TSTP Solution File: GRP128-2.006 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP128-2.006 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 22:26:09 EDT 2022
% Result : Unsatisfiable 0.88s 0.80s
% Output : Proof 1.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP128-2.006 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 15:23:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.88/0.80 % SZS status Unsatisfiable
% 0.88/0.80 % SZS output start Proof
% 0.88/0.80 tff(product_type, type, (
% 0.88/0.80 product: ( $i * $i * $i ) > $o)).
% 0.88/0.80 tff(e_6_type, type, (
% 0.88/0.80 e_6: $i)).
% 0.88/0.80 tff(e_3_type, type, (
% 0.88/0.80 e_3: $i)).
% 0.88/0.80 tff(e_5_type, type, (
% 0.88/0.80 e_5: $i)).
% 0.88/0.80 tff(e_4_type, type, (
% 0.88/0.80 e_4: $i)).
% 0.88/0.80 tff(e_1_type, type, (
% 0.88/0.80 e_1: $i)).
% 0.88/0.80 tff(equalish_type, type, (
% 0.88/0.80 equalish: ( $i * $i ) > $o)).
% 0.88/0.80 tff(e_2_type, type, (
% 0.88/0.80 e_2: $i)).
% 0.88/0.80 tff(next_type, type, (
% 0.88/0.80 next: ( $i * $i ) > $o)).
% 0.88/0.80 tff(greater_type, type, (
% 0.88/0.80 greater: ( $i * $i ) > $o)).
% 0.88/0.80 tff(group_element_type, type, (
% 0.88/0.80 group_element: $i > $o)).
% 0.88/0.80 tff(1,assumption,(product(e_5, e_1, e_6)), introduced(assumption)).
% 0.88/0.80 tff(2,assumption,(product(e_5, e_3, e_6)), introduced(assumption)).
% 0.88/0.80 tff(3,plain,
% 0.88/0.80 (^[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))))),
% 0.88/0.80 inference(bind,[status(th)],[])).
% 0.88/0.80 tff(4,plain,
% 0.88/0.80 (![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)))),
% 0.88/0.80 inference(quant_intro,[status(thm)],[3])).
% 0.88/0.80 tff(5,plain,
% 0.88/0.80 (![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)))),
% 0.88/0.80 inference(rewrite,[status(thm)],[])).
% 0.88/0.80 tff(6,plain,
% 0.88/0.80 (^[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)))))),
% 0.88/0.80 inference(bind,[status(th)],[])).
% 0.88/0.80 tff(7,plain,
% 0.88/0.80 (![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)))),
% 0.88/0.80 inference(quant_intro,[status(thm)],[6])).
% 0.88/0.80 tff(8,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.88/0.80 tff(9,plain,
% 0.88/0.80 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.88/0.80 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.88/0.80 tff(10,plain,
% 0.88/0.80 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.88/0.80 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.88/0.80 tff(11,plain,(
% 0.88/0.80 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.88/0.80 inference(skolemize,[status(sab)],[10])).
% 0.88/0.80 tff(12,plain,
% 0.88/0.80 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.88/0.80 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.88/0.80 tff(13,plain,
% 0.88/0.80 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.88/0.80 inference(rewrite,[status(thm)],[])).
% 0.88/0.80 tff(14,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.88/0.80 tff(15,plain,
% 0.88/0.80 (~equalish(e_3, e_1)),
% 0.88/0.80 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.88/0.80 tff(16,plain,
% 0.88/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_5, e_1, e_6)) | (~product(e_5, 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_1) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_3, e_6)))),
% 0.88/0.80 inference(rewrite,[status(thm)],[])).
% 0.88/0.80 tff(17,plain,
% 0.88/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_3, e_6)))),
% 0.88/0.80 inference(quant_inst,[status(thm)],[])).
% 0.88/0.80 tff(18,plain,
% 0.88/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_3, e_6))),
% 0.88/0.80 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.88/0.80 tff(19,plain,
% 0.88/0.80 ($false),
% 0.88/0.80 inference(unit_resolution,[status(thm)],[18, 15, 12, 1, 2])).
% 0.88/0.80 tff(20,plain,((~product(e_5, e_3, e_6)) | (~product(e_5, e_1, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.80 tff(21,plain,
% 0.88/0.80 (~product(e_5, e_3, e_6)),
% 0.88/0.80 inference(unit_resolution,[status(thm)],[20, 1])).
% 0.88/0.80 tff(22,assumption,(product(e_5, e_6, e_5)), introduced(assumption)).
% 0.88/0.80 tff(23,assumption,(~product(e_5, e_5, e_5)), introduced(assumption)).
% 0.88/0.80 tff(24,plain,
% 0.88/0.80 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))))),
% 0.88/0.80 inference(bind,[status(th)],[])).
% 0.88/0.80 tff(25,plain,
% 0.88/0.80 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.88/0.80 inference(quant_intro,[status(thm)],[24])).
% 0.88/0.80 tff(26,plain,
% 0.88/0.80 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.88/0.80 inference(rewrite,[status(thm)],[])).
% 0.88/0.80 tff(27,plain,
% 0.88/0.80 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))))),
% 0.88/0.80 inference(bind,[status(th)],[])).
% 0.88/0.80 tff(28,plain,
% 0.88/0.80 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.88/0.80 inference(quant_intro,[status(thm)],[27])).
% 0.88/0.80 tff(29,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.88/0.80 tff(30,plain,
% 0.88/0.80 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.88/0.80 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.88/0.80 tff(31,plain,
% 0.88/0.80 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.88/0.80 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.88/0.80 tff(32,plain,(
% 0.88/0.80 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.88/0.80 inference(skolemize,[status(sab)],[31])).
% 0.88/0.80 tff(33,plain,
% 0.88/0.80 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.88/0.80 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.88/0.80 tff(34,plain,
% 0.88/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)))),
% 0.88/0.80 inference(rewrite,[status(thm)],[])).
% 0.88/0.80 tff(35,plain,
% 0.88/0.80 ((product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_6, e_5))) <=> (product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)))),
% 0.88/0.80 inference(rewrite,[status(thm)],[])).
% 0.88/0.80 tff(36,plain,
% 0.88/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5))))),
% 0.88/0.80 inference(monotonicity,[status(thm)],[35])).
% 0.88/0.80 tff(37,plain,
% 0.88/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)))),
% 0.88/0.80 inference(transitivity,[status(thm)],[36, 34])).
% 0.88/0.80 tff(38,plain,
% 0.88/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_6, e_5)))),
% 0.88/0.80 inference(quant_inst,[status(thm)],[])).
% 0.88/0.80 tff(39,plain,
% 0.88/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5))),
% 0.88/0.80 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.88/0.80 tff(40,plain,
% 0.88/0.80 ($false),
% 0.88/0.80 inference(unit_resolution,[status(thm)],[39, 33, 23, 22])).
% 0.88/0.80 tff(41,plain,(product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.80 tff(42,plain,
% 0.88/0.80 (product(e_5, e_5, e_5)),
% 0.88/0.80 inference(unit_resolution,[status(thm)],[41, 22])).
% 0.88/0.80 tff(43,plain,
% 0.88/0.80 ((~equalish(e_5, e_6)) <=> (~equalish(e_5, e_6))),
% 0.88/0.80 inference(rewrite,[status(thm)],[])).
% 0.88/0.80 tff(44,axiom,(~equalish(e_5, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_6')).
% 0.88/0.80 tff(45,plain,
% 0.88/0.80 (~equalish(e_5, e_6)),
% 0.88/0.80 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.88/0.80 tff(46,plain,
% 0.88/0.80 (((~![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_5, e_5, e_5)) | (~product(e_5, 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_5, e_6) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_6, e_5)))),
% 0.88/0.80 inference(rewrite,[status(thm)],[])).
% 0.88/0.80 tff(47,plain,
% 0.88/0.80 ((equalish(e_5, e_6) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_5, e_5))) <=> (equalish(e_5, e_6) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_6, e_5)))),
% 0.88/0.80 inference(rewrite,[status(thm)],[])).
% 0.88/0.80 tff(48,plain,
% 0.88/0.80 (((~![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_5, e_6, e_5)) | (~product(e_5, 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_5, e_5, e_5)) | (~product(e_5, e_6, e_5))))),
% 0.88/0.80 inference(monotonicity,[status(thm)],[47])).
% 0.88/0.80 tff(49,plain,
% 0.88/0.80 (((~![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_5, e_6, e_5)) | (~product(e_5, 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_5, e_5, e_5)) | (~product(e_5, e_6, e_5)))),
% 0.88/0.80 inference(transitivity,[status(thm)],[48, 46])).
% 0.88/0.80 tff(50,plain,
% 0.88/0.80 ((~![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_5, e_6, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.88/0.80 inference(quant_inst,[status(thm)],[])).
% 0.88/0.80 tff(51,plain,
% 0.88/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_6, e_5))),
% 0.88/0.80 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.88/0.80 tff(52,plain,
% 0.88/0.80 ($false),
% 0.88/0.80 inference(unit_resolution,[status(thm)],[51, 45, 12, 42, 22])).
% 0.88/0.80 tff(53,plain,(~product(e_5, e_6, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.80 tff(54,assumption,(~product(e_1, e_3, e_5)), introduced(assumption)).
% 0.88/0.80 tff(55,assumption,(~product(e_4, e_3, e_6)), introduced(assumption)).
% 0.88/0.80 tff(56,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.88/0.80 tff(57,plain,
% 0.88/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)))),
% 0.88/0.80 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(58,plain,
% 0.88/0.81 ((product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)))),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(59,plain,
% 0.88/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2))))),
% 0.88/0.81 inference(monotonicity,[status(thm)],[58])).
% 0.88/0.81 tff(60,plain,
% 0.88/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)))),
% 0.88/0.81 inference(transitivity,[status(thm)],[59, 57])).
% 0.88/0.81 tff(61,plain,
% 0.88/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.88/0.81 inference(quant_inst,[status(thm)],[])).
% 0.88/0.81 tff(62,plain,
% 0.88/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2))),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.88/0.81 tff(63,plain,
% 0.88/0.81 (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2))),
% 0.88/0.81 inference(unit_resolution,[status(thm)],[62, 33])).
% 0.88/0.81 tff(64,plain,
% 0.88/0.81 (product(e_2, e_2, e_2)),
% 0.88/0.81 inference(unit_resolution,[status(thm)],[63, 56])).
% 0.88/0.81 tff(65,plain,
% 0.88/0.81 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(66,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.88/0.81 tff(67,plain,
% 0.88/0.81 (~equalish(e_1, e_2)),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.88/0.81 tff(68,plain,
% 0.88/0.81 (((~![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)))),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(69,plain,
% 0.88/0.81 ((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)))),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(70,plain,
% 0.88/0.81 (((~![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))))),
% 0.88/0.81 inference(monotonicity,[status(thm)],[69])).
% 0.88/0.81 tff(71,plain,
% 0.88/0.81 (((~![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)))),
% 0.88/0.81 inference(transitivity,[status(thm)],[70, 68])).
% 0.88/0.81 tff(72,plain,
% 0.88/0.81 ((~![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)))),
% 0.88/0.81 inference(quant_inst,[status(thm)],[])).
% 0.88/0.81 tff(73,plain,
% 0.88/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.88/0.81 tff(74,plain,
% 0.88/0.81 ($false),
% 0.88/0.81 inference(unit_resolution,[status(thm)],[73, 67, 12, 56, 64])).
% 0.88/0.81 tff(75,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.81 tff(76,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.88/0.81 tff(77,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.88/0.81 tff(78,plain,
% 0.88/0.81 (^[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))))),
% 0.88/0.81 inference(bind,[status(th)],[])).
% 0.88/0.81 tff(79,plain,
% 0.88/0.81 (![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)))),
% 0.88/0.81 inference(quant_intro,[status(thm)],[78])).
% 0.88/0.81 tff(80,plain,
% 0.88/0.81 (![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)))),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(81,plain,
% 0.88/0.81 (^[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)))))),
% 0.88/0.81 inference(bind,[status(th)],[])).
% 0.88/0.81 tff(82,plain,
% 0.88/0.81 (![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)))),
% 0.88/0.81 inference(quant_intro,[status(thm)],[81])).
% 0.88/0.81 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')).
% 0.88/0.81 tff(84,plain,
% 0.88/0.81 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.88/0.81 tff(85,plain,
% 0.88/0.81 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.88/0.81 tff(86,plain,(
% 0.88/0.81 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.88/0.81 inference(skolemize,[status(sab)],[85])).
% 0.88/0.81 tff(87,plain,
% 0.88/0.81 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.88/0.81 tff(88,plain,
% 0.88/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(89,plain,
% 0.88/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.88/0.81 inference(quant_inst,[status(thm)],[])).
% 0.88/0.81 tff(90,plain,
% 0.88/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.88/0.81 tff(91,plain,
% 0.88/0.81 ($false),
% 0.88/0.81 inference(unit_resolution,[status(thm)],[90, 67, 87, 77, 76])).
% 0.88/0.81 tff(92,plain,((~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.81 tff(93,plain,
% 0.88/0.81 (~product(e_1, e_1, e_1)),
% 0.88/0.81 inference(unit_resolution,[status(thm)],[92, 76])).
% 0.88/0.81 tff(94,plain,
% 0.88/0.81 (^[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))))),
% 0.88/0.81 inference(bind,[status(th)],[])).
% 0.88/0.81 tff(95,plain,
% 0.88/0.81 (![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)))),
% 0.88/0.81 inference(quant_intro,[status(thm)],[94])).
% 0.88/0.81 tff(96,plain,
% 0.88/0.81 (![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)))),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(97,plain,
% 0.88/0.81 (^[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)))))),
% 0.88/0.81 inference(bind,[status(th)],[])).
% 0.88/0.81 tff(98,plain,
% 0.88/0.81 (![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)))),
% 0.88/0.81 inference(quant_intro,[status(thm)],[97])).
% 0.88/0.81 tff(99,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')).
% 0.88/0.81 tff(100,plain,
% 0.88/0.81 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.88/0.81 tff(101,plain,
% 0.88/0.81 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.88/0.81 tff(102,plain,(
% 0.88/0.81 ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.88/0.81 inference(skolemize,[status(sab)],[101])).
% 0.88/0.81 tff(103,plain,
% 0.88/0.81 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.88/0.81 tff(104,plain,
% 0.88/0.81 (greater(e_6, e_2) <=> greater(e_6, e_2)),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(105,axiom,(greater(e_6, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_greater_e_2')).
% 0.88/0.81 tff(106,plain,
% 0.88/0.81 (greater(e_6, e_2)),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.88/0.81 tff(107,plain,
% 0.88/0.81 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(108,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.88/0.81 tff(109,plain,
% 0.88/0.81 (next(e_1, e_2)),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.88/0.81 tff(110,plain,
% 0.88/0.81 (((~![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)))),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(111,plain,
% 0.88/0.81 ((~![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)))),
% 0.88/0.81 inference(quant_inst,[status(thm)],[])).
% 0.88/0.81 tff(112,plain,
% 0.88/0.81 ((~![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))),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.88/0.81 tff(113,plain,
% 0.88/0.81 (~product(e_1, e_1, e_6)),
% 0.88/0.81 inference(unit_resolution,[status(thm)],[112, 109, 106, 103])).
% 0.88/0.81 tff(114,plain,
% 0.88/0.81 (greater(e_5, e_2) <=> greater(e_5, e_2)),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(115,axiom,(greater(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_2')).
% 0.88/0.81 tff(116,plain,
% 0.88/0.81 (greater(e_5, e_2)),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.88/0.81 tff(117,plain,
% 0.88/0.81 (((~![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)))),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(118,plain,
% 0.88/0.81 ((~![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)))),
% 0.88/0.81 inference(quant_inst,[status(thm)],[])).
% 0.88/0.81 tff(119,plain,
% 0.88/0.81 ((~![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))),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.88/0.81 tff(120,plain,
% 0.88/0.81 (~product(e_1, e_1, e_5)),
% 0.88/0.81 inference(unit_resolution,[status(thm)],[119, 109, 116, 103])).
% 0.88/0.81 tff(121,plain,
% 0.88/0.81 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(122,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.88/0.81 tff(123,plain,
% 0.88/0.81 (greater(e_4, e_2)),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.88/0.81 tff(124,plain,
% 0.88/0.81 (((~![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)))),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(125,plain,
% 0.88/0.81 ((~![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)))),
% 0.88/0.81 inference(quant_inst,[status(thm)],[])).
% 0.88/0.81 tff(126,plain,
% 0.88/0.81 ((~![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))),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.88/0.81 tff(127,plain,
% 0.88/0.81 (~product(e_1, e_1, e_4)),
% 0.88/0.81 inference(unit_resolution,[status(thm)],[126, 109, 123, 103])).
% 0.88/0.81 tff(128,plain,
% 0.88/0.81 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(129,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.88/0.81 tff(130,plain,
% 0.88/0.81 (greater(e_3, e_2)),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.88/0.81 tff(131,plain,
% 0.88/0.81 (((~![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)))),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(132,plain,
% 0.88/0.81 ((~![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)))),
% 0.88/0.81 inference(quant_inst,[status(thm)],[])).
% 0.88/0.81 tff(133,plain,
% 0.88/0.81 ((~![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))),
% 0.88/0.81 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.88/0.81 tff(134,plain,
% 0.88/0.81 (~product(e_1, e_1, e_3)),
% 0.88/0.81 inference(unit_resolution,[status(thm)],[133, 109, 130, 103])).
% 0.88/0.81 tff(135,plain,
% 0.88/0.81 (^[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))))),
% 0.88/0.81 inference(bind,[status(th)],[])).
% 0.88/0.81 tff(136,plain,
% 0.88/0.81 (![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))) <=> ![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)))),
% 0.88/0.81 inference(quant_intro,[status(thm)],[135])).
% 0.88/0.81 tff(137,plain,
% 0.88/0.81 (![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))) <=> ![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)))),
% 0.88/0.81 inference(rewrite,[status(thm)],[])).
% 0.88/0.81 tff(138,plain,
% 0.88/0.81 (^[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)))))),
% 0.88/0.82 inference(bind,[status(th)],[])).
% 0.88/0.82 tff(139,plain,
% 0.88/0.82 (![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)))),
% 0.88/0.82 inference(quant_intro,[status(thm)],[138])).
% 0.88/0.82 tff(140,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')).
% 0.88/0.82 tff(141,plain,
% 0.88/0.82 (![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)))),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.88/0.82 tff(142,plain,
% 0.88/0.82 (![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)))),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.88/0.82 tff(143,plain,(
% 0.88/0.82 ![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)))),
% 0.88/0.82 inference(skolemize,[status(sab)],[142])).
% 0.88/0.82 tff(144,plain,
% 0.88/0.82 (![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)))),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.88/0.82 tff(145,plain,
% 0.88/0.82 (group_element(e_1) <=> group_element(e_1)),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(146,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.88/0.82 tff(147,plain,
% 0.88/0.82 (group_element(e_1)),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.88/0.82 tff(148,plain,
% 0.88/0.82 (((~![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_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_6) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_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_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_6) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(149,plain,
% 0.88/0.82 ((product(e_1, e_1, e_6) | product(e_1, e_1, e_5) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1))) <=> (product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_6) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(150,plain,
% 0.88/0.82 (((~![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_1, e_6) | product(e_1, e_1, e_5) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_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_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_6) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))))),
% 0.88/0.82 inference(monotonicity,[status(thm)],[149])).
% 0.88/0.82 tff(151,plain,
% 0.88/0.82 (((~![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_1, e_6) | product(e_1, e_1, e_5) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_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_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_6) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.88/0.82 inference(transitivity,[status(thm)],[150, 148])).
% 0.88/0.82 tff(152,plain,
% 0.88/0.82 ((~![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_1, e_6) | product(e_1, e_1, e_5) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))),
% 0.88/0.82 inference(quant_inst,[status(thm)],[])).
% 0.88/0.82 tff(153,plain,
% 0.88/0.82 ((~![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_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_6) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.88/0.82 tff(154,plain,
% 0.88/0.82 (product(e_1, e_1, e_2) | product(e_1, e_1, e_1)),
% 0.88/0.82 inference(unit_resolution,[status(thm)],[153, 147, 144, 134, 127, 120, 113])).
% 0.88/0.82 tff(155,plain,
% 0.88/0.82 (product(e_1, e_1, e_2)),
% 0.88/0.82 inference(unit_resolution,[status(thm)],[154, 93])).
% 0.88/0.82 tff(156,plain,
% 0.88/0.82 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)))),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(157,plain,
% 0.88/0.82 ((product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_1, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)))),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(158,plain,
% 0.88/0.82 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1))))),
% 0.88/0.82 inference(monotonicity,[status(thm)],[157])).
% 0.88/0.82 tff(159,plain,
% 0.88/0.82 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)))),
% 0.88/0.82 inference(transitivity,[status(thm)],[158, 156])).
% 0.88/0.82 tff(160,plain,
% 0.88/0.82 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.88/0.82 inference(quant_inst,[status(thm)],[])).
% 0.88/0.82 tff(161,plain,
% 0.88/0.82 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1))),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.88/0.82 tff(162,plain,
% 0.88/0.82 ((~product(e_1, e_1, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1))),
% 0.88/0.82 inference(unit_resolution,[status(thm)],[161, 33])).
% 0.88/0.82 tff(163,plain,
% 0.88/0.82 (product(e_1, e_2, e_1)),
% 0.88/0.82 inference(unit_resolution,[status(thm)],[162, 155, 76])).
% 0.88/0.82 tff(164,plain,
% 0.88/0.82 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(165,plain,
% 0.88/0.82 ((product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1))) <=> (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(166,plain,
% 0.88/0.82 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1))))),
% 0.88/0.82 inference(monotonicity,[status(thm)],[165])).
% 0.88/0.82 tff(167,plain,
% 0.88/0.82 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.88/0.82 inference(transitivity,[status(thm)],[166, 164])).
% 0.88/0.82 tff(168,plain,
% 0.88/0.82 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.88/0.82 inference(quant_inst,[status(thm)],[])).
% 0.88/0.82 tff(169,plain,
% 0.88/0.82 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1))),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.88/0.82 tff(170,plain,
% 0.88/0.82 ($false),
% 0.88/0.82 inference(unit_resolution,[status(thm)],[169, 33, 93, 163])).
% 0.88/0.82 tff(171,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.82 tff(172,plain,
% 0.88/0.82 (greater(e_6, e_3) <=> greater(e_6, e_3)),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(173,axiom,(greater(e_6, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_greater_e_3')).
% 0.88/0.82 tff(174,plain,
% 0.88/0.82 (greater(e_6, e_3)),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.88/0.82 tff(175,plain,
% 0.88/0.82 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(176,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.88/0.82 tff(177,plain,
% 0.88/0.82 (next(e_2, e_3)),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.88/0.82 tff(178,plain,
% 0.88/0.82 (((~![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)))),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(179,plain,
% 0.88/0.82 ((~![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)))),
% 0.88/0.82 inference(quant_inst,[status(thm)],[])).
% 0.88/0.82 tff(180,plain,
% 0.88/0.82 ((~![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))),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.88/0.82 tff(181,plain,
% 0.88/0.82 (~product(e_2, e_1, e_6)),
% 0.88/0.82 inference(unit_resolution,[status(thm)],[180, 177, 174, 103])).
% 0.88/0.82 tff(182,plain,
% 0.88/0.82 (greater(e_5, e_3) <=> greater(e_5, e_3)),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(183,axiom,(greater(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_3')).
% 0.88/0.82 tff(184,plain,
% 0.88/0.82 (greater(e_5, e_3)),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.88/0.82 tff(185,plain,
% 0.88/0.82 (((~![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)))),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(186,plain,
% 0.88/0.82 ((~![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)))),
% 0.88/0.82 inference(quant_inst,[status(thm)],[])).
% 0.88/0.82 tff(187,plain,
% 0.88/0.82 ((~![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))),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.88/0.82 tff(188,plain,
% 0.88/0.82 (~product(e_2, e_1, e_5)),
% 0.88/0.82 inference(unit_resolution,[status(thm)],[187, 177, 184, 103])).
% 0.88/0.82 tff(189,plain,
% 0.88/0.82 (greater(e_4, e_3) <=> greater(e_4, e_3)),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(190,axiom,(greater(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_3')).
% 0.88/0.82 tff(191,plain,
% 0.88/0.82 (greater(e_4, e_3)),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.88/0.82 tff(192,plain,
% 0.88/0.82 (((~![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)))),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(193,plain,
% 0.88/0.82 ((~![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)))),
% 0.88/0.82 inference(quant_inst,[status(thm)],[])).
% 0.88/0.82 tff(194,plain,
% 0.88/0.82 ((~![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))),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.88/0.82 tff(195,plain,
% 0.88/0.82 (~product(e_2, e_1, e_4)),
% 0.88/0.82 inference(unit_resolution,[status(thm)],[194, 177, 191, 103])).
% 0.88/0.82 tff(196,plain,
% 0.88/0.82 (group_element(e_2) <=> group_element(e_2)),
% 0.88/0.82 inference(rewrite,[status(thm)],[])).
% 0.88/0.82 tff(197,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.88/0.82 tff(198,plain,
% 0.88/0.82 (group_element(e_2)),
% 0.88/0.82 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.88/0.83 tff(199,plain,
% 0.88/0.83 (((~![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)))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(200,plain,
% 0.88/0.83 ((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)))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(201,plain,
% 0.88/0.83 (((~![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))))),
% 0.88/0.83 inference(monotonicity,[status(thm)],[200])).
% 0.88/0.83 tff(202,plain,
% 0.88/0.83 (((~![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)))),
% 0.88/0.83 inference(transitivity,[status(thm)],[201, 199])).
% 0.88/0.83 tff(203,plain,
% 0.88/0.83 ((~![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)))),
% 0.88/0.83 inference(quant_inst,[status(thm)],[])).
% 0.88/0.83 tff(204,plain,
% 0.88/0.83 ((~![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))),
% 0.88/0.83 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.88/0.83 tff(205,plain,
% 0.88/0.83 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.88/0.83 inference(unit_resolution,[status(thm)],[204, 147, 198, 144, 195, 188, 181])).
% 0.88/0.83 tff(206,plain,
% 0.88/0.83 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2)),
% 0.88/0.83 inference(unit_resolution,[status(thm)],[205, 171])).
% 0.88/0.83 tff(207,plain,
% 0.88/0.83 (product(e_2, e_1, e_3)),
% 0.88/0.83 inference(unit_resolution,[status(thm)],[206, 75])).
% 0.88/0.83 tff(208,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.88/0.83 tff(209,assumption,(product(e_3, e_3, e_3)), introduced(assumption)).
% 0.88/0.83 tff(210,plain,
% 0.88/0.83 (((~![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_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(211,plain,
% 0.88/0.83 ((~![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_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.88/0.83 inference(quant_inst,[status(thm)],[])).
% 0.88/0.83 tff(212,plain,
% 0.88/0.83 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3))),
% 0.88/0.83 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.88/0.83 tff(213,plain,
% 0.88/0.83 ($false),
% 0.88/0.83 inference(unit_resolution,[status(thm)],[212, 15, 12, 208, 209])).
% 0.88/0.83 tff(214,plain,((~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.83 tff(215,plain,
% 0.88/0.83 (~product(e_3, e_3, e_3)),
% 0.88/0.83 inference(unit_resolution,[status(thm)],[214, 208])).
% 0.88/0.83 tff(216,plain,
% 0.88/0.83 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(217,plain,
% 0.88/0.83 ((product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_1, e_3))) <=> ((~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(218,plain,
% 0.88/0.83 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3)))),
% 0.88/0.83 inference(monotonicity,[status(thm)],[217])).
% 0.88/0.83 tff(219,plain,
% 0.88/0.83 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3))),
% 0.88/0.83 inference(transitivity,[status(thm)],[218, 216])).
% 0.88/0.83 tff(220,plain,
% 0.88/0.83 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.88/0.83 inference(quant_inst,[status(thm)],[])).
% 0.88/0.83 tff(221,plain,
% 0.88/0.83 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3)),
% 0.88/0.83 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.88/0.83 tff(222,plain,
% 0.88/0.83 ($false),
% 0.88/0.83 inference(unit_resolution,[status(thm)],[221, 33, 208, 215])).
% 0.88/0.83 tff(223,plain,(~product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.83 tff(224,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.88/0.83 tff(225,plain,
% 0.88/0.83 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(226,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.88/0.83 tff(227,plain,
% 0.88/0.83 (~equalish(e_2, e_3)),
% 0.88/0.83 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.88/0.83 tff(228,plain,
% 0.88/0.83 (((~![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)))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(229,plain,
% 0.88/0.83 ((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)))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(230,plain,
% 0.88/0.83 (((~![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))))),
% 0.88/0.83 inference(monotonicity,[status(thm)],[229])).
% 0.88/0.83 tff(231,plain,
% 0.88/0.83 (((~![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)))),
% 0.88/0.83 inference(transitivity,[status(thm)],[230, 228])).
% 0.88/0.83 tff(232,plain,
% 0.88/0.83 ((~![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)))),
% 0.88/0.83 inference(quant_inst,[status(thm)],[])).
% 0.88/0.83 tff(233,plain,
% 0.88/0.83 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.88/0.83 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.88/0.83 tff(234,plain,
% 0.88/0.83 ($false),
% 0.88/0.83 inference(unit_resolution,[status(thm)],[233, 227, 87, 56, 224])).
% 0.88/0.83 tff(235,plain,((~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.83 tff(236,plain,
% 0.88/0.83 (~product(e_2, e_1, e_2)),
% 0.88/0.83 inference(unit_resolution,[status(thm)],[235, 224])).
% 0.88/0.83 tff(237,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.88/0.83 tff(238,plain,
% 0.88/0.83 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(239,plain,
% 0.88/0.83 ((product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2))) <=> (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(240,plain,
% 0.88/0.83 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2))))),
% 0.88/0.83 inference(monotonicity,[status(thm)],[239])).
% 0.88/0.83 tff(241,plain,
% 0.88/0.83 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)))),
% 0.88/0.83 inference(transitivity,[status(thm)],[240, 238])).
% 0.88/0.83 tff(242,plain,
% 0.88/0.83 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.88/0.83 inference(quant_inst,[status(thm)],[])).
% 0.88/0.83 tff(243,plain,
% 0.88/0.83 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2))),
% 0.88/0.83 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.88/0.83 tff(244,plain,
% 0.88/0.83 (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2))),
% 0.88/0.83 inference(unit_resolution,[status(thm)],[243, 33])).
% 0.88/0.83 tff(245,plain,
% 0.88/0.83 (product(e_2, e_2, e_2)),
% 0.88/0.83 inference(unit_resolution,[status(thm)],[244, 237])).
% 0.88/0.83 tff(246,plain,
% 0.88/0.83 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(247,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.88/0.83 tff(248,plain,
% 0.88/0.83 (~equalish(e_3, e_2)),
% 0.88/0.83 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.88/0.83 tff(249,plain,
% 0.88/0.83 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, 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_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(250,plain,
% 0.88/0.83 ((equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2))) <=> (equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(251,plain,
% 0.88/0.83 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.88/0.83 inference(monotonicity,[status(thm)],[250])).
% 0.88/0.83 tff(252,plain,
% 0.88/0.83 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.88/0.83 inference(transitivity,[status(thm)],[251, 249])).
% 0.88/0.83 tff(253,plain,
% 0.88/0.83 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.88/0.83 inference(quant_inst,[status(thm)],[])).
% 0.88/0.83 tff(254,plain,
% 0.88/0.83 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2))),
% 0.88/0.83 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.88/0.83 tff(255,plain,
% 0.88/0.83 ($false),
% 0.88/0.83 inference(unit_resolution,[status(thm)],[254, 248, 12, 237, 245])).
% 0.88/0.83 tff(256,plain,(~product(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.83 tff(257,plain,
% 0.88/0.83 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(258,plain,
% 0.88/0.83 ((product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3))) <=> (product(e_2, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.88/0.83 inference(rewrite,[status(thm)],[])).
% 0.88/0.83 tff(259,plain,
% 0.88/0.83 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.88/0.84 inference(monotonicity,[status(thm)],[258])).
% 0.88/0.84 tff(260,plain,
% 0.88/0.84 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.88/0.84 inference(transitivity,[status(thm)],[259, 257])).
% 0.88/0.84 tff(261,plain,
% 0.88/0.84 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.88/0.84 inference(quant_inst,[status(thm)],[])).
% 0.88/0.84 tff(262,plain,
% 0.88/0.84 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2))),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.88/0.84 tff(263,plain,
% 0.88/0.84 (product(e_2, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2))),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[262, 33])).
% 0.88/0.84 tff(264,plain,
% 0.88/0.84 (~product(e_2, e_1, e_3)),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[263, 224, 256])).
% 0.88/0.84 tff(265,plain,
% 0.88/0.84 ($false),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[206, 264, 236])).
% 0.88/0.84 tff(266,plain,(~product(e_3, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.84 tff(267,assumption,(~product(e_3, e_1, e_3)), introduced(assumption)).
% 0.88/0.84 tff(268,assumption,(~product(e_3, e_1, e_2)), introduced(assumption)).
% 0.88/0.84 tff(269,assumption,(~product(e_3, e_1, e_4)), introduced(assumption)).
% 0.88/0.84 tff(270,plain,
% 0.88/0.84 (greater(e_6, e_4) <=> greater(e_6, e_4)),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(271,axiom,(greater(e_6, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_greater_e_4')).
% 0.88/0.84 tff(272,plain,
% 0.88/0.84 (greater(e_6, e_4)),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.88/0.84 tff(273,plain,
% 0.88/0.84 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(274,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.88/0.84 tff(275,plain,
% 0.88/0.84 (next(e_3, e_4)),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.88/0.84 tff(276,plain,
% 0.88/0.84 (((~![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)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(277,plain,
% 0.88/0.84 ((~![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)))),
% 0.88/0.84 inference(quant_inst,[status(thm)],[])).
% 0.88/0.84 tff(278,plain,
% 0.88/0.84 ((~![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))),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.88/0.84 tff(279,plain,
% 0.88/0.84 (~product(e_3, e_1, e_6)),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[278, 275, 272, 103])).
% 0.88/0.84 tff(280,plain,
% 0.88/0.84 (greater(e_5, e_4) <=> greater(e_5, e_4)),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(281,axiom,(greater(e_5, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_4')).
% 0.88/0.84 tff(282,plain,
% 0.88/0.84 (greater(e_5, e_4)),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.88/0.84 tff(283,plain,
% 0.88/0.84 (((~![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)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(284,plain,
% 0.88/0.84 ((~![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)))),
% 0.88/0.84 inference(quant_inst,[status(thm)],[])).
% 0.88/0.84 tff(285,plain,
% 0.88/0.84 ((~![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))),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.88/0.84 tff(286,plain,
% 0.88/0.84 (~product(e_3, e_1, e_5)),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[285, 275, 282, 103])).
% 0.88/0.84 tff(287,plain,
% 0.88/0.84 (group_element(e_3) <=> group_element(e_3)),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(288,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.88/0.84 tff(289,plain,
% 0.88/0.84 (group_element(e_3)),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.88/0.84 tff(290,plain,
% 0.88/0.84 (((~![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)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(291,plain,
% 0.88/0.84 ((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)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(292,plain,
% 0.88/0.84 (((~![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))))),
% 0.88/0.84 inference(monotonicity,[status(thm)],[291])).
% 0.88/0.84 tff(293,plain,
% 0.88/0.84 (((~![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)))),
% 0.88/0.84 inference(transitivity,[status(thm)],[292, 290])).
% 0.88/0.84 tff(294,plain,
% 0.88/0.84 ((~![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)))),
% 0.88/0.84 inference(quant_inst,[status(thm)],[])).
% 0.88/0.84 tff(295,plain,
% 0.88/0.84 ((~![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))),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.88/0.84 tff(296,plain,
% 0.88/0.84 (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)),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[295, 147, 289, 144, 286, 279])).
% 0.88/0.84 tff(297,plain,
% 0.88/0.84 (product(e_3, e_1, e_1)),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[296, 269, 268, 267])).
% 0.88/0.84 tff(298,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.88/0.84 tff(299,plain,
% 0.88/0.84 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(300,plain,
% 0.88/0.84 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.88/0.84 inference(quant_inst,[status(thm)],[])).
% 0.88/0.84 tff(301,plain,
% 0.88/0.84 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.88/0.84 tff(302,plain,
% 0.88/0.84 ($false),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[301, 15, 87, 298, 224])).
% 0.88/0.84 tff(303,plain,((~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.84 tff(304,plain,
% 0.88/0.84 (~product(e_3, e_1, e_2)),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[303, 298])).
% 0.88/0.84 tff(305,plain,
% 0.88/0.84 (product(e_3, e_1, e_1)),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[296, 304, 269, 267])).
% 0.88/0.84 tff(306,plain,
% 0.88/0.84 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_1)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(307,plain,
% 0.88/0.84 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_1)))),
% 0.88/0.84 inference(quant_inst,[status(thm)],[])).
% 0.88/0.84 tff(308,plain,
% 0.88/0.84 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_1))),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.88/0.84 tff(309,plain,
% 0.88/0.84 ($false),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[308, 33, 298, 304, 305])).
% 0.88/0.84 tff(310,plain,((~product(e_1, e_1, e_2)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.84 tff(311,plain,
% 0.88/0.84 (~product(e_1, e_1, e_2)),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[310, 269, 267])).
% 0.88/0.84 tff(312,plain,
% 0.88/0.84 (product(e_1, e_1, e_1)),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[154, 311])).
% 0.88/0.84 tff(313,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.88/0.84 tff(314,plain,
% 0.88/0.84 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(315,plain,
% 0.88/0.84 ((equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))) <=> (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(316,plain,
% 0.88/0.84 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.88/0.84 inference(monotonicity,[status(thm)],[315])).
% 0.88/0.84 tff(317,plain,
% 0.88/0.84 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.88/0.84 inference(transitivity,[status(thm)],[316, 314])).
% 0.88/0.84 tff(318,plain,
% 0.88/0.84 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.88/0.84 inference(quant_inst,[status(thm)],[])).
% 0.88/0.84 tff(319,plain,
% 0.88/0.84 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.88/0.84 tff(320,plain,
% 0.88/0.84 ($false),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[319, 15, 87, 77, 313])).
% 0.88/0.84 tff(321,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.84 tff(322,plain,
% 0.88/0.84 ($false),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[321, 312, 297])).
% 0.88/0.84 tff(323,plain,(product(e_3, e_1, e_4) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.84 tff(324,plain,
% 0.88/0.84 (product(e_3, e_1, e_4)),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[323, 266, 223])).
% 0.88/0.84 tff(325,plain,
% 0.88/0.84 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(326,plain,
% 0.88/0.84 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3)))),
% 0.88/0.84 inference(quant_inst,[status(thm)],[])).
% 0.88/0.84 tff(327,plain,
% 0.88/0.84 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3))),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.88/0.84 tff(328,plain,
% 0.88/0.84 (product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3))),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[327, 33])).
% 0.88/0.84 tff(329,plain,
% 0.88/0.84 (product(e_2, e_3, e_4) | (~product(e_2, e_1, e_3))),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[328, 324])).
% 0.88/0.84 tff(330,plain,
% 0.88/0.84 (product(e_2, e_3, e_4)),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[329, 207])).
% 0.88/0.84 tff(331,assumption,(product(e_4, e_2, e_4)), introduced(assumption)).
% 0.88/0.84 tff(332,assumption,(product(e_4, e_4, e_4)), introduced(assumption)).
% 0.88/0.84 tff(333,plain,
% 0.88/0.84 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(334,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.88/0.84 tff(335,plain,
% 0.88/0.84 (~equalish(e_4, e_2)),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.88/0.84 tff(336,plain,
% 0.88/0.84 (((~![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_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_4, e_2) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(337,plain,
% 0.88/0.84 ((equalish(e_4, e_2) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4))) <=> (equalish(e_4, e_2) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(338,plain,
% 0.88/0.84 (((~![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_4, e_2, 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_4, e_2) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4))))),
% 0.88/0.84 inference(monotonicity,[status(thm)],[337])).
% 0.88/0.84 tff(339,plain,
% 0.88/0.84 (((~![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_4, e_2, 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_4, e_2) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.88/0.84 inference(transitivity,[status(thm)],[338, 336])).
% 0.88/0.84 tff(340,plain,
% 0.88/0.84 ((~![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_4, e_2, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.88/0.84 inference(quant_inst,[status(thm)],[])).
% 0.88/0.84 tff(341,plain,
% 0.88/0.84 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4))),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.88/0.84 tff(342,plain,
% 0.88/0.84 ($false),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[341, 335, 12, 331, 332])).
% 0.88/0.84 tff(343,plain,((~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.84 tff(344,plain,
% 0.88/0.84 (~product(e_4, e_4, e_4)),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[343, 331])).
% 0.88/0.84 tff(345,plain,
% 0.88/0.84 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_4) | (~product(e_4, e_2, e_4)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(346,plain,
% 0.88/0.84 ((product(e_4, e_4, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_2, e_4))) <=> (product(e_4, e_4, e_4) | (~product(e_4, e_2, e_4)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(347,plain,
% 0.88/0.84 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_2, e_4))))),
% 0.88/0.84 inference(monotonicity,[status(thm)],[346])).
% 0.88/0.84 tff(348,plain,
% 0.88/0.84 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_4) | (~product(e_4, e_2, e_4)))),
% 0.88/0.84 inference(transitivity,[status(thm)],[347, 345])).
% 0.88/0.84 tff(349,plain,
% 0.88/0.84 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.88/0.84 inference(quant_inst,[status(thm)],[])).
% 0.88/0.84 tff(350,plain,
% 0.88/0.84 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_4) | (~product(e_4, e_2, e_4))),
% 0.88/0.84 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.88/0.84 tff(351,plain,
% 0.88/0.84 ($false),
% 0.88/0.84 inference(unit_resolution,[status(thm)],[350, 33, 331, 344])).
% 0.88/0.84 tff(352,plain,(~product(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.84 tff(353,plain,
% 0.88/0.84 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_2)) | product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_2)) | product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(354,plain,
% 0.88/0.84 ((product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_4, e_3, e_2))) <=> ((~product(e_4, e_3, e_2)) | product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4)))),
% 0.88/0.84 inference(rewrite,[status(thm)],[])).
% 0.88/0.84 tff(355,plain,
% 0.88/0.84 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_2)) | product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4))))),
% 0.88/0.84 inference(monotonicity,[status(thm)],[354])).
% 0.88/0.84 tff(356,plain,
% 0.88/0.84 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_2)) | product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4)))),
% 0.88/0.84 inference(transitivity,[status(thm)],[355, 353])).
% 0.88/0.84 tff(357,plain,
% 0.88/0.84 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_4, e_3, e_2)))),
% 0.88/0.85 inference(quant_inst,[status(thm)],[])).
% 0.88/0.85 tff(358,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_2)) | product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.88/0.85 tff(359,plain,
% 0.88/0.85 ((~product(e_4, e_3, e_2)) | product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4))),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[358, 33])).
% 0.88/0.85 tff(360,plain,
% 0.88/0.85 ((~product(e_4, e_3, e_2)) | (~product(e_2, e_3, e_4))),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[359, 352])).
% 0.88/0.85 tff(361,plain,
% 0.88/0.85 (~product(e_4, e_3, e_2)),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[360, 330])).
% 0.88/0.85 tff(362,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.88/0.85 tff(363,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.88/0.85 tff(364,plain,
% 0.88/0.85 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(365,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.88/0.85 tff(366,plain,
% 0.88/0.85 (~equalish(e_4, e_1)),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.88/0.85 tff(367,plain,
% 0.88/0.85 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, 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_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(368,plain,
% 0.88/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.88/0.85 inference(quant_inst,[status(thm)],[])).
% 0.88/0.85 tff(369,plain,
% 0.88/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.88/0.85 tff(370,plain,
% 0.88/0.85 ($false),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[369, 366, 12, 363, 362])).
% 0.88/0.85 tff(371,plain,((~product(e_2, e_4, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.85 tff(372,plain,
% 0.88/0.85 (~product(e_2, e_4, e_3)),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[371, 207])).
% 0.88/0.85 tff(373,assumption,(~product(e_2, e_4, e_3)), introduced(assumption)).
% 0.88/0.85 tff(374,assumption,(product(e_2, e_3, e_4)), introduced(assumption)).
% 0.88/0.85 tff(375,assumption,(product(e_4, e_3, e_3)), introduced(assumption)).
% 0.88/0.85 tff(376,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_4, e_3, e_3)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_4, e_3) | (~product(e_4, e_3, e_3)) | (~product(e_2, e_3, e_4)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(377,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_4, e_3, e_3)) | (~product(e_2, e_3, e_4)))),
% 0.88/0.85 inference(quant_inst,[status(thm)],[])).
% 0.88/0.85 tff(378,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_4, e_3) | (~product(e_4, e_3, e_3)) | (~product(e_2, e_3, e_4))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.88/0.85 tff(379,plain,
% 0.88/0.85 ($false),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[378, 33, 375, 374, 373])).
% 0.88/0.85 tff(380,plain,((~product(e_4, e_3, e_3)) | (~product(e_2, e_3, e_4)) | product(e_2, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.85 tff(381,plain,
% 0.88/0.85 (~product(e_4, e_3, e_3)),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[380, 330, 372])).
% 0.88/0.85 tff(382,assumption,(~product(e_4, e_3, e_3)), introduced(assumption)).
% 0.88/0.85 tff(383,assumption,(~product(e_4, e_3, e_2)), introduced(assumption)).
% 0.88/0.85 tff(384,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.88/0.85 tff(385,plain,
% 0.88/0.85 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_4, 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_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(386,plain,
% 0.88/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.88/0.85 inference(quant_inst,[status(thm)],[])).
% 0.88/0.85 tff(387,plain,
% 0.88/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_2))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.88/0.85 tff(388,plain,
% 0.88/0.85 ($false),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[387, 366, 87, 298, 384])).
% 0.88/0.85 tff(389,plain,((~product(e_4, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.85 tff(390,plain,
% 0.88/0.85 (~product(e_4, e_1, e_2)),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[389, 298])).
% 0.88/0.85 tff(391,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(392,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1)))),
% 0.88/0.85 inference(quant_inst,[status(thm)],[])).
% 0.88/0.85 tff(393,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.88/0.85 tff(394,plain,
% 0.88/0.85 (product(e_4, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1))),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[393, 33])).
% 0.88/0.85 tff(395,plain,
% 0.88/0.85 (~product(e_4, e_1, e_1)),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[394, 298, 390])).
% 0.88/0.85 tff(396,assumption,(product(e_4, e_3, e_4)), introduced(assumption)).
% 0.88/0.85 tff(397,plain,
% 0.88/0.85 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(398,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.88/0.85 tff(399,plain,
% 0.88/0.85 (~equalish(e_4, e_3)),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.88/0.85 tff(400,plain,
% 0.88/0.85 (((~![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_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(401,plain,
% 0.88/0.85 ((~![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_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.88/0.85 inference(quant_inst,[status(thm)],[])).
% 0.88/0.85 tff(402,plain,
% 0.88/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.88/0.85 tff(403,plain,
% 0.88/0.85 ($false),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[402, 399, 12, 396, 332])).
% 0.88/0.85 tff(404,plain,((~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.85 tff(405,plain,
% 0.88/0.85 (~product(e_4, e_4, e_4)),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[404, 396])).
% 0.88/0.85 tff(406,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_4) | (~product(e_4, e_3, e_4)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(407,plain,
% 0.88/0.85 ((product(e_4, e_4, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_4))) <=> (product(e_4, e_4, e_4) | (~product(e_4, e_3, e_4)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(408,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_3, e_4))))),
% 0.88/0.85 inference(monotonicity,[status(thm)],[407])).
% 0.88/0.85 tff(409,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_4) | (~product(e_4, e_3, e_4)))),
% 0.88/0.85 inference(transitivity,[status(thm)],[408, 406])).
% 0.88/0.85 tff(410,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_4)))),
% 0.88/0.85 inference(quant_inst,[status(thm)],[])).
% 0.88/0.85 tff(411,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_4) | (~product(e_4, e_3, e_4))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.88/0.85 tff(412,plain,
% 0.88/0.85 ($false),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[411, 33, 396, 405])).
% 0.88/0.85 tff(413,plain,(~product(e_4, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.85 tff(414,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_3)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(415,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_3)))),
% 0.88/0.85 inference(quant_inst,[status(thm)],[])).
% 0.88/0.85 tff(416,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_3))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.88/0.85 tff(417,plain,
% 0.88/0.85 (~product(e_4, e_1, e_3)),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[416, 33, 324, 413])).
% 0.88/0.85 tff(418,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.88/0.85 tff(419,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.88/0.85 tff(420,plain,
% 0.88/0.85 (((~![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_4, e_1, e_4)) | (~product(e_3, 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_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(421,plain,
% 0.88/0.85 ((equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4))) <=> (equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(422,plain,
% 0.88/0.85 (((~![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_1, e_4)) | (~product(e_4, 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_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))))),
% 0.88/0.85 inference(monotonicity,[status(thm)],[421])).
% 0.88/0.85 tff(423,plain,
% 0.88/0.85 (((~![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_1, e_4)) | (~product(e_4, 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_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.88/0.85 inference(transitivity,[status(thm)],[422, 420])).
% 0.88/0.85 tff(424,plain,
% 0.88/0.85 ((~![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_1, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.88/0.85 inference(quant_inst,[status(thm)],[])).
% 0.88/0.85 tff(425,plain,
% 0.88/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[424, 423])).
% 0.88/0.85 tff(426,plain,
% 0.88/0.85 ($false),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[425, 399, 87, 419, 418])).
% 0.88/0.85 tff(427,plain,((~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.85 tff(428,plain,
% 0.88/0.85 (~product(e_4, e_1, e_4)),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[427, 324])).
% 0.88/0.85 tff(429,assumption,(~product(e_4, e_1, e_1)), introduced(assumption)).
% 0.88/0.85 tff(430,assumption,(product(e_4, e_3, e_1)), introduced(assumption)).
% 0.88/0.85 tff(431,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.88/0.85 tff(432,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(433,plain,
% 0.88/0.85 ((product(e_4, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_4, e_3, e_1))) <=> (product(e_4, e_1, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(434,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_1))))),
% 0.88/0.85 inference(monotonicity,[status(thm)],[433])).
% 0.88/0.85 tff(435,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.88/0.85 inference(transitivity,[status(thm)],[434, 432])).
% 0.88/0.85 tff(436,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.88/0.85 inference(quant_inst,[status(thm)],[])).
% 0.88/0.85 tff(437,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_1))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.88/0.85 tff(438,plain,
% 0.88/0.85 ($false),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[437, 33, 429, 430, 431])).
% 0.88/0.85 tff(439,plain,((~product(e_1, e_3, e_1)) | product(e_4, e_1, e_1) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.85 tff(440,plain,
% 0.88/0.85 (~product(e_1, e_3, e_1)),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[439, 430, 429])).
% 0.88/0.85 tff(441,assumption,(~product(e_4, e_1, e_4)), introduced(assumption)).
% 0.88/0.85 tff(442,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.88/0.85 tff(443,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_4)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(444,plain,
% 0.88/0.85 ((product(e_4, e_1, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_3, e_1))) <=> (product(e_4, e_1, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_4)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(445,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_4))))),
% 0.88/0.85 inference(monotonicity,[status(thm)],[444])).
% 0.88/0.85 tff(446,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_4)))),
% 0.88/0.85 inference(transitivity,[status(thm)],[445, 443])).
% 0.88/0.85 tff(447,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_3, e_1)))),
% 0.88/0.85 inference(quant_inst,[status(thm)],[])).
% 0.88/0.85 tff(448,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_4))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.88/0.85 tff(449,plain,
% 0.88/0.85 ($false),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[448, 33, 441, 430, 442])).
% 0.88/0.85 tff(450,plain,((~product(e_1, e_3, e_4)) | product(e_4, e_1, e_4) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.85 tff(451,plain,
% 0.88/0.85 (~product(e_1, e_3, e_4)),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[450, 430, 441])).
% 0.88/0.85 tff(452,assumption,(~product(e_4, e_1, e_3)), introduced(assumption)).
% 0.88/0.85 tff(453,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.88/0.85 tff(454,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_3)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(455,plain,
% 0.88/0.85 ((product(e_4, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_4, e_3, e_1))) <=> (product(e_4, e_1, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_3)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(456,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_3))))),
% 0.88/0.85 inference(monotonicity,[status(thm)],[455])).
% 0.88/0.85 tff(457,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_3)))),
% 0.88/0.85 inference(transitivity,[status(thm)],[456, 454])).
% 0.88/0.85 tff(458,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_4, e_3, e_1)))),
% 0.88/0.85 inference(quant_inst,[status(thm)],[])).
% 0.88/0.85 tff(459,plain,
% 0.88/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_3))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.88/0.85 tff(460,plain,
% 0.88/0.85 ($false),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[459, 33, 452, 430, 453])).
% 0.88/0.85 tff(461,plain,((~product(e_1, e_3, e_3)) | product(e_4, e_1, e_3) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.85 tff(462,plain,
% 0.88/0.85 (~product(e_1, e_3, e_3)),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[461, 430, 452])).
% 0.88/0.85 tff(463,assumption,(~product(e_4, e_1, e_2)), introduced(assumption)).
% 0.88/0.85 tff(464,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.88/0.85 tff(465,plain,
% 0.88/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(466,plain,
% 0.88/0.85 ((product(e_4, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_1))) <=> (product(e_4, e_1, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.88/0.86 inference(rewrite,[status(thm)],[])).
% 0.88/0.86 tff(467,plain,
% 0.88/0.86 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_2))))),
% 0.88/0.86 inference(monotonicity,[status(thm)],[466])).
% 0.88/0.86 tff(468,plain,
% 0.88/0.86 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.88/0.86 inference(transitivity,[status(thm)],[467, 465])).
% 0.88/0.86 tff(469,plain,
% 0.88/0.86 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_1)))),
% 0.88/0.86 inference(quant_inst,[status(thm)],[])).
% 0.88/0.86 tff(470,plain,
% 0.88/0.86 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_2))),
% 0.88/0.86 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.88/0.86 tff(471,plain,
% 0.88/0.86 ($false),
% 0.88/0.86 inference(unit_resolution,[status(thm)],[470, 33, 463, 430, 464])).
% 0.88/0.86 tff(472,plain,((~product(e_1, e_3, e_2)) | product(e_4, e_1, e_2) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.86 tff(473,plain,
% 0.88/0.86 (~product(e_1, e_3, e_2)),
% 0.88/0.86 inference(unit_resolution,[status(thm)],[472, 430, 463])).
% 0.88/0.86 tff(474,plain,
% 0.88/0.86 (((~![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_4) | product(e_1, e_3, e_6) | 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_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_4) | product(e_1, e_3, e_6) | 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_3, e_1))),
% 0.88/0.86 inference(rewrite,[status(thm)],[])).
% 0.88/0.86 tff(475,plain,
% 0.88/0.86 ((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_4) | product(e_1, e_3, e_6) | 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_3, e_1))),
% 0.88/0.86 inference(rewrite,[status(thm)],[])).
% 0.88/0.86 tff(476,plain,
% 0.88/0.86 (((~![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_4) | product(e_1, e_3, e_6) | 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_3, e_1)))),
% 0.88/0.86 inference(monotonicity,[status(thm)],[475])).
% 0.88/0.86 tff(477,plain,
% 0.88/0.86 (((~![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_4) | product(e_1, e_3, e_6) | 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_3, e_1))),
% 0.88/0.86 inference(transitivity,[status(thm)],[476, 474])).
% 0.88/0.86 tff(478,plain,
% 0.88/0.86 ((~![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)))),
% 0.88/0.86 inference(quant_inst,[status(thm)],[])).
% 0.88/0.86 tff(479,plain,
% 0.88/0.86 ((~![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_4) | product(e_1, e_3, e_6) | 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_3, e_1)),
% 0.88/0.86 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.88/0.86 tff(480,plain,
% 0.88/0.86 (product(e_1, e_3, e_4) | product(e_1, e_3, e_6) | 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_3, e_1)),
% 0.88/0.86 inference(unit_resolution,[status(thm)],[479, 147, 289, 144])).
% 0.88/0.86 tff(481,plain,
% 0.88/0.86 (product(e_1, e_3, e_6)),
% 0.88/0.86 inference(unit_resolution,[status(thm)],[480, 473, 462, 54, 451, 440])).
% 0.88/0.86 tff(482,plain,
% 0.88/0.86 (greater(e_6, e_5) <=> greater(e_6, e_5)),
% 0.88/0.86 inference(rewrite,[status(thm)],[])).
% 0.88/0.86 tff(483,axiom,(greater(e_6, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_greater_e_5')).
% 0.88/0.86 tff(484,plain,
% 0.88/0.86 (greater(e_6, e_5)),
% 0.88/0.86 inference(modus_ponens,[status(thm)],[483, 482])).
% 0.88/0.86 tff(485,plain,
% 0.88/0.86 (next(e_4, e_5) <=> next(e_4, e_5)),
% 0.88/0.86 inference(rewrite,[status(thm)],[])).
% 0.88/0.86 tff(486,axiom,(next(e_4, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_then_e_5')).
% 0.88/0.86 tff(487,plain,
% 0.88/0.86 (next(e_4, e_5)),
% 0.88/0.86 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.88/0.86 tff(488,plain,
% 0.88/0.86 (((~![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)))),
% 0.88/0.86 inference(rewrite,[status(thm)],[])).
% 0.88/0.86 tff(489,plain,
% 0.88/0.86 ((~![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)))),
% 0.88/0.86 inference(quant_inst,[status(thm)],[])).
% 0.88/0.86 tff(490,plain,
% 0.88/0.86 ((~![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))),
% 0.88/0.86 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.88/0.86 tff(491,plain,
% 0.88/0.86 (~product(e_4, e_1, e_6)),
% 0.88/0.86 inference(unit_resolution,[status(thm)],[490, 487, 484, 103])).
% 0.88/0.86 tff(492,plain,
% 0.88/0.86 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_6) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_6)))),
% 0.88/0.86 inference(rewrite,[status(thm)],[])).
% 0.88/0.86 tff(493,plain,
% 0.88/0.86 ((product(e_4, e_1, e_6) | (~product(e_1, e_3, e_6)) | (~product(e_4, e_3, e_1))) <=> (product(e_4, e_1, e_6) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_6)))),
% 0.88/0.86 inference(rewrite,[status(thm)],[])).
% 0.88/0.86 tff(494,plain,
% 0.88/0.86 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_1, e_3, e_6)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_6))))),
% 0.88/0.86 inference(monotonicity,[status(thm)],[493])).
% 0.88/0.86 tff(495,plain,
% 0.88/0.86 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_1, e_3, e_6)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_6) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_6)))),
% 0.88/0.86 inference(transitivity,[status(thm)],[494, 492])).
% 0.88/0.86 tff(496,plain,
% 0.88/0.86 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_1, e_3, e_6)) | (~product(e_4, e_3, e_1)))),
% 0.88/0.86 inference(quant_inst,[status(thm)],[])).
% 0.88/0.86 tff(497,plain,
% 0.88/0.86 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_6) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_3, e_6))),
% 0.88/0.86 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.88/0.86 tff(498,plain,
% 0.88/0.86 ($false),
% 0.88/0.86 inference(unit_resolution,[status(thm)],[497, 33, 491, 430, 481])).
% 0.88/0.86 tff(499,plain,((~product(e_4, e_3, e_1)) | product(e_1, e_3, e_5) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.86 tff(500,plain,
% 0.88/0.86 ((~product(e_4, e_3, e_1)) | product(e_1, e_3, e_5) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.88/0.86 inference(unit_resolution,[status(thm)],[499, 428, 417])).
% 0.88/0.86 tff(501,plain,
% 0.88/0.86 (~product(e_4, e_3, e_1)),
% 0.88/0.86 inference(unit_resolution,[status(thm)],[500, 395, 54, 390])).
% 0.88/0.86 tff(502,assumption,(~product(e_4, e_1, e_5)), introduced(assumption)).
% 0.88/0.86 tff(503,plain,
% 0.88/0.86 (group_element(e_4) <=> group_element(e_4)),
% 0.88/0.86 inference(rewrite,[status(thm)],[])).
% 0.88/0.86 tff(504,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.88/0.86 tff(505,plain,
% 0.88/0.86 (group_element(e_4)),
% 0.88/0.86 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.88/0.86 tff(506,plain,
% 0.88/0.86 (((~![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)))),
% 0.88/0.86 inference(rewrite,[status(thm)],[])).
% 0.88/0.86 tff(507,plain,
% 0.88/0.86 ((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)))),
% 0.88/0.86 inference(rewrite,[status(thm)],[])).
% 0.88/0.86 tff(508,plain,
% 0.88/0.86 (((~![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))))),
% 0.88/0.86 inference(monotonicity,[status(thm)],[507])).
% 0.88/0.86 tff(509,plain,
% 0.88/0.86 (((~![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)))),
% 0.88/0.86 inference(transitivity,[status(thm)],[508, 506])).
% 0.88/0.86 tff(510,plain,
% 0.88/0.86 ((~![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)))),
% 0.88/0.86 inference(quant_inst,[status(thm)],[])).
% 0.88/0.86 tff(511,plain,
% 0.88/0.86 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_4, e_1, e_6) | (~group_element(e_1)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4))),
% 0.88/0.86 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.88/0.86 tff(512,plain,
% 0.88/0.86 (product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.88/0.86 inference(unit_resolution,[status(thm)],[511, 147, 505, 144, 491])).
% 0.88/0.86 tff(513,plain,
% 0.88/0.86 ($false),
% 0.88/0.86 inference(unit_resolution,[status(thm)],[512, 395, 390, 441, 452, 502])).
% 0.88/0.86 tff(514,plain,((~product(e_1, e_1, e_2)) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.86 tff(515,plain,
% 0.88/0.86 ((~product(e_1, e_1, e_2)) | product(e_4, e_1, e_5)),
% 0.88/0.86 inference(unit_resolution,[status(thm)],[514, 428, 417])).
% 0.88/0.86 tff(516,plain,
% 0.88/0.86 (product(e_4, e_1, e_5)),
% 0.88/0.86 inference(unit_resolution,[status(thm)],[515, 298])).
% 0.88/0.86 tff(517,assumption,(product(e_4, e_3, e_5)), introduced(assumption)).
% 0.88/0.86 tff(518,assumption,(product(e_4, e_1, e_5)), introduced(assumption)).
% 0.88/0.86 tff(519,plain,
% 0.88/0.86 (((~![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_3, e_5)) | (~product(e_4, e_1, 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_3, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.88/0.86 inference(rewrite,[status(thm)],[])).
% 0.88/0.86 tff(520,plain,
% 0.88/0.86 ((equalish(e_3, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_3, e_5))) <=> (equalish(e_3, e_1) | (~product(e_4, e_3, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.88/0.86 inference(rewrite,[status(thm)],[])).
% 0.88/0.86 tff(521,plain,
% 0.88/0.86 (((~![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_3, e_5)) | (~product(e_4, e_1, e_5))))),
% 0.95/0.86 inference(monotonicity,[status(thm)],[520])).
% 0.95/0.86 tff(522,plain,
% 0.95/0.86 (((~![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_3, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.95/0.86 inference(transitivity,[status(thm)],[521, 519])).
% 0.95/0.86 tff(523,plain,
% 0.95/0.86 ((~![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)))),
% 0.95/0.86 inference(quant_inst,[status(thm)],[])).
% 0.95/0.86 tff(524,plain,
% 0.95/0.86 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_4, e_3, e_5)) | (~product(e_4, e_1, e_5))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.95/0.86 tff(525,plain,
% 0.95/0.86 ($false),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[524, 15, 12, 518, 517])).
% 0.95/0.86 tff(526,plain,((~product(e_4, e_3, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.95/0.86 tff(527,plain,
% 0.95/0.86 (~product(e_4, e_3, e_5)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[526, 516])).
% 0.95/0.86 tff(528,plain,
% 0.95/0.86 (((~![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_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_6) | product(e_4, e_3, e_5) | product(e_4, 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_4)) | 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_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(529,plain,
% 0.95/0.86 ((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_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(530,plain,
% 0.95/0.86 (((~![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_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1)))),
% 0.95/0.86 inference(monotonicity,[status(thm)],[529])).
% 0.95/0.86 tff(531,plain,
% 0.95/0.86 (((~![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_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1))),
% 0.95/0.87 inference(transitivity,[status(thm)],[530, 528])).
% 0.95/0.87 tff(532,plain,
% 0.95/0.87 ((~![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)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(533,plain,
% 0.95/0.87 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[532, 531])).
% 0.95/0.87 tff(534,plain,
% 0.95/0.87 (product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[533, 289, 505, 144])).
% 0.95/0.87 tff(535,plain,
% 0.95/0.87 (product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[534, 413])).
% 0.95/0.87 tff(536,plain,
% 0.95/0.87 ($false),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[535, 527, 501, 55, 383, 382])).
% 0.95/0.87 tff(537,plain,((~product(e_1, e_1, e_2)) | product(e_4, e_3, e_6) | product(e_4, e_3, e_2) | product(e_4, e_3, e_3) | product(e_1, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.95/0.87 tff(538,plain,
% 0.95/0.87 (~product(e_1, e_1, e_2)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[537, 383, 55, 382, 54])).
% 0.95/0.87 tff(539,plain,
% 0.95/0.87 (product(e_1, e_1, e_1)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[154, 538])).
% 0.95/0.87 tff(540,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.95/0.87 tff(541,plain,
% 0.95/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(542,plain,
% 0.95/0.87 ((equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))) <=> (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(543,plain,
% 0.95/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[542])).
% 0.95/0.87 tff(544,plain,
% 0.95/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[543, 541])).
% 0.95/0.87 tff(545,plain,
% 0.95/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(546,plain,
% 0.95/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.95/0.87 tff(547,plain,
% 0.95/0.87 ($false),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[546, 366, 87, 77, 540])).
% 0.95/0.87 tff(548,plain,((~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.95/0.87 tff(549,plain,
% 0.95/0.87 (~product(e_4, e_1, e_1)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[548, 539])).
% 0.95/0.87 tff(550,plain,
% 0.95/0.87 (product(e_4, e_1, e_5) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[512, 428, 417])).
% 0.95/0.87 tff(551,plain,
% 0.95/0.87 (product(e_4, e_1, e_5)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[550, 463, 549])).
% 0.95/0.87 tff(552,plain,
% 0.95/0.87 (~product(e_4, e_3, e_1)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[500, 463, 54, 549])).
% 0.95/0.87 tff(553,plain,
% 0.95/0.87 (product(e_4, e_3, e_5)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[535, 552, 55, 382, 383])).
% 0.95/0.87 tff(554,plain,
% 0.95/0.87 ($false),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[526, 553, 551])).
% 0.95/0.87 tff(555,plain,(product(e_4, e_1, e_2) | product(e_4, e_3, e_6) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_1, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.95/0.87 tff(556,plain,
% 0.95/0.87 (product(e_4, e_1, e_2) | product(e_4, e_3, e_6) | product(e_1, e_3, e_5)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[555, 381, 361])).
% 0.95/0.87 tff(557,plain,
% 0.95/0.87 (product(e_4, e_1, e_2)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[556, 55, 54])).
% 0.95/0.87 tff(558,assumption,(product(e_5, e_1, e_2)), introduced(assumption)).
% 0.95/0.87 tff(559,plain,
% 0.95/0.87 ((~equalish(e_5, e_4)) <=> (~equalish(e_5, e_4))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(560,axiom,(~equalish(e_5, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_4')).
% 0.95/0.87 tff(561,plain,
% 0.95/0.87 (~equalish(e_5, e_4)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.95/0.87 tff(562,plain,
% 0.95/0.87 (((~![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_5, e_1, e_2)) | (~product(e_4, 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_5, e_4) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(563,plain,
% 0.95/0.87 ((equalish(e_5, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_5, e_1, e_2))) <=> (equalish(e_5, e_4) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(564,plain,
% 0.95/0.87 (((~![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_1, e_2)) | (~product(e_5, 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_5, e_4) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_2))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[563])).
% 0.95/0.87 tff(565,plain,
% 0.95/0.87 (((~![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_1, e_2)) | (~product(e_5, 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_5, e_4) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[564, 562])).
% 0.95/0.87 tff(566,plain,
% 0.95/0.87 ((~![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_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(567,plain,
% 0.95/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_2))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[566, 565])).
% 0.96/0.87 tff(568,plain,
% 0.96/0.87 ($false),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[567, 561, 87, 384, 558])).
% 0.96/0.87 tff(569,plain,((~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.87 tff(570,plain,
% 0.96/0.87 (~product(e_5, e_1, e_2)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[569, 557])).
% 0.96/0.87 tff(571,plain,
% 0.96/0.87 ((~product(e_1, e_1, e_2)) | product(e_4, e_3, e_6) | product(e_1, e_3, e_5)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[537, 361, 381])).
% 0.96/0.87 tff(572,plain,
% 0.96/0.87 (~product(e_1, e_1, e_2)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[571, 55, 54])).
% 0.96/0.87 tff(573,plain,
% 0.96/0.87 (product(e_1, e_1, e_1)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[154, 572])).
% 0.96/0.87 tff(574,assumption,(product(e_5, e_1, e_1)), introduced(assumption)).
% 0.96/0.87 tff(575,plain,
% 0.96/0.87 ((~equalish(e_5, e_1)) <=> (~equalish(e_5, e_1))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(576,axiom,(~equalish(e_5, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_1')).
% 0.96/0.87 tff(577,plain,
% 0.96/0.87 (~equalish(e_5, e_1)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[576, 575])).
% 0.96/0.87 tff(578,plain,
% 0.96/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, 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_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(579,plain,
% 0.96/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))),
% 0.96/0.87 inference(quant_inst,[status(thm)],[])).
% 0.96/0.87 tff(580,plain,
% 0.96/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[579, 578])).
% 0.96/0.87 tff(581,plain,
% 0.96/0.87 ($false),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[580, 577, 87, 77, 574])).
% 0.96/0.87 tff(582,plain,((~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.87 tff(583,plain,
% 0.96/0.87 (~product(e_5, e_1, e_1)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[582, 573])).
% 0.96/0.87 tff(584,assumption,(product(e_5, e_1, e_3)), introduced(assumption)).
% 0.96/0.87 tff(585,plain,
% 0.96/0.87 ((~equalish(e_5, e_2)) <=> (~equalish(e_5, e_2))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(586,axiom,(~equalish(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_2')).
% 0.96/0.87 tff(587,plain,
% 0.96/0.87 (~equalish(e_5, e_2)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.96/0.87 tff(588,plain,
% 0.96/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, 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_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(589,plain,
% 0.96/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3)))),
% 0.96/0.87 inference(quant_inst,[status(thm)],[])).
% 0.96/0.87 tff(590,plain,
% 0.96/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[589, 588])).
% 0.96/0.87 tff(591,plain,
% 0.96/0.87 ($false),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[590, 587, 87, 363, 584])).
% 0.96/0.87 tff(592,plain,((~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.87 tff(593,plain,
% 0.96/0.87 (~product(e_5, e_1, e_3)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[592, 207])).
% 0.96/0.87 tff(594,assumption,(product(e_5, e_1, e_4)), introduced(assumption)).
% 0.96/0.87 tff(595,plain,
% 0.96/0.87 ((~equalish(e_5, e_3)) <=> (~equalish(e_5, e_3))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(596,axiom,(~equalish(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_3')).
% 0.96/0.87 tff(597,plain,
% 0.96/0.87 (~equalish(e_5, e_3)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.96/0.87 tff(598,plain,
% 0.96/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, 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_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(599,plain,
% 0.96/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.96/0.87 inference(quant_inst,[status(thm)],[])).
% 0.96/0.87 tff(600,plain,
% 0.96/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[599, 598])).
% 0.96/0.87 tff(601,plain,
% 0.96/0.87 ($false),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[600, 597, 87, 419, 594])).
% 0.96/0.87 tff(602,plain,((~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.87 tff(603,plain,
% 0.96/0.87 (~product(e_5, e_1, e_4)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[602, 324])).
% 0.96/0.87 tff(604,assumption,(product(e_5, e_1, e_5)), introduced(assumption)).
% 0.96/0.87 tff(605,assumption,(product(e_5, e_5, e_5)), introduced(assumption)).
% 0.96/0.87 tff(606,plain,
% 0.96/0.87 (((~![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_5, e_1, e_5)) | (~product(e_5, 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_1) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(607,plain,
% 0.96/0.87 ((~![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_5, e_1, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.96/0.87 inference(quant_inst,[status(thm)],[])).
% 0.96/0.87 tff(608,plain,
% 0.96/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_5, e_5))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.96/0.87 tff(609,plain,
% 0.96/0.87 ($false),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[608, 577, 12, 604, 605])).
% 0.96/0.87 tff(610,plain,((~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.87 tff(611,plain,
% 0.96/0.87 (~product(e_5, e_5, e_5)),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[610, 604])).
% 0.96/0.87 tff(612,plain,
% 0.96/0.87 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(613,plain,
% 0.96/0.87 ((product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_1, e_5))) <=> (product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(614,plain,
% 0.96/0.87 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5))))),
% 0.96/0.87 inference(monotonicity,[status(thm)],[613])).
% 0.96/0.87 tff(615,plain,
% 0.96/0.87 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)))),
% 0.96/0.87 inference(transitivity,[status(thm)],[614, 612])).
% 0.96/0.87 tff(616,plain,
% 0.96/0.87 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.96/0.87 inference(quant_inst,[status(thm)],[])).
% 0.96/0.87 tff(617,plain,
% 0.96/0.87 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[616, 615])).
% 0.96/0.87 tff(618,plain,
% 0.96/0.87 ($false),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[617, 33, 604, 611])).
% 0.96/0.87 tff(619,plain,(~product(e_5, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.96/0.87 tff(620,plain,
% 0.96/0.87 (group_element(e_5) <=> group_element(e_5)),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(621,axiom,(group_element(e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_5')).
% 0.96/0.87 tff(622,plain,
% 0.96/0.87 (group_element(e_5)),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[621, 620])).
% 0.96/0.87 tff(623,plain,
% 0.96/0.87 (((~![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_3) | product(e_5, e_1, e_6) | product(e_5, e_1, e_4) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | product(e_5, 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_5)) | product(e_5, e_1, e_3) | product(e_5, e_1, e_6) | product(e_5, e_1, e_4) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | product(e_5, e_1, e_5))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(624,plain,
% 0.96/0.87 ((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_3) | product(e_5, e_1, e_6) | product(e_5, e_1, e_4) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | product(e_5, e_1, e_5))),
% 0.96/0.87 inference(rewrite,[status(thm)],[])).
% 0.96/0.87 tff(625,plain,
% 0.96/0.87 (((~![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_3) | product(e_5, e_1, e_6) | product(e_5, e_1, e_4) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | product(e_5, e_1, e_5)))),
% 0.96/0.87 inference(monotonicity,[status(thm)],[624])).
% 0.96/0.87 tff(626,plain,
% 0.96/0.87 (((~![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_3) | product(e_5, e_1, e_6) | product(e_5, e_1, e_4) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | product(e_5, e_1, e_5))),
% 0.96/0.88 inference(transitivity,[status(thm)],[625, 623])).
% 0.96/0.88 tff(627,plain,
% 0.96/0.88 ((~![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)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(628,plain,
% 0.96/0.88 ((~![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_3) | product(e_5, e_1, e_6) | product(e_5, e_1, e_4) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | product(e_5, e_1, e_5)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[627, 626])).
% 0.96/0.88 tff(629,plain,
% 0.96/0.88 (product(e_5, e_1, e_3) | product(e_5, e_1, e_6) | product(e_5, e_1, e_4) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | product(e_5, e_1, e_5)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[628, 147, 622, 144])).
% 0.96/0.88 tff(630,plain,
% 0.96/0.88 (product(e_5, e_1, e_3) | product(e_5, e_1, e_6) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[629, 619, 603])).
% 0.96/0.88 tff(631,plain,
% 0.96/0.88 (product(e_5, e_1, e_6) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[630, 593])).
% 0.96/0.88 tff(632,plain,
% 0.96/0.88 (product(e_5, e_1, e_6)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[631, 583, 570])).
% 0.96/0.88 tff(633,assumption,(product(e_6, e_1, e_6)), introduced(assumption)).
% 0.96/0.88 tff(634,plain,
% 0.96/0.88 ((~equalish(e_6, e_5)) <=> (~equalish(e_6, e_5))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(635,axiom,(~equalish(e_6, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_5')).
% 0.96/0.88 tff(636,plain,
% 0.96/0.88 (~equalish(e_6, e_5)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.96/0.88 tff(637,plain,
% 0.96/0.88 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, e_1, e_6)) | (~product(e_6, e_1, 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_5) | (~product(e_5, e_1, e_6)) | (~product(e_6, e_1, e_6)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(638,plain,
% 0.96/0.88 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, e_1, e_6)) | (~product(e_6, e_1, e_6)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(639,plain,
% 0.96/0.88 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_5) | (~product(e_5, e_1, e_6)) | (~product(e_6, e_1, e_6))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[638, 637])).
% 0.96/0.88 tff(640,plain,
% 0.96/0.88 ($false),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[639, 636, 87, 1, 633])).
% 0.96/0.88 tff(641,plain,((~product(e_6, e_1, e_6)) | (~product(e_5, e_1, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.88 tff(642,plain,
% 0.96/0.88 (~product(e_6, e_1, e_6)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[641, 632])).
% 0.96/0.88 tff(643,plain,
% 0.96/0.88 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_5, e_6, e_5))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_5, e_6, e_5))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(644,plain,
% 0.96/0.88 ((product(e_5, e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6))) <=> ((~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_5, e_6, e_5))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(645,plain,
% 0.96/0.88 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_5, e_6, e_5)))),
% 0.96/0.88 inference(monotonicity,[status(thm)],[644])).
% 0.96/0.88 tff(646,plain,
% 0.96/0.88 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_5, e_6, e_5))),
% 0.96/0.88 inference(transitivity,[status(thm)],[645, 643])).
% 0.96/0.88 tff(647,plain,
% 0.96/0.88 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(648,plain,
% 0.96/0.88 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_5, e_6, e_5)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[647, 646])).
% 0.96/0.88 tff(649,plain,
% 0.96/0.88 ((~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_5, e_6, e_5)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[648, 33])).
% 0.96/0.88 tff(650,plain,
% 0.96/0.88 (~product(e_6, e_1, e_5)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[649, 632, 53])).
% 0.96/0.88 tff(651,assumption,(product(e_6, e_1, e_3)), introduced(assumption)).
% 0.96/0.88 tff(652,plain,
% 0.96/0.88 ((~equalish(e_6, e_2)) <=> (~equalish(e_6, e_2))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(653,axiom,(~equalish(e_6, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_2')).
% 0.96/0.88 tff(654,plain,
% 0.96/0.88 (~equalish(e_6, e_2)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[653, 652])).
% 0.96/0.88 tff(655,plain,
% 0.96/0.88 (((~![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)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(656,plain,
% 0.96/0.88 ((~![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)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(657,plain,
% 0.96/0.88 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_6, e_1, e_3))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.96/0.88 tff(658,plain,
% 0.96/0.88 ($false),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[657, 654, 87, 363, 651])).
% 0.96/0.88 tff(659,plain,((~product(e_6, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.88 tff(660,plain,
% 0.96/0.88 (~product(e_6, e_1, e_3)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[659, 207])).
% 0.96/0.88 tff(661,assumption,(~product(e_6, e_1, e_6)), introduced(assumption)).
% 0.96/0.88 tff(662,assumption,(~product(e_6, e_1, e_5)), introduced(assumption)).
% 0.96/0.88 tff(663,assumption,(~product(e_6, e_1, e_3)), introduced(assumption)).
% 0.96/0.88 tff(664,plain,
% 0.96/0.88 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(665,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.96/0.88 tff(666,plain,
% 0.96/0.88 (~equalish(e_2, e_1)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[665, 664])).
% 0.96/0.88 tff(667,plain,
% 0.96/0.88 (((~![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_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_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(668,plain,
% 0.96/0.88 ((~![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_2)) | (~product(e_2, e_1, e_2)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(669,plain,
% 0.96/0.88 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[668, 667])).
% 0.96/0.88 tff(670,plain,
% 0.96/0.88 ($false),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[669, 666, 87, 298, 56])).
% 0.96/0.88 tff(671,plain,((~product(e_2, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.88 tff(672,plain,
% 0.96/0.88 (~product(e_1, e_1, e_2)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[671, 56])).
% 0.96/0.88 tff(673,plain,
% 0.96/0.88 (product(e_1, e_1, e_1)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[154, 672])).
% 0.96/0.88 tff(674,assumption,(product(e_6, e_1, e_2)), introduced(assumption)).
% 0.96/0.88 tff(675,plain,
% 0.96/0.88 (((~![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_2)) | (~product(e_6, 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_6, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_6, e_1, e_2)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(676,plain,
% 0.96/0.88 ((~![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_2)) | (~product(e_6, e_1, e_2)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(677,plain,
% 0.96/0.88 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_6, e_1, e_2))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[676, 675])).
% 0.96/0.88 tff(678,plain,
% 0.96/0.88 ($false),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[677, 654, 87, 56, 674])).
% 0.96/0.88 tff(679,plain,((~product(e_6, e_1, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.88 tff(680,plain,
% 0.96/0.88 (~product(e_6, e_1, e_2)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[679, 56])).
% 0.96/0.88 tff(681,assumption,(product(e_6, e_1, e_4)), introduced(assumption)).
% 0.96/0.88 tff(682,plain,
% 0.96/0.88 ((~equalish(e_6, e_3)) <=> (~equalish(e_6, e_3))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(683,axiom,(~equalish(e_6, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_3')).
% 0.96/0.88 tff(684,plain,
% 0.96/0.88 (~equalish(e_6, e_3)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.96/0.88 tff(685,plain,
% 0.96/0.88 (((~![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)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(686,plain,
% 0.96/0.88 ((~![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)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(687,plain,
% 0.96/0.88 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_4))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[686, 685])).
% 0.96/0.88 tff(688,plain,
% 0.96/0.88 ($false),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[687, 684, 87, 419, 681])).
% 0.96/0.88 tff(689,plain,((~product(e_6, e_1, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.88 tff(690,plain,
% 0.96/0.88 (~product(e_6, e_1, e_4)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[689, 324])).
% 0.96/0.88 tff(691,plain,
% 0.96/0.88 (group_element(e_6) <=> group_element(e_6)),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(692,axiom,(group_element(e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_6')).
% 0.96/0.88 tff(693,plain,
% 0.96/0.88 (group_element(e_6)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[692, 691])).
% 0.96/0.88 tff(694,plain,
% 0.96/0.88 (((~![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_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_6) | (~group_element(e_6)) | 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)) | 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_6) | (~group_element(e_6)) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(695,plain,
% 0.96/0.88 ((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)) | 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_6) | (~group_element(e_6)) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(696,plain,
% 0.96/0.88 (((~![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)) | 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_6) | (~group_element(e_6)) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5)))),
% 0.96/0.88 inference(monotonicity,[status(thm)],[695])).
% 0.96/0.88 tff(697,plain,
% 0.96/0.88 (((~![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)) | 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_6) | (~group_element(e_6)) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5))),
% 0.96/0.88 inference(transitivity,[status(thm)],[696, 694])).
% 0.96/0.88 tff(698,plain,
% 0.96/0.88 ((~![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)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(699,plain,
% 0.96/0.88 ((~![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_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_6) | (~group_element(e_6)) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[698, 697])).
% 0.96/0.88 tff(700,plain,
% 0.96/0.88 (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_6) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[699, 147, 693, 144])).
% 0.96/0.88 tff(701,plain,
% 0.96/0.88 (product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_6) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[700, 690])).
% 0.96/0.88 tff(702,plain,
% 0.96/0.88 (product(e_6, e_1, e_1)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[701, 680, 661, 662, 663])).
% 0.96/0.88 tff(703,assumption,(product(e_6, e_1, e_1)), introduced(assumption)).
% 0.96/0.88 tff(704,plain,
% 0.96/0.88 ((~equalish(e_6, e_1)) <=> (~equalish(e_6, e_1))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(705,axiom,(~equalish(e_6, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_1')).
% 0.96/0.88 tff(706,plain,
% 0.96/0.88 (~equalish(e_6, e_1)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.96/0.88 tff(707,plain,
% 0.96/0.88 (((~![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)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(708,plain,
% 0.96/0.88 ((~![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)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(709,plain,
% 0.96/0.88 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_6, e_1, e_1))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.96/0.88 tff(710,plain,
% 0.96/0.88 ($false),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[709, 706, 87, 77, 703])).
% 0.96/0.88 tff(711,plain,((~product(e_6, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.88 tff(712,plain,
% 0.96/0.88 ($false),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[711, 702, 673])).
% 0.96/0.88 tff(713,plain,((~product(e_2, e_1, e_2)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.96/0.88 tff(714,plain,
% 0.96/0.88 (~product(e_2, e_1, e_2)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[713, 663, 662, 661])).
% 0.96/0.88 tff(715,plain,
% 0.96/0.88 (product(e_2, e_1, e_3)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[206, 714])).
% 0.96/0.88 tff(716,plain,
% 0.96/0.88 (~product(e_2, e_4, e_3)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[371, 715])).
% 0.96/0.88 tff(717,plain,
% 0.96/0.88 (product(e_2, e_3, e_4)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[329, 715])).
% 0.96/0.88 tff(718,plain,
% 0.96/0.88 (~product(e_4, e_3, e_3)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[380, 717, 716])).
% 0.96/0.88 tff(719,plain,
% 0.96/0.88 (~product(e_4, e_3, e_2)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[360, 717])).
% 0.96/0.88 tff(720,plain,
% 0.96/0.88 (~product(e_1, e_1, e_2)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[537, 719, 55, 718, 54])).
% 0.96/0.88 tff(721,plain,
% 0.96/0.88 (product(e_1, e_1, e_1)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[154, 720])).
% 0.96/0.88 tff(722,plain,
% 0.96/0.88 (~product(e_4, e_1, e_1)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[548, 721])).
% 0.96/0.88 tff(723,plain,
% 0.96/0.88 (~product(e_6, e_1, e_1)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[711, 721])).
% 0.96/0.88 tff(724,plain,
% 0.96/0.88 (product(e_6, e_1, e_2)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[701, 723, 661, 662, 663])).
% 0.96/0.88 tff(725,plain,
% 0.96/0.88 (((~![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_2)) | (~product(e_6, 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_6, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_6, e_1, e_2)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(726,plain,
% 0.96/0.88 ((~![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_2)) | (~product(e_6, e_1, e_2)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(727,plain,
% 0.96/0.89 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_6, e_1, e_2))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[726, 725])).
% 0.96/0.89 tff(728,plain,
% 0.96/0.89 ($false),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[727, 706, 87, 298, 674])).
% 0.96/0.89 tff(729,plain,((~product(e_6, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.89 tff(730,plain,
% 0.96/0.89 (~product(e_1, e_1, e_2)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[729, 674])).
% 0.96/0.89 tff(731,plain,
% 0.96/0.89 (product(e_1, e_1, e_1)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[154, 730])).
% 0.96/0.89 tff(732,plain,
% 0.96/0.89 (~product(e_3, e_1, e_1)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[321, 731])).
% 0.96/0.89 tff(733,plain,
% 0.96/0.89 (product(e_3, e_1, e_4)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[296, 732, 268, 267])).
% 0.96/0.89 tff(734,plain,
% 0.96/0.89 (~product(e_4, e_1, e_4)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[427, 733])).
% 0.96/0.89 tff(735,plain,
% 0.96/0.89 (product(e_4, e_1, e_2)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[512, 734, 502, 452, 429])).
% 0.96/0.89 tff(736,plain,
% 0.96/0.89 ((~equalish(e_6, e_4)) <=> (~equalish(e_6, e_4))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(737,axiom,(~equalish(e_6, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_4')).
% 0.96/0.89 tff(738,plain,
% 0.96/0.89 (~equalish(e_6, e_4)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.96/0.89 tff(739,plain,
% 0.96/0.89 (((~![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_2)) | (~product(e_6, 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_6, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_6, e_1, e_2)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(740,plain,
% 0.96/0.89 ((~![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_2)) | (~product(e_6, e_1, e_2)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(741,plain,
% 0.96/0.89 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_6, e_1, e_2))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.96/0.89 tff(742,plain,
% 0.96/0.89 ($false),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[741, 738, 87, 735, 674])).
% 0.96/0.89 tff(743,plain,((~product(e_6, e_1, e_2)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.96/0.89 tff(744,plain,
% 0.96/0.89 ((~product(e_6, e_1, e_2)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_1)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[743, 223, 266, 417])).
% 0.96/0.89 tff(745,plain,
% 0.96/0.89 (product(e_4, e_1, e_5)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[744, 724, 722])).
% 0.96/0.89 tff(746,assumption,(product(e_4, e_4, e_5)), introduced(assumption)).
% 0.96/0.89 tff(747,plain,
% 0.96/0.89 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, 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_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_4, e_5)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(748,plain,
% 0.96/0.89 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_4, e_5)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(749,plain,
% 0.96/0.89 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_4, e_5))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[748, 747])).
% 0.96/0.89 tff(750,plain,
% 0.96/0.89 ($false),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[749, 366, 12, 518, 746])).
% 0.96/0.89 tff(751,plain,((~product(e_4, e_4, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.89 tff(752,plain,
% 0.96/0.89 (~product(e_4, e_4, e_5)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[751, 745])).
% 0.96/0.89 tff(753,plain,
% 0.96/0.89 (~product(e_4, e_3, e_5)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[526, 745])).
% 0.96/0.89 tff(754,plain,
% 0.96/0.89 (product(e_4, e_3, e_1)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[535, 753, 55, 719, 718])).
% 0.96/0.89 tff(755,assumption,(product(e_4, e_2, e_1)), introduced(assumption)).
% 0.96/0.89 tff(756,plain,
% 0.96/0.89 (((~![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_4, e_3, e_1)) | (~product(e_4, 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_3) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(757,plain,
% 0.96/0.89 ((~![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_4, e_3, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(758,plain,
% 0.96/0.89 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_2, e_1))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[757, 756])).
% 0.96/0.89 tff(759,plain,
% 0.96/0.89 ($false),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[758, 227, 12, 430, 755])).
% 0.96/0.89 tff(760,plain,((~product(e_4, e_2, e_1)) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.89 tff(761,plain,
% 0.96/0.89 (~product(e_4, e_2, e_1)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[760, 754])).
% 0.96/0.89 tff(762,assumption,(~product(e_3, e_4, e_5)), introduced(assumption)).
% 0.96/0.89 tff(763,plain,
% 0.96/0.89 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5)) | product(e_3, e_4, e_5))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5)) | product(e_3, e_4, e_5))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(764,plain,
% 0.96/0.89 ((product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_3, e_1, e_4))) <=> ((~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5)) | product(e_3, e_4, e_5))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(765,plain,
% 0.96/0.89 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5)) | product(e_3, e_4, e_5)))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[764])).
% 0.96/0.89 tff(766,plain,
% 0.96/0.89 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5)) | product(e_3, e_4, e_5))),
% 0.96/0.89 inference(transitivity,[status(thm)],[765, 763])).
% 0.96/0.89 tff(767,plain,
% 0.96/0.89 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_3, e_1, e_4)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(768,plain,
% 0.96/0.89 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5)) | product(e_3, e_4, e_5)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.96/0.89 tff(769,plain,
% 0.96/0.89 ($false),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[768, 33, 419, 518, 762])).
% 0.96/0.89 tff(770,plain,(product(e_3, e_4, e_5) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.89 tff(771,plain,
% 0.96/0.89 (product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5))),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[770, 324])).
% 0.96/0.89 tff(772,plain,
% 0.96/0.89 (product(e_3, e_4, e_5)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[771, 745])).
% 0.96/0.89 tff(773,assumption,(product(e_3, e_4, e_5)), introduced(assumption)).
% 0.96/0.89 tff(774,assumption,(product(e_2, e_4, e_5)), introduced(assumption)).
% 0.96/0.89 tff(775,plain,
% 0.96/0.89 (((~![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_4, e_5)) | (~product(e_3, e_4, e_5)))) <=> ((~![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_4, e_5)) | (~product(e_3, e_4, e_5)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(776,plain,
% 0.96/0.89 ((equalish(e_2, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_2, e_4, e_5))) <=> (equalish(e_2, e_3) | (~product(e_2, e_4, e_5)) | (~product(e_3, e_4, e_5)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(777,plain,
% 0.96/0.89 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_2, e_4, e_5)))) <=> ((~![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_4, e_5)) | (~product(e_3, e_4, e_5))))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[776])).
% 0.96/0.89 tff(778,plain,
% 0.96/0.89 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_2, e_4, e_5)))) <=> ((~![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_4, e_5)) | (~product(e_3, e_4, e_5)))),
% 0.96/0.89 inference(transitivity,[status(thm)],[777, 775])).
% 0.96/0.89 tff(779,plain,
% 0.96/0.89 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_2, e_4, e_5)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(780,plain,
% 0.96/0.89 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_4, e_5)) | (~product(e_3, e_4, e_5))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[779, 778])).
% 0.96/0.89 tff(781,plain,
% 0.96/0.89 ($false),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[780, 227, 87, 774, 773])).
% 0.96/0.89 tff(782,plain,((~product(e_2, e_4, e_5)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.89 tff(783,plain,
% 0.96/0.89 (~product(e_2, e_4, e_5)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[782, 772])).
% 0.96/0.89 tff(784,assumption,(product(e_2, e_4, e_4)), introduced(assumption)).
% 0.96/0.89 tff(785,plain,
% 0.96/0.89 (((~![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_2, e_4, e_4)) | (~product(e_2, 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_4, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(786,plain,
% 0.96/0.89 ((equalish(e_4, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_4, e_4))) <=> (equalish(e_4, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(787,plain,
% 0.96/0.89 (((~![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_2, e_3, e_4)) | (~product(e_2, 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_2, e_4, e_4)) | (~product(e_2, e_3, e_4))))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[786])).
% 0.96/0.89 tff(788,plain,
% 0.96/0.89 (((~![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_2, e_3, e_4)) | (~product(e_2, 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_2, e_4, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.96/0.89 inference(transitivity,[status(thm)],[787, 785])).
% 0.96/0.89 tff(789,plain,
% 0.96/0.89 ((~![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_2, e_3, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(790,plain,
% 0.96/0.89 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_2, e_3, e_4))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.96/0.89 tff(791,plain,
% 0.96/0.89 ($false),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[790, 399, 12, 374, 784])).
% 0.96/0.89 tff(792,plain,((~product(e_2, e_4, e_4)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.89 tff(793,plain,
% 0.96/0.89 (~product(e_2, e_4, e_4)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[792, 717])).
% 0.96/0.89 tff(794,plain,
% 0.96/0.89 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_6)) | product(e_4, e_5, e_6) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_6)) | product(e_4, e_5, e_6) | (~product(e_4, e_1, e_5)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(795,plain,
% 0.96/0.89 ((product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_4, e_1, e_5))) <=> ((~product(e_5, e_1, e_6)) | product(e_4, e_5, e_6) | (~product(e_4, e_1, e_5)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(796,plain,
% 0.96/0.89 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_6)) | product(e_4, e_5, e_6) | (~product(e_4, e_1, e_5))))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[795])).
% 0.96/0.89 tff(797,plain,
% 0.96/0.89 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_6)) | product(e_4, e_5, e_6) | (~product(e_4, e_1, e_5)))),
% 0.96/0.89 inference(transitivity,[status(thm)],[796, 794])).
% 0.96/0.89 tff(798,plain,
% 0.96/0.89 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_4, e_1, e_5)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(799,plain,
% 0.96/0.89 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_6)) | product(e_4, e_5, e_6) | (~product(e_4, e_1, e_5))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[798, 797])).
% 0.96/0.89 tff(800,plain,
% 0.96/0.89 ((~product(e_5, e_1, e_6)) | product(e_4, e_5, e_6) | (~product(e_4, e_1, e_5))),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[799, 33])).
% 0.96/0.89 tff(801,plain,
% 0.96/0.89 (product(e_4, e_5, e_6)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[800, 745, 1])).
% 0.96/0.89 tff(802,assumption,(product(e_4, e_2, e_6)), introduced(assumption)).
% 0.96/0.89 tff(803,assumption,(product(e_4, e_5, e_6)), introduced(assumption)).
% 0.96/0.89 tff(804,plain,
% 0.96/0.89 (((~![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_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_5, e_2) | (~product(e_4, e_5, e_6)) | (~product(e_4, e_2, e_6)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(805,plain,
% 0.96/0.89 ((equalish(e_5, e_2) | (~product(e_4, e_2, e_6)) | (~product(e_4, e_5, e_6))) <=> (equalish(e_5, e_2) | (~product(e_4, e_5, e_6)) | (~product(e_4, e_2, e_6)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(806,plain,
% 0.96/0.89 (((~![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_4, e_2, e_6)) | (~product(e_4, 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_4, e_5, e_6)) | (~product(e_4, e_2, e_6))))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[805])).
% 0.96/0.89 tff(807,plain,
% 0.96/0.89 (((~![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_4, e_2, e_6)) | (~product(e_4, 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_4, e_5, e_6)) | (~product(e_4, e_2, e_6)))),
% 0.96/0.89 inference(transitivity,[status(thm)],[806, 804])).
% 0.96/0.89 tff(808,plain,
% 0.96/0.89 ((~![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_4, e_2, e_6)) | (~product(e_4, e_5, e_6)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(809,plain,
% 0.96/0.89 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_4, e_5, e_6)) | (~product(e_4, e_2, e_6))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[808, 807])).
% 0.96/0.89 tff(810,plain,
% 0.96/0.89 ($false),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[809, 587, 12, 803, 802])).
% 0.96/0.89 tff(811,plain,((~product(e_4, e_5, e_6)) | (~product(e_4, e_2, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.89 tff(812,plain,
% 0.96/0.89 (~product(e_4, e_2, e_6)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[811, 801])).
% 0.96/0.89 tff(813,assumption,(~product(e_4, e_2, e_1)), introduced(assumption)).
% 0.96/0.89 tff(814,assumption,(product(e_4, e_4, e_2)), introduced(assumption)).
% 0.96/0.89 tff(815,assumption,(~product(e_4, e_2, e_6)), introduced(assumption)).
% 0.96/0.89 tff(816,assumption,(~product(e_2, e_4, e_5)), introduced(assumption)).
% 0.96/0.89 tff(817,assumption,(~product(e_2, e_4, e_4)), introduced(assumption)).
% 0.96/0.89 tff(818,assumption,(~product(e_2, e_4, e_1)), introduced(assumption)).
% 0.96/0.89 tff(819,assumption,(product(e_2, e_4, e_2)), introduced(assumption)).
% 0.96/0.89 tff(820,plain,
% 0.96/0.89 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(821,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.96/0.89 tff(822,plain,
% 0.96/0.89 (~equalish(e_2, e_4)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[821, 820])).
% 0.96/0.89 tff(823,plain,
% 0.96/0.89 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_4, e_2)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(824,plain,
% 0.96/0.89 ((equalish(e_2, e_4) | (~product(e_4, e_4, e_2)) | (~product(e_2, e_4, e_2))) <=> (equalish(e_2, e_4) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_4, e_2)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(825,plain,
% 0.96/0.89 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_4, e_2))))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[824])).
% 0.96/0.89 tff(826,plain,
% 0.96/0.89 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_4, e_2)))),
% 0.96/0.89 inference(transitivity,[status(thm)],[825, 823])).
% 0.96/0.90 tff(827,plain,
% 0.96/0.90 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(828,plain,
% 0.96/0.90 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_4, e_2))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[827, 826])).
% 0.96/0.90 tff(829,plain,
% 0.96/0.90 ($false),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[828, 822, 87, 819, 814])).
% 0.96/0.90 tff(830,plain,((~product(e_2, e_4, e_2)) | (~product(e_4, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.90 tff(831,plain,
% 0.96/0.90 (~product(e_2, e_4, e_2)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[830, 814])).
% 0.96/0.90 tff(832,plain,
% 0.96/0.90 (((~![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_2, e_4, e_6) | product(e_2, e_4, e_5) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, 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_2)) | (~group_element(e_4)) | product(e_2, e_4, e_6) | product(e_2, e_4, e_5) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(833,plain,
% 0.96/0.90 ((product(e_2, e_4, e_6) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_6) | product(e_2, e_4, e_5) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(834,plain,
% 0.96/0.90 (((~![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_4, e_6) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_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_2, e_4, e_6) | product(e_2, e_4, e_5) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1)))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[833])).
% 0.96/0.90 tff(835,plain,
% 0.96/0.90 (((~![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_4, e_6) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_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_2, e_4, e_6) | product(e_2, e_4, e_5) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1))),
% 0.96/0.90 inference(transitivity,[status(thm)],[834, 832])).
% 0.96/0.90 tff(836,plain,
% 0.96/0.90 ((~![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_4, e_6) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(837,plain,
% 0.96/0.90 ((~![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_2, e_4, e_6) | product(e_2, e_4, e_5) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1)),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.96/0.90 tff(838,plain,
% 0.96/0.90 (product(e_2, e_4, e_6) | product(e_2, e_4, e_5) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[837, 198, 505, 144])).
% 0.96/0.90 tff(839,plain,
% 0.96/0.90 (product(e_2, e_4, e_6)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[838, 831, 373, 817, 818, 816])).
% 0.96/0.90 tff(840,plain,
% 0.96/0.90 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_6)) | product(e_4, e_2, e_6) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_6)) | product(e_4, e_2, e_6) | (~product(e_4, e_4, e_2)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(841,plain,
% 0.96/0.90 ((product(e_4, e_2, e_6) | (~product(e_2, e_4, e_6)) | (~product(e_4, e_4, e_2))) <=> ((~product(e_2, e_4, e_6)) | product(e_4, e_2, e_6) | (~product(e_4, e_4, e_2)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(842,plain,
% 0.96/0.90 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_6) | (~product(e_2, e_4, e_6)) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_6)) | product(e_4, e_2, e_6) | (~product(e_4, e_4, e_2))))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[841])).
% 0.96/0.90 tff(843,plain,
% 0.96/0.90 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_6) | (~product(e_2, e_4, e_6)) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_6)) | product(e_4, e_2, e_6) | (~product(e_4, e_4, e_2)))),
% 0.96/0.90 inference(transitivity,[status(thm)],[842, 840])).
% 0.96/0.90 tff(844,plain,
% 0.96/0.90 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_6) | (~product(e_2, e_4, e_6)) | (~product(e_4, e_4, e_2)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(845,plain,
% 0.96/0.90 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_6)) | product(e_4, e_2, e_6) | (~product(e_4, e_4, e_2))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[844, 843])).
% 0.96/0.90 tff(846,plain,
% 0.96/0.90 ($false),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[845, 33, 839, 814, 815])).
% 0.96/0.90 tff(847,plain,((~product(e_4, e_4, e_2)) | product(e_4, e_2, e_6) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.96/0.90 tff(848,plain,
% 0.96/0.90 (product(e_2, e_4, e_1)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[847, 814, 373, 817, 816, 815])).
% 0.96/0.90 tff(849,plain,
% 0.96/0.90 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_4, e_2, e_1) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_1)) | product(e_4, e_2, e_1) | (~product(e_4, e_4, e_2)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(850,plain,
% 0.96/0.90 ((product(e_4, e_2, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_2))) <=> ((~product(e_2, e_4, e_1)) | product(e_4, e_2, e_1) | (~product(e_4, e_4, e_2)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(851,plain,
% 0.96/0.90 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_4, e_2, e_1) | (~product(e_4, e_4, e_2))))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[850])).
% 0.96/0.90 tff(852,plain,
% 0.96/0.90 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_1)) | product(e_4, e_2, e_1) | (~product(e_4, e_4, e_2)))),
% 0.96/0.90 inference(transitivity,[status(thm)],[851, 849])).
% 0.96/0.90 tff(853,plain,
% 0.96/0.90 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_2)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(854,plain,
% 0.96/0.90 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_1)) | product(e_4, e_2, e_1) | (~product(e_4, e_4, e_2))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[853, 852])).
% 0.96/0.90 tff(855,plain,
% 0.96/0.90 ($false),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[854, 33, 848, 814, 813])).
% 0.96/0.90 tff(856,plain,((~product(e_4, e_4, e_2)) | product(e_4, e_2, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_5) | product(e_4, e_2, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.96/0.90 tff(857,plain,
% 0.96/0.90 (~product(e_4, e_4, e_2)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[856, 812, 716, 793, 783, 761])).
% 0.96/0.90 tff(858,assumption,(product(e_4, e_4, e_1)), introduced(assumption)).
% 0.96/0.90 tff(859,plain,
% 0.96/0.90 (((~![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_4, e_4, e_1)) | (~product(e_4, 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_4, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(860,plain,
% 0.96/0.90 ((equalish(e_4, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_4, e_1))) <=> (equalish(e_4, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(861,plain,
% 0.96/0.90 (((~![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_4, e_3, e_1)) | (~product(e_4, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_3, e_1))))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[860])).
% 0.96/0.90 tff(862,plain,
% 0.96/0.90 (((~![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_4, e_3, e_1)) | (~product(e_4, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.96/0.90 inference(transitivity,[status(thm)],[861, 859])).
% 0.96/0.90 tff(863,plain,
% 0.96/0.90 ((~![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_4, e_3, e_1)) | (~product(e_4, e_4, e_1)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(864,plain,
% 0.96/0.90 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_3, e_1))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[863, 862])).
% 0.96/0.90 tff(865,plain,
% 0.96/0.90 ($false),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[864, 399, 12, 430, 858])).
% 0.96/0.90 tff(866,plain,((~product(e_4, e_4, e_1)) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.90 tff(867,plain,
% 0.96/0.90 (~product(e_4, e_4, e_1)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[866, 754])).
% 0.96/0.90 tff(868,assumption,(product(e_4, e_4, e_6)), introduced(assumption)).
% 0.96/0.90 tff(869,plain,
% 0.96/0.90 ((~equalish(e_4, e_5)) <=> (~equalish(e_4, e_5))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(870,axiom,(~equalish(e_4, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_5')).
% 0.96/0.90 tff(871,plain,
% 0.96/0.90 (~equalish(e_4, e_5)),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[870, 869])).
% 0.96/0.90 tff(872,plain,
% 0.96/0.90 (((~![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_4, e_5, e_6)) | (~product(e_4, 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_5) | (~product(e_4, e_5, e_6)) | (~product(e_4, e_4, e_6)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(873,plain,
% 0.96/0.90 ((~![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_4, e_5, e_6)) | (~product(e_4, e_4, e_6)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(874,plain,
% 0.96/0.90 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_4, e_5, e_6)) | (~product(e_4, e_4, e_6))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.96/0.90 tff(875,plain,
% 0.96/0.90 ($false),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[874, 871, 12, 803, 868])).
% 0.96/0.90 tff(876,plain,((~product(e_4, e_4, e_6)) | (~product(e_4, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.90 tff(877,plain,
% 0.96/0.90 (~product(e_4, e_4, e_6)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[876, 801])).
% 0.96/0.90 tff(878,plain,
% 0.96/0.90 (product(e_4, e_1, e_2)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[500, 754, 54, 722])).
% 0.96/0.90 tff(879,assumption,(~product(e_4, e_2, e_3)), introduced(assumption)).
% 0.96/0.90 tff(880,plain,
% 0.96/0.90 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_4, e_2, e_3) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_4, e_2, e_3) | (~product(e_4, e_1, e_2)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(881,plain,
% 0.96/0.90 ((product(e_4, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_2))) <=> ((~product(e_2, e_1, e_3)) | product(e_4, e_2, e_3) | (~product(e_4, e_1, e_2)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(882,plain,
% 0.96/0.90 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_4, e_2, e_3) | (~product(e_4, e_1, e_2))))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[881])).
% 0.96/0.90 tff(883,plain,
% 0.96/0.90 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_4, e_2, e_3) | (~product(e_4, e_1, e_2)))),
% 0.96/0.90 inference(transitivity,[status(thm)],[882, 880])).
% 0.96/0.90 tff(884,plain,
% 0.96/0.90 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_2)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(885,plain,
% 0.96/0.90 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_4, e_2, e_3) | (~product(e_4, e_1, e_2))),
% 0.99/0.90 inference(modus_ponens,[status(thm)],[884, 883])).
% 0.99/0.90 tff(886,plain,
% 0.99/0.90 ($false),
% 0.99/0.90 inference(unit_resolution,[status(thm)],[885, 33, 363, 384, 879])).
% 0.99/0.90 tff(887,plain,(product(e_4, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.90 tff(888,plain,
% 0.99/0.90 (product(e_4, e_2, e_3)),
% 0.99/0.90 inference(unit_resolution,[status(thm)],[887, 878, 715])).
% 0.99/0.90 tff(889,assumption,(product(e_4, e_2, e_3)), introduced(assumption)).
% 0.99/0.90 tff(890,assumption,(product(e_4, e_4, e_3)), introduced(assumption)).
% 0.99/0.90 tff(891,plain,
% 0.99/0.90 (((~![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_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_4) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.99/0.90 inference(rewrite,[status(thm)],[])).
% 0.99/0.90 tff(892,plain,
% 0.99/0.90 ((~![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_3)) | (~product(e_4, e_2, e_3)))),
% 0.99/0.90 inference(quant_inst,[status(thm)],[])).
% 0.99/0.90 tff(893,plain,
% 0.99/0.90 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_2, e_3))),
% 0.99/0.90 inference(modus_ponens,[status(thm)],[892, 891])).
% 0.99/0.90 tff(894,plain,
% 0.99/0.90 ($false),
% 0.99/0.90 inference(unit_resolution,[status(thm)],[893, 822, 12, 890, 889])).
% 0.99/0.90 tff(895,plain,((~product(e_4, e_2, e_3)) | (~product(e_4, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.90 tff(896,plain,
% 0.99/0.90 (~product(e_4, e_4, e_3)),
% 0.99/0.90 inference(unit_resolution,[status(thm)],[895, 888])).
% 0.99/0.90 tff(897,plain,
% 0.99/0.90 (((~![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)) | product(e_4, e_4, e_3) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_4, e_2) | product(e_4, e_4, e_4) | product(e_4, 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)) | product(e_4, e_4, e_3) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_4, e_2) | product(e_4, e_4, e_4) | product(e_4, e_4, e_5))),
% 0.99/0.90 inference(rewrite,[status(thm)],[])).
% 0.99/0.90 tff(898,plain,
% 0.99/0.90 ((product(e_4, e_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_4) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_4))) <=> ((~group_element(e_4)) | product(e_4, e_4, e_3) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_4, e_2) | product(e_4, e_4, e_4) | product(e_4, e_4, e_5))),
% 0.99/0.90 inference(rewrite,[status(thm)],[])).
% 0.99/0.90 tff(899,plain,
% 0.99/0.90 (((~![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_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_4) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1) | (~group_element(e_4)) | (~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)) | product(e_4, e_4, e_3) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_4, e_2) | product(e_4, e_4, e_4) | product(e_4, e_4, e_5)))),
% 0.99/0.90 inference(monotonicity,[status(thm)],[898])).
% 0.99/0.90 tff(900,plain,
% 0.99/0.90 (((~![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_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_4) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1) | (~group_element(e_4)) | (~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)) | product(e_4, e_4, e_3) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_4, e_2) | product(e_4, e_4, e_4) | product(e_4, e_4, e_5))),
% 0.99/0.91 inference(transitivity,[status(thm)],[899, 897])).
% 0.99/0.91 tff(901,plain,
% 0.99/0.91 ((~![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_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_4) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_4)))),
% 0.99/0.91 inference(quant_inst,[status(thm)],[])).
% 0.99/0.91 tff(902,plain,
% 0.99/0.91 ((~![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)) | product(e_4, e_4, e_3) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_4, e_2) | product(e_4, e_4, e_4) | product(e_4, e_4, e_5)),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[901, 900])).
% 0.99/0.91 tff(903,plain,
% 0.99/0.91 (product(e_4, e_4, e_3) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_4, e_2) | product(e_4, e_4, e_4) | product(e_4, e_4, e_5)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[902, 505, 144])).
% 0.99/0.91 tff(904,plain,
% 0.99/0.91 (product(e_4, e_4, e_4)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[903, 896, 877, 867, 857, 752])).
% 0.99/0.91 tff(905,assumption,(product(e_4, e_6, e_1)), introduced(assumption)).
% 0.99/0.91 tff(906,plain,
% 0.99/0.91 (((~![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_1)) | (~product(e_4, e_6, e_1)))) <=> ((~![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_1)) | (~product(e_4, e_6, e_1)))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(907,plain,
% 0.99/0.91 ((~![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_1)) | (~product(e_4, e_6, e_1)))),
% 0.99/0.91 inference(quant_inst,[status(thm)],[])).
% 0.99/0.91 tff(908,plain,
% 0.99/0.91 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_6, e_1))),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[907, 906])).
% 0.99/0.91 tff(909,plain,
% 0.99/0.91 ($false),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[908, 684, 12, 430, 905])).
% 0.99/0.91 tff(910,plain,((~product(e_4, e_6, e_1)) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.91 tff(911,plain,
% 0.99/0.91 (~product(e_4, e_6, e_1)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[910, 754])).
% 0.99/0.91 tff(912,assumption,(product(e_4, e_6, e_5)), introduced(assumption)).
% 0.99/0.91 tff(913,plain,
% 0.99/0.91 (((~![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)))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(914,plain,
% 0.99/0.91 ((~![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)))),
% 0.99/0.91 inference(quant_inst,[status(thm)],[])).
% 0.99/0.91 tff(915,plain,
% 0.99/0.91 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_6, e_5))),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[914, 913])).
% 0.99/0.91 tff(916,plain,
% 0.99/0.91 ($false),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[915, 706, 12, 518, 912])).
% 0.99/0.91 tff(917,plain,((~product(e_4, e_6, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.91 tff(918,plain,
% 0.99/0.91 (~product(e_4, e_6, e_5)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[917, 745])).
% 0.99/0.91 tff(919,assumption,(product(e_4, e_6, e_2)), introduced(assumption)).
% 0.99/0.91 tff(920,plain,
% 0.99/0.91 (((~![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)))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(921,plain,
% 0.99/0.91 ((~![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)))),
% 0.99/0.91 inference(quant_inst,[status(thm)],[])).
% 0.99/0.91 tff(922,plain,
% 0.99/0.91 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_6, e_2))),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[921, 920])).
% 0.99/0.91 tff(923,plain,
% 0.99/0.91 ($false),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[922, 706, 12, 384, 919])).
% 0.99/0.91 tff(924,plain,((~product(e_4, e_6, e_2)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.91 tff(925,plain,
% 0.99/0.91 (~product(e_4, e_6, e_2)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[924, 878])).
% 0.99/0.91 tff(926,assumption,(product(e_4, e_6, e_6)), introduced(assumption)).
% 0.99/0.91 tff(927,plain,
% 0.99/0.91 (((~![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_6)) | (~product(e_4, 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_4, e_5, e_6)) | (~product(e_4, e_6, e_6)))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(928,plain,
% 0.99/0.91 ((~![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_6)) | (~product(e_4, e_6, e_6)))),
% 0.99/0.91 inference(quant_inst,[status(thm)],[])).
% 0.99/0.91 tff(929,plain,
% 0.99/0.91 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_4, e_5, e_6)) | (~product(e_4, e_6, e_6))),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[928, 927])).
% 0.99/0.91 tff(930,plain,
% 0.99/0.91 ($false),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[929, 636, 12, 803, 926])).
% 0.99/0.91 tff(931,plain,((~product(e_4, e_6, e_6)) | (~product(e_4, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.91 tff(932,plain,
% 0.99/0.91 (~product(e_4, e_6, e_6)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[931, 801])).
% 0.99/0.91 tff(933,assumption,(product(e_4, e_6, e_3)), introduced(assumption)).
% 0.99/0.91 tff(934,plain,
% 0.99/0.91 (((~![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_4, e_2, 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_2) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_6, e_3)))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(935,plain,
% 0.99/0.91 ((~![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_4, e_2, e_3)) | (~product(e_4, e_6, e_3)))),
% 0.99/0.91 inference(quant_inst,[status(thm)],[])).
% 0.99/0.91 tff(936,plain,
% 0.99/0.91 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_6, e_3))),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[935, 934])).
% 0.99/0.91 tff(937,plain,
% 0.99/0.91 ($false),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[936, 654, 12, 889, 933])).
% 0.99/0.91 tff(938,plain,((~product(e_4, e_6, e_3)) | (~product(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.91 tff(939,plain,
% 0.99/0.91 (~product(e_4, e_6, e_3)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[938, 888])).
% 0.99/0.91 tff(940,plain,
% 0.99/0.91 (((~![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))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(941,plain,
% 0.99/0.91 ((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))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(942,plain,
% 0.99/0.91 (((~![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)))),
% 0.99/0.91 inference(monotonicity,[status(thm)],[941])).
% 0.99/0.91 tff(943,plain,
% 0.99/0.91 (((~![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))),
% 0.99/0.91 inference(transitivity,[status(thm)],[942, 940])).
% 0.99/0.91 tff(944,plain,
% 0.99/0.91 ((~![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)))),
% 0.99/0.91 inference(quant_inst,[status(thm)],[])).
% 0.99/0.91 tff(945,plain,
% 0.99/0.91 ((~![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)),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[944, 943])).
% 0.99/0.91 tff(946,plain,
% 0.99/0.91 (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)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[945, 505, 693, 144])).
% 0.99/0.91 tff(947,plain,
% 0.99/0.91 (product(e_4, e_6, e_4)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[946, 939, 932, 925, 918, 911])).
% 0.99/0.91 tff(948,assumption,(product(e_4, e_6, e_4)), introduced(assumption)).
% 0.99/0.91 tff(949,plain,
% 0.99/0.91 (((~![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)))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(950,plain,
% 0.99/0.91 ((~![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)))),
% 0.99/0.91 inference(quant_inst,[status(thm)],[])).
% 0.99/0.91 tff(951,plain,
% 0.99/0.91 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_6, e_4))),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[950, 949])).
% 0.99/0.91 tff(952,plain,
% 0.99/0.91 ($false),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[951, 738, 12, 332, 948])).
% 0.99/0.91 tff(953,plain,((~product(e_4, e_6, e_4)) | (~product(e_4, e_4, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.91 tff(954,plain,
% 0.99/0.91 ($false),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[953, 947, 904])).
% 0.99/0.91 tff(955,plain,(product(e_6, e_1, e_3) | product(e_1, e_3, e_5) | product(e_4, e_3, e_6) | (~product(e_5, e_1, e_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.99/0.91 tff(956,plain,
% 0.99/0.91 (product(e_1, e_3, e_5) | product(e_4, e_3, e_6) | (~product(e_5, e_1, e_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_5)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[955, 660])).
% 0.99/0.91 tff(957,plain,
% 0.99/0.91 ($false),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[956, 650, 642, 54, 632, 55])).
% 0.99/0.91 tff(958,plain,(product(e_4, e_3, e_6) | product(e_1, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.99/0.91 tff(959,plain,
% 0.99/0.91 (product(e_4, e_3, e_6)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[958, 54])).
% 0.99/0.91 tff(960,assumption,(product(e_1, e_3, e_6)), introduced(assumption)).
% 0.99/0.91 tff(961,assumption,(product(e_4, e_3, e_6)), introduced(assumption)).
% 0.99/0.91 tff(962,plain,
% 0.99/0.91 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_4, e_3, e_6)) | (~product(e_1, 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_4, e_3, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(963,plain,
% 0.99/0.91 ((equalish(e_4, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_4, e_3, e_6))) <=> (equalish(e_4, e_1) | (~product(e_4, e_3, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(964,plain,
% 0.99/0.91 (((~![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_4, e_3, e_6)) | (~product(e_1, e_3, e_6))))),
% 0.99/0.91 inference(monotonicity,[status(thm)],[963])).
% 0.99/0.91 tff(965,plain,
% 0.99/0.91 (((~![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_4, e_3, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.99/0.91 inference(transitivity,[status(thm)],[964, 962])).
% 0.99/0.91 tff(966,plain,
% 0.99/0.91 ((~![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)))),
% 0.99/0.91 inference(quant_inst,[status(thm)],[])).
% 0.99/0.91 tff(967,plain,
% 0.99/0.91 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_3, e_6)) | (~product(e_1, e_3, e_6))),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[966, 965])).
% 0.99/0.91 tff(968,plain,
% 0.99/0.91 ($false),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[967, 366, 87, 961, 960])).
% 0.99/0.91 tff(969,plain,((~product(e_4, e_3, e_6)) | (~product(e_1, e_3, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.91 tff(970,plain,
% 0.99/0.91 (~product(e_1, e_3, e_6)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[969, 959])).
% 0.99/0.91 tff(971,assumption,(product(e_3, e_3, e_6)), introduced(assumption)).
% 0.99/0.91 tff(972,plain,
% 0.99/0.91 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(973,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.99/0.91 tff(974,plain,
% 0.99/0.91 (~equalish(e_3, e_4)),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[973, 972])).
% 0.99/0.91 tff(975,plain,
% 0.99/0.91 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_3, e_6)) | (~product(e_3, 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_3, e_4) | (~product(e_4, e_3, e_6)) | (~product(e_3, e_3, e_6)))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(976,plain,
% 0.99/0.91 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_3, e_6)) | (~product(e_3, e_3, e_6)))),
% 0.99/0.91 inference(quant_inst,[status(thm)],[])).
% 0.99/0.91 tff(977,plain,
% 0.99/0.91 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_3, e_6)) | (~product(e_3, e_3, e_6))),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[976, 975])).
% 0.99/0.91 tff(978,plain,
% 0.99/0.91 ($false),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[977, 974, 87, 961, 971])).
% 0.99/0.91 tff(979,plain,((~product(e_3, e_3, e_6)) | (~product(e_4, e_3, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.91 tff(980,plain,
% 0.99/0.91 (~product(e_3, e_3, e_6)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[979, 959])).
% 0.99/0.91 tff(981,assumption,(~product(e_2, e_4, e_6)), introduced(assumption)).
% 0.99/0.91 tff(982,plain,
% 0.99/0.91 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_6)) | product(e_2, e_4, e_6) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_6)) | product(e_2, e_4, e_6) | (~product(e_2, e_3, e_4)))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(983,plain,
% 0.99/0.91 ((product(e_2, e_4, e_6) | (~product(e_4, e_3, e_6)) | (~product(e_2, e_3, e_4))) <=> ((~product(e_4, e_3, e_6)) | product(e_2, e_4, e_6) | (~product(e_2, e_3, e_4)))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(984,plain,
% 0.99/0.91 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_6) | (~product(e_4, e_3, e_6)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_6)) | product(e_2, e_4, e_6) | (~product(e_2, e_3, e_4))))),
% 0.99/0.91 inference(monotonicity,[status(thm)],[983])).
% 0.99/0.91 tff(985,plain,
% 0.99/0.91 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_6) | (~product(e_4, e_3, e_6)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_6)) | product(e_2, e_4, e_6) | (~product(e_2, e_3, e_4)))),
% 0.99/0.91 inference(transitivity,[status(thm)],[984, 982])).
% 0.99/0.91 tff(986,plain,
% 0.99/0.91 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_6) | (~product(e_4, e_3, e_6)) | (~product(e_2, e_3, e_4)))),
% 0.99/0.91 inference(quant_inst,[status(thm)],[])).
% 0.99/0.91 tff(987,plain,
% 0.99/0.91 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_6)) | product(e_2, e_4, e_6) | (~product(e_2, e_3, e_4))),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[986, 985])).
% 0.99/0.91 tff(988,plain,
% 0.99/0.91 ($false),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[987, 33, 961, 374, 981])).
% 0.99/0.91 tff(989,plain,((~product(e_4, e_3, e_6)) | (~product(e_2, e_3, e_4)) | product(e_2, e_4, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.99/0.91 tff(990,plain,
% 0.99/0.91 ((~product(e_4, e_3, e_6)) | product(e_2, e_4, e_6)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[989, 330])).
% 0.99/0.91 tff(991,plain,
% 0.99/0.91 (product(e_2, e_4, e_6)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[990, 959])).
% 0.99/0.91 tff(992,assumption,(product(e_2, e_4, e_6)), introduced(assumption)).
% 0.99/0.91 tff(993,assumption,(product(e_5, e_4, e_6)), introduced(assumption)).
% 0.99/0.91 tff(994,plain,
% 0.99/0.91 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_4, e_6)) | (~product(e_5, e_4, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_4, e_6)) | (~product(e_5, e_4, e_6)))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(995,plain,
% 0.99/0.91 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_4, e_6)) | (~product(e_5, e_4, e_6)))),
% 0.99/0.91 inference(quant_inst,[status(thm)],[])).
% 0.99/0.91 tff(996,plain,
% 0.99/0.91 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_4, e_6)) | (~product(e_5, e_4, e_6))),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[995, 994])).
% 0.99/0.91 tff(997,plain,
% 0.99/0.91 ($false),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[996, 587, 87, 993, 992])).
% 0.99/0.91 tff(998,plain,((~product(e_5, e_4, e_6)) | (~product(e_2, e_4, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.91 tff(999,plain,
% 0.99/0.91 (~product(e_5, e_4, e_6)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[998, 991])).
% 0.99/0.91 tff(1000,assumption,(~product(e_5, e_1, e_6)), introduced(assumption)).
% 0.99/0.91 tff(1001,plain,
% 0.99/0.91 (~product(e_1, e_1, e_2)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[515, 502])).
% 0.99/0.91 tff(1002,plain,
% 0.99/0.91 (product(e_1, e_1, e_1)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[154, 1001])).
% 0.99/0.91 tff(1003,plain,
% 0.99/0.91 (~product(e_4, e_1, e_1)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[548, 1002])).
% 0.99/0.91 tff(1004,plain,
% 0.99/0.91 (product(e_4, e_1, e_2)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[550, 1003, 502])).
% 0.99/0.91 tff(1005,plain,
% 0.99/0.91 (~product(e_5, e_1, e_1)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[582, 1002])).
% 0.99/0.91 tff(1006,plain,
% 0.99/0.91 (product(e_5, e_1, e_2)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[631, 1005, 1000])).
% 0.99/0.91 tff(1007,plain,
% 0.99/0.91 ($false),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[569, 1006, 1004])).
% 0.99/0.91 tff(1008,plain,(product(e_4, e_1, e_5) | product(e_5, e_1, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.99/0.91 tff(1009,plain,
% 0.99/0.91 (product(e_4, e_1, e_5)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[1008, 1000])).
% 0.99/0.91 tff(1010,plain,
% 0.99/0.91 (product(e_3, e_4, e_5)),
% 0.99/0.91 inference(unit_resolution,[status(thm)],[771, 1009])).
% 0.99/0.91 tff(1011,assumption,(product(e_1, e_4, e_5)), introduced(assumption)).
% 0.99/0.91 tff(1012,plain,
% 0.99/0.91 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.99/0.91 inference(rewrite,[status(thm)],[])).
% 0.99/0.91 tff(1013,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.99/0.91 tff(1014,plain,
% 0.99/0.91 (~equalish(e_1, e_3)),
% 0.99/0.91 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 0.99/0.91 tff(1015,plain,
% 0.99/0.91 (((~![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_4, e_5)) | (~product(e_3, e_4, 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_3) | (~product(e_1, e_4, e_5)) | (~product(e_3, e_4, e_5)))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1016,plain,
% 0.99/0.92 ((equalish(e_1, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_1, e_4, e_5))) <=> (equalish(e_1, e_3) | (~product(e_1, e_4, e_5)) | (~product(e_3, e_4, e_5)))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1017,plain,
% 0.99/0.92 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_1, e_4, 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_3) | (~product(e_1, e_4, e_5)) | (~product(e_3, e_4, e_5))))),
% 0.99/0.92 inference(monotonicity,[status(thm)],[1016])).
% 0.99/0.92 tff(1018,plain,
% 0.99/0.92 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_1, e_4, 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_3) | (~product(e_1, e_4, e_5)) | (~product(e_3, e_4, e_5)))),
% 0.99/0.92 inference(transitivity,[status(thm)],[1017, 1015])).
% 0.99/0.92 tff(1019,plain,
% 0.99/0.92 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_1, e_4, e_5)))),
% 0.99/0.92 inference(quant_inst,[status(thm)],[])).
% 0.99/0.92 tff(1020,plain,
% 0.99/0.92 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_4, e_5)) | (~product(e_3, e_4, e_5))),
% 0.99/0.92 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 0.99/0.92 tff(1021,plain,
% 0.99/0.92 ($false),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1020, 1014, 87, 1011, 773])).
% 0.99/0.92 tff(1022,plain,((~product(e_1, e_4, e_5)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.92 tff(1023,plain,
% 0.99/0.92 (~product(e_1, e_4, e_5)),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1022, 1010])).
% 0.99/0.92 tff(1024,assumption,(~product(e_1, e_3, e_6)), introduced(assumption)).
% 0.99/0.92 tff(1025,assumption,(~product(e_3, e_3, e_6)), introduced(assumption)).
% 0.99/0.92 tff(1026,assumption,(~product(e_5, e_4, e_6)), introduced(assumption)).
% 0.99/0.92 tff(1027,assumption,(~product(e_1, e_3, e_1)), introduced(assumption)).
% 0.99/0.92 tff(1028,plain,
% 0.99/0.92 (((~![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_3, e_4)) | (~product(e_1, e_3, 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_2) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1029,plain,
% 0.99/0.92 ((~![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_3, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.99/0.92 inference(quant_inst,[status(thm)],[])).
% 0.99/0.92 tff(1030,plain,
% 0.99/0.92 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_4))),
% 0.99/0.92 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 0.99/0.92 tff(1031,plain,
% 0.99/0.92 ($false),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1030, 67, 87, 374, 442])).
% 0.99/0.92 tff(1032,plain,((~product(e_1, e_3, e_4)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.92 tff(1033,plain,
% 0.99/0.92 (~product(e_1, e_3, e_4)),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1032, 330])).
% 0.99/0.92 tff(1034,assumption,(~product(e_1, e_3, e_2)), introduced(assumption)).
% 0.99/0.92 tff(1035,assumption,(~product(e_1, e_3, e_4)), introduced(assumption)).
% 0.99/0.92 tff(1036,plain,
% 0.99/0.92 (product(e_1, e_3, e_3)),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[480, 54, 1035, 1024, 1034, 1027])).
% 0.99/0.92 tff(1037,assumption,(product(e_3, e_3, e_2)), introduced(assumption)).
% 0.99/0.92 tff(1038,plain,
% 0.99/0.92 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1039,plain,
% 0.99/0.92 ((product(e_1, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3))) <=> (product(e_1, e_3, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1040,plain,
% 0.99/0.92 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2))))),
% 0.99/0.92 inference(monotonicity,[status(thm)],[1039])).
% 0.99/0.92 tff(1041,plain,
% 0.99/0.92 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.99/0.92 inference(transitivity,[status(thm)],[1040, 1038])).
% 0.99/0.92 tff(1042,plain,
% 0.99/0.92 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)))),
% 0.99/0.92 inference(quant_inst,[status(thm)],[])).
% 0.99/0.92 tff(1043,plain,
% 0.99/0.92 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2))),
% 0.99/0.92 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 0.99/0.92 tff(1044,plain,
% 0.99/0.92 ($false),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1043, 33, 453, 1034, 1037])).
% 0.99/0.92 tff(1045,plain,((~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)) | product(e_1, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.99/0.92 tff(1046,plain,
% 0.99/0.92 (~product(e_3, e_3, e_2)),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1045, 1036, 1034])).
% 0.99/0.92 tff(1047,assumption,(product(e_3, e_3, e_4)), introduced(assumption)).
% 0.99/0.92 tff(1048,plain,
% 0.99/0.92 (((~![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_3, e_1, e_4)) | (~product(e_3, 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_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_4)))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1049,plain,
% 0.99/0.92 ((~![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_3, e_1, e_4)) | (~product(e_3, e_3, e_4)))),
% 0.99/0.92 inference(quant_inst,[status(thm)],[])).
% 0.99/0.92 tff(1050,plain,
% 0.99/0.92 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_4))),
% 0.99/0.92 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 0.99/0.92 tff(1051,plain,
% 0.99/0.92 ($false),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1050, 15, 12, 324, 1047])).
% 0.99/0.92 tff(1052,plain,(~product(e_3, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.99/0.92 tff(1053,assumption,(~product(e_3, e_3, e_5)), introduced(assumption)).
% 0.99/0.92 tff(1054,assumption,(~product(e_3, e_3, e_2)), introduced(assumption)).
% 0.99/0.92 tff(1055,plain,
% 0.99/0.92 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3)))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1056,plain,
% 0.99/0.92 ((product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1))) <=> (product(e_3, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3)))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1057,plain,
% 0.99/0.92 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3))))),
% 0.99/0.92 inference(monotonicity,[status(thm)],[1056])).
% 0.99/0.92 tff(1058,plain,
% 0.99/0.92 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3)))),
% 0.99/0.92 inference(transitivity,[status(thm)],[1057, 1055])).
% 0.99/0.92 tff(1059,plain,
% 0.99/0.92 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.99/0.92 inference(quant_inst,[status(thm)],[])).
% 0.99/0.92 tff(1060,plain,
% 0.99/0.92 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3))),
% 0.99/0.92 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 0.99/0.92 tff(1061,plain,
% 0.99/0.92 (~product(e_3, e_3, e_1)),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1060, 33, 267, 453])).
% 0.99/0.92 tff(1062,assumption,(~product(e_3, e_3, e_4)), introduced(assumption)).
% 0.99/0.92 tff(1063,plain,
% 0.99/0.92 (((~![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)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_6) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, 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)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_6) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1064,plain,
% 0.99/0.92 ((product(e_3, e_3, e_6) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_6) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1065,plain,
% 0.99/0.92 (((~![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_3, e_6) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~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)))) | ((~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_6) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3)))),
% 0.99/0.92 inference(monotonicity,[status(thm)],[1064])).
% 0.99/0.92 tff(1066,plain,
% 0.99/0.92 (((~![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_3, e_6) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~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)))) | (~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_6) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3))),
% 0.99/0.92 inference(transitivity,[status(thm)],[1065, 1063])).
% 0.99/0.92 tff(1067,plain,
% 0.99/0.92 ((~![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_3, e_6) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3)))),
% 0.99/0.92 inference(quant_inst,[status(thm)],[])).
% 0.99/0.92 tff(1068,plain,
% 0.99/0.92 ((~![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)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_6) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3)),
% 0.99/0.92 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 0.99/0.92 tff(1069,plain,
% 0.99/0.92 (product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_5) | product(e_3, e_3, e_3)),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1068, 289, 144, 1025, 1062])).
% 0.99/0.92 tff(1070,plain,
% 0.99/0.92 (product(e_3, e_3, e_3)),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1069, 1061, 1054, 1053])).
% 0.99/0.92 tff(1071,plain,
% 0.99/0.92 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_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_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1072,plain,
% 0.99/0.92 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.99/0.92 inference(quant_inst,[status(thm)],[])).
% 0.99/0.92 tff(1073,plain,
% 0.99/0.92 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.99/0.92 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 0.99/0.92 tff(1074,plain,
% 0.99/0.92 ($false),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1073, 15, 87, 453, 1070])).
% 0.99/0.92 tff(1075,plain,((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_2) | product(e_3, e_3, e_5) | product(e_3, e_3, e_6) | product(e_3, e_3, e_4) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.99/0.92 tff(1076,plain,
% 0.99/0.92 ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_2) | product(e_3, e_3, e_5) | product(e_3, e_3, e_6) | product(e_3, e_3, e_4)),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1075, 223])).
% 0.99/0.92 tff(1077,plain,
% 0.99/0.92 ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_2) | product(e_3, e_3, e_5) | product(e_3, e_3, e_6)),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1076, 1052])).
% 0.99/0.92 tff(1078,plain,
% 0.99/0.92 (product(e_3, e_3, e_5)),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1077, 1046, 1025, 1036])).
% 0.99/0.92 tff(1079,plain,
% 0.99/0.92 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_5) | (~product(e_3, e_3, e_5)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_5) | (~product(e_3, e_3, e_5)) | (~product(e_1, e_3, e_3)))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1080,plain,
% 0.99/0.92 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_5) | (~product(e_3, e_3, e_5)) | (~product(e_1, e_3, e_3)))),
% 0.99/0.92 inference(quant_inst,[status(thm)],[])).
% 0.99/0.92 tff(1081,plain,
% 0.99/0.92 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_5) | (~product(e_3, e_3, e_5)) | (~product(e_1, e_3, e_3))),
% 0.99/0.92 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 0.99/0.92 tff(1082,plain,
% 0.99/0.92 ($false),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1081, 33, 54, 1036, 1078])).
% 0.99/0.92 tff(1083,plain,(product(e_1, e_3, e_5) | product(e_3, e_3, e_6) | product(e_1, e_3, e_2) | product(e_1, e_3, e_4) | product(e_1, e_3, e_6) | product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.99/0.92 tff(1084,plain,
% 0.99/0.92 (product(e_1, e_3, e_5) | product(e_3, e_3, e_6) | product(e_1, e_3, e_2) | product(e_1, e_3, e_6) | product(e_1, e_3, e_1)),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1083, 1033])).
% 0.99/0.92 tff(1085,plain,
% 0.99/0.92 (product(e_1, e_3, e_2)),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1084, 1027, 1024, 1025, 54])).
% 0.99/0.92 tff(1086,assumption,(product(e_6, e_3, e_2)), introduced(assumption)).
% 0.99/0.92 tff(1087,plain,
% 0.99/0.92 ((~equalish(e_1, e_6)) <=> (~equalish(e_1, e_6))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1088,axiom,(~equalish(e_1, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_6')).
% 0.99/0.92 tff(1089,plain,
% 0.99/0.92 (~equalish(e_1, e_6)),
% 0.99/0.92 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 0.99/0.92 tff(1090,plain,
% 0.99/0.92 (((~![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_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_1, e_6) | (~product(e_1, e_3, e_2)) | (~product(e_6, e_3, e_2)))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1091,plain,
% 0.99/0.92 ((equalish(e_1, e_6) | (~product(e_6, e_3, e_2)) | (~product(e_1, e_3, e_2))) <=> (equalish(e_1, e_6) | (~product(e_1, e_3, e_2)) | (~product(e_6, e_3, e_2)))),
% 0.99/0.92 inference(rewrite,[status(thm)],[])).
% 0.99/0.92 tff(1092,plain,
% 0.99/0.92 (((~![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_3, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_6) | (~product(e_1, e_3, e_2)) | (~product(e_6, e_3, e_2))))),
% 0.99/0.92 inference(monotonicity,[status(thm)],[1091])).
% 0.99/0.92 tff(1093,plain,
% 0.99/0.92 (((~![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_3, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_6) | (~product(e_1, e_3, e_2)) | (~product(e_6, e_3, e_2)))),
% 0.99/0.92 inference(transitivity,[status(thm)],[1092, 1090])).
% 0.99/0.92 tff(1094,plain,
% 0.99/0.92 ((~![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_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.99/0.92 inference(quant_inst,[status(thm)],[])).
% 0.99/0.92 tff(1095,plain,
% 0.99/0.92 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_6) | (~product(e_1, e_3, e_2)) | (~product(e_6, e_3, e_2))),
% 0.99/0.92 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 0.99/0.92 tff(1096,plain,
% 0.99/0.92 ($false),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1095, 1089, 87, 464, 1086])).
% 0.99/0.92 tff(1097,plain,((~product(e_1, e_3, e_2)) | (~product(e_6, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.92 tff(1098,plain,
% 0.99/0.92 (~product(e_6, e_3, e_2)),
% 0.99/0.92 inference(unit_resolution,[status(thm)],[1097, 1085])).
% 0.99/0.92 tff(1099,assumption,(product(e_6, e_3, e_5)), introduced(assumption)).
% 0.99/0.92 tff(1100,assumption,(product(e_6, e_1, e_5)), introduced(assumption)).
% 0.99/0.92 tff(1101,plain,
% 0.99/0.93 (((~![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_6, e_1, 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_1) | (~product(e_6, e_1, e_5)) | (~product(e_6, e_3, e_5)))),
% 0.99/0.93 inference(rewrite,[status(thm)],[])).
% 0.99/0.93 tff(1102,plain,
% 0.99/0.93 ((~![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_6, e_1, e_5)) | (~product(e_6, e_3, e_5)))),
% 0.99/0.93 inference(quant_inst,[status(thm)],[])).
% 0.99/0.93 tff(1103,plain,
% 0.99/0.93 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_6, e_1, e_5)) | (~product(e_6, e_3, e_5))),
% 0.99/0.93 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 0.99/0.93 tff(1104,plain,
% 0.99/0.93 ($false),
% 0.99/0.93 inference(unit_resolution,[status(thm)],[1103, 15, 12, 1100, 1099])).
% 0.99/0.93 tff(1105,plain,((~product(e_6, e_3, e_5)) | (~product(e_6, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.99/0.93 tff(1106,plain,
% 0.99/0.93 (~product(e_6, e_1, e_5)),
% 0.99/0.93 inference(unit_resolution,[status(thm)],[1105, 1099])).
% 0.99/0.93 tff(1107,plain,
% 0.99/0.93 (~product(e_6, e_1, e_1)),
% 0.99/0.93 inference(unit_resolution,[status(thm)],[711, 1002])).
% 0.99/0.93 tff(1108,plain,
% 0.99/0.93 (~product(e_6, e_1, e_2)),
% 0.99/0.93 inference(unit_resolution,[status(thm)],[744, 1003, 502])).
% 0.99/0.93 tff(1109,plain,
% 0.99/0.93 (product(e_6, e_1, e_2) | product(e_6, e_1, e_6) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5)),
% 0.99/0.93 inference(unit_resolution,[status(thm)],[701, 660])).
% 0.99/0.93 tff(1110,plain,
% 0.99/0.93 ($false),
% 0.99/0.93 inference(unit_resolution,[status(thm)],[1109, 1108, 1107, 662, 661])).
% 0.99/0.93 tff(1111,plain,(product(e_4, e_1, e_5) | product(e_6, e_1, e_5) | product(e_6, e_1, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.99/0.93 tff(1112,plain,
% 0.99/0.93 (product(e_6, e_1, e_6)),
% 0.99/0.93 inference(unit_resolution,[status(thm)],[1111, 502, 662])).
% 0.99/0.93 tff(1113,plain,
% 0.99/0.93 (~product(e_5, e_1, e_6)),
% 0.99/0.93 inference(unit_resolution,[status(thm)],[641, 1112])).
% 0.99/0.93 tff(1114,plain,
% 0.99/0.93 (product(e_5, e_1, e_2)),
% 0.99/0.93 inference(unit_resolution,[status(thm)],[631, 1005, 1113])).
% 0.99/0.93 tff(1115,plain,
% 0.99/0.93 ($false),
% 0.99/0.93 inference(unit_resolution,[status(thm)],[569, 1114, 1004])).
% 0.99/0.93 tff(1116,plain,(product(e_4, e_1, e_5) | product(e_6, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.99/0.93 tff(1117,plain,
% 0.99/0.93 (product(e_4, e_1, e_5)),
% 0.99/0.93 inference(unit_resolution,[status(thm)],[1116, 1106])).
% 0.99/0.93 tff(1118,plain,
% 0.99/0.93 (~product(e_4, e_6, e_5)),
% 0.99/0.93 inference(unit_resolution,[status(thm)],[917, 1117])).
% 0.99/0.93 tff(1119,assumption,(~product(e_4, e_6, e_5)), introduced(assumption)).
% 0.99/0.93 tff(1120,plain,
% 0.99/0.93 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_6)) | product(e_4, e_6, e_5) | (~product(e_6, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_6)) | product(e_4, e_6, e_5) | (~product(e_6, e_3, e_5)))),
% 0.99/0.93 inference(rewrite,[status(thm)],[])).
% 0.99/0.93 tff(1121,plain,
% 0.99/0.93 ((product(e_4, e_6, e_5) | (~product(e_6, e_3, e_5)) | (~product(e_4, e_3, e_6))) <=> ((~product(e_4, e_3, e_6)) | product(e_4, e_6, e_5) | (~product(e_6, e_3, e_5)))),
% 0.99/0.93 inference(rewrite,[status(thm)],[])).
% 0.99/0.93 tff(1122,plain,
% 0.99/0.93 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_6, e_5) | (~product(e_6, e_3, e_5)) | (~product(e_4, e_3, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_6)) | product(e_4, e_6, e_5) | (~product(e_6, e_3, e_5))))),
% 0.99/0.93 inference(monotonicity,[status(thm)],[1121])).
% 0.99/0.93 tff(1123,plain,
% 0.99/0.93 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_6, e_5) | (~product(e_6, e_3, e_5)) | (~product(e_4, e_3, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_6)) | product(e_4, e_6, e_5) | (~product(e_6, e_3, e_5)))),
% 1.02/0.93 inference(transitivity,[status(thm)],[1122, 1120])).
% 1.02/0.93 tff(1124,plain,
% 1.02/0.93 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_6, e_5) | (~product(e_6, e_3, e_5)) | (~product(e_4, e_3, e_6)))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1125,plain,
% 1.02/0.93 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_6)) | product(e_4, e_6, e_5) | (~product(e_6, e_3, e_5))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1124, 1123])).
% 1.02/0.93 tff(1126,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1125, 33, 961, 1119, 1099])).
% 1.02/0.93 tff(1127,plain,((~product(e_6, e_3, e_5)) | (~product(e_4, e_3, e_6)) | product(e_4, e_6, e_5)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1128,plain,
% 1.02/0.93 (~product(e_4, e_3, e_6)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1127, 1118, 1099])).
% 1.02/0.93 tff(1129,plain,
% 1.02/0.93 (product(e_4, e_1, e_2)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[556, 1128, 54])).
% 1.02/0.93 tff(1130,plain,
% 1.02/0.93 (~product(e_5, e_1, e_2)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[569, 1129])).
% 1.02/0.93 tff(1131,plain,
% 1.02/0.93 (~product(e_1, e_1, e_2)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[571, 1128, 54])).
% 1.02/0.93 tff(1132,plain,
% 1.02/0.93 (product(e_1, e_1, e_1)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[154, 1131])).
% 1.02/0.93 tff(1133,plain,
% 1.02/0.93 (~product(e_5, e_1, e_1)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[582, 1132])).
% 1.02/0.93 tff(1134,plain,
% 1.02/0.93 (product(e_5, e_1, e_6)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[631, 1133, 1130])).
% 1.02/0.93 tff(1135,plain,
% 1.02/0.93 (~product(e_6, e_1, e_6)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[641, 1134])).
% 1.02/0.93 tff(1136,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[956, 1135, 1134, 54, 1106, 1128])).
% 1.02/0.93 tff(1137,plain,((~product(e_6, e_3, e_5)) | product(e_1, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1138,plain,
% 1.02/0.93 (~product(e_6, e_3, e_5)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1137, 54])).
% 1.02/0.93 tff(1139,plain,
% 1.02/0.93 (((~![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_1, e_5)) | (~product(e_4, 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_6, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1140,plain,
% 1.02/0.93 ((equalish(e_6, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_6, e_1, e_5))) <=> (equalish(e_6, e_4) | (~product(e_6, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1141,plain,
% 1.02/0.93 (((~![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_6, e_1, e_5)) | (~product(e_4, e_1, e_5))))),
% 1.02/0.93 inference(monotonicity,[status(thm)],[1140])).
% 1.02/0.93 tff(1142,plain,
% 1.02/0.93 (((~![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_6, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 1.02/0.93 inference(transitivity,[status(thm)],[1141, 1139])).
% 1.02/0.93 tff(1143,plain,
% 1.02/0.93 ((~![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)))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1144,plain,
% 1.02/0.93 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_6, e_1, e_5)) | (~product(e_4, e_1, e_5))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 1.02/0.93 tff(1145,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1144, 738, 87, 518, 1100])).
% 1.02/0.93 tff(1146,plain,((~product(e_6, e_1, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1147,plain,
% 1.02/0.93 (~product(e_6, e_1, e_5)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1146, 1009])).
% 1.02/0.93 tff(1148,assumption,(~product(e_5, e_1, e_3)), introduced(assumption)).
% 1.02/0.93 tff(1149,plain,
% 1.02/0.93 (~product(e_5, e_1, e_1)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[582, 731])).
% 1.02/0.93 tff(1150,plain,
% 1.02/0.93 (product(e_5, e_1, e_2)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[629, 1149, 619, 1148, 1000, 603])).
% 1.02/0.93 tff(1151,plain,
% 1.02/0.93 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_6, 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_6, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_6, e_1, e_2)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1152,plain,
% 1.02/0.93 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_6, e_1, e_2)))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1153,plain,
% 1.02/0.93 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_6, e_1, e_2))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 1.02/0.93 tff(1154,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1153, 636, 87, 1150, 674])).
% 1.02/0.93 tff(1155,plain,((~product(e_6, e_1, e_2)) | product(e_5, e_1, e_3) | product(e_5, e_1, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1156,plain,
% 1.02/0.93 (~product(e_6, e_1, e_2)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1155, 1000, 1148])).
% 1.02/0.93 tff(1157,plain,
% 1.02/0.93 (~product(e_1, e_1, e_1)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[582, 574])).
% 1.02/0.93 tff(1158,plain,
% 1.02/0.93 (product(e_1, e_1, e_2)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[154, 1157])).
% 1.02/0.93 tff(1159,plain,
% 1.02/0.93 (~product(e_2, e_1, e_2)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[671, 1158])).
% 1.02/0.93 tff(1160,assumption,(~product(e_6, e_1, e_2)), introduced(assumption)).
% 1.02/0.93 tff(1161,plain,
% 1.02/0.93 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_6, e_1, e_1)) | (~product(e_5, 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_5) | (~product(e_6, e_1, e_1)) | (~product(e_5, e_1, e_1)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1162,plain,
% 1.02/0.93 ((equalish(e_6, e_5) | (~product(e_5, e_1, e_1)) | (~product(e_6, e_1, e_1))) <=> (equalish(e_6, e_5) | (~product(e_6, e_1, e_1)) | (~product(e_5, e_1, e_1)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1163,plain,
% 1.02/0.93 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, 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_5) | (~product(e_6, e_1, e_1)) | (~product(e_5, e_1, e_1))))),
% 1.02/0.93 inference(monotonicity,[status(thm)],[1162])).
% 1.02/0.93 tff(1164,plain,
% 1.02/0.93 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, 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_5) | (~product(e_6, e_1, e_1)) | (~product(e_5, e_1, e_1)))),
% 1.02/0.93 inference(transitivity,[status(thm)],[1163, 1161])).
% 1.02/0.93 tff(1165,plain,
% 1.02/0.93 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, e_1, e_1)) | (~product(e_6, e_1, e_1)))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1166,plain,
% 1.02/0.93 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_5) | (~product(e_6, e_1, e_1)) | (~product(e_5, e_1, e_1))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 1.02/0.93 tff(1167,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1166, 636, 87, 574, 703])).
% 1.02/0.93 tff(1168,plain,((~product(e_6, e_1, e_1)) | (~product(e_5, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1169,plain,
% 1.02/0.93 (~product(e_6, e_1, e_1)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1168, 574])).
% 1.02/0.93 tff(1170,plain,
% 1.02/0.93 (product(e_6, e_1, e_3)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[701, 1169, 661, 662, 1160])).
% 1.02/0.93 tff(1171,plain,
% 1.02/0.93 (~product(e_2, e_1, e_3)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[659, 1170])).
% 1.02/0.93 tff(1172,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[206, 1171, 1159])).
% 1.02/0.93 tff(1173,plain,((~product(e_5, e_1, e_1)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1174,plain,
% 1.02/0.93 (~product(e_5, e_1, e_1)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1173, 1156, 662, 661])).
% 1.02/0.93 tff(1175,plain,
% 1.02/0.93 (product(e_5, e_1, e_2)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[630, 1174, 1148, 1000])).
% 1.02/0.93 tff(1176,plain,
% 1.02/0.93 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_5, 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_5, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1177,plain,
% 1.02/0.93 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1178,plain,
% 1.02/0.93 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_5, e_1, e_2))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 1.02/0.93 tff(1179,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1178, 587, 87, 56, 558])).
% 1.02/0.93 tff(1180,plain,((~product(e_5, e_1, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1181,plain,
% 1.02/0.93 (~product(e_2, e_1, e_2)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1180, 1175])).
% 1.02/0.93 tff(1182,assumption,(~product(e_5, e_1, e_1)), introduced(assumption)).
% 1.02/0.93 tff(1183,plain,
% 1.02/0.93 (product(e_5, e_1, e_2)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[629, 1000, 619, 1148, 1182, 603])).
% 1.02/0.93 tff(1184,plain,
% 1.02/0.93 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, 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_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1185,plain,
% 1.02/0.93 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1186,plain,
% 1.02/0.93 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 1.02/0.93 tff(1187,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1186, 577, 87, 298, 558])).
% 1.02/0.93 tff(1188,plain,((~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1189,plain,
% 1.02/0.93 (~product(e_1, e_1, e_2)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1188, 1183])).
% 1.02/0.93 tff(1190,plain,
% 1.02/0.93 (product(e_6, e_1, e_1)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[700, 1156, 690, 662, 663, 661])).
% 1.02/0.93 tff(1191,plain,
% 1.02/0.93 (~product(e_1, e_1, e_1)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[711, 1190])).
% 1.02/0.93 tff(1192,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[154, 1191, 1189])).
% 1.02/0.93 tff(1193,plain,(product(e_5, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_3) | product(e_6, e_1, e_6) | product(e_5, e_1, e_3) | product(e_5, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1194,plain,
% 1.02/0.93 (product(e_6, e_1, e_3)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1193, 1174, 661, 662, 1148, 1000])).
% 1.02/0.93 tff(1195,plain,
% 1.02/0.93 (~product(e_2, e_1, e_3)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[659, 1194])).
% 1.02/0.93 tff(1196,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[206, 1195, 1181])).
% 1.02/0.93 tff(1197,plain,(product(e_5, e_1, e_6) | product(e_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_5, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1198,plain,
% 1.02/0.93 (product(e_5, e_1, e_6) | product(e_6, e_1, e_6) | product(e_6, e_1, e_5)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1197, 593])).
% 1.02/0.93 tff(1199,plain,
% 1.02/0.93 (product(e_6, e_1, e_6)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1198, 1147, 1000])).
% 1.02/0.93 tff(1200,assumption,(product(e_6, e_3, e_6)), introduced(assumption)).
% 1.02/0.93 tff(1201,plain,
% 1.02/0.93 (((~![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_6, e_1, e_6)) | (~product(e_6, 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_1) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_3, e_6)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1202,plain,
% 1.02/0.93 ((~![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_6, e_1, e_6)) | (~product(e_6, e_3, e_6)))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1203,plain,
% 1.02/0.93 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_3, e_6))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 1.02/0.93 tff(1204,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1203, 15, 12, 633, 1200])).
% 1.02/0.93 tff(1205,plain,((~product(e_6, e_3, e_6)) | (~product(e_6, e_1, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1206,plain,
% 1.02/0.93 (~product(e_6, e_3, e_6)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1205, 1199])).
% 1.02/0.93 tff(1207,plain,
% 1.02/0.93 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1208,plain,
% 1.02/0.93 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1209,plain,
% 1.02/0.93 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 1.02/0.93 tff(1210,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1209, 15, 87, 464, 1037])).
% 1.02/0.93 tff(1211,plain,((~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1212,plain,
% 1.02/0.93 (~product(e_3, e_3, e_2)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1211, 1085])).
% 1.02/0.93 tff(1213,assumption,(product(e_3, e_3, e_5)), introduced(assumption)).
% 1.02/0.93 tff(1214,plain,
% 1.02/0.93 (((~![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_3, e_3, e_5)) | (~product(e_3, 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_3, e_4) | (~product(e_3, e_3, e_5)) | (~product(e_3, e_4, e_5)))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1215,plain,
% 1.02/0.94 ((equalish(e_3, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_3, e_5))) <=> (equalish(e_3, e_4) | (~product(e_3, e_3, e_5)) | (~product(e_3, e_4, e_5)))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1216,plain,
% 1.02/0.94 (((~![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_3, e_4, e_5)) | (~product(e_3, 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_4) | (~product(e_3, e_3, e_5)) | (~product(e_3, e_4, e_5))))),
% 1.02/0.94 inference(monotonicity,[status(thm)],[1215])).
% 1.02/0.94 tff(1217,plain,
% 1.02/0.94 (((~![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_3, e_4, e_5)) | (~product(e_3, 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_4) | (~product(e_3, e_3, e_5)) | (~product(e_3, e_4, e_5)))),
% 1.02/0.94 inference(transitivity,[status(thm)],[1216, 1214])).
% 1.02/0.94 tff(1218,plain,
% 1.02/0.94 ((~![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_3, e_4, e_5)) | (~product(e_3, e_3, e_5)))),
% 1.02/0.94 inference(quant_inst,[status(thm)],[])).
% 1.02/0.94 tff(1219,plain,
% 1.02/0.94 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_3, e_3, e_5)) | (~product(e_3, e_4, e_5))),
% 1.02/0.94 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 1.02/0.94 tff(1220,plain,
% 1.02/0.94 ($false),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1219, 974, 12, 1213, 773])).
% 1.02/0.94 tff(1221,plain,((~product(e_3, e_3, e_5)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.94 tff(1222,plain,
% 1.02/0.94 (~product(e_3, e_3, e_5)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1221, 1010])).
% 1.02/0.94 tff(1223,plain,
% 1.02/0.94 (~product(e_1, e_3, e_3)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1077, 1212, 1025, 1222])).
% 1.02/0.94 tff(1224,assumption,(product(e_3, e_3, e_1)), introduced(assumption)).
% 1.02/0.94 tff(1225,assumption,(~product(e_1, e_3, e_3)), introduced(assumption)).
% 1.02/0.94 tff(1226,plain,
% 1.02/0.94 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_6) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_6)))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1227,plain,
% 1.02/0.94 ((product(e_3, e_1, e_6) | (~product(e_1, e_3, e_6)) | (~product(e_3, e_3, e_1))) <=> (product(e_3, e_1, e_6) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_6)))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1228,plain,
% 1.02/0.94 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_1, e_3, e_6)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_6))))),
% 1.02/0.94 inference(monotonicity,[status(thm)],[1227])).
% 1.02/0.94 tff(1229,plain,
% 1.02/0.94 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_1, e_3, e_6)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_6) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_6)))),
% 1.02/0.94 inference(transitivity,[status(thm)],[1228, 1226])).
% 1.02/0.94 tff(1230,plain,
% 1.02/0.94 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_1, e_3, e_6)) | (~product(e_3, e_3, e_1)))),
% 1.02/0.94 inference(quant_inst,[status(thm)],[])).
% 1.02/0.94 tff(1231,plain,
% 1.02/0.94 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_6) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_6))),
% 1.02/0.94 inference(modus_ponens,[status(thm)],[1230, 1229])).
% 1.02/0.94 tff(1232,plain,
% 1.02/0.94 ($false),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1231, 33, 279, 960, 1224])).
% 1.02/0.94 tff(1233,plain,((~product(e_1, e_3, e_6)) | (~product(e_3, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.94 tff(1234,plain,
% 1.02/0.94 (~product(e_1, e_3, e_6)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1233, 1224])).
% 1.02/0.94 tff(1235,plain,
% 1.02/0.94 (product(e_1, e_3, e_2)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[480, 1234, 54, 1035, 1225, 1027])).
% 1.02/0.94 tff(1236,plain,
% 1.02/0.94 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_2)))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1237,plain,
% 1.02/0.94 ((product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_1))) <=> (product(e_3, e_1, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_2)))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1238,plain,
% 1.02/0.94 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_2))))),
% 1.02/0.94 inference(monotonicity,[status(thm)],[1237])).
% 1.02/0.94 tff(1239,plain,
% 1.02/0.94 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_2)))),
% 1.02/0.94 inference(transitivity,[status(thm)],[1238, 1236])).
% 1.02/0.94 tff(1240,plain,
% 1.02/0.94 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_1)))),
% 1.02/0.94 inference(quant_inst,[status(thm)],[])).
% 1.02/0.94 tff(1241,plain,
% 1.02/0.94 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_2))),
% 1.02/0.94 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 1.02/0.94 tff(1242,plain,
% 1.02/0.94 ($false),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1241, 33, 266, 1235, 1224])).
% 1.02/0.94 tff(1243,plain,((~product(e_3, e_3, e_1)) | 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)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.94 tff(1244,plain,
% 1.02/0.94 ((~product(e_3, e_3, e_1)) | product(e_1, e_3, e_5) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1243, 1033])).
% 1.02/0.94 tff(1245,plain,
% 1.02/0.94 (~product(e_3, e_3, e_1)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1244, 1223, 54, 1027])).
% 1.02/0.94 tff(1246,plain,
% 1.02/0.94 (product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_6) | product(e_3, e_3, e_5) | product(e_3, e_3, e_3)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1068, 289, 144, 1052])).
% 1.02/0.94 tff(1247,plain,
% 1.02/0.94 (product(e_3, e_3, e_3)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1246, 1245, 1025, 1222, 1212])).
% 1.02/0.94 tff(1248,assumption,(product(e_6, e_3, e_3)), introduced(assumption)).
% 1.02/0.94 tff(1249,plain,
% 1.02/0.94 (((~![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)))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1250,plain,
% 1.02/0.94 ((~![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)))),
% 1.02/0.94 inference(quant_inst,[status(thm)],[])).
% 1.02/0.94 tff(1251,plain,
% 1.02/0.94 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_6, e_3, e_3))),
% 1.02/0.94 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 1.02/0.94 tff(1252,plain,
% 1.02/0.94 ($false),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1251, 684, 87, 1248, 209])).
% 1.02/0.94 tff(1253,plain,((~product(e_6, e_3, e_3)) | (~product(e_3, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.94 tff(1254,plain,
% 1.02/0.94 (~product(e_6, e_3, e_3)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1253, 1247])).
% 1.02/0.94 tff(1255,assumption,(product(e_6, e_3, e_4)), introduced(assumption)).
% 1.02/0.94 tff(1256,plain,
% 1.02/0.94 (((~![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_3, e_4)) | (~product(e_6, e_3, 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_2) | (~product(e_2, e_3, e_4)) | (~product(e_6, e_3, e_4)))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1257,plain,
% 1.02/0.94 ((~![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_3, e_4)) | (~product(e_6, e_3, e_4)))),
% 1.02/0.94 inference(quant_inst,[status(thm)],[])).
% 1.02/0.94 tff(1258,plain,
% 1.02/0.94 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_6, e_3, e_4))),
% 1.02/0.94 inference(modus_ponens,[status(thm)],[1257, 1256])).
% 1.02/0.94 tff(1259,plain,
% 1.02/0.94 ($false),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1258, 654, 87, 374, 1255])).
% 1.02/0.94 tff(1260,plain,((~product(e_6, e_3, e_4)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.94 tff(1261,plain,
% 1.02/0.94 (~product(e_6, e_3, e_4)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1260, 330])).
% 1.02/0.94 tff(1262,assumption,(~product(e_6, e_3, e_4)), introduced(assumption)).
% 1.02/0.94 tff(1263,assumption,(~product(e_6, e_3, e_1)), introduced(assumption)).
% 1.02/0.94 tff(1264,assumption,(~product(e_6, e_3, e_2)), introduced(assumption)).
% 1.02/0.94 tff(1265,assumption,(~product(e_6, e_3, e_6)), introduced(assumption)).
% 1.02/0.94 tff(1266,assumption,(~product(e_6, e_3, e_3)), introduced(assumption)).
% 1.02/0.94 tff(1267,assumption,(~product(e_6, e_3, e_5)), introduced(assumption)).
% 1.02/0.94 tff(1268,plain,
% 1.02/0.94 (((~![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)) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | (~group_element(e_6)) | 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_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)) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | (~group_element(e_6)) | 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_1))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1269,plain,
% 1.02/0.94 ((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)) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | (~group_element(e_6)) | 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_1))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1270,plain,
% 1.02/0.94 (((~![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)) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | (~group_element(e_6)) | 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_1)))),
% 1.02/0.94 inference(monotonicity,[status(thm)],[1269])).
% 1.02/0.94 tff(1271,plain,
% 1.02/0.94 (((~![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)) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | (~group_element(e_6)) | 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_1))),
% 1.02/0.94 inference(transitivity,[status(thm)],[1270, 1268])).
% 1.02/0.94 tff(1272,plain,
% 1.02/0.94 ((~![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)))),
% 1.02/0.94 inference(quant_inst,[status(thm)],[])).
% 1.02/0.94 tff(1273,plain,
% 1.02/0.94 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | (~group_element(e_6)) | product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_4) | product(e_6, e_3, e_1)),
% 1.02/0.94 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 1.02/0.94 tff(1274,plain,
% 1.02/0.94 ($false),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1273, 289, 693, 144, 1267, 1266, 1265, 1264, 1263, 1262])).
% 1.02/0.94 tff(1275,plain,(product(e_6, e_3, e_3) | product(e_6, e_3, e_5) | product(e_6, e_3, e_6) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1) | product(e_6, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.94 tff(1276,plain,
% 1.02/0.94 (product(e_6, e_3, e_3) | product(e_6, e_3, e_5) | product(e_6, e_3, e_6) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1275, 1261])).
% 1.02/0.94 tff(1277,plain,
% 1.02/0.94 (product(e_6, e_3, e_1)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1276, 1254, 1206, 1138, 1098])).
% 1.02/0.94 tff(1278,assumption,(product(e_1, e_4, e_2)), introduced(assumption)).
% 1.02/0.94 tff(1279,plain,
% 1.02/0.94 (((~![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)))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1280,plain,
% 1.02/0.94 ((~![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)))),
% 1.02/0.94 inference(quant_inst,[status(thm)],[])).
% 1.02/0.94 tff(1281,plain,
% 1.02/0.94 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_4, e_2))),
% 1.02/0.94 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 1.02/0.94 tff(1282,plain,
% 1.02/0.94 ($false),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1281, 399, 12, 464, 1278])).
% 1.02/0.94 tff(1283,plain,((~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.94 tff(1284,plain,
% 1.02/0.94 (~product(e_1, e_4, e_2)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1283, 1085])).
% 1.02/0.94 tff(1285,plain,
% 1.02/0.94 (~product(e_2, e_4, e_5)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[782, 1010])).
% 1.02/0.94 tff(1286,assumption,(product(e_6, e_4, e_5)), introduced(assumption)).
% 1.02/0.94 tff(1287,plain,
% 1.02/0.94 (((~![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_4, e_5)) | (~product(e_6, e_4, 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_3) | (~product(e_3, e_4, e_5)) | (~product(e_6, e_4, e_5)))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1288,plain,
% 1.02/0.94 ((~![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_4, e_5)) | (~product(e_6, e_4, e_5)))),
% 1.02/0.94 inference(quant_inst,[status(thm)],[])).
% 1.02/0.94 tff(1289,plain,
% 1.02/0.94 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_6, e_4, e_5))),
% 1.02/0.94 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 1.02/0.94 tff(1290,plain,
% 1.02/0.94 ($false),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1289, 684, 87, 1286, 773])).
% 1.02/0.94 tff(1291,plain,((~product(e_6, e_4, e_5)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.94 tff(1292,plain,
% 1.02/0.94 (~product(e_6, e_4, e_5)),
% 1.02/0.94 inference(unit_resolution,[status(thm)],[1291, 1010])).
% 1.02/0.94 tff(1293,assumption,(~product(e_1, e_2, e_4)), introduced(assumption)).
% 1.02/0.94 tff(1294,plain,
% 1.02/0.94 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_2)) | product(e_1, e_2, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_2)) | product(e_1, e_2, e_4))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1295,plain,
% 1.02/0.94 ((product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_2))) <=> ((~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_2)) | product(e_1, e_2, e_4))),
% 1.02/0.94 inference(rewrite,[status(thm)],[])).
% 1.02/0.94 tff(1296,plain,
% 1.02/0.94 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_2)) | product(e_1, e_2, e_4)))),
% 1.02/0.94 inference(monotonicity,[status(thm)],[1295])).
% 1.02/0.94 tff(1297,plain,
% 1.02/0.94 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_2)) | product(e_1, e_2, e_4))),
% 1.02/0.94 inference(transitivity,[status(thm)],[1296, 1294])).
% 1.02/0.94 tff(1298,plain,
% 1.02/0.94 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_2)))),
% 1.02/0.94 inference(quant_inst,[status(thm)],[])).
% 1.02/0.94 tff(1299,plain,
% 1.02/0.94 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_2)) | product(e_1, e_2, e_4)),
% 1.02/0.94 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 1.02/0.95 tff(1300,plain,
% 1.02/0.95 ($false),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1299, 33, 374, 464, 1293])).
% 1.02/0.95 tff(1301,plain,(product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.95 tff(1302,plain,
% 1.02/0.95 (product(e_1, e_2, e_4) | (~product(e_1, e_3, e_2))),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1301, 330])).
% 1.02/0.95 tff(1303,plain,
% 1.02/0.95 (product(e_1, e_2, e_4)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1302, 1085])).
% 1.02/0.95 tff(1304,assumption,(product(e_1, e_2, e_4)), introduced(assumption)).
% 1.02/0.95 tff(1305,assumption,(product(e_1, e_4, e_4)), introduced(assumption)).
% 1.02/0.95 tff(1306,plain,
% 1.02/0.95 (((~![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_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_4, e_2) | (~product(e_1, e_4, e_4)) | (~product(e_1, e_2, e_4)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1307,plain,
% 1.02/0.95 ((equalish(e_4, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_4, e_4))) <=> (equalish(e_4, e_2) | (~product(e_1, e_4, e_4)) | (~product(e_1, e_2, e_4)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1308,plain,
% 1.02/0.95 (((~![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_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_2) | (~product(e_1, e_4, e_4)) | (~product(e_1, e_2, e_4))))),
% 1.02/0.95 inference(monotonicity,[status(thm)],[1307])).
% 1.02/0.95 tff(1309,plain,
% 1.02/0.95 (((~![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_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_2) | (~product(e_1, e_4, e_4)) | (~product(e_1, e_2, e_4)))),
% 1.02/0.95 inference(transitivity,[status(thm)],[1308, 1306])).
% 1.02/0.95 tff(1310,plain,
% 1.02/0.95 ((~![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_4)) | (~product(e_1, e_4, e_4)))),
% 1.02/0.95 inference(quant_inst,[status(thm)],[])).
% 1.02/0.95 tff(1311,plain,
% 1.02/0.95 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_1, e_4, e_4)) | (~product(e_1, e_2, e_4))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 1.02/0.95 tff(1312,plain,
% 1.02/0.95 ($false),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1311, 335, 12, 1305, 1304])).
% 1.02/0.95 tff(1313,plain,((~product(e_1, e_4, e_4)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.95 tff(1314,plain,
% 1.02/0.95 (~product(e_1, e_4, e_4)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1313, 1303])).
% 1.02/0.95 tff(1315,assumption,(product(e_5, e_4, e_5)), introduced(assumption)).
% 1.02/0.95 tff(1316,plain,
% 1.02/0.95 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_5, e_4, e_5)) | (~product(e_3, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_4, e_5)) | (~product(e_3, e_4, e_5)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1317,plain,
% 1.02/0.95 ((equalish(e_5, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_5))) <=> (equalish(e_5, e_3) | (~product(e_5, e_4, e_5)) | (~product(e_3, e_4, e_5)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1318,plain,
% 1.02/0.95 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_5, e_4, e_5)) | (~product(e_3, e_4, e_5))))),
% 1.02/0.95 inference(monotonicity,[status(thm)],[1317])).
% 1.02/0.95 tff(1319,plain,
% 1.02/0.95 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_4, e_5)) | (~product(e_3, e_4, e_5)))),
% 1.02/0.95 inference(transitivity,[status(thm)],[1318, 1316])).
% 1.02/0.95 tff(1320,plain,
% 1.02/0.95 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_5)))),
% 1.02/0.95 inference(quant_inst,[status(thm)],[])).
% 1.02/0.95 tff(1321,plain,
% 1.02/0.95 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_4, e_5)) | (~product(e_3, e_4, e_5))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 1.02/0.95 tff(1322,plain,
% 1.02/0.95 ($false),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1321, 597, 87, 1315, 773])).
% 1.02/0.95 tff(1323,plain,((~product(e_5, e_4, e_5)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.95 tff(1324,plain,
% 1.02/0.95 (~product(e_5, e_4, e_5)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1323, 1010])).
% 1.02/0.95 tff(1325,plain,
% 1.02/0.95 (~product(e_4, e_4, e_5)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[751, 1009])).
% 1.02/0.95 tff(1326,assumption,(product(e_3, e_5, e_3)), introduced(assumption)).
% 1.02/0.95 tff(1327,plain,
% 1.02/0.95 (((~![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_3, e_3, e_3)) | (~product(e_3, 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_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1328,plain,
% 1.02/0.95 ((~![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_3, e_3, e_3)) | (~product(e_3, e_5, e_3)))),
% 1.02/0.95 inference(quant_inst,[status(thm)],[])).
% 1.02/0.95 tff(1329,plain,
% 1.02/0.95 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[1328, 1327])).
% 1.02/0.95 tff(1330,plain,
% 1.02/0.95 ($false),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1329, 597, 12, 1326, 209])).
% 1.02/0.95 tff(1331,plain,((~product(e_3, e_5, e_3)) | (~product(e_3, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.95 tff(1332,plain,
% 1.02/0.95 (~product(e_3, e_5, e_3)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1331, 1247])).
% 1.02/0.95 tff(1333,assumption,(~product(e_3, e_5, e_3)), introduced(assumption)).
% 1.02/0.95 tff(1334,assumption,(product(e_5, e_4, e_3)), introduced(assumption)).
% 1.02/0.95 tff(1335,plain,
% 1.02/0.95 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_5)) | product(e_3, e_5, e_3) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_3) | (~product(e_5, e_4, e_3)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1336,plain,
% 1.02/0.95 ((product(e_3, e_5, e_3) | (~product(e_5, e_4, e_3)) | (~product(e_3, e_4, e_5))) <=> ((~product(e_3, e_4, e_5)) | product(e_3, e_5, e_3) | (~product(e_5, e_4, e_3)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1337,plain,
% 1.02/0.95 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_3) | (~product(e_5, e_4, e_3)) | (~product(e_3, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_5)) | product(e_3, e_5, e_3) | (~product(e_5, e_4, e_3))))),
% 1.02/0.95 inference(monotonicity,[status(thm)],[1336])).
% 1.02/0.95 tff(1338,plain,
% 1.02/0.95 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_3) | (~product(e_5, e_4, e_3)) | (~product(e_3, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_3) | (~product(e_5, e_4, e_3)))),
% 1.02/0.95 inference(transitivity,[status(thm)],[1337, 1335])).
% 1.02/0.95 tff(1339,plain,
% 1.02/0.95 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_3) | (~product(e_5, e_4, e_3)) | (~product(e_3, e_4, e_5)))),
% 1.02/0.95 inference(quant_inst,[status(thm)],[])).
% 1.02/0.95 tff(1340,plain,
% 1.02/0.95 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_3) | (~product(e_5, e_4, e_3))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[1339, 1338])).
% 1.02/0.95 tff(1341,plain,
% 1.02/0.95 ($false),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1340, 33, 1334, 773, 1333])).
% 1.02/0.95 tff(1342,plain,(product(e_3, e_5, e_3) | (~product(e_5, e_4, e_3)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.95 tff(1343,plain,
% 1.02/0.95 (~product(e_5, e_4, e_3)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1342, 1332, 1010])).
% 1.02/0.95 tff(1344,plain,
% 1.02/0.95 (~product(e_4, e_1, e_2)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[569, 558])).
% 1.02/0.95 tff(1345,plain,
% 1.02/0.95 (product(e_4, e_3, e_6)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[556, 1344, 54])).
% 1.02/0.95 tff(1346,plain,
% 1.02/0.95 (((~![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_4, e_3, 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_3) | (~product(e_4, e_3, e_6)) | (~product(e_4, e_2, e_6)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1347,plain,
% 1.02/0.95 ((~![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_4, e_3, e_6)) | (~product(e_4, e_2, e_6)))),
% 1.02/0.95 inference(quant_inst,[status(thm)],[])).
% 1.02/0.95 tff(1348,plain,
% 1.02/0.95 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_4, e_3, e_6)) | (~product(e_4, e_2, e_6))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 1.02/0.95 tff(1349,plain,
% 1.02/0.95 ($false),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1348, 227, 12, 961, 802])).
% 1.02/0.95 tff(1350,plain,((~product(e_4, e_2, e_6)) | (~product(e_4, e_3, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.95 tff(1351,plain,
% 1.02/0.95 (~product(e_4, e_2, e_6)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1350, 1345])).
% 1.02/0.95 tff(1352,assumption,(product(e_6, e_3, e_1)), introduced(assumption)).
% 1.02/0.95 tff(1353,assumption,(~product(e_4, e_6, e_1)), introduced(assumption)).
% 1.02/0.95 tff(1354,plain,
% 1.02/0.95 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_6)) | (~product(e_6, e_3, e_1)) | product(e_4, e_6, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_6)) | (~product(e_6, e_3, e_1)) | product(e_4, e_6, e_1))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1355,plain,
% 1.02/0.95 ((product(e_4, e_6, e_1) | (~product(e_6, e_3, e_1)) | (~product(e_4, e_3, e_6))) <=> ((~product(e_4, e_3, e_6)) | (~product(e_6, e_3, e_1)) | product(e_4, e_6, e_1))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1356,plain,
% 1.02/0.95 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_6, e_1) | (~product(e_6, e_3, e_1)) | (~product(e_4, e_3, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_6)) | (~product(e_6, e_3, e_1)) | product(e_4, e_6, e_1)))),
% 1.02/0.95 inference(monotonicity,[status(thm)],[1355])).
% 1.02/0.95 tff(1357,plain,
% 1.02/0.95 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_6, e_1) | (~product(e_6, e_3, e_1)) | (~product(e_4, e_3, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_6)) | (~product(e_6, e_3, e_1)) | product(e_4, e_6, e_1))),
% 1.02/0.95 inference(transitivity,[status(thm)],[1356, 1354])).
% 1.02/0.95 tff(1358,plain,
% 1.02/0.95 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_6, e_1) | (~product(e_6, e_3, e_1)) | (~product(e_4, e_3, e_6)))),
% 1.02/0.95 inference(quant_inst,[status(thm)],[])).
% 1.02/0.95 tff(1359,plain,
% 1.02/0.95 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_6)) | (~product(e_6, e_3, e_1)) | product(e_4, e_6, e_1)),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 1.02/0.95 tff(1360,plain,
% 1.02/0.95 ($false),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1359, 33, 961, 1353, 1352])).
% 1.02/0.95 tff(1361,plain,((~product(e_6, e_3, e_1)) | (~product(e_4, e_3, e_6)) | product(e_4, e_6, e_1)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.95 tff(1362,plain,
% 1.02/0.95 (product(e_4, e_6, e_1)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1361, 1345, 1352])).
% 1.02/0.95 tff(1363,plain,
% 1.02/0.95 (((~![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_4, e_6, e_1)) | (~product(e_4, 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_6, e_2) | (~product(e_4, e_6, e_1)) | (~product(e_4, e_2, e_1)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1364,plain,
% 1.02/0.95 ((equalish(e_6, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_6, e_1))) <=> (equalish(e_6, e_2) | (~product(e_4, e_6, e_1)) | (~product(e_4, e_2, e_1)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1365,plain,
% 1.02/0.95 (((~![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_4, e_2, e_1)) | (~product(e_4, e_6, e_1)))) <=> ((~![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_4, e_6, e_1)) | (~product(e_4, e_2, e_1))))),
% 1.02/0.95 inference(monotonicity,[status(thm)],[1364])).
% 1.02/0.95 tff(1366,plain,
% 1.02/0.95 (((~![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_4, e_2, e_1)) | (~product(e_4, e_6, e_1)))) <=> ((~![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_4, e_6, e_1)) | (~product(e_4, e_2, e_1)))),
% 1.02/0.95 inference(transitivity,[status(thm)],[1365, 1363])).
% 1.02/0.95 tff(1367,plain,
% 1.02/0.95 ((~![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_4, e_2, e_1)) | (~product(e_4, e_6, e_1)))),
% 1.02/0.95 inference(quant_inst,[status(thm)],[])).
% 1.02/0.95 tff(1368,plain,
% 1.02/0.95 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_2) | (~product(e_4, e_6, e_1)) | (~product(e_4, e_2, e_1))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 1.02/0.95 tff(1369,plain,
% 1.02/0.95 ($false),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1368, 654, 12, 755, 905])).
% 1.02/0.95 tff(1370,plain,((~product(e_4, e_6, e_1)) | (~product(e_4, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.95 tff(1371,plain,
% 1.02/0.95 (~product(e_4, e_2, e_1)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1370, 1362])).
% 1.02/0.95 tff(1372,plain,
% 1.02/0.95 (~product(e_2, e_4, e_4)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[792, 330])).
% 1.02/0.95 tff(1373,plain,
% 1.02/0.95 ((~product(e_4, e_4, e_2)) | product(e_4, e_2, e_1) | product(e_2, e_4, e_5) | product(e_4, e_2, e_6)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[856, 1372, 372])).
% 1.02/0.95 tff(1374,plain,
% 1.02/0.95 (~product(e_4, e_4, e_2)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1373, 1371, 816, 1351])).
% 1.02/0.95 tff(1375,plain,
% 1.02/0.95 (((~![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_4, e_3, e_6)) | (~product(e_4, 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_3) | (~product(e_4, e_3, e_6)) | (~product(e_4, e_4, e_6)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1376,plain,
% 1.02/0.95 ((~![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_4, e_3, e_6)) | (~product(e_4, e_4, e_6)))),
% 1.02/0.95 inference(quant_inst,[status(thm)],[])).
% 1.02/0.95 tff(1377,plain,
% 1.02/0.95 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_4, e_3, e_6)) | (~product(e_4, e_4, e_6))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 1.02/0.95 tff(1378,plain,
% 1.02/0.95 ($false),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1377, 399, 12, 961, 868])).
% 1.02/0.95 tff(1379,plain,((~product(e_4, e_4, e_6)) | (~product(e_4, e_3, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.95 tff(1380,plain,
% 1.02/0.95 (~product(e_4, e_4, e_6)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1379, 1345])).
% 1.02/0.95 tff(1381,assumption,(~product(e_4, e_4, e_5)), introduced(assumption)).
% 1.02/0.95 tff(1382,assumption,(~product(e_5, e_4, e_3)), introduced(assumption)).
% 1.02/0.95 tff(1383,plain,
% 1.02/0.95 (~product(e_1, e_1, e_2)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1188, 558])).
% 1.02/0.95 tff(1384,plain,
% 1.02/0.95 (product(e_1, e_1, e_1)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[154, 1383])).
% 1.02/0.95 tff(1385,assumption,(product(e_1, e_4, e_1)), introduced(assumption)).
% 1.02/0.95 tff(1386,plain,
% 1.02/0.95 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1387,plain,
% 1.02/0.95 ((equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1))) <=> (equalish(e_4, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1388,plain,
% 1.02/0.95 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1))))),
% 1.02/0.95 inference(monotonicity,[status(thm)],[1387])).
% 1.02/0.95 tff(1389,plain,
% 1.02/0.95 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 1.02/0.95 inference(transitivity,[status(thm)],[1388, 1386])).
% 1.02/0.95 tff(1390,plain,
% 1.02/0.95 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 1.02/0.95 inference(quant_inst,[status(thm)],[])).
% 1.02/0.95 tff(1391,plain,
% 1.02/0.95 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 1.02/0.95 tff(1392,plain,
% 1.02/0.95 ($false),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1391, 366, 12, 77, 1385])).
% 1.02/0.95 tff(1393,plain,((~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.95 tff(1394,plain,
% 1.02/0.95 (~product(e_1, e_4, e_1)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1393, 1384])).
% 1.02/0.95 tff(1395,assumption,(~product(e_6, e_4, e_5)), introduced(assumption)).
% 1.02/0.95 tff(1396,plain,
% 1.02/0.95 (product(e_2, e_4, e_6)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[990, 1345])).
% 1.02/0.95 tff(1397,assumption,(product(e_1, e_4, e_6)), introduced(assumption)).
% 1.02/0.95 tff(1398,plain,
% 1.02/0.95 (((~![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_4, e_6)) | (~product(e_1, e_4, 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_2) | (~product(e_2, e_4, e_6)) | (~product(e_1, e_4, e_6)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1399,plain,
% 1.02/0.95 ((~![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_4, e_6)) | (~product(e_1, e_4, e_6)))),
% 1.02/0.95 inference(quant_inst,[status(thm)],[])).
% 1.02/0.95 tff(1400,plain,
% 1.02/0.95 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_4, e_6)) | (~product(e_1, e_4, e_6))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[1399, 1398])).
% 1.02/0.95 tff(1401,plain,
% 1.02/0.95 ($false),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1400, 67, 87, 992, 1397])).
% 1.02/0.95 tff(1402,plain,((~product(e_1, e_4, e_6)) | (~product(e_2, e_4, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.95 tff(1403,plain,
% 1.02/0.95 (~product(e_1, e_4, e_6)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[1402, 1396])).
% 1.02/0.95 tff(1404,assumption,(~product(e_1, e_4, e_5)), introduced(assumption)).
% 1.02/0.95 tff(1405,assumption,(~product(e_1, e_4, e_4)), introduced(assumption)).
% 1.02/0.95 tff(1406,assumption,(~product(e_1, e_4, e_2)), introduced(assumption)).
% 1.02/0.95 tff(1407,plain,
% 1.02/0.95 (((~![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_2) | 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))) <=> ((~![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_2) | 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))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1408,plain,
% 1.02/0.95 ((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_2) | 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))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(1409,plain,
% 1.02/0.95 (((~![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_2) | 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)))),
% 1.02/0.95 inference(monotonicity,[status(thm)],[1408])).
% 1.02/0.95 tff(1410,plain,
% 1.02/0.95 (((~![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_2) | 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))),
% 1.02/0.96 inference(transitivity,[status(thm)],[1409, 1407])).
% 1.02/0.96 tff(1411,plain,
% 1.02/0.96 ((~![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)))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(1412,plain,
% 1.02/0.96 ((~![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_2) | 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)),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 1.02/0.96 tff(1413,plain,
% 1.02/0.96 (product(e_1, e_4, e_2) | 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)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1412, 147, 505, 144])).
% 1.02/0.96 tff(1414,plain,
% 1.02/0.96 (product(e_1, e_4, e_3)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1413, 1403, 1405, 1406, 1394, 1404])).
% 1.02/0.96 tff(1415,assumption,(product(e_1, e_4, e_3)), introduced(assumption)).
% 1.02/0.96 tff(1416,assumption,(product(e_6, e_4, e_3)), introduced(assumption)).
% 1.02/0.96 tff(1417,plain,
% 1.02/0.96 (((~![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_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_6, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_6, e_4, e_3)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1418,plain,
% 1.02/0.96 ((~![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_4, e_3)) | (~product(e_6, e_4, e_3)))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(1419,plain,
% 1.02/0.96 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_6, e_4, e_3))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 1.02/0.96 tff(1420,plain,
% 1.02/0.96 ($false),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1419, 706, 87, 1416, 1415])).
% 1.02/0.96 tff(1421,plain,((~product(e_6, e_4, e_3)) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.96 tff(1422,plain,
% 1.02/0.96 (~product(e_6, e_4, e_3)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1421, 1414])).
% 1.02/0.96 tff(1423,assumption,(~product(e_1, e_4, e_6)), introduced(assumption)).
% 1.02/0.96 tff(1424,assumption,(~product(e_1, e_4, e_1)), introduced(assumption)).
% 1.02/0.96 tff(1425,assumption,(product(e_6, e_4, e_1)), introduced(assumption)).
% 1.02/0.96 tff(1426,plain,
% 1.02/0.96 (((~![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_1)) | (~product(e_6, e_4, 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_4) | (~product(e_4, e_4, e_1)) | (~product(e_6, e_4, e_1)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1427,plain,
% 1.02/0.96 ((~![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_1)) | (~product(e_6, e_4, e_1)))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(1428,plain,
% 1.02/0.96 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_6, e_4, e_1))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[1427, 1426])).
% 1.02/0.96 tff(1429,plain,
% 1.02/0.96 ($false),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1428, 738, 87, 858, 1425])).
% 1.02/0.96 tff(1430,plain,((~product(e_6, e_4, e_1)) | (~product(e_4, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.96 tff(1431,plain,
% 1.02/0.96 (~product(e_6, e_4, e_1)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1430, 858])).
% 1.02/0.96 tff(1432,assumption,(product(e_2, e_4, e_1)), introduced(assumption)).
% 1.02/0.96 tff(1433,plain,
% 1.02/0.96 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_2, e_4, 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_4) | (~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_1)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1434,plain,
% 1.02/0.96 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_1)))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(1435,plain,
% 1.02/0.96 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_1))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 1.02/0.96 tff(1436,plain,
% 1.02/0.96 ($false),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1435, 822, 87, 858, 1432])).
% 1.02/0.96 tff(1437,plain,((~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.96 tff(1438,plain,
% 1.02/0.96 (~product(e_2, e_4, e_1)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1437, 858])).
% 1.02/0.96 tff(1439,plain,
% 1.02/0.96 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_4)) | product(e_2, e_4, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_4)) | product(e_2, e_4, e_1))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1440,plain,
% 1.02/0.96 ((product(e_2, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_4))) <=> ((~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_4)) | product(e_2, e_4, e_1))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1441,plain,
% 1.02/0.96 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_4)) | product(e_2, e_4, e_1)))),
% 1.02/0.96 inference(monotonicity,[status(thm)],[1440])).
% 1.02/0.96 tff(1442,plain,
% 1.02/0.96 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_4)) | product(e_2, e_4, e_1))),
% 1.02/0.96 inference(transitivity,[status(thm)],[1441, 1439])).
% 1.02/0.96 tff(1443,plain,
% 1.02/0.96 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_4)))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(1444,plain,
% 1.02/0.96 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_4)) | product(e_2, e_4, e_1)),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 1.02/0.96 tff(1445,plain,
% 1.02/0.96 (~product(e_2, e_4, e_4)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1444, 33, 858, 1438])).
% 1.02/0.96 tff(1446,plain,
% 1.02/0.96 (product(e_2, e_4, e_2)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[838, 981, 818, 373, 816, 817])).
% 1.02/0.96 tff(1447,plain,
% 1.02/0.96 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_4, e_2)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1448,plain,
% 1.02/0.96 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_4, e_2)))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(1449,plain,
% 1.02/0.96 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_4, e_2))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[1448, 1447])).
% 1.02/0.96 tff(1450,plain,
% 1.02/0.96 ($false),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1449, 366, 12, 56, 819])).
% 1.02/0.96 tff(1451,plain,((~product(e_2, e_4, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.96 tff(1452,plain,
% 1.02/0.96 (~product(e_2, e_1, e_2)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1451, 1446])).
% 1.02/0.96 tff(1453,plain,
% 1.02/0.96 (product(e_2, e_1, e_3)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[206, 1452])).
% 1.02/0.96 tff(1454,plain,
% 1.02/0.96 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1455,plain,
% 1.02/0.96 ((equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1456,plain,
% 1.02/0.96 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))))),
% 1.02/0.96 inference(monotonicity,[status(thm)],[1455])).
% 1.02/0.96 tff(1457,plain,
% 1.02/0.96 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 1.02/0.96 inference(transitivity,[status(thm)],[1456, 1454])).
% 1.02/0.96 tff(1458,plain,
% 1.02/0.96 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(1459,plain,
% 1.02/0.96 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[1458, 1457])).
% 1.02/0.96 tff(1460,plain,
% 1.02/0.96 ($false),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1459, 248, 87, 363, 208])).
% 1.02/0.96 tff(1461,plain,((~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.96 tff(1462,plain,
% 1.02/0.96 (~product(e_3, e_1, e_3)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1461, 1453])).
% 1.02/0.96 tff(1463,plain,
% 1.02/0.96 (((~![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_2, e_4, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_3, e_2)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1464,plain,
% 1.02/0.96 ((~![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_2, e_4, e_2)) | (~product(e_2, e_3, e_2)))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(1465,plain,
% 1.02/0.96 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_3, e_2))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 1.02/0.96 tff(1466,plain,
% 1.02/0.96 ($false),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1465, 974, 12, 237, 819])).
% 1.02/0.96 tff(1467,plain,((~product(e_2, e_3, e_2)) | (~product(e_2, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.96 tff(1468,plain,
% 1.02/0.96 (~product(e_2, e_3, e_2)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1467, 1446])).
% 1.02/0.96 tff(1469,plain,
% 1.02/0.96 (~product(e_3, e_1, e_2)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[263, 1468, 1453])).
% 1.02/0.96 tff(1470,plain,
% 1.02/0.96 (product(e_3, e_1, e_4)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[323, 1469, 1462])).
% 1.02/0.96 tff(1471,plain,
% 1.02/0.96 (product(e_2, e_3, e_4)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[328, 1470, 1453])).
% 1.02/0.96 tff(1472,plain,
% 1.02/0.96 (~product(e_4, e_3, e_3)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[380, 1471, 373])).
% 1.02/0.96 tff(1473,plain,
% 1.02/0.96 (((~![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_3, e_4)) | (~product(e_4, e_3, e_4)))) <=> ((~![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_3, e_4)) | (~product(e_4, e_3, e_4)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1474,plain,
% 1.02/0.96 ((~![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_3, e_4)) | (~product(e_4, e_3, e_4)))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(1475,plain,
% 1.02/0.96 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_4, e_3, e_4))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[1474, 1473])).
% 1.02/0.96 tff(1476,plain,
% 1.02/0.96 ($false),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1475, 335, 87, 396, 374])).
% 1.02/0.96 tff(1477,plain,((~product(e_4, e_3, e_4)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.96 tff(1478,plain,
% 1.02/0.96 (~product(e_4, e_3, e_4)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1477, 1471])).
% 1.02/0.96 tff(1479,plain,
% 1.02/0.96 (~product(e_4, e_3, e_2)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[360, 1471])).
% 1.02/0.96 tff(1480,plain,
% 1.02/0.96 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_4)) | product(e_2, e_4, e_1) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_3, e_4)) | product(e_2, e_4, e_1) | (~product(e_4, e_3, e_1)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1481,plain,
% 1.02/0.96 ((product(e_2, e_4, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_2, e_3, e_4))) <=> ((~product(e_2, e_3, e_4)) | product(e_2, e_4, e_1) | (~product(e_4, e_3, e_1)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1482,plain,
% 1.02/0.96 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_4)) | product(e_2, e_4, e_1) | (~product(e_4, e_3, e_1))))),
% 1.02/0.96 inference(monotonicity,[status(thm)],[1481])).
% 1.02/0.96 tff(1483,plain,
% 1.02/0.96 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_3, e_4)) | product(e_2, e_4, e_1) | (~product(e_4, e_3, e_1)))),
% 1.02/0.96 inference(transitivity,[status(thm)],[1482, 1480])).
% 1.02/0.96 tff(1484,plain,
% 1.02/0.96 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_2, e_3, e_4)))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(1485,plain,
% 1.02/0.96 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_3, e_4)) | product(e_2, e_4, e_1) | (~product(e_4, e_3, e_1))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 1.02/0.96 tff(1486,plain,
% 1.02/0.96 ($false),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1485, 33, 430, 374, 818])).
% 1.02/0.96 tff(1487,plain,((~product(e_4, e_3, e_1)) | (~product(e_2, e_3, e_4)) | product(e_2, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.96 tff(1488,plain,
% 1.02/0.96 (~product(e_4, e_3, e_1)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1487, 1471, 818])).
% 1.02/0.96 tff(1489,plain,
% 1.02/0.96 (~product(e_4, e_3, e_6)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[989, 1471, 981])).
% 1.02/0.96 tff(1490,plain,
% 1.02/0.96 (product(e_4, e_3, e_5)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[534, 1489, 1488, 1479, 1478, 1472])).
% 1.02/0.96 tff(1491,plain,
% 1.02/0.96 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_5) | (~product(e_4, e_3, e_5)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_4, e_5) | (~product(e_4, e_3, e_5)) | (~product(e_2, e_3, e_4)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1492,plain,
% 1.02/0.96 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_5) | (~product(e_4, e_3, e_5)) | (~product(e_2, e_3, e_4)))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(1493,plain,
% 1.02/0.96 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_4, e_5) | (~product(e_4, e_3, e_5)) | (~product(e_2, e_3, e_4))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 1.02/0.96 tff(1494,plain,
% 1.02/0.96 ($false),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1493, 33, 1490, 1471, 816])).
% 1.02/0.96 tff(1495,plain,(product(e_2, e_4, e_6) | product(e_2, e_4, e_5) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.96 tff(1496,plain,
% 1.02/0.96 (product(e_2, e_4, e_6)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1495, 1445, 373, 1438, 816])).
% 1.02/0.96 tff(1497,assumption,(product(e_6, e_4, e_6)), introduced(assumption)).
% 1.02/0.96 tff(1498,plain,
% 1.02/0.96 (((~![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_4, e_6)) | (~product(e_6, e_4, 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_2) | (~product(e_2, e_4, e_6)) | (~product(e_6, e_4, e_6)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(1499,plain,
% 1.02/0.96 ((~![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_4, e_6)) | (~product(e_6, e_4, e_6)))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(1500,plain,
% 1.02/0.96 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_2) | (~product(e_2, e_4, e_6)) | (~product(e_6, e_4, e_6))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[1499, 1498])).
% 1.02/0.96 tff(1501,plain,
% 1.02/0.96 ($false),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1500, 654, 87, 992, 1497])).
% 1.02/0.96 tff(1502,plain,((~product(e_6, e_4, e_6)) | (~product(e_2, e_4, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.96 tff(1503,plain,
% 1.02/0.96 (~product(e_6, e_4, e_6)),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[1502, 1496])).
% 1.02/0.96 tff(1504,assumption,(~product(e_6, e_4, e_3)), introduced(assumption)).
% 1.02/0.96 tff(1505,plain,
% 1.02/0.96 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_1)) | product(e_6, e_4, e_1) | (~product(e_6, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_1)) | product(e_6, e_4, e_1) | (~product(e_6, e_4, e_4)))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(1506,plain,
% 1.02/0.97 ((product(e_6, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_6, e_4, e_4))) <=> ((~product(e_4, e_4, e_1)) | product(e_6, e_4, e_1) | (~product(e_6, e_4, e_4)))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(1507,plain,
% 1.02/0.97 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_6, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_1)) | product(e_6, e_4, e_1) | (~product(e_6, e_4, e_4))))),
% 1.02/0.97 inference(monotonicity,[status(thm)],[1506])).
% 1.02/0.97 tff(1508,plain,
% 1.02/0.97 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_6, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_1)) | product(e_6, e_4, e_1) | (~product(e_6, e_4, e_4)))),
% 1.02/0.97 inference(transitivity,[status(thm)],[1507, 1505])).
% 1.02/0.97 tff(1509,plain,
% 1.02/0.97 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_6, e_4, e_4)))),
% 1.02/0.97 inference(quant_inst,[status(thm)],[])).
% 1.02/0.97 tff(1510,plain,
% 1.02/0.97 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_1)) | product(e_6, e_4, e_1) | (~product(e_6, e_4, e_4))),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 1.02/0.97 tff(1511,plain,
% 1.02/0.97 (~product(e_6, e_4, e_4)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1510, 33, 858, 1431])).
% 1.02/0.97 tff(1512,plain,
% 1.02/0.97 (((~![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_5) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_1) | product(e_6, e_4, e_4) | product(e_6, e_4, 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_4)) | (~group_element(e_6)) | product(e_6, e_4, e_5) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_1) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(1513,plain,
% 1.02/0.97 ((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_5) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_1) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(1514,plain,
% 1.02/0.97 (((~![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_5) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_1) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3)))),
% 1.02/0.97 inference(monotonicity,[status(thm)],[1513])).
% 1.02/0.97 tff(1515,plain,
% 1.02/0.97 (((~![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_5) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_1) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3))),
% 1.02/0.97 inference(transitivity,[status(thm)],[1514, 1512])).
% 1.02/0.97 tff(1516,plain,
% 1.02/0.97 ((~![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)))),
% 1.02/0.97 inference(quant_inst,[status(thm)],[])).
% 1.02/0.97 tff(1517,plain,
% 1.02/0.97 ((~![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_5) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_1) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3)),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[1516, 1515])).
% 1.02/0.97 tff(1518,plain,
% 1.02/0.97 (product(e_6, e_4, e_5) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_1) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1517, 505, 693, 144])).
% 1.02/0.97 tff(1519,plain,
% 1.02/0.97 (product(e_6, e_4, e_2)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1518, 1511, 1504, 1395, 1503, 1431])).
% 1.02/0.97 tff(1520,assumption,(product(e_6, e_4, e_2)), introduced(assumption)).
% 1.02/0.97 tff(1521,plain,
% 1.02/0.97 (((~![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_4, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_6) | (~product(e_6, e_4, e_2)) | (~product(e_1, e_4, e_2)))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(1522,plain,
% 1.02/0.97 ((~![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_4, e_2)) | (~product(e_1, e_4, e_2)))),
% 1.02/0.97 inference(quant_inst,[status(thm)],[])).
% 1.02/0.97 tff(1523,plain,
% 1.02/0.97 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_6) | (~product(e_6, e_4, e_2)) | (~product(e_1, e_4, e_2))),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 1.02/0.97 tff(1524,plain,
% 1.02/0.97 ($false),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1523, 1089, 87, 1520, 1278])).
% 1.02/0.97 tff(1525,plain,((~product(e_1, e_4, e_2)) | (~product(e_6, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.97 tff(1526,plain,
% 1.02/0.97 (~product(e_1, e_4, e_2)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1525, 1519])).
% 1.02/0.97 tff(1527,plain,
% 1.02/0.97 (product(e_1, e_4, e_3)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1413, 1526, 1424, 1405, 1423, 1404])).
% 1.02/0.97 tff(1528,plain,
% 1.02/0.97 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_3)))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(1529,plain,
% 1.02/0.97 ((product(e_4, e_1, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_4, e_1))) <=> (product(e_4, e_1, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_3)))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(1530,plain,
% 1.02/0.97 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_3))))),
% 1.02/0.97 inference(monotonicity,[status(thm)],[1529])).
% 1.02/0.97 tff(1531,plain,
% 1.02/0.97 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_3)))),
% 1.02/0.97 inference(transitivity,[status(thm)],[1530, 1528])).
% 1.02/0.97 tff(1532,plain,
% 1.02/0.97 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_4, e_1)))),
% 1.02/0.97 inference(quant_inst,[status(thm)],[])).
% 1.02/0.97 tff(1533,plain,
% 1.02/0.97 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_3))),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 1.02/0.97 tff(1534,plain,
% 1.02/0.97 ($false),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1533, 33, 417, 858, 1527])).
% 1.02/0.97 tff(1535,plain,((~product(e_4, e_4, e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4) | product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_6, e_4, e_3) | product(e_6, e_4, e_5) | product(e_2, e_4, e_3) | product(e_2, e_4, e_5)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.97 tff(1536,plain,
% 1.02/0.97 ((~product(e_4, e_4, e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4) | product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_6, e_4, e_3) | product(e_6, e_4, e_5) | product(e_2, e_4, e_5)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1535, 372])).
% 1.02/0.97 tff(1537,plain,
% 1.02/0.97 (~product(e_4, e_4, e_1)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1536, 1422, 1405, 1404, 1403, 1395, 1394, 816])).
% 1.02/0.97 tff(1538,assumption,(product(e_5, e_4, e_2)), introduced(assumption)).
% 1.02/0.97 tff(1539,plain,
% 1.02/0.97 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_5, 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_1) | (~product(e_5, e_1, e_2)) | (~product(e_5, e_4, e_2)))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(1540,plain,
% 1.02/0.97 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_5, e_4, e_2)))),
% 1.02/0.97 inference(quant_inst,[status(thm)],[])).
% 1.02/0.97 tff(1541,plain,
% 1.02/0.97 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_5, e_4, e_2))),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 1.02/0.97 tff(1542,plain,
% 1.02/0.97 ($false),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1541, 366, 12, 1538, 558])).
% 1.02/0.97 tff(1543,plain,((~product(e_5, e_4, e_2)) | (~product(e_5, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.97 tff(1544,plain,
% 1.02/0.97 (~product(e_5, e_4, e_2)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1543, 558])).
% 1.02/0.97 tff(1545,assumption,(~product(e_5, e_4, e_5)), introduced(assumption)).
% 1.02/0.97 tff(1546,plain,
% 1.02/0.97 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_1, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_1)))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(1547,plain,
% 1.02/0.97 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_1)))),
% 1.02/0.97 inference(quant_inst,[status(thm)],[])).
% 1.02/0.97 tff(1548,plain,
% 1.02/0.97 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_1, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_1))),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 1.02/0.97 tff(1549,plain,
% 1.02/0.97 (product(e_5, e_1, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_1))),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1548, 33])).
% 1.02/0.97 tff(1550,plain,
% 1.02/0.97 ((~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_1))),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1549, 593])).
% 1.02/0.97 tff(1551,plain,
% 1.02/0.97 (~product(e_5, e_4, e_1)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1550, 1414])).
% 1.02/0.97 tff(1552,plain,
% 1.02/0.97 (((~![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)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, 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_4)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_1) | (~group_element(e_5)))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(1553,plain,
% 1.02/0.97 ((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)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_1) | (~group_element(e_5)))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(1554,plain,
% 1.02/0.97 (((~![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)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_1) | (~group_element(e_5))))),
% 1.02/0.97 inference(monotonicity,[status(thm)],[1553])).
% 1.02/0.97 tff(1555,plain,
% 1.02/0.97 (((~![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)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_1) | (~group_element(e_5)))),
% 1.02/0.97 inference(transitivity,[status(thm)],[1554, 1552])).
% 1.02/0.97 tff(1556,plain,
% 1.02/0.97 ((~![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)))),
% 1.02/0.97 inference(quant_inst,[status(thm)],[])).
% 1.02/0.97 tff(1557,plain,
% 1.02/0.97 ((~![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)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_1) | (~group_element(e_5))),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 1.02/0.97 tff(1558,plain,
% 1.02/0.97 (product(e_5, e_4, e_2) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_1)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1557, 505, 622, 144])).
% 1.02/0.97 tff(1559,plain,
% 1.02/0.97 (product(e_5, e_4, e_4)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1558, 1551, 1545, 1026, 1544, 1382])).
% 1.02/0.97 tff(1560,assumption,(~product(e_4, e_4, e_2)), introduced(assumption)).
% 1.02/0.97 tff(1561,assumption,(~product(e_4, e_4, e_1)), introduced(assumption)).
% 1.02/0.97 tff(1562,assumption,(~product(e_4, e_4, e_6)), introduced(assumption)).
% 1.02/0.97 tff(1563,assumption,(product(e_5, e_4, e_4)), introduced(assumption)).
% 1.02/0.97 tff(1564,plain,
% 1.02/0.97 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_3) | (~product(e_4, e_4, e_3)) | (~product(e_5, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_3) | (~product(e_4, e_4, e_3)) | (~product(e_5, e_4, e_4)))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(1565,plain,
% 1.02/0.97 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_3) | (~product(e_4, e_4, e_3)) | (~product(e_5, e_4, e_4)))),
% 1.02/0.97 inference(quant_inst,[status(thm)],[])).
% 1.02/0.97 tff(1566,plain,
% 1.02/0.97 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_3) | (~product(e_4, e_4, e_3)) | (~product(e_5, e_4, e_4))),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 1.02/0.97 tff(1567,plain,
% 1.02/0.97 (product(e_5, e_4, e_3) | (~product(e_4, e_4, e_3)) | (~product(e_5, e_4, e_4))),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1566, 33])).
% 1.02/0.97 tff(1568,plain,
% 1.02/0.97 (~product(e_4, e_4, e_3)),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1567, 1563, 1382])).
% 1.02/0.97 tff(1569,plain,
% 1.02/0.97 (((~![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)))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(1570,plain,
% 1.02/0.97 ((~![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)))),
% 1.02/0.97 inference(quant_inst,[status(thm)],[])).
% 1.02/0.97 tff(1571,plain,
% 1.02/0.97 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4))),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[1570, 1569])).
% 1.02/0.97 tff(1572,plain,
% 1.02/0.97 ($false),
% 1.02/0.97 inference(unit_resolution,[status(thm)],[1571, 561, 87, 1563, 332])).
% 1.02/0.97 tff(1573,plain,((~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1574,plain,
% 1.02/0.98 (~product(e_4, e_4, e_4)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1573, 1563])).
% 1.02/0.98 tff(1575,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[903, 1574, 1568, 1562, 1561, 1560, 1381])).
% 1.02/0.98 tff(1576,plain,((~product(e_5, e_4, e_4)) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_4, e_2) | product(e_4, e_4, e_5) | product(e_5, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1577,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1576, 1559, 1537, 1382, 1381, 1380, 1374])).
% 1.02/0.98 tff(1578,plain,((~product(e_5, e_1, e_2)) | product(e_5, e_4, e_3) | product(e_4, e_4, e_5) | product(e_5, e_4, e_5) | product(e_5, e_4, e_6) | product(e_1, e_4, e_4) | product(e_1, e_4, e_5) | product(e_6, e_4, e_5) | product(e_2, e_4, e_5) | product(e_1, e_4, e_2) | (~product(e_6, e_3, e_1)) | product(e_1, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1579,plain,
% 1.02/0.98 (~product(e_5, e_1, e_2)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1578, 1343, 1325, 1324, 1026, 1314, 1023, 1292, 1285, 1284, 1277, 54])).
% 1.02/0.98 tff(1580,plain,
% 1.02/0.98 (product(e_5, e_1, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[631, 1579, 1000])).
% 1.02/0.98 tff(1581,assumption,(~product(e_4, e_5, e_1)), introduced(assumption)).
% 1.02/0.98 tff(1582,plain,
% 1.02/0.98 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_5, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_1)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1583,plain,
% 1.02/0.98 ((product(e_4, e_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_4, e_1, e_5))) <=> (product(e_4, e_5, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_1)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1584,plain,
% 1.02/0.98 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_1))))),
% 1.02/0.98 inference(monotonicity,[status(thm)],[1583])).
% 1.02/0.98 tff(1585,plain,
% 1.02/0.98 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_5, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_1)))),
% 1.02/0.98 inference(transitivity,[status(thm)],[1584, 1582])).
% 1.02/0.98 tff(1586,plain,
% 1.02/0.98 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_4, e_1, e_5)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(1587,plain,
% 1.02/0.98 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_5, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_1))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1586, 1585])).
% 1.02/0.98 tff(1588,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1587, 33, 518, 574, 1581])).
% 1.02/0.98 tff(1589,plain,(product(e_4, e_5, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1590,plain,
% 1.02/0.98 (product(e_4, e_5, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1589, 1580, 1009])).
% 1.02/0.98 tff(1591,assumption,(product(e_4, e_5, e_1)), introduced(assumption)).
% 1.02/0.98 tff(1592,plain,
% 1.02/0.98 (((~![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_6, e_1)) | (~product(e_4, e_5, e_1)))) <=> ((~![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_6, e_1)) | (~product(e_4, e_5, e_1)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1593,plain,
% 1.02/0.98 ((equalish(e_6, e_5) | (~product(e_4, e_5, e_1)) | (~product(e_4, e_6, e_1))) <=> (equalish(e_6, e_5) | (~product(e_4, e_6, e_1)) | (~product(e_4, e_5, e_1)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1594,plain,
% 1.02/0.98 (((~![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_1)) | (~product(e_4, e_6, e_1)))) <=> ((~![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_6, e_1)) | (~product(e_4, e_5, e_1))))),
% 1.02/0.98 inference(monotonicity,[status(thm)],[1593])).
% 1.02/0.98 tff(1595,plain,
% 1.02/0.98 (((~![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_1)) | (~product(e_4, e_6, e_1)))) <=> ((~![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_6, e_1)) | (~product(e_4, e_5, e_1)))),
% 1.02/0.98 inference(transitivity,[status(thm)],[1594, 1592])).
% 1.02/0.98 tff(1596,plain,
% 1.02/0.98 ((~![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_1)) | (~product(e_4, e_6, e_1)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(1597,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_4, e_6, e_1)) | (~product(e_4, e_5, e_1))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1596, 1595])).
% 1.02/0.98 tff(1598,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1597, 636, 12, 1591, 905])).
% 1.02/0.98 tff(1599,plain,((~product(e_4, e_6, e_1)) | (~product(e_4, e_5, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1600,plain,
% 1.02/0.98 (~product(e_4, e_6, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1599, 1590])).
% 1.02/0.98 tff(1601,plain,
% 1.02/0.98 (~product(e_1, e_1, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[582, 1580])).
% 1.02/0.98 tff(1602,plain,
% 1.02/0.98 (product(e_1, e_1, e_2)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[154, 1601])).
% 1.02/0.98 tff(1603,plain,
% 1.02/0.98 (product(e_4, e_3, e_6)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[571, 1602, 54])).
% 1.02/0.98 tff(1604,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1361, 1603, 1600, 1277])).
% 1.02/0.98 tff(1605,plain,(product(e_1, e_3, e_1) | product(e_1, e_3, e_5) | product(e_5, e_1, e_6) | product(e_5, e_4, e_6) | product(e_3, e_3, e_6) | product(e_1, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1606,plain,
% 1.02/0.98 (product(e_1, e_3, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1605, 54, 1000, 1026, 1025, 1024])).
% 1.02/0.98 tff(1607,plain,
% 1.02/0.98 (((~![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_1)) | (~product(e_1, 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_1, e_4, e_1)) | (~product(e_1, e_3, e_1)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1608,plain,
% 1.02/0.98 ((~![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_1)) | (~product(e_1, e_3, e_1)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(1609,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_3, e_1))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 1.02/0.98 tff(1610,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1609, 974, 12, 431, 1385])).
% 1.02/0.98 tff(1611,plain,((~product(e_1, e_3, e_1)) | (~product(e_1, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1612,plain,
% 1.02/0.98 (~product(e_1, e_4, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1611, 1606])).
% 1.02/0.98 tff(1613,plain,
% 1.02/0.98 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, 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_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1614,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(1615,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 1.02/0.98 tff(1616,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1615, 15, 12, 77, 431])).
% 1.02/0.98 tff(1617,plain,((~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1618,plain,
% 1.02/0.98 (~product(e_1, e_1, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1617, 1606])).
% 1.02/0.98 tff(1619,plain,
% 1.02/0.98 (product(e_1, e_1, e_2)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[154, 1618])).
% 1.02/0.98 tff(1620,plain,
% 1.02/0.98 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_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_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_4, e_2)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1621,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_4, e_2)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(1622,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_4, e_2))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 1.02/0.98 tff(1623,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1622, 366, 12, 298, 1278])).
% 1.02/0.98 tff(1624,plain,((~product(e_1, e_4, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1625,plain,
% 1.02/0.98 (~product(e_1, e_4, e_2)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1624, 1619])).
% 1.02/0.98 tff(1626,plain,
% 1.02/0.98 (product(e_4, e_3, e_6)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[571, 1619, 54])).
% 1.02/0.98 tff(1627,plain,
% 1.02/0.98 (product(e_2, e_4, e_6)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[990, 1626])).
% 1.02/0.98 tff(1628,plain,
% 1.02/0.98 (~product(e_1, e_4, e_6)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1402, 1627])).
% 1.02/0.98 tff(1629,plain,
% 1.02/0.98 (~product(e_4, e_2, e_6)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1350, 1626])).
% 1.02/0.98 tff(1630,plain,
% 1.02/0.98 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_6, e_1, 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_1) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_4, e_6)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1631,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_4, e_6)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(1632,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_4, e_6))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 1.02/0.98 tff(1633,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1632, 366, 12, 633, 1497])).
% 1.02/0.98 tff(1634,plain,((~product(e_6, e_4, e_6)) | (~product(e_6, e_1, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1635,plain,
% 1.02/0.98 (~product(e_6, e_4, e_6)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1634, 1199])).
% 1.02/0.98 tff(1636,plain,
% 1.02/0.98 (~product(e_4, e_4, e_6)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1379, 1626])).
% 1.02/0.98 tff(1637,plain,
% 1.02/0.98 (~product(e_5, e_1, e_2)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1188, 1619])).
% 1.02/0.98 tff(1638,plain,
% 1.02/0.98 (product(e_5, e_1, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[631, 1637, 1000])).
% 1.02/0.98 tff(1639,plain,
% 1.02/0.98 (product(e_4, e_5, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1589, 1638, 1009])).
% 1.02/0.98 tff(1640,plain,
% 1.02/0.98 ((~equalish(e_2, e_5)) <=> (~equalish(e_2, e_5))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1641,axiom,(~equalish(e_2, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_5')).
% 1.02/0.98 tff(1642,plain,
% 1.02/0.98 (~equalish(e_2, e_5)),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 1.02/0.98 tff(1643,plain,
% 1.02/0.98 (((~![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_1)) | (~product(e_4, 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_5) | (~product(e_4, e_5, e_1)) | (~product(e_4, e_2, e_1)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1644,plain,
% 1.02/0.98 ((~![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_1)) | (~product(e_4, e_2, e_1)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(1645,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_4, e_5, e_1)) | (~product(e_4, e_2, e_1))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1644, 1643])).
% 1.02/0.98 tff(1646,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1645, 1642, 12, 1591, 755])).
% 1.02/0.98 tff(1647,plain,((~product(e_4, e_2, e_1)) | (~product(e_4, e_5, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1648,plain,
% 1.02/0.98 (~product(e_4, e_2, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1647, 1639])).
% 1.02/0.98 tff(1649,plain,
% 1.02/0.98 (~product(e_4, e_4, e_2)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1373, 1648, 1285, 1629])).
% 1.02/0.98 tff(1650,assumption,(product(e_2, e_5, e_4)), introduced(assumption)).
% 1.02/0.98 tff(1651,plain,
% 1.02/0.98 (((~![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_2, e_3, e_4)) | (~product(e_2, 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_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_5, e_4)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1652,plain,
% 1.02/0.98 ((~![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_2, e_3, e_4)) | (~product(e_2, e_5, e_4)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(1653,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_5, e_4))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 1.02/0.98 tff(1654,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1653, 597, 12, 374, 1650])).
% 1.02/0.98 tff(1655,plain,((~product(e_2, e_5, e_4)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1656,plain,
% 1.02/0.98 (~product(e_2, e_5, e_4)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1655, 330])).
% 1.02/0.98 tff(1657,plain,
% 1.02/0.98 (product(e_3, e_4, e_5)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[770, 518, 324])).
% 1.02/0.98 tff(1658,plain,
% 1.02/0.98 (~product(e_1, e_4, e_5)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1022, 1657])).
% 1.02/0.98 tff(1659,plain,
% 1.02/0.98 (~product(e_4, e_4, e_5)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[751, 518])).
% 1.02/0.98 tff(1660,assumption,(~product(e_4, e_4, e_4)), introduced(assumption)).
% 1.02/0.98 tff(1661,plain,
% 1.02/0.98 (~product(e_5, e_1, e_2)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1188, 298])).
% 1.02/0.98 tff(1662,plain,
% 1.02/0.98 (product(e_5, e_1, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[629, 1661, 619, 1148, 1000, 603])).
% 1.02/0.98 tff(1663,plain,
% 1.02/0.98 (product(e_4, e_5, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1589, 1662, 518])).
% 1.02/0.98 tff(1664,plain,
% 1.02/0.98 (((~![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_1)) | (~product(e_4, e_5, e_1)))) <=> ((~![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_1)) | (~product(e_4, e_5, e_1)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1665,plain,
% 1.02/0.98 ((~![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_1)) | (~product(e_4, e_5, e_1)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(1666,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_5, e_1))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 1.02/0.98 tff(1667,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1666, 561, 12, 858, 1591])).
% 1.02/0.98 tff(1668,plain,((~product(e_4, e_5, e_1)) | (~product(e_4, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1669,plain,
% 1.02/0.98 (~product(e_4, e_4, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1668, 1663])).
% 1.02/0.98 tff(1670,plain,
% 1.02/0.98 (product(e_4, e_4, e_3)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[903, 1669, 1660, 1562, 1560, 1659])).
% 1.02/0.98 tff(1671,plain,
% 1.02/0.98 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1672,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 1.02/0.98 tff(1673,plain,
% 1.02/0.98 (~equalish(e_1, e_4)),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1672, 1671])).
% 1.02/0.98 tff(1674,plain,
% 1.02/0.98 (((~![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_3)) | (~product(e_1, 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_1, e_4) | (~product(e_4, e_4, e_3)) | (~product(e_1, e_4, e_3)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1675,plain,
% 1.02/0.98 ((~![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_3)) | (~product(e_1, e_4, e_3)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(1676,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_3)) | (~product(e_1, e_4, e_3))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1675, 1674])).
% 1.02/0.98 tff(1677,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1676, 1673, 87, 890, 1415])).
% 1.02/0.98 tff(1678,plain,((~product(e_1, e_4, e_3)) | (~product(e_4, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1679,plain,
% 1.02/0.98 (~product(e_1, e_4, e_3)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1678, 1670])).
% 1.02/0.98 tff(1680,plain,
% 1.02/0.98 (~product(e_1, e_4, e_2)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1624, 298])).
% 1.02/0.98 tff(1681,assumption,(~product(e_2, e_5, e_4)), introduced(assumption)).
% 1.02/0.98 tff(1682,assumption,(product(e_4, e_2, e_5)), introduced(assumption)).
% 1.02/0.98 tff(1683,plain,
% 1.02/0.98 (((~![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)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1684,plain,
% 1.02/0.98 ((~![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)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(1685,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_2, e_5))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1684, 1683])).
% 1.02/0.98 tff(1686,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1685, 666, 12, 518, 1682])).
% 1.02/0.98 tff(1687,plain,((~product(e_4, e_2, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1688,plain,
% 1.02/0.98 (~product(e_4, e_2, e_5)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1687, 518])).
% 1.02/0.98 tff(1689,plain,
% 1.02/0.98 (~product(e_5, e_4, e_5)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1323, 1657])).
% 1.02/0.98 tff(1690,assumption,(product(e_5, e_4, e_1)), introduced(assumption)).
% 1.02/0.98 tff(1691,plain,
% 1.02/0.98 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_5, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_5, e_1, e_1)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1692,plain,
% 1.02/0.98 ((equalish(e_4, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_5, e_4, e_1))) <=> (equalish(e_4, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_5, e_1, e_1)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1693,plain,
% 1.02/0.98 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_5, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_5, e_1, e_1))))),
% 1.02/0.98 inference(monotonicity,[status(thm)],[1692])).
% 1.02/0.98 tff(1694,plain,
% 1.02/0.98 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_5, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_5, e_1, e_1)))),
% 1.02/0.98 inference(transitivity,[status(thm)],[1693, 1691])).
% 1.02/0.98 tff(1695,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_5, e_4, e_1)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(1696,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_5, e_1, e_1))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1695, 1694])).
% 1.02/0.98 tff(1697,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1696, 366, 12, 1690, 574])).
% 1.02/0.98 tff(1698,plain,((~product(e_5, e_4, e_1)) | (~product(e_5, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.98 tff(1699,plain,
% 1.02/0.98 (~product(e_5, e_4, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1698, 1662])).
% 1.02/0.98 tff(1700,plain,
% 1.02/0.98 (~product(e_6, e_1, e_1)),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[1168, 1662])).
% 1.02/0.98 tff(1701,plain,
% 1.02/0.98 (((~![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_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_6, e_4) | (~product(e_4, e_4, e_3)) | (~product(e_6, e_4, e_3)))),
% 1.02/0.98 inference(rewrite,[status(thm)],[])).
% 1.02/0.98 tff(1702,plain,
% 1.02/0.98 ((~![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_3)) | (~product(e_6, e_4, e_3)))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(1703,plain,
% 1.02/0.98 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_4, e_3)) | (~product(e_6, e_4, e_3))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 1.02/0.99 tff(1704,plain,
% 1.02/0.99 ($false),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1703, 738, 87, 890, 1416])).
% 1.02/0.99 tff(1705,plain,((~product(e_6, e_4, e_3)) | (~product(e_4, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.99 tff(1706,plain,
% 1.02/0.99 (~product(e_6, e_4, e_3)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1705, 1670])).
% 1.02/0.99 tff(1707,assumption,(~product(e_6, e_4, e_6)), introduced(assumption)).
% 1.02/0.99 tff(1708,plain,
% 1.02/0.99 (((~![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_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_4) | (~product(e_4, e_4, e_3)) | (~product(e_5, e_4, e_3)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1709,plain,
% 1.02/0.99 ((~![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_3)) | (~product(e_5, e_4, e_3)))),
% 1.02/0.99 inference(quant_inst,[status(thm)],[])).
% 1.02/0.99 tff(1710,plain,
% 1.02/0.99 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_3)) | (~product(e_5, e_4, e_3))),
% 1.02/0.99 inference(modus_ponens,[status(thm)],[1709, 1708])).
% 1.02/0.99 tff(1711,plain,
% 1.02/0.99 ($false),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1710, 561, 87, 1334, 890])).
% 1.02/0.99 tff(1712,plain,((~product(e_5, e_4, e_3)) | (~product(e_4, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.99 tff(1713,plain,
% 1.02/0.99 (~product(e_5, e_4, e_3)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1712, 1670])).
% 1.02/0.99 tff(1714,plain,
% 1.02/0.99 (~product(e_2, e_4, e_5)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[782, 1657])).
% 1.02/0.99 tff(1715,plain,
% 1.02/0.99 (~product(e_6, e_1, e_5)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1146, 518])).
% 1.02/0.99 tff(1716,plain,
% 1.02/0.99 (product(e_6, e_1, e_6)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[700, 1700, 690, 1715, 663, 1156])).
% 1.02/0.99 tff(1717,assumption,(product(e_6, e_2, e_6)), introduced(assumption)).
% 1.02/0.99 tff(1718,plain,
% 1.02/0.99 (((~![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_2, 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_2, e_1) | (~product(e_6, e_2, e_6)) | (~product(e_6, e_1, e_6)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1719,plain,
% 1.02/0.99 ((equalish(e_2, e_1) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_2, e_6))) <=> (equalish(e_2, e_1) | (~product(e_6, e_2, e_6)) | (~product(e_6, e_1, e_6)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1720,plain,
% 1.02/0.99 (((~![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_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_1) | (~product(e_6, e_2, e_6)) | (~product(e_6, e_1, e_6))))),
% 1.02/0.99 inference(monotonicity,[status(thm)],[1719])).
% 1.02/0.99 tff(1721,plain,
% 1.02/0.99 (((~![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_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_1) | (~product(e_6, e_2, e_6)) | (~product(e_6, e_1, e_6)))),
% 1.02/0.99 inference(transitivity,[status(thm)],[1720, 1718])).
% 1.02/0.99 tff(1722,plain,
% 1.02/0.99 ((~![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_6)) | (~product(e_6, e_2, e_6)))),
% 1.02/0.99 inference(quant_inst,[status(thm)],[])).
% 1.02/0.99 tff(1723,plain,
% 1.02/0.99 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_6, e_2, e_6)) | (~product(e_6, e_1, e_6))),
% 1.02/0.99 inference(modus_ponens,[status(thm)],[1722, 1721])).
% 1.02/0.99 tff(1724,plain,
% 1.02/0.99 ($false),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1723, 666, 12, 633, 1717])).
% 1.02/0.99 tff(1725,plain,((~product(e_6, e_2, e_6)) | (~product(e_6, e_1, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.99 tff(1726,plain,
% 1.02/0.99 (~product(e_6, e_2, e_6)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1725, 1716])).
% 1.02/0.99 tff(1727,plain,
% 1.02/0.99 (~product(e_6, e_4, e_5)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1291, 1657])).
% 1.02/0.99 tff(1728,assumption,(product(e_6, e_4, e_4)), introduced(assumption)).
% 1.02/0.99 tff(1729,plain,
% 1.02/0.99 (((~![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)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1730,plain,
% 1.02/0.99 ((~![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)))),
% 1.02/0.99 inference(quant_inst,[status(thm)],[])).
% 1.02/0.99 tff(1731,plain,
% 1.02/0.99 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_6, e_4, e_4))),
% 1.02/0.99 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 1.02/0.99 tff(1732,plain,
% 1.02/0.99 ($false),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1731, 738, 87, 332, 1728])).
% 1.02/0.99 tff(1733,plain,((~product(e_6, e_4, e_4)) | (~product(e_4, e_4, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.99 tff(1734,plain,
% 1.02/0.99 (~product(e_4, e_4, e_4)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1733, 1728])).
% 1.02/0.99 tff(1735,plain,
% 1.02/0.99 (product(e_4, e_4, e_3)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[903, 1734, 1381, 1560, 1562, 1561])).
% 1.02/0.99 tff(1736,plain,
% 1.02/0.99 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_3)) | product(e_6, e_4, e_3) | (~product(e_6, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_3)) | product(e_6, e_4, e_3) | (~product(e_6, e_4, e_4)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1737,plain,
% 1.02/0.99 ((product(e_6, e_4, e_3) | (~product(e_4, e_4, e_3)) | (~product(e_6, e_4, e_4))) <=> ((~product(e_4, e_4, e_3)) | product(e_6, e_4, e_3) | (~product(e_6, e_4, e_4)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1738,plain,
% 1.02/0.99 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_4, e_3) | (~product(e_4, e_4, e_3)) | (~product(e_6, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_3)) | product(e_6, e_4, e_3) | (~product(e_6, e_4, e_4))))),
% 1.02/0.99 inference(monotonicity,[status(thm)],[1737])).
% 1.02/0.99 tff(1739,plain,
% 1.02/0.99 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_4, e_3) | (~product(e_4, e_4, e_3)) | (~product(e_6, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_3)) | product(e_6, e_4, e_3) | (~product(e_6, e_4, e_4)))),
% 1.02/0.99 inference(transitivity,[status(thm)],[1738, 1736])).
% 1.02/0.99 tff(1740,plain,
% 1.02/0.99 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_4, e_3) | (~product(e_4, e_4, e_3)) | (~product(e_6, e_4, e_4)))),
% 1.02/0.99 inference(quant_inst,[status(thm)],[])).
% 1.02/0.99 tff(1741,plain,
% 1.02/0.99 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_3)) | product(e_6, e_4, e_3) | (~product(e_6, e_4, e_4))),
% 1.02/0.99 inference(modus_ponens,[status(thm)],[1740, 1739])).
% 1.02/0.99 tff(1742,plain,
% 1.02/0.99 ($false),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1741, 33, 1735, 1728, 1504])).
% 1.02/0.99 tff(1743,plain,((~product(e_6, e_4, e_4)) | product(e_6, e_4, e_3) | product(e_4, e_4, e_5) | product(e_4, e_4, e_2) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.99 tff(1744,plain,
% 1.02/0.99 (~product(e_6, e_4, e_4)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1743, 1706, 1560, 1659, 1562, 1669])).
% 1.02/0.99 tff(1745,assumption,(~product(e_6, e_1, e_1)), introduced(assumption)).
% 1.02/0.99 tff(1746,assumption,(~product(e_6, e_4, e_4)), introduced(assumption)).
% 1.02/0.99 tff(1747,assumption,(~product(e_5, e_4, e_1)), introduced(assumption)).
% 1.02/0.99 tff(1748,assumption,(~product(e_4, e_2, e_5)), introduced(assumption)).
% 1.02/0.99 tff(1749,assumption,(~product(e_6, e_2, e_6)), introduced(assumption)).
% 1.02/0.99 tff(1750,assumption,(~product(e_4, e_4, e_3)), introduced(assumption)).
% 1.02/0.99 tff(1751,assumption,(~product(e_6, e_4, e_1)), introduced(assumption)).
% 1.02/0.99 tff(1752,plain,
% 1.02/0.99 (product(e_6, e_4, e_2)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1518, 1504, 1395, 1707, 1746, 1751])).
% 1.02/0.99 tff(1753,plain,
% 1.02/0.99 (product(e_2, e_4, e_2)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[838, 818, 373, 817, 816, 981])).
% 1.02/0.99 tff(1754,plain,
% 1.02/0.99 (((~![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_4, e_2)) | (~product(e_6, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_6, e_4, e_2)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1755,plain,
% 1.02/0.99 ((~![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_4, e_2)) | (~product(e_6, e_4, e_2)))),
% 1.02/0.99 inference(quant_inst,[status(thm)],[])).
% 1.02/0.99 tff(1756,plain,
% 1.02/0.99 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_6, e_4, e_2))),
% 1.02/0.99 inference(modus_ponens,[status(thm)],[1755, 1754])).
% 1.02/0.99 tff(1757,plain,
% 1.02/0.99 ($false),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1756, 654, 87, 819, 1520])).
% 1.02/0.99 tff(1758,plain,((~product(e_6, e_4, e_2)) | (~product(e_2, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.99 tff(1759,plain,
% 1.02/0.99 (~product(e_6, e_4, e_2)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1758, 1753])).
% 1.02/0.99 tff(1760,plain,
% 1.02/0.99 (product(e_2, e_4, e_5)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[847, 814, 373, 817, 818, 815])).
% 1.02/0.99 tff(1761,plain,
% 1.02/0.99 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_5)) | product(e_4, e_2, e_5) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_5)) | product(e_4, e_2, e_5) | (~product(e_4, e_4, e_2)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1762,plain,
% 1.02/0.99 ((product(e_4, e_2, e_5) | (~product(e_2, e_4, e_5)) | (~product(e_4, e_4, e_2))) <=> ((~product(e_2, e_4, e_5)) | product(e_4, e_2, e_5) | (~product(e_4, e_4, e_2)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1763,plain,
% 1.02/0.99 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_5) | (~product(e_2, e_4, e_5)) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_5)) | product(e_4, e_2, e_5) | (~product(e_4, e_4, e_2))))),
% 1.02/0.99 inference(monotonicity,[status(thm)],[1762])).
% 1.02/0.99 tff(1764,plain,
% 1.02/0.99 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_5) | (~product(e_2, e_4, e_5)) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_5)) | product(e_4, e_2, e_5) | (~product(e_4, e_4, e_2)))),
% 1.02/0.99 inference(transitivity,[status(thm)],[1763, 1761])).
% 1.02/0.99 tff(1765,plain,
% 1.02/0.99 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_5) | (~product(e_2, e_4, e_5)) | (~product(e_4, e_4, e_2)))),
% 1.02/0.99 inference(quant_inst,[status(thm)],[])).
% 1.02/0.99 tff(1766,plain,
% 1.02/0.99 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_5)) | product(e_4, e_2, e_5) | (~product(e_4, e_4, e_2))),
% 1.02/0.99 inference(modus_ponens,[status(thm)],[1765, 1764])).
% 1.02/0.99 tff(1767,plain,
% 1.02/0.99 ($false),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1766, 33, 1760, 814, 1748])).
% 1.02/0.99 tff(1768,plain,((~product(e_4, e_4, e_2)) | product(e_4, e_2, e_5) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_4, e_2, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.99 tff(1769,plain,
% 1.02/0.99 (~product(e_4, e_4, e_2)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1768, 818, 373, 817, 1748, 815])).
% 1.02/0.99 tff(1770,plain,
% 1.02/0.99 (product(e_4, e_4, e_4)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[903, 1769, 1381, 1750, 1562, 1561])).
% 1.02/0.99 tff(1771,plain,
% 1.02/0.99 (~product(e_6, e_4, e_4)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1733, 1770])).
% 1.02/0.99 tff(1772,plain,
% 1.02/0.99 ($false),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1518, 1771, 1759, 1395, 1707, 1751, 1504])).
% 1.02/0.99 tff(1773,plain,(product(e_2, e_4, e_1) | product(e_6, e_4, e_5) | product(e_6, e_4, e_6) | product(e_6, e_4, e_1) | product(e_6, e_4, e_3) | product(e_4, e_4, e_5) | product(e_4, e_4, e_3) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_5) | product(e_2, e_4, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.99 tff(1774,plain,
% 1.02/0.99 (product(e_2, e_4, e_6)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1773, 1504, 1707, 818, 1750, 1381, 1395, 1562, 1561, 373, 817, 816, 1751, 1748, 815])).
% 1.02/0.99 tff(1775,plain,
% 1.02/0.99 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_6)) | product(e_6, e_2, e_6) | (~product(e_6, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_6)) | product(e_6, e_2, e_6) | (~product(e_6, e_4, e_2)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1776,plain,
% 1.02/0.99 ((product(e_6, e_2, e_6) | (~product(e_2, e_4, e_6)) | (~product(e_6, e_4, e_2))) <=> ((~product(e_2, e_4, e_6)) | product(e_6, e_2, e_6) | (~product(e_6, e_4, e_2)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1777,plain,
% 1.02/0.99 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_2, e_6) | (~product(e_2, e_4, e_6)) | (~product(e_6, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_6)) | product(e_6, e_2, e_6) | (~product(e_6, e_4, e_2))))),
% 1.02/0.99 inference(monotonicity,[status(thm)],[1776])).
% 1.02/0.99 tff(1778,plain,
% 1.02/0.99 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_2, e_6) | (~product(e_2, e_4, e_6)) | (~product(e_6, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_6)) | product(e_6, e_2, e_6) | (~product(e_6, e_4, e_2)))),
% 1.02/0.99 inference(transitivity,[status(thm)],[1777, 1775])).
% 1.02/0.99 tff(1779,plain,
% 1.02/0.99 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_2, e_6) | (~product(e_2, e_4, e_6)) | (~product(e_6, e_4, e_2)))),
% 1.02/0.99 inference(quant_inst,[status(thm)],[])).
% 1.02/0.99 tff(1780,plain,
% 1.02/0.99 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_6)) | product(e_6, e_2, e_6) | (~product(e_6, e_4, e_2))),
% 1.02/0.99 inference(modus_ponens,[status(thm)],[1779, 1778])).
% 1.02/0.99 tff(1781,plain,
% 1.02/0.99 ($false),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1780, 33, 1774, 1752, 1749])).
% 1.02/0.99 tff(1782,plain,(product(e_6, e_4, e_3) | product(e_6, e_2, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_6) | product(e_6, e_4, e_4) | product(e_6, e_4, e_1) | product(e_2, e_4, e_1) | product(e_4, e_4, e_3) | product(e_4, e_4, e_5) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_5) | product(e_4, e_2, e_5) | product(e_4, e_2, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.99 tff(1783,plain,
% 1.02/0.99 (product(e_6, e_4, e_1)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1782, 1750, 1395, 1707, 1504, 1749, 818, 1746, 1381, 1562, 1561, 373, 817, 816, 1748, 815])).
% 1.02/0.99 tff(1784,plain,
% 1.02/0.99 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_1)) | product(e_6, e_1, e_1) | (~product(e_6, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_4, e_1)) | product(e_6, e_1, e_1) | (~product(e_6, e_4, e_1)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1785,plain,
% 1.02/0.99 ((product(e_6, e_1, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_6, e_4, e_1))) <=> ((~product(e_1, e_4, e_1)) | product(e_6, e_1, e_1) | (~product(e_6, e_4, e_1)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1786,plain,
% 1.02/0.99 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_1, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_6, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_1)) | product(e_6, e_1, e_1) | (~product(e_6, e_4, e_1))))),
% 1.02/0.99 inference(monotonicity,[status(thm)],[1785])).
% 1.02/0.99 tff(1787,plain,
% 1.02/0.99 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_1, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_6, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_4, e_1)) | product(e_6, e_1, e_1) | (~product(e_6, e_4, e_1)))),
% 1.02/0.99 inference(transitivity,[status(thm)],[1786, 1784])).
% 1.02/0.99 tff(1788,plain,
% 1.02/0.99 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_1, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_6, e_4, e_1)))),
% 1.02/0.99 inference(quant_inst,[status(thm)],[])).
% 1.02/0.99 tff(1789,plain,
% 1.02/0.99 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_4, e_1)) | product(e_6, e_1, e_1) | (~product(e_6, e_4, e_1))),
% 1.02/0.99 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 1.02/0.99 tff(1790,plain,
% 1.02/0.99 ($false),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1789, 33, 1385, 1745, 1425])).
% 1.02/0.99 tff(1791,plain,((~product(e_1, e_4, e_1)) | product(e_6, e_1, e_1) | (~product(e_6, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.99 tff(1792,plain,
% 1.02/0.99 (~product(e_1, e_4, e_1)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[1791, 1783, 1745])).
% 1.02/0.99 tff(1793,plain,
% 1.02/0.99 (product(e_4, e_4, e_4)),
% 1.02/0.99 inference(unit_resolution,[status(thm)],[903, 1750, 1381, 1560, 1562, 1561])).
% 1.02/0.99 tff(1794,plain,
% 1.02/0.99 (((~![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)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1795,plain,
% 1.02/0.99 ((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)))),
% 1.02/0.99 inference(rewrite,[status(thm)],[])).
% 1.02/0.99 tff(1796,plain,
% 1.02/0.99 (((~![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))))),
% 1.02/1.00 inference(monotonicity,[status(thm)],[1795])).
% 1.02/1.00 tff(1797,plain,
% 1.02/1.00 (((~![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)))),
% 1.02/1.00 inference(transitivity,[status(thm)],[1796, 1794])).
% 1.02/1.00 tff(1798,plain,
% 1.02/1.00 ((~![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)))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(1799,plain,
% 1.02/1.00 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 1.02/1.00 tff(1800,plain,
% 1.02/1.00 ($false),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1799, 1673, 87, 1305, 332])).
% 1.02/1.00 tff(1801,plain,((~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.00 tff(1802,plain,
% 1.02/1.00 (~product(e_1, e_4, e_4)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1801, 1793])).
% 1.02/1.00 tff(1803,plain,
% 1.02/1.00 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_1, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_6, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_6, e_1, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_6, e_4, e_1)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(1804,plain,
% 1.02/1.00 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_1, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_6, e_4, e_1)))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(1805,plain,
% 1.02/1.00 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_6, e_1, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_6, e_4, e_1))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[1804, 1803])).
% 1.02/1.00 tff(1806,plain,
% 1.02/1.00 ($false),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1805, 33, 663, 1425, 1415])).
% 1.02/1.00 tff(1807,plain,((~product(e_1, e_4, e_3)) | product(e_6, e_1, e_3) | (~product(e_6, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.00 tff(1808,plain,
% 1.02/1.00 (~product(e_1, e_4, e_3)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1807, 1783, 663])).
% 1.02/1.00 tff(1809,plain,
% 1.02/1.00 (product(e_1, e_4, e_6)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1413, 1808, 1406, 1404, 1802, 1792])).
% 1.02/1.00 tff(1810,plain,
% 1.02/1.00 (~product(e_2, e_4, e_6)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1402, 1809])).
% 1.02/1.00 tff(1811,plain,
% 1.02/1.00 (product(e_2, e_4, e_2)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[838, 1810, 373, 817, 816, 818])).
% 1.02/1.00 tff(1812,plain,
% 1.02/1.00 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_5)) | product(e_2, e_5, e_4) | (~product(e_5, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_5)) | product(e_2, e_5, e_4) | (~product(e_5, e_4, e_4)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(1813,plain,
% 1.02/1.00 ((product(e_2, e_5, e_4) | (~product(e_5, e_4, e_4)) | (~product(e_2, e_4, e_5))) <=> ((~product(e_2, e_4, e_5)) | product(e_2, e_5, e_4) | (~product(e_5, e_4, e_4)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(1814,plain,
% 1.02/1.00 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_4) | (~product(e_5, e_4, e_4)) | (~product(e_2, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_5)) | product(e_2, e_5, e_4) | (~product(e_5, e_4, e_4))))),
% 1.02/1.00 inference(monotonicity,[status(thm)],[1813])).
% 1.02/1.00 tff(1815,plain,
% 1.02/1.00 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_4) | (~product(e_5, e_4, e_4)) | (~product(e_2, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_5)) | product(e_2, e_5, e_4) | (~product(e_5, e_4, e_4)))),
% 1.02/1.00 inference(transitivity,[status(thm)],[1814, 1812])).
% 1.02/1.00 tff(1816,plain,
% 1.02/1.00 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_4) | (~product(e_5, e_4, e_4)) | (~product(e_2, e_4, e_5)))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(1817,plain,
% 1.02/1.00 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_5)) | product(e_2, e_5, e_4) | (~product(e_5, e_4, e_4))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[1816, 1815])).
% 1.02/1.00 tff(1818,plain,
% 1.02/1.00 ($false),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1817, 33, 1563, 1681, 774])).
% 1.02/1.00 tff(1819,plain,((~product(e_5, e_4, e_4)) | product(e_2, e_5, e_4) | (~product(e_2, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.00 tff(1820,plain,
% 1.02/1.00 (~product(e_2, e_4, e_5)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1819, 1563, 1681])).
% 1.02/1.00 tff(1821,plain,
% 1.02/1.00 (~product(e_4, e_4, e_2)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[847, 1820, 373, 817, 818, 815])).
% 1.02/1.00 tff(1822,plain,
% 1.02/1.00 (product(e_4, e_4, e_4)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[903, 1821, 1381, 1750, 1562, 1561])).
% 1.02/1.00 tff(1823,plain,
% 1.02/1.00 (((~![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_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_4, e_5) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(1824,plain,
% 1.02/1.00 ((equalish(e_4, e_5) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_4))) <=> (equalish(e_4, e_5) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(1825,plain,
% 1.02/1.00 (((~![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_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_4, e_5) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4))))),
% 1.02/1.00 inference(monotonicity,[status(thm)],[1824])).
% 1.02/1.00 tff(1826,plain,
% 1.02/1.00 (((~![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_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_4, e_5) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))),
% 1.02/1.00 inference(transitivity,[status(thm)],[1825, 1823])).
% 1.02/1.00 tff(1827,plain,
% 1.02/1.00 ((~![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_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(1828,plain,
% 1.02/1.00 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[1827, 1826])).
% 1.02/1.00 tff(1829,plain,
% 1.02/1.00 ($false),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1828, 871, 87, 1563, 1822])).
% 1.02/1.00 tff(1830,plain,((~product(e_5, e_4, e_4)) | product(e_4, e_4, e_5) | product(e_4, e_4, e_3) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_4, e_2, e_6) | product(e_2, e_5, e_4)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.00 tff(1831,plain,
% 1.02/1.00 (~product(e_5, e_4, e_4)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1830, 1750, 818, 1562, 1561, 373, 817, 1381, 815, 1681])).
% 1.02/1.00 tff(1832,plain,
% 1.02/1.00 ((~equalish(e_1, e_5)) <=> (~equalish(e_1, e_5))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(1833,axiom,(~equalish(e_1, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_5')).
% 1.02/1.00 tff(1834,plain,
% 1.02/1.00 (~equalish(e_1, e_5)),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 1.02/1.00 tff(1835,plain,
% 1.02/1.00 (((~![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_4, e_6)) | (~product(e_1, e_4, 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_5) | (~product(e_5, e_4, e_6)) | (~product(e_1, e_4, e_6)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(1836,plain,
% 1.02/1.00 ((~![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_4, e_6)) | (~product(e_1, e_4, e_6)))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(1837,plain,
% 1.02/1.00 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_5) | (~product(e_5, e_4, e_6)) | (~product(e_1, e_4, e_6))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[1836, 1835])).
% 1.02/1.00 tff(1838,plain,
% 1.02/1.00 ($false),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1837, 1834, 87, 993, 1397])).
% 1.02/1.00 tff(1839,plain,((~product(e_1, e_4, e_6)) | (~product(e_5, e_4, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.00 tff(1840,plain,
% 1.02/1.00 (~product(e_5, e_4, e_6)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1839, 1809])).
% 1.02/1.00 tff(1841,plain,
% 1.02/1.00 (product(e_5, e_4, e_2)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1558, 1840, 1747, 1545, 1382, 1831])).
% 1.02/1.00 tff(1842,plain,
% 1.02/1.00 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_5, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_5, e_4, e_2)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(1843,plain,
% 1.02/1.00 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_5, e_4, e_2)))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(1844,plain,
% 1.02/1.00 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_5, e_4, e_2))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 1.02/1.00 tff(1845,plain,
% 1.02/1.00 ($false),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1844, 587, 87, 1538, 819])).
% 1.02/1.00 tff(1846,plain,((~product(e_5, e_4, e_2)) | (~product(e_2, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.00 tff(1847,plain,
% 1.02/1.00 ($false),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1846, 1841, 1811])).
% 1.02/1.00 tff(1848,plain,(product(e_4, e_4, e_3) | product(e_5, e_4, e_1) | product(e_5, e_4, e_5) | product(e_5, e_4, e_3) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_5) | product(e_2, e_4, e_1) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_6, e_1, e_3) | product(e_6, e_1, e_1) | product(e_6, e_4, e_5) | product(e_6, e_4, e_6) | product(e_6, e_4, e_3) | product(e_6, e_2, e_6) | product(e_6, e_4, e_4) | product(e_4, e_4, e_5) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_2, e_5) | product(e_4, e_2, e_6) | product(e_2, e_5, e_4) | product(e_4, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.00 tff(1849,plain,
% 1.02/1.00 (product(e_4, e_4, e_3)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1848, 1746, 1545, 1382, 373, 817, 816, 818, 1406, 1404, 663, 1745, 1395, 1707, 1504, 1749, 1747, 1381, 1562, 1561, 1748, 815, 1681, 1560])).
% 1.02/1.00 tff(1850,plain,
% 1.02/1.00 (~product(e_5, e_4, e_4)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1567, 1849, 1382])).
% 1.02/1.00 tff(1851,plain,
% 1.02/1.00 (~product(e_2, e_4, e_2)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1758, 1520])).
% 1.02/1.00 tff(1852,plain,
% 1.02/1.00 (product(e_2, e_4, e_6)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[838, 1851, 373, 817, 816, 818])).
% 1.02/1.00 tff(1853,assumption,(~product(e_5, e_4, e_4)), introduced(assumption)).
% 1.02/1.00 tff(1854,plain,
% 1.02/1.00 (((~![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_2)) | (~product(e_6, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_5, e_4, e_2)) | (~product(e_6, e_4, e_2)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(1855,plain,
% 1.02/1.00 ((equalish(e_5, e_6) | (~product(e_6, e_4, e_2)) | (~product(e_5, e_4, e_2))) <=> (equalish(e_5, e_6) | (~product(e_5, e_4, e_2)) | (~product(e_6, e_4, e_2)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(1856,plain,
% 1.02/1.00 (((~![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_2)) | (~product(e_5, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_5, e_4, e_2)) | (~product(e_6, e_4, e_2))))),
% 1.02/1.00 inference(monotonicity,[status(thm)],[1855])).
% 1.02/1.00 tff(1857,plain,
% 1.02/1.00 (((~![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_2)) | (~product(e_5, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_5, e_4, e_2)) | (~product(e_6, e_4, e_2)))),
% 1.02/1.00 inference(transitivity,[status(thm)],[1856, 1854])).
% 1.02/1.00 tff(1858,plain,
% 1.02/1.00 ((~![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_2)) | (~product(e_5, e_4, e_2)))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(1859,plain,
% 1.02/1.00 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_5, e_4, e_2)) | (~product(e_6, e_4, e_2))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[1858, 1857])).
% 1.02/1.00 tff(1860,plain,
% 1.02/1.00 ($false),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1859, 45, 87, 1538, 1520])).
% 1.02/1.00 tff(1861,plain,((~product(e_5, e_4, e_2)) | (~product(e_6, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.00 tff(1862,plain,
% 1.02/1.00 (~product(e_5, e_4, e_2)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1861, 1520])).
% 1.02/1.00 tff(1863,plain,
% 1.02/1.00 (product(e_5, e_4, e_6)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1558, 1862, 1747, 1545, 1382, 1853])).
% 1.02/1.00 tff(1864,plain,
% 1.02/1.00 ($false),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[998, 1863, 1852])).
% 1.02/1.00 tff(1865,plain,((~product(e_6, e_4, e_2)) | product(e_5, e_4, e_1) | product(e_5, e_4, e_5) | product(e_5, e_4, e_3) | product(e_5, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_5) | product(e_2, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.00 tff(1866,plain,
% 1.02/1.00 (~product(e_6, e_4, e_2)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1865, 1850, 1545, 1382, 1747, 373, 817, 816, 818])).
% 1.02/1.00 tff(1867,plain,
% 1.02/1.00 (product(e_6, e_4, e_1)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1518, 1866, 1395, 1707, 1504, 1746])).
% 1.02/1.00 tff(1868,plain,
% 1.02/1.00 (~product(e_1, e_4, e_1)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1791, 1867, 1745])).
% 1.02/1.00 tff(1869,plain,
% 1.02/1.00 (~product(e_1, e_4, e_3)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1678, 1849])).
% 1.02/1.00 tff(1870,assumption,(~product(e_6, e_1, e_4)), introduced(assumption)).
% 1.02/1.00 tff(1871,plain,
% 1.02/1.00 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_6, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_6, e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_6, e_4, e_1)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(1872,plain,
% 1.02/1.00 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_6, e_4, e_1)))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(1873,plain,
% 1.02/1.00 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_6, e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_6, e_4, e_1))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[1872, 1871])).
% 1.02/1.00 tff(1874,plain,
% 1.02/1.00 ($false),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1873, 33, 1305, 1870, 1425])).
% 1.02/1.00 tff(1875,plain,((~product(e_1, e_4, e_4)) | product(e_6, e_1, e_4) | (~product(e_6, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.00 tff(1876,plain,
% 1.02/1.00 (~product(e_1, e_4, e_4)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1875, 1867, 1870])).
% 1.02/1.00 tff(1877,plain,
% 1.02/1.00 (product(e_1, e_4, e_6)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1413, 1876, 1406, 1404, 1869, 1868])).
% 1.02/1.00 tff(1878,plain,
% 1.02/1.00 (~product(e_2, e_4, e_6)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1402, 1877])).
% 1.02/1.00 tff(1879,plain,
% 1.02/1.00 (product(e_2, e_4, e_2)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[838, 1878, 373, 817, 816, 818])).
% 1.02/1.00 tff(1880,plain,
% 1.02/1.00 (~product(e_5, e_4, e_6)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1839, 1877])).
% 1.02/1.00 tff(1881,plain,
% 1.02/1.00 (product(e_5, e_4, e_2)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1558, 1880, 1747, 1545, 1382, 1850])).
% 1.02/1.00 tff(1882,plain,
% 1.02/1.00 ($false),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1846, 1881, 1879])).
% 1.02/1.00 tff(1883,plain,(product(e_6, e_4, e_4) | product(e_5, e_4, e_1) | product(e_5, e_4, e_5) | product(e_5, e_4, e_3) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_5) | product(e_2, e_4, e_1) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_6, e_1, e_4) | product(e_6, e_1, e_1) | product(e_6, e_4, e_5) | product(e_6, e_4, e_6) | product(e_6, e_4, e_3) | product(e_6, e_1, e_3) | product(e_6, e_2, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_2, e_5) | product(e_4, e_2, e_6) | product(e_2, e_5, e_4) | product(e_4, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.00 tff(1884,plain,
% 1.02/1.00 (product(e_2, e_4, e_1)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1883, 1744, 1727, 817, 1726, 373, 1714, 1713, 690, 1707, 1706, 1700, 1699, 1689, 1658, 663, 815, 1688, 1562, 1669, 1680, 1659, 1681, 1560])).
% 1.02/1.00 tff(1885,plain,
% 1.02/1.00 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_2, e_4, e_1)))),
% 1.02/1.00 inference(rewrite,[status(thm)],[])).
% 1.02/1.00 tff(1886,plain,
% 1.02/1.00 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_2, e_4, e_1)))),
% 1.02/1.00 inference(quant_inst,[status(thm)],[])).
% 1.02/1.00 tff(1887,plain,
% 1.02/1.00 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_2, e_4, e_1))),
% 1.02/1.00 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 1.02/1.00 tff(1888,plain,
% 1.02/1.00 ($false),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1887, 33, 171, 1385, 1432])).
% 1.02/1.00 tff(1889,plain,((~product(e_1, e_4, e_1)) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.00 tff(1890,plain,
% 1.02/1.00 (~product(e_1, e_4, e_1)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1889, 1884])).
% 1.02/1.00 tff(1891,assumption,(~product(e_5, e_4, e_2)), introduced(assumption)).
% 1.02/1.00 tff(1892,plain,
% 1.02/1.00 (~product(e_5, e_4, e_4)),
% 1.02/1.00 inference(unit_resolution,[status(thm)],[1567, 1382, 890])).
% 1.02/1.00 tff(1893,plain,
% 1.02/1.01 ($false),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1558, 1892, 1382, 1747, 1891, 1026, 1545])).
% 1.02/1.01 tff(1894,plain,(product(e_5, e_4, e_3) | product(e_5, e_4, e_1) | product(e_5, e_4, e_2) | product(e_5, e_4, e_6) | product(e_5, e_4, e_5) | (~product(e_4, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.01 tff(1895,plain,
% 1.02/1.01 (product(e_5, e_4, e_2)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1894, 1670, 1026, 1689, 1699, 1713])).
% 1.02/1.01 tff(1896,plain,
% 1.02/1.01 (~product(e_6, e_4, e_2)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1861, 1895])).
% 1.02/1.01 tff(1897,plain,
% 1.02/1.01 (product(e_6, e_4, e_1)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1518, 1896, 1706, 1727, 1744, 1707])).
% 1.02/1.01 tff(1898,plain,
% 1.02/1.01 (~product(e_1, e_4, e_4)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1875, 1897, 690])).
% 1.02/1.01 tff(1899,plain,
% 1.02/1.01 ($false),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1413, 1898, 1890, 1423, 1680, 1679, 1658])).
% 1.02/1.01 tff(1900,plain,((~product(e_1, e_1, e_2)) | product(e_1, e_4, e_6) | product(e_6, e_4, e_6) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_6, e_1, e_3) | product(e_4, e_2, e_6) | product(e_4, e_4, e_6) | product(e_2, e_5, e_4) | product(e_4, e_4, e_2) | product(e_5, e_4, e_6) | product(e_4, e_4, e_4) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_3) | product(e_5, e_1, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.01 tff(1901,plain,
% 1.02/1.01 ((~product(e_1, e_1, e_2)) | product(e_1, e_4, e_6) | product(e_6, e_4, e_6) | product(e_4, e_2, e_6) | product(e_4, e_4, e_6) | product(e_4, e_4, e_2) | product(e_5, e_4, e_6) | product(e_4, e_4, e_4) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_6)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1900, 372, 1372, 660, 1656, 593])).
% 1.02/1.01 tff(1902,plain,
% 1.02/1.01 (product(e_4, e_4, e_4)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1901, 1649, 1619, 1628, 1636, 1026, 1635, 1629, 1009, 1000])).
% 1.02/1.01 tff(1903,plain,
% 1.02/1.01 (~product(e_1, e_4, e_4)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1801, 1902])).
% 1.02/1.01 tff(1904,plain,
% 1.02/1.01 (product(e_1, e_4, e_3)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1413, 1903, 1628, 1625, 1612, 1023])).
% 1.02/1.01 tff(1905,plain,
% 1.02/1.01 (~product(e_6, e_4, e_4)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1733, 1902])).
% 1.02/1.01 tff(1906,plain,
% 1.02/1.01 (~product(e_5, e_4, e_4)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1573, 1902])).
% 1.02/1.01 tff(1907,assumption,(~product(e_6, e_4, e_2)), introduced(assumption)).
% 1.02/1.01 tff(1908,plain,
% 1.02/1.01 (~product(e_6, e_4, e_3)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1421, 1415])).
% 1.02/1.01 tff(1909,plain,
% 1.02/1.01 (~product(e_6, e_4, e_1)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1807, 1415, 663])).
% 1.02/1.01 tff(1910,plain,
% 1.02/1.01 ($false),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1518, 1909, 1908, 1907, 1395, 1746, 1707])).
% 1.02/1.01 tff(1911,plain,((~product(e_1, e_4, e_3)) | product(e_6, e_4, e_2) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_6) | product(e_6, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.01 tff(1912,plain,
% 1.02/1.01 (product(e_6, e_4, e_2)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1911, 1415, 663, 1395, 1707, 1746])).
% 1.02/1.01 tff(1913,plain,
% 1.02/1.01 (~product(e_5, e_4, e_1)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1549, 1415, 1148])).
% 1.02/1.01 tff(1914,plain,
% 1.02/1.01 (((~![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_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_1, e_5) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_3)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1915,plain,
% 1.02/1.01 ((equalish(e_1, e_5) | (~product(e_5, e_4, e_3)) | (~product(e_1, e_4, e_3))) <=> (equalish(e_1, e_5) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_3)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1916,plain,
% 1.02/1.01 (((~![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_4, e_3)) | (~product(e_1, 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_1, e_5) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_3))))),
% 1.02/1.01 inference(monotonicity,[status(thm)],[1915])).
% 1.02/1.01 tff(1917,plain,
% 1.02/1.01 (((~![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_4, e_3)) | (~product(e_1, 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_1, e_5) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_3)))),
% 1.02/1.01 inference(transitivity,[status(thm)],[1916, 1914])).
% 1.02/1.01 tff(1918,plain,
% 1.02/1.01 ((~![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_4, e_3)) | (~product(e_1, e_4, e_3)))),
% 1.02/1.01 inference(quant_inst,[status(thm)],[])).
% 1.02/1.01 tff(1919,plain,
% 1.02/1.01 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_5) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_3))),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.02/1.01 tff(1920,plain,
% 1.02/1.01 ($false),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1919, 1834, 87, 1334, 1415])).
% 1.02/1.01 tff(1921,plain,((~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.01 tff(1922,plain,
% 1.02/1.01 (~product(e_5, e_4, e_3)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1921, 1415])).
% 1.02/1.01 tff(1923,plain,
% 1.02/1.01 (product(e_5, e_4, e_2)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1558, 1922, 1545, 1853, 1026, 1913])).
% 1.02/1.01 tff(1924,plain,
% 1.02/1.01 ($false),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1861, 1923, 1912])).
% 1.02/1.01 tff(1925,plain,((~product(e_1, e_4, e_3)) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_6) | product(e_5, e_1, e_3) | product(e_6, e_1, e_3) | product(e_6, e_4, e_5) | product(e_6, e_4, e_6) | product(e_6, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.01 tff(1926,plain,
% 1.02/1.01 ((~product(e_1, e_4, e_3)) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_6) | product(e_6, e_4, e_4)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1925, 660, 593])).
% 1.02/1.01 tff(1927,plain,
% 1.02/1.01 ($false),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1926, 1906, 1905, 1324, 1026, 1292, 1635, 1904])).
% 1.02/1.01 tff(1928,plain,(product(e_1, e_3, e_5) | product(e_5, e_4, e_6) | product(e_5, e_1, e_6) | product(e_3, e_3, e_6) | product(e_1, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.01 tff(1929,plain,
% 1.02/1.01 (product(e_5, e_1, e_6)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1928, 999, 54, 980, 970])).
% 1.02/1.01 tff(1930,plain,
% 1.02/1.01 (~product(e_6, e_1, e_5)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[649, 1929, 53])).
% 1.02/1.01 tff(1931,plain,
% 1.02/1.01 ((~equalish(e_3, e_5)) <=> (~equalish(e_3, e_5))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1932,axiom,(~equalish(e_3, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_5')).
% 1.02/1.01 tff(1933,plain,
% 1.02/1.01 (~equalish(e_3, e_5)),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 1.02/1.01 tff(1934,plain,
% 1.02/1.01 (((~![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_4, e_3, e_6)) | (~product(e_4, 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_3, e_5) | (~product(e_4, e_3, e_6)) | (~product(e_4, e_5, e_6)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1935,plain,
% 1.02/1.01 ((equalish(e_3, e_5) | (~product(e_4, e_5, e_6)) | (~product(e_4, e_3, e_6))) <=> (equalish(e_3, e_5) | (~product(e_4, e_3, e_6)) | (~product(e_4, e_5, e_6)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1936,plain,
% 1.02/1.01 (((~![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_4, e_5, e_6)) | (~product(e_4, 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_4, e_3, e_6)) | (~product(e_4, e_5, e_6))))),
% 1.02/1.01 inference(monotonicity,[status(thm)],[1935])).
% 1.02/1.01 tff(1937,plain,
% 1.02/1.01 (((~![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_4, e_5, e_6)) | (~product(e_4, 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_4, e_3, e_6)) | (~product(e_4, e_5, e_6)))),
% 1.02/1.01 inference(transitivity,[status(thm)],[1936, 1934])).
% 1.02/1.01 tff(1938,plain,
% 1.02/1.01 ((~![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_4, e_5, e_6)) | (~product(e_4, e_3, e_6)))),
% 1.02/1.01 inference(quant_inst,[status(thm)],[])).
% 1.02/1.01 tff(1939,plain,
% 1.02/1.01 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_4, e_3, e_6)) | (~product(e_4, e_5, e_6))),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[1938, 1937])).
% 1.02/1.01 tff(1940,plain,
% 1.02/1.01 ($false),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1939, 1933, 12, 961, 803])).
% 1.02/1.01 tff(1941,plain,((~product(e_4, e_3, e_6)) | (~product(e_4, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.01 tff(1942,plain,
% 1.02/1.01 (~product(e_4, e_5, e_6)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1941, 959])).
% 1.02/1.01 tff(1943,plain,
% 1.02/1.01 (~product(e_4, e_1, e_5)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[800, 1929, 1942])).
% 1.02/1.01 tff(1944,plain,
% 1.02/1.01 ($false),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1116, 1943, 1930])).
% 1.02/1.01 tff(1945,plain,(product(e_1, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.01 tff(1946,assumption,(product(e_5, e_3, e_5)), introduced(assumption)).
% 1.02/1.01 tff(1947,assumption,(product(e_1, e_3, e_5)), introduced(assumption)).
% 1.02/1.01 tff(1948,plain,
% 1.02/1.01 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_3, e_5)) | (~product(e_5, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_1, e_3, e_5)) | (~product(e_5, e_3, e_5)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1949,plain,
% 1.02/1.01 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_3, e_5)) | (~product(e_5, e_3, e_5)))),
% 1.02/1.01 inference(quant_inst,[status(thm)],[])).
% 1.02/1.01 tff(1950,plain,
% 1.02/1.01 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_1, e_3, e_5)) | (~product(e_5, e_3, e_5))),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[1949, 1948])).
% 1.02/1.01 tff(1951,plain,
% 1.02/1.01 ($false),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1950, 577, 87, 1947, 1946])).
% 1.02/1.01 tff(1952,plain,((~product(e_5, e_3, e_5)) | (~product(e_1, e_3, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.01 tff(1953,plain,
% 1.02/1.01 (~product(e_5, e_3, e_5)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1952, 1945])).
% 1.02/1.01 tff(1954,plain,
% 1.02/1.01 (((~![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_5)) | (~product(e_6, e_3, 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_3, e_5)) | (~product(e_6, e_3, e_5)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1955,plain,
% 1.02/1.01 ((~![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_5)) | (~product(e_6, e_3, e_5)))),
% 1.02/1.01 inference(quant_inst,[status(thm)],[])).
% 1.02/1.01 tff(1956,plain,
% 1.02/1.01 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_3, e_5)) | (~product(e_6, e_3, e_5))),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[1955, 1954])).
% 1.02/1.01 tff(1957,plain,
% 1.02/1.01 ($false),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1956, 706, 87, 1947, 1099])).
% 1.02/1.01 tff(1958,plain,((~product(e_6, e_3, e_5)) | (~product(e_1, e_3, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.01 tff(1959,plain,
% 1.02/1.01 (~product(e_6, e_3, e_5)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1958, 1945])).
% 1.02/1.01 tff(1960,plain,
% 1.02/1.01 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_5)) | product(e_5, e_1, e_5) | (~product(e_5, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_5)) | product(e_5, e_1, e_5) | (~product(e_5, e_3, e_1)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1961,plain,
% 1.02/1.01 ((product(e_5, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_5, e_3, e_1))) <=> ((~product(e_1, e_3, e_5)) | product(e_5, e_1, e_5) | (~product(e_5, e_3, e_1)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1962,plain,
% 1.02/1.01 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_5, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_5)) | product(e_5, e_1, e_5) | (~product(e_5, e_3, e_1))))),
% 1.02/1.01 inference(monotonicity,[status(thm)],[1961])).
% 1.02/1.01 tff(1963,plain,
% 1.02/1.01 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_5, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_5)) | product(e_5, e_1, e_5) | (~product(e_5, e_3, e_1)))),
% 1.02/1.01 inference(transitivity,[status(thm)],[1962, 1960])).
% 1.02/1.01 tff(1964,plain,
% 1.02/1.01 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_5, e_3, e_1)))),
% 1.02/1.01 inference(quant_inst,[status(thm)],[])).
% 1.02/1.01 tff(1965,plain,
% 1.02/1.01 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_5)) | product(e_5, e_1, e_5) | (~product(e_5, e_3, e_1))),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[1964, 1963])).
% 1.02/1.01 tff(1966,plain,
% 1.02/1.01 (~product(e_5, e_3, e_1)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1965, 33, 1945, 619])).
% 1.02/1.01 tff(1967,plain,
% 1.02/1.01 (~product(e_6, e_1, e_5)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[649, 1, 53])).
% 1.02/1.01 tff(1968,plain,
% 1.02/1.01 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_5)) | product(e_6, e_1, e_5) | (~product(e_6, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_5)) | product(e_6, e_1, e_5) | (~product(e_6, e_3, e_1)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1969,plain,
% 1.02/1.01 ((product(e_6, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_6, e_3, e_1))) <=> ((~product(e_1, e_3, e_5)) | product(e_6, e_1, e_5) | (~product(e_6, e_3, e_1)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1970,plain,
% 1.02/1.01 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_6, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_5)) | product(e_6, e_1, e_5) | (~product(e_6, e_3, e_1))))),
% 1.02/1.01 inference(monotonicity,[status(thm)],[1969])).
% 1.02/1.01 tff(1971,plain,
% 1.02/1.01 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_6, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_5)) | product(e_6, e_1, e_5) | (~product(e_6, e_3, e_1)))),
% 1.02/1.01 inference(transitivity,[status(thm)],[1970, 1968])).
% 1.02/1.01 tff(1972,plain,
% 1.02/1.01 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_6, e_3, e_1)))),
% 1.02/1.01 inference(quant_inst,[status(thm)],[])).
% 1.02/1.01 tff(1973,plain,
% 1.02/1.01 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_5)) | product(e_6, e_1, e_5) | (~product(e_6, e_3, e_1))),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 1.02/1.01 tff(1974,plain,
% 1.02/1.01 ($false),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1973, 33, 1947, 662, 1352])).
% 1.02/1.01 tff(1975,plain,((~product(e_1, e_3, e_5)) | product(e_6, e_1, e_5) | (~product(e_6, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.01 tff(1976,plain,
% 1.02/1.01 (~product(e_6, e_3, e_1)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1975, 1967, 1945])).
% 1.02/1.01 tff(1977,assumption,(product(e_5, e_3, e_4)), introduced(assumption)).
% 1.02/1.01 tff(1978,plain,
% 1.02/1.01 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_5, e_3, 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_2) | (~product(e_2, e_3, e_4)) | (~product(e_5, e_3, e_4)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1979,plain,
% 1.02/1.01 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_5, e_3, e_4)))),
% 1.02/1.01 inference(quant_inst,[status(thm)],[])).
% 1.02/1.01 tff(1980,plain,
% 1.02/1.01 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_5, e_3, e_4))),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 1.02/1.01 tff(1981,plain,
% 1.02/1.01 ($false),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1980, 587, 87, 374, 1977])).
% 1.02/1.01 tff(1982,plain,((~product(e_5, e_3, e_4)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.01 tff(1983,plain,
% 1.02/1.01 (~product(e_5, e_3, e_4)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1982, 330])).
% 1.02/1.01 tff(1984,assumption,(~product(e_5, e_3, e_1)), introduced(assumption)).
% 1.02/1.01 tff(1985,assumption,(~product(e_5, e_3, e_6)), introduced(assumption)).
% 1.02/1.01 tff(1986,assumption,(~product(e_5, e_3, e_5)), introduced(assumption)).
% 1.02/1.01 tff(1987,plain,
% 1.02/1.01 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_6)) | product(e_5, e_3, e_6) | (~product(e_5, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_6)) | product(e_5, e_3, e_6) | (~product(e_5, e_3, e_3)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1988,plain,
% 1.02/1.01 ((product(e_5, e_3, e_6) | (~product(e_3, e_3, e_6)) | (~product(e_5, e_3, e_3))) <=> ((~product(e_3, e_3, e_6)) | product(e_5, e_3, e_6) | (~product(e_5, e_3, e_3)))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1989,plain,
% 1.02/1.01 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_6) | (~product(e_3, e_3, e_6)) | (~product(e_5, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_6)) | product(e_5, e_3, e_6) | (~product(e_5, e_3, e_3))))),
% 1.02/1.01 inference(monotonicity,[status(thm)],[1988])).
% 1.02/1.01 tff(1990,plain,
% 1.02/1.01 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_6) | (~product(e_3, e_3, e_6)) | (~product(e_5, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_6)) | product(e_5, e_3, e_6) | (~product(e_5, e_3, e_3)))),
% 1.02/1.01 inference(transitivity,[status(thm)],[1989, 1987])).
% 1.02/1.01 tff(1991,plain,
% 1.02/1.01 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_6) | (~product(e_3, e_3, e_6)) | (~product(e_5, e_3, e_3)))),
% 1.02/1.01 inference(quant_inst,[status(thm)],[])).
% 1.02/1.01 tff(1992,plain,
% 1.02/1.01 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_6)) | product(e_5, e_3, e_6) | (~product(e_5, e_3, e_3))),
% 1.02/1.01 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 1.02/1.01 tff(1993,plain,
% 1.02/1.01 (~product(e_5, e_3, e_3)),
% 1.02/1.01 inference(unit_resolution,[status(thm)],[1992, 33, 971, 1985])).
% 1.02/1.01 tff(1994,assumption,(~product(e_5, e_3, e_4)), introduced(assumption)).
% 1.02/1.01 tff(1995,plain,
% 1.02/1.01 (((~![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_5)) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_6) | product(e_5, e_3, e_1) | product(e_5, e_3, 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_3)) | (~group_element(e_5)) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_6) | product(e_5, e_3, e_1) | product(e_5, e_3, e_5))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1996,plain,
% 1.02/1.01 ((product(e_5, e_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_5))) <=> ((~group_element(e_3)) | (~group_element(e_5)) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_6) | product(e_5, e_3, e_1) | product(e_5, e_3, e_5))),
% 1.02/1.01 inference(rewrite,[status(thm)],[])).
% 1.02/1.01 tff(1997,plain,
% 1.02/1.01 (((~![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_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)) | (~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_3)) | (~group_element(e_5)) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_6) | product(e_5, e_3, e_1) | product(e_5, e_3, e_5)))),
% 1.02/1.01 inference(monotonicity,[status(thm)],[1996])).
% 1.02/1.01 tff(1998,plain,
% 1.02/1.01 (((~![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_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)) | (~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_3)) | (~group_element(e_5)) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_6) | product(e_5, e_3, e_1) | product(e_5, e_3, e_5))),
% 1.02/1.01 inference(transitivity,[status(thm)],[1997, 1995])).
% 1.02/1.01 tff(1999,plain,
% 1.02/1.01 ((~![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_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_5)))),
% 1.02/1.01 inference(quant_inst,[status(thm)],[])).
% 1.02/1.01 tff(2000,plain,
% 1.02/1.01 ((~![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_5)) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_6) | product(e_5, e_3, e_1) | product(e_5, e_3, e_5)),
% 1.02/1.02 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 1.02/1.02 tff(2001,plain,
% 1.02/1.02 (product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_6) | product(e_5, e_3, e_1) | product(e_5, e_3, e_5)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2000, 289, 622, 144, 1994])).
% 1.02/1.02 tff(2002,plain,
% 1.02/1.02 (product(e_5, e_3, e_2)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2001, 1993, 1986, 1985, 1984])).
% 1.02/1.02 tff(2003,assumption,(product(e_5, e_3, e_2)), introduced(assumption)).
% 1.02/1.02 tff(2004,plain,
% 1.02/1.02 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, 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_5) | (~product(e_5, e_3, e_2)) | (~product(e_6, e_3, e_2)))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(2005,plain,
% 1.02/1.02 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, e_3, e_2)) | (~product(e_6, e_3, e_2)))),
% 1.02/1.02 inference(quant_inst,[status(thm)],[])).
% 1.02/1.02 tff(2006,plain,
% 1.02/1.02 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_5) | (~product(e_5, e_3, e_2)) | (~product(e_6, e_3, e_2))),
% 1.02/1.02 inference(modus_ponens,[status(thm)],[2005, 2004])).
% 1.02/1.02 tff(2007,plain,
% 1.02/1.02 ($false),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2006, 636, 87, 1086, 2003])).
% 1.02/1.02 tff(2008,plain,((~product(e_6, e_3, e_2)) | (~product(e_5, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.02 tff(2009,plain,
% 1.02/1.02 (~product(e_6, e_3, e_2)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2008, 2002])).
% 1.02/1.02 tff(2010,plain,
% 1.02/1.02 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_6)) | product(e_6, e_3, e_6) | (~product(e_6, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_6)) | product(e_6, e_3, e_6) | (~product(e_6, e_3, e_3)))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(2011,plain,
% 1.02/1.02 ((product(e_6, e_3, e_6) | (~product(e_3, e_3, e_6)) | (~product(e_6, e_3, e_3))) <=> ((~product(e_3, e_3, e_6)) | product(e_6, e_3, e_6) | (~product(e_6, e_3, e_3)))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(2012,plain,
% 1.02/1.02 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_3, e_6) | (~product(e_3, e_3, e_6)) | (~product(e_6, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_6)) | product(e_6, e_3, e_6) | (~product(e_6, e_3, e_3))))),
% 1.02/1.02 inference(monotonicity,[status(thm)],[2011])).
% 1.02/1.02 tff(2013,plain,
% 1.02/1.02 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_3, e_6) | (~product(e_3, e_3, e_6)) | (~product(e_6, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_6)) | product(e_6, e_3, e_6) | (~product(e_6, e_3, e_3)))),
% 1.02/1.02 inference(transitivity,[status(thm)],[2012, 2010])).
% 1.02/1.02 tff(2014,plain,
% 1.02/1.02 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_3, e_6) | (~product(e_3, e_3, e_6)) | (~product(e_6, e_3, e_3)))),
% 1.02/1.02 inference(quant_inst,[status(thm)],[])).
% 1.02/1.02 tff(2015,plain,
% 1.02/1.02 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_6)) | product(e_6, e_3, e_6) | (~product(e_6, e_3, e_3))),
% 1.02/1.02 inference(modus_ponens,[status(thm)],[2014, 2013])).
% 1.02/1.02 tff(2016,plain,
% 1.02/1.02 ($false),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2015, 33, 971, 1248, 1265])).
% 1.02/1.02 tff(2017,plain,((~product(e_3, e_3, e_6)) | (~product(e_6, e_3, e_3)) | product(e_6, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.02 tff(2018,plain,
% 1.02/1.02 (~product(e_6, e_3, e_3)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2017, 1265, 971])).
% 1.02/1.02 tff(2019,plain,
% 1.02/1.02 (product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_1)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[1273, 289, 693, 144, 1262])).
% 1.02/1.02 tff(2020,plain,
% 1.02/1.02 ($false),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2019, 2018, 1265, 1267, 1264, 1263])).
% 1.02/1.02 tff(2021,plain,(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) | product(e_6, e_3, e_4) | (~product(e_3, e_3, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.02 tff(2022,plain,
% 1.02/1.02 (product(e_6, e_3, e_6)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2021, 2009, 1267, 1263, 1262, 971])).
% 1.02/1.02 tff(2023,plain,
% 1.02/1.02 (((~![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_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_3) | (~product(e_3, e_3, e_6)) | (~product(e_6, e_3, e_6)))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(2024,plain,
% 1.02/1.02 ((~![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_6)) | (~product(e_6, e_3, e_6)))),
% 1.02/1.02 inference(quant_inst,[status(thm)],[])).
% 1.02/1.02 tff(2025,plain,
% 1.02/1.02 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_3) | (~product(e_3, e_3, e_6)) | (~product(e_6, e_3, e_6))),
% 1.02/1.02 inference(modus_ponens,[status(thm)],[2024, 2023])).
% 1.02/1.02 tff(2026,plain,
% 1.02/1.02 ($false),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2025, 684, 87, 971, 2022])).
% 1.02/1.02 tff(2027,plain,((~product(e_3, e_3, e_6)) | product(e_6, e_3, e_5) | product(e_6, e_3, e_1) | product(e_6, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_5, e_3, e_1) | product(e_5, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.02 tff(2028,plain,
% 1.02/1.02 ((~product(e_3, e_3, e_6)) | product(e_6, e_3, e_5) | product(e_6, e_3, e_1) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_5, e_3, e_1)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2027, 1261, 1983])).
% 1.02/1.02 tff(2029,plain,
% 1.02/1.02 (~product(e_3, e_3, e_6)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2028, 1976, 1953, 1966, 21, 1959])).
% 1.02/1.02 tff(2030,plain,
% 1.02/1.02 (product(e_4, e_1, e_5)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[1116, 1967])).
% 1.02/1.02 tff(2031,plain,
% 1.02/1.02 (~product(e_4, e_3, e_5)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[526, 2030])).
% 1.02/1.02 tff(2032,assumption,(~product(e_4, e_3, e_5)), introduced(assumption)).
% 1.02/1.02 tff(2033,plain,
% 1.02/1.02 (~product(e_4, e_3, e_6)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[969, 960])).
% 1.02/1.02 tff(2034,plain,
% 1.02/1.02 (product(e_4, e_3, e_1)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[535, 2033, 383, 382, 2032])).
% 1.02/1.02 tff(2035,plain,
% 1.02/1.02 ($false),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[497, 33, 491, 2034, 960])).
% 1.02/1.02 tff(2036,plain,((~product(e_1, e_3, e_6)) | product(e_4, e_3, e_2) | product(e_4, e_3, e_3) | product(e_4, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.02 tff(2037,plain,
% 1.02/1.02 ((~product(e_1, e_3, e_6)) | product(e_4, e_3, e_5)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2036, 381, 361])).
% 1.02/1.02 tff(2038,plain,
% 1.02/1.02 (~product(e_1, e_3, e_6)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2037, 2031])).
% 1.02/1.02 tff(2039,plain,
% 1.02/1.02 (~product(e_6, e_1, e_6)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[1205, 1200])).
% 1.02/1.02 tff(2040,plain,
% 1.02/1.02 (((~![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_6)) | (~product(e_4, 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_3) | (~product(e_4, e_3, e_6)) | (~product(e_4, e_6, e_6)))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(2041,plain,
% 1.02/1.02 ((~![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_6)) | (~product(e_4, e_6, e_6)))),
% 1.02/1.02 inference(quant_inst,[status(thm)],[])).
% 1.02/1.02 tff(2042,plain,
% 1.02/1.02 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_3) | (~product(e_4, e_3, e_6)) | (~product(e_4, e_6, e_6))),
% 1.02/1.02 inference(modus_ponens,[status(thm)],[2041, 2040])).
% 1.02/1.02 tff(2043,plain,
% 1.02/1.02 ($false),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2042, 684, 12, 961, 926])).
% 1.02/1.02 tff(2044,plain,((~product(e_4, e_6, e_6)) | (~product(e_4, e_3, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.02 tff(2045,plain,
% 1.02/1.02 (~product(e_4, e_6, e_6)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2044, 961])).
% 1.02/1.02 tff(2046,plain,
% 1.02/1.02 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_6)) | product(e_4, e_6, e_6) | (~product(e_6, e_3, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_6)) | product(e_4, e_6, e_6) | (~product(e_6, e_3, e_6)))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(2047,plain,
% 1.02/1.02 ((product(e_4, e_6, e_6) | (~product(e_6, e_3, e_6)) | (~product(e_4, e_3, e_6))) <=> ((~product(e_4, e_3, e_6)) | product(e_4, e_6, e_6) | (~product(e_6, e_3, e_6)))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(2048,plain,
% 1.02/1.02 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_6, e_6) | (~product(e_6, e_3, e_6)) | (~product(e_4, e_3, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_6)) | product(e_4, e_6, e_6) | (~product(e_6, e_3, e_6))))),
% 1.02/1.02 inference(monotonicity,[status(thm)],[2047])).
% 1.02/1.02 tff(2049,plain,
% 1.02/1.02 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_6, e_6) | (~product(e_6, e_3, e_6)) | (~product(e_4, e_3, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_6)) | product(e_4, e_6, e_6) | (~product(e_6, e_3, e_6)))),
% 1.02/1.02 inference(transitivity,[status(thm)],[2048, 2046])).
% 1.02/1.02 tff(2050,plain,
% 1.02/1.02 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_6, e_6) | (~product(e_6, e_3, e_6)) | (~product(e_4, e_3, e_6)))),
% 1.02/1.02 inference(quant_inst,[status(thm)],[])).
% 1.02/1.02 tff(2051,plain,
% 1.02/1.02 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_6)) | product(e_4, e_6, e_6) | (~product(e_6, e_3, e_6))),
% 1.02/1.02 inference(modus_ponens,[status(thm)],[2050, 2049])).
% 1.02/1.02 tff(2052,plain,
% 1.02/1.02 ($false),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2051, 33, 961, 2045, 1200])).
% 1.02/1.02 tff(2053,plain,((~product(e_6, e_3, e_6)) | (~product(e_4, e_3, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.02 tff(2054,plain,
% 1.02/1.02 (~product(e_4, e_3, e_6)),
% 1.02/1.02 inference(unit_resolution,[status(thm)],[2053, 1200])).
% 1.02/1.02 tff(2055,assumption,(product(e_6, e_5, e_6)), introduced(assumption)).
% 1.02/1.02 tff(2056,plain,
% 1.02/1.02 (((~![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_6, e_3, e_6)) | (~product(e_6, 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_3) | (~product(e_6, e_3, e_6)) | (~product(e_6, e_5, e_6)))),
% 1.02/1.02 inference(rewrite,[status(thm)],[])).
% 1.02/1.02 tff(2057,plain,
% 1.02/1.02 ((~![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_6, e_3, e_6)) | (~product(e_6, e_5, e_6)))),
% 1.11/1.02 inference(quant_inst,[status(thm)],[])).
% 1.11/1.02 tff(2058,plain,
% 1.11/1.02 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_3) | (~product(e_6, e_3, e_6)) | (~product(e_6, e_5, e_6))),
% 1.11/1.02 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 1.11/1.02 tff(2059,plain,
% 1.11/1.02 ($false),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[2058, 597, 12, 2055, 1200])).
% 1.11/1.02 tff(2060,plain,((~product(e_6, e_5, e_6)) | (~product(e_6, e_3, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.02 tff(2061,plain,
% 1.11/1.02 (~product(e_6, e_5, e_6)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[2060, 1200])).
% 1.11/1.02 tff(2062,assumption,(~product(e_6, e_5, e_6)), introduced(assumption)).
% 1.11/1.02 tff(2063,plain,
% 1.11/1.02 (~product(e_5, e_1, e_1)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[582, 539])).
% 1.11/1.02 tff(2064,plain,
% 1.11/1.02 (product(e_4, e_1, e_2)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[555, 383, 382, 55, 54])).
% 1.11/1.02 tff(2065,plain,
% 1.11/1.02 (~product(e_5, e_1, e_2)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[569, 2064])).
% 1.11/1.02 tff(2066,plain,
% 1.11/1.02 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_4, 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_4) | (~product(e_2, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 1.11/1.02 inference(rewrite,[status(thm)],[])).
% 1.11/1.02 tff(2067,plain,
% 1.11/1.02 ((equalish(e_2, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_1, e_2))) <=> (equalish(e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 1.11/1.02 inference(rewrite,[status(thm)],[])).
% 1.11/1.02 tff(2068,plain,
% 1.11/1.02 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_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_4) | (~product(e_2, e_1, e_2)) | (~product(e_4, e_1, e_2))))),
% 1.11/1.02 inference(monotonicity,[status(thm)],[2067])).
% 1.11/1.02 tff(2069,plain,
% 1.11/1.02 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_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_4) | (~product(e_2, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 1.11/1.02 inference(transitivity,[status(thm)],[2068, 2066])).
% 1.11/1.02 tff(2070,plain,
% 1.11/1.02 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 1.11/1.02 inference(quant_inst,[status(thm)],[])).
% 1.11/1.02 tff(2071,plain,
% 1.11/1.02 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_4, e_1, e_2))),
% 1.11/1.02 inference(modus_ponens,[status(thm)],[2070, 2069])).
% 1.11/1.02 tff(2072,plain,
% 1.11/1.02 ($false),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[2071, 822, 87, 56, 384])).
% 1.11/1.02 tff(2073,plain,((~product(e_2, e_1, e_2)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.02 tff(2074,plain,
% 1.11/1.02 (~product(e_2, e_1, e_2)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[2073, 2064])).
% 1.11/1.02 tff(2075,plain,
% 1.11/1.02 (product(e_2, e_1, e_3)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[206, 2074])).
% 1.11/1.02 tff(2076,plain,
% 1.11/1.02 (~product(e_5, e_1, e_3)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[592, 2075])).
% 1.11/1.02 tff(2077,plain,
% 1.11/1.02 (product(e_5, e_1, e_6)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[630, 2076, 2065, 2063])).
% 1.11/1.02 tff(2078,plain,
% 1.11/1.02 (~product(e_6, e_1, e_3)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[659, 2075])).
% 1.11/1.02 tff(2079,plain,
% 1.11/1.02 (product(e_6, e_1, e_5)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[955, 2077, 55, 54, 661, 2078])).
% 1.11/1.02 tff(2080,plain,
% 1.11/1.02 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_6, e_5, e_6))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_6, e_5, e_6))),
% 1.11/1.02 inference(rewrite,[status(thm)],[])).
% 1.11/1.02 tff(2081,plain,
% 1.11/1.02 ((product(e_6, e_5, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_6, e_1, e_5))) <=> ((~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_6, e_5, e_6))),
% 1.11/1.02 inference(rewrite,[status(thm)],[])).
% 1.11/1.02 tff(2082,plain,
% 1.11/1.02 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_5, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_6, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_6, e_5, e_6)))),
% 1.11/1.02 inference(monotonicity,[status(thm)],[2081])).
% 1.11/1.02 tff(2083,plain,
% 1.11/1.02 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_5, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_6, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_6, e_5, e_6))),
% 1.11/1.02 inference(transitivity,[status(thm)],[2082, 2080])).
% 1.11/1.02 tff(2084,plain,
% 1.11/1.02 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_5, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_6, e_1, e_5)))),
% 1.11/1.02 inference(quant_inst,[status(thm)],[])).
% 1.11/1.02 tff(2085,plain,
% 1.11/1.02 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_6, e_5, e_6)),
% 1.11/1.02 inference(modus_ponens,[status(thm)],[2084, 2083])).
% 1.11/1.02 tff(2086,plain,
% 1.11/1.02 ((~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)) | product(e_6, e_5, e_6)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[2085, 33])).
% 1.11/1.02 tff(2087,plain,
% 1.11/1.02 ($false),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[2086, 2079, 2077, 2062])).
% 1.11/1.02 tff(2088,plain,(product(e_4, e_3, e_2) | product(e_6, e_5, e_6) | product(e_4, e_3, e_6) | product(e_1, e_3, e_5) | product(e_6, e_1, e_6) | product(e_4, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.02 tff(2089,plain,
% 1.11/1.02 (product(e_6, e_5, e_6) | product(e_4, e_3, e_6) | product(e_1, e_3, e_5) | product(e_6, e_1, e_6)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[2088, 381, 361])).
% 1.11/1.02 tff(2090,plain,
% 1.11/1.02 (product(e_1, e_3, e_5)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[2089, 2061, 2039, 2054])).
% 1.11/1.02 tff(2091,plain,
% 1.11/1.02 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_3, e_3, e_1)))),
% 1.11/1.02 inference(rewrite,[status(thm)],[])).
% 1.11/1.02 tff(2092,plain,
% 1.11/1.02 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_3, e_3, e_1)))),
% 1.11/1.02 inference(quant_inst,[status(thm)],[])).
% 1.11/1.02 tff(2093,plain,
% 1.11/1.02 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_3, e_3, e_1))),
% 1.11/1.02 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 1.11/1.02 tff(2094,plain,
% 1.11/1.02 (~product(e_3, e_3, e_1)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[2093, 33, 286, 2090])).
% 1.11/1.02 tff(2095,plain,
% 1.11/1.02 (~product(e_5, e_3, e_1)),
% 1.11/1.02 inference(unit_resolution,[status(thm)],[1965, 33, 2090, 619])).
% 1.11/1.02 tff(2096,assumption,(~product(e_5, e_3, e_2)), introduced(assumption)).
% 1.11/1.02 tff(2097,plain,
% 1.11/1.02 (product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2000, 289, 622, 144, 1986, 1985, 1994])).
% 1.11/1.03 tff(2098,plain,
% 1.11/1.03 (product(e_5, e_3, e_3)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2097, 1984, 2096])).
% 1.11/1.03 tff(2099,assumption,(~product(e_3, e_3, e_1)), introduced(assumption)).
% 1.11/1.03 tff(2100,plain,
% 1.11/1.03 (product(e_5, e_3, e_3) | product(e_5, e_3, e_2)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2000, 289, 622, 144, 1986, 1985, 1994, 1984])).
% 1.11/1.03 tff(2101,plain,
% 1.11/1.03 (product(e_5, e_3, e_3)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2100, 2096])).
% 1.11/1.03 tff(2102,assumption,(product(e_5, e_3, e_3)), introduced(assumption)).
% 1.11/1.03 tff(2103,plain,
% 1.11/1.03 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, 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_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2104,plain,
% 1.11/1.03 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))),
% 1.11/1.03 inference(quant_inst,[status(thm)],[])).
% 1.11/1.03 tff(2105,plain,
% 1.11/1.03 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3))),
% 1.11/1.03 inference(modus_ponens,[status(thm)],[2104, 2103])).
% 1.11/1.03 tff(2106,plain,
% 1.11/1.03 ($false),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2105, 597, 87, 209, 2102])).
% 1.11/1.03 tff(2107,plain,((~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.03 tff(2108,plain,
% 1.11/1.03 (~product(e_3, e_3, e_3)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2107, 2101])).
% 1.11/1.03 tff(2109,plain,
% 1.11/1.03 (product(e_3, e_3, e_2)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[1246, 2108, 1025, 1053, 2099])).
% 1.11/1.03 tff(2110,plain,
% 1.11/1.03 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_5, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_5, e_3, e_3)))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2111,plain,
% 1.11/1.03 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_5, e_3, e_3)))),
% 1.11/1.03 inference(quant_inst,[status(thm)],[])).
% 1.11/1.03 tff(2112,plain,
% 1.11/1.03 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_5, e_3, e_3))),
% 1.11/1.03 inference(modus_ponens,[status(thm)],[2111, 2110])).
% 1.11/1.03 tff(2113,plain,
% 1.11/1.03 ($false),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2112, 33, 2109, 2096, 2101])).
% 1.11/1.03 tff(2114,plain,(product(e_5, e_3, e_2) | product(e_3, e_3, e_6) | product(e_3, e_3, e_5) | product(e_3, e_3, e_1) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_5, e_3, e_4) | product(e_5, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.03 tff(2115,plain,
% 1.11/1.03 (product(e_3, e_3, e_5)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2114, 1984, 1986, 1025, 2099, 1985, 1994, 2096])).
% 1.11/1.03 tff(2116,plain,
% 1.11/1.03 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_5)) | product(e_5, e_3, e_5) | (~product(e_5, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_5)) | product(e_5, e_3, e_5) | (~product(e_5, e_3, e_3)))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2117,plain,
% 1.11/1.03 ((product(e_5, e_3, e_5) | (~product(e_3, e_3, e_5)) | (~product(e_5, e_3, e_3))) <=> ((~product(e_3, e_3, e_5)) | product(e_5, e_3, e_5) | (~product(e_5, e_3, e_3)))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2118,plain,
% 1.11/1.03 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_5) | (~product(e_3, e_3, e_5)) | (~product(e_5, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_5)) | product(e_5, e_3, e_5) | (~product(e_5, e_3, e_3))))),
% 1.11/1.03 inference(monotonicity,[status(thm)],[2117])).
% 1.11/1.03 tff(2119,plain,
% 1.11/1.03 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_5) | (~product(e_3, e_3, e_5)) | (~product(e_5, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_5)) | product(e_5, e_3, e_5) | (~product(e_5, e_3, e_3)))),
% 1.11/1.03 inference(transitivity,[status(thm)],[2118, 2116])).
% 1.11/1.03 tff(2120,plain,
% 1.11/1.03 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_5) | (~product(e_3, e_3, e_5)) | (~product(e_5, e_3, e_3)))),
% 1.11/1.03 inference(quant_inst,[status(thm)],[])).
% 1.11/1.03 tff(2121,plain,
% 1.11/1.03 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_5)) | product(e_5, e_3, e_5) | (~product(e_5, e_3, e_3))),
% 1.11/1.03 inference(modus_ponens,[status(thm)],[2120, 2119])).
% 1.11/1.03 tff(2122,plain,
% 1.11/1.03 ($false),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2121, 33, 2115, 1986, 2098])).
% 1.11/1.03 tff(2123,plain,(product(e_5, e_3, e_1) | product(e_5, e_3, e_5) | product(e_5, e_3, e_2) | product(e_5, e_3, e_6) | product(e_5, e_3, e_4) | product(e_3, e_3, e_6) | product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.03 tff(2124,plain,
% 1.11/1.03 (product(e_5, e_3, e_1) | product(e_5, e_3, e_5) | product(e_5, e_3, e_2) | product(e_5, e_3, e_6) | product(e_3, e_3, e_6) | product(e_3, e_3, e_1)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2123, 1983])).
% 1.11/1.03 tff(2125,plain,
% 1.11/1.03 (product(e_5, e_3, e_2)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2124, 2095, 1025, 1986, 1985, 2094])).
% 1.11/1.03 tff(2126,plain,
% 1.11/1.03 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_5)) | product(e_1, e_5, e_2) | (~product(e_5, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_5)) | product(e_1, e_5, e_2) | (~product(e_5, e_3, e_2)))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2127,plain,
% 1.11/1.03 ((product(e_1, e_5, e_2) | (~product(e_5, e_3, e_2)) | (~product(e_1, e_3, e_5))) <=> ((~product(e_1, e_3, e_5)) | product(e_1, e_5, e_2) | (~product(e_5, e_3, e_2)))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2128,plain,
% 1.11/1.03 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_5, e_2) | (~product(e_5, e_3, e_2)) | (~product(e_1, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_5)) | product(e_1, e_5, e_2) | (~product(e_5, e_3, e_2))))),
% 1.11/1.03 inference(monotonicity,[status(thm)],[2127])).
% 1.11/1.03 tff(2129,plain,
% 1.11/1.03 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_5, e_2) | (~product(e_5, e_3, e_2)) | (~product(e_1, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_5)) | product(e_1, e_5, e_2) | (~product(e_5, e_3, e_2)))),
% 1.11/1.03 inference(transitivity,[status(thm)],[2128, 2126])).
% 1.11/1.03 tff(2130,plain,
% 1.11/1.03 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_5, e_2) | (~product(e_5, e_3, e_2)) | (~product(e_1, e_3, e_5)))),
% 1.11/1.03 inference(quant_inst,[status(thm)],[])).
% 1.11/1.03 tff(2131,plain,
% 1.11/1.03 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_5)) | product(e_1, e_5, e_2) | (~product(e_5, e_3, e_2))),
% 1.11/1.03 inference(modus_ponens,[status(thm)],[2130, 2129])).
% 1.11/1.03 tff(2132,plain,
% 1.11/1.03 ((~product(e_1, e_3, e_5)) | product(e_1, e_5, e_2) | (~product(e_5, e_3, e_2))),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2131, 33])).
% 1.11/1.03 tff(2133,plain,
% 1.11/1.03 (product(e_1, e_5, e_2)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2132, 2125, 2090])).
% 1.11/1.03 tff(2134,assumption,(product(e_1, e_5, e_2)), introduced(assumption)).
% 1.11/1.03 tff(2135,assumption,(product(e_3, e_5, e_2)), introduced(assumption)).
% 1.11/1.03 tff(2136,plain,
% 1.11/1.03 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_5, e_2)) | (~product(e_1, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_5, e_2)) | (~product(e_1, e_5, e_2)))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2137,plain,
% 1.11/1.03 ((equalish(e_3, e_1) | (~product(e_1, e_5, e_2)) | (~product(e_3, e_5, e_2))) <=> (equalish(e_3, e_1) | (~product(e_3, e_5, e_2)) | (~product(e_1, e_5, e_2)))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2138,plain,
% 1.11/1.03 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_5, e_2)) | (~product(e_3, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_5, e_2)) | (~product(e_1, e_5, e_2))))),
% 1.11/1.03 inference(monotonicity,[status(thm)],[2137])).
% 1.11/1.03 tff(2139,plain,
% 1.11/1.03 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_5, e_2)) | (~product(e_3, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_5, e_2)) | (~product(e_1, e_5, e_2)))),
% 1.11/1.03 inference(transitivity,[status(thm)],[2138, 2136])).
% 1.11/1.03 tff(2140,plain,
% 1.11/1.03 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_5, e_2)) | (~product(e_3, e_5, e_2)))),
% 1.11/1.03 inference(quant_inst,[status(thm)],[])).
% 1.11/1.03 tff(2141,plain,
% 1.11/1.03 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_5, e_2)) | (~product(e_1, e_5, e_2))),
% 1.11/1.03 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 1.11/1.03 tff(2142,plain,
% 1.11/1.03 ($false),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2141, 15, 87, 2135, 2134])).
% 1.11/1.03 tff(2143,plain,((~product(e_3, e_5, e_2)) | (~product(e_1, e_5, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.03 tff(2144,plain,
% 1.11/1.03 (~product(e_3, e_5, e_2)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2143, 2133])).
% 1.11/1.03 tff(2145,plain,
% 1.11/1.03 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_5, 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_5, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_5, e_3, e_2)))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2146,plain,
% 1.11/1.03 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_5, e_3, e_2)))),
% 1.11/1.03 inference(quant_inst,[status(thm)],[])).
% 1.11/1.03 tff(2147,plain,
% 1.11/1.03 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_5, e_3, e_2))),
% 1.11/1.03 inference(modus_ponens,[status(thm)],[2146, 2145])).
% 1.11/1.03 tff(2148,plain,
% 1.11/1.03 ($false),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2147, 597, 87, 1037, 2003])).
% 1.11/1.03 tff(2149,plain,((~product(e_5, e_3, e_2)) | (~product(e_3, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.03 tff(2150,plain,
% 1.11/1.03 (~product(e_3, e_3, e_2)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2149, 2125])).
% 1.11/1.03 tff(2151,plain,
% 1.11/1.03 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_5)) | (~product(e_3, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_5)) | (~product(e_3, e_3, e_5)))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2152,plain,
% 1.11/1.03 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_5)) | (~product(e_3, e_3, e_5)))),
% 1.11/1.03 inference(quant_inst,[status(thm)],[])).
% 1.11/1.03 tff(2153,plain,
% 1.11/1.03 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_5)) | (~product(e_3, e_3, e_5))),
% 1.11/1.03 inference(modus_ponens,[status(thm)],[2152, 2151])).
% 1.11/1.03 tff(2154,plain,
% 1.11/1.03 ($false),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2153, 15, 87, 1947, 1213])).
% 1.11/1.03 tff(2155,plain,((~product(e_3, e_3, e_5)) | (~product(e_1, e_3, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.03 tff(2156,plain,
% 1.11/1.03 (~product(e_3, e_3, e_5)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2155, 1947])).
% 1.11/1.03 tff(2157,assumption,(~product(e_3, e_3, e_3)), introduced(assumption)).
% 1.11/1.03 tff(2158,plain,
% 1.11/1.03 (product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_6) | product(e_3, e_3, e_5)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[1068, 289, 144, 1062, 2157])).
% 1.11/1.03 tff(2159,plain,
% 1.11/1.03 (product(e_3, e_3, e_1)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2158, 2156, 1025, 1054])).
% 1.11/1.03 tff(2160,plain,
% 1.11/1.03 ($false),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2093, 33, 286, 1947, 2159])).
% 1.11/1.03 tff(2161,plain,((~product(e_1, e_3, e_5)) | product(e_3, e_3, e_6) | product(e_3, e_3, e_2) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.03 tff(2162,plain,
% 1.11/1.03 ((~product(e_1, e_3, e_5)) | product(e_3, e_3, e_6) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2161, 1052])).
% 1.11/1.03 tff(2163,plain,
% 1.11/1.03 (product(e_3, e_3, e_3)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2162, 2150, 1025, 2090])).
% 1.11/1.03 tff(2164,plain,
% 1.11/1.03 (~product(e_3, e_5, e_3)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[1331, 2163])).
% 1.11/1.03 tff(2165,plain,
% 1.11/1.03 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_3, e_5, e_1)) | (~product(e_1, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_3, e_5, e_1)) | (~product(e_1, e_5, e_2)))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2166,plain,
% 1.11/1.03 ((product(e_3, e_1, e_2) | (~product(e_1, e_5, e_2)) | (~product(e_3, e_5, e_1))) <=> (product(e_3, e_1, e_2) | (~product(e_3, e_5, e_1)) | (~product(e_1, e_5, e_2)))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2167,plain,
% 1.11/1.03 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_5, e_2)) | (~product(e_3, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_3, e_5, e_1)) | (~product(e_1, e_5, e_2))))),
% 1.11/1.03 inference(monotonicity,[status(thm)],[2166])).
% 1.11/1.03 tff(2168,plain,
% 1.11/1.03 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_5, e_2)) | (~product(e_3, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_3, e_5, e_1)) | (~product(e_1, e_5, e_2)))),
% 1.11/1.03 inference(transitivity,[status(thm)],[2167, 2165])).
% 1.11/1.03 tff(2169,plain,
% 1.11/1.03 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_5, e_2)) | (~product(e_3, e_5, e_1)))),
% 1.11/1.03 inference(quant_inst,[status(thm)],[])).
% 1.11/1.03 tff(2170,plain,
% 1.11/1.03 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_3, e_5, e_1)) | (~product(e_1, e_5, e_2))),
% 1.11/1.03 inference(modus_ponens,[status(thm)],[2169, 2168])).
% 1.11/1.03 tff(2171,plain,
% 1.11/1.03 (~product(e_3, e_5, e_1)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2170, 33, 266, 2133])).
% 1.11/1.03 tff(2172,plain,
% 1.11/1.03 (product(e_5, e_1, e_6)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[1198, 662, 661])).
% 1.11/1.03 tff(2173,plain,
% 1.11/1.03 (product(e_4, e_1, e_5)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[1111, 662, 661])).
% 1.11/1.03 tff(2174,plain,
% 1.11/1.03 (product(e_4, e_5, e_6)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[800, 2173, 2172])).
% 1.11/1.03 tff(2175,plain,
% 1.11/1.03 (~product(e_4, e_2, e_6)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[811, 2174])).
% 1.11/1.03 tff(2176,plain,
% 1.11/1.03 (product(e_3, e_4, e_5)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[771, 2173])).
% 1.11/1.03 tff(2177,plain,
% 1.11/1.03 (~product(e_2, e_4, e_5)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[782, 2176])).
% 1.11/1.03 tff(2178,plain,
% 1.11/1.03 (~product(e_4, e_3, e_5)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[526, 2173])).
% 1.11/1.03 tff(2179,plain,
% 1.11/1.03 (product(e_4, e_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[535, 361, 381])).
% 1.11/1.03 tff(2180,plain,
% 1.11/1.03 (product(e_4, e_3, e_1)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2179, 2178, 55])).
% 1.11/1.03 tff(2181,plain,
% 1.11/1.03 (~product(e_4, e_2, e_1)),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[760, 2180])).
% 1.11/1.03 tff(2182,assumption,(~product(e_3, e_5, e_2)), introduced(assumption)).
% 1.11/1.03 tff(2183,plain,
% 1.11/1.03 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_2))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2184,plain,
% 1.11/1.03 ((product(e_3, e_5, e_2) | (~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_5))) <=> ((~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_2))),
% 1.11/1.03 inference(rewrite,[status(thm)],[])).
% 1.11/1.03 tff(2185,plain,
% 1.11/1.03 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_2) | (~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_2)))),
% 1.11/1.03 inference(monotonicity,[status(thm)],[2184])).
% 1.11/1.03 tff(2186,plain,
% 1.11/1.03 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_2) | (~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_2))),
% 1.11/1.03 inference(transitivity,[status(thm)],[2185, 2183])).
% 1.11/1.03 tff(2187,plain,
% 1.11/1.03 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_2) | (~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_5)))),
% 1.11/1.03 inference(quant_inst,[status(thm)],[])).
% 1.11/1.03 tff(2188,plain,
% 1.11/1.03 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_2)),
% 1.11/1.03 inference(modus_ponens,[status(thm)],[2187, 2186])).
% 1.11/1.03 tff(2189,plain,
% 1.11/1.03 ($false),
% 1.11/1.03 inference(unit_resolution,[status(thm)],[2188, 33, 1538, 773, 2182])).
% 1.11/1.03 tff(2190,plain,(product(e_3, e_5, e_2) | (~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.04 tff(2191,plain,
% 1.11/1.04 (~product(e_5, e_4, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2190, 2176, 2182])).
% 1.11/1.04 tff(2192,assumption,(~product(e_3, e_5, e_1)), introduced(assumption)).
% 1.11/1.04 tff(2193,plain,
% 1.11/1.04 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_1)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_4, e_1)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_1))),
% 1.11/1.04 inference(rewrite,[status(thm)],[])).
% 1.11/1.04 tff(2194,plain,
% 1.11/1.04 ((product(e_3, e_5, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_3, e_4, e_5))) <=> ((~product(e_5, e_4, e_1)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_1))),
% 1.11/1.04 inference(rewrite,[status(thm)],[])).
% 1.11/1.04 tff(2195,plain,
% 1.11/1.04 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_3, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_1)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_1)))),
% 1.11/1.04 inference(monotonicity,[status(thm)],[2194])).
% 1.11/1.04 tff(2196,plain,
% 1.11/1.04 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_3, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_4, e_1)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_1))),
% 1.11/1.04 inference(transitivity,[status(thm)],[2195, 2193])).
% 1.11/1.04 tff(2197,plain,
% 1.11/1.04 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_3, e_4, e_5)))),
% 1.11/1.04 inference(quant_inst,[status(thm)],[])).
% 1.11/1.04 tff(2198,plain,
% 1.11/1.04 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_4, e_1)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_1)),
% 1.11/1.04 inference(modus_ponens,[status(thm)],[2197, 2196])).
% 1.11/1.04 tff(2199,plain,
% 1.11/1.04 ((~product(e_5, e_4, e_1)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2198, 33])).
% 1.11/1.04 tff(2200,plain,
% 1.11/1.04 (~product(e_5, e_4, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2199, 2176, 2192])).
% 1.11/1.04 tff(2201,plain,
% 1.11/1.04 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_5, e_1, e_6)) | (~product(e_5, 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_1) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_4, e_6)))),
% 1.11/1.04 inference(rewrite,[status(thm)],[])).
% 1.11/1.04 tff(2202,plain,
% 1.11/1.04 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_4, e_6)))),
% 1.11/1.04 inference(quant_inst,[status(thm)],[])).
% 1.11/1.04 tff(2203,plain,
% 1.11/1.04 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_4, e_6))),
% 1.11/1.04 inference(modus_ponens,[status(thm)],[2202, 2201])).
% 1.11/1.04 tff(2204,plain,
% 1.11/1.04 ($false),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2203, 366, 12, 993, 1])).
% 1.11/1.04 tff(2205,plain,((~product(e_5, e_4, e_6)) | (~product(e_5, e_1, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.04 tff(2206,plain,
% 1.11/1.04 (~product(e_5, e_4, e_6)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2205, 2172])).
% 1.11/1.04 tff(2207,plain,
% 1.11/1.04 (~product(e_3, e_1, e_3)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1461, 363])).
% 1.11/1.04 tff(2208,plain,
% 1.11/1.04 (~product(e_6, e_1, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[711, 77])).
% 1.11/1.04 tff(2209,plain,
% 1.11/1.04 (~product(e_6, e_1, e_3)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[659, 363])).
% 1.11/1.04 tff(2210,plain,
% 1.11/1.04 (~product(e_3, e_1, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[321, 77])).
% 1.11/1.04 tff(2211,plain,
% 1.11/1.04 (product(e_3, e_1, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[296, 2210, 268, 2207])).
% 1.11/1.04 tff(2212,plain,
% 1.11/1.04 (~product(e_6, e_1, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[689, 2211])).
% 1.11/1.04 tff(2213,plain,
% 1.11/1.04 (product(e_6, e_1, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[700, 2212, 661, 1715, 2209, 2208])).
% 1.11/1.04 tff(2214,plain,
% 1.11/1.04 (~product(e_5, e_1, e_3)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[592, 363])).
% 1.11/1.04 tff(2215,plain,
% 1.11/1.04 (~product(e_5, e_1, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[602, 2211])).
% 1.11/1.04 tff(2216,plain,
% 1.11/1.04 (~product(e_5, e_1, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[582, 77])).
% 1.11/1.04 tff(2217,plain,
% 1.11/1.04 (((~![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_5, e_1, e_5)) | (~product(e_4, 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_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 1.11/1.04 inference(rewrite,[status(thm)],[])).
% 1.11/1.04 tff(2218,plain,
% 1.11/1.04 ((equalish(e_5, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_5))) <=> (equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 1.11/1.04 inference(rewrite,[status(thm)],[])).
% 1.11/1.04 tff(2219,plain,
% 1.11/1.04 (((~![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_1, e_5)) | (~product(e_5, 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_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5))))),
% 1.11/1.04 inference(monotonicity,[status(thm)],[2218])).
% 1.11/1.04 tff(2220,plain,
% 1.11/1.04 (((~![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_1, e_5)) | (~product(e_5, 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_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 1.11/1.04 inference(transitivity,[status(thm)],[2219, 2217])).
% 1.11/1.04 tff(2221,plain,
% 1.11/1.04 ((~![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_1, e_5)) | (~product(e_5, e_1, e_5)))),
% 1.11/1.04 inference(quant_inst,[status(thm)],[])).
% 1.11/1.04 tff(2222,plain,
% 1.11/1.04 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5))),
% 1.11/1.04 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 1.11/1.04 tff(2223,plain,
% 1.11/1.04 ($false),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2222, 561, 87, 518, 604])).
% 1.11/1.04 tff(2224,plain,((~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.04 tff(2225,plain,
% 1.11/1.04 (~product(e_5, e_1, e_5)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2224, 518])).
% 1.11/1.04 tff(2226,plain,
% 1.11/1.04 (product(e_2, e_3, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[328, 2211, 363])).
% 1.11/1.04 tff(2227,plain,
% 1.11/1.04 (~product(e_4, e_3, e_3)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[380, 2226, 373])).
% 1.11/1.04 tff(2228,plain,
% 1.11/1.04 (~product(e_4, e_3, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1477, 2226])).
% 1.11/1.04 tff(2229,plain,
% 1.11/1.04 (~product(e_4, e_3, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[360, 2226])).
% 1.11/1.04 tff(2230,plain,
% 1.11/1.04 (~product(e_4, e_3, e_5)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[526, 518])).
% 1.11/1.04 tff(2231,plain,
% 1.11/1.04 (~product(e_4, e_3, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1487, 2226, 818])).
% 1.11/1.04 tff(2232,plain,
% 1.11/1.04 (product(e_4, e_3, e_6)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[534, 2231, 2230, 2229, 2228, 2227])).
% 1.11/1.04 tff(2233,plain,
% 1.11/1.04 (~product(e_4, e_5, e_6)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1941, 2232])).
% 1.11/1.04 tff(2234,plain,
% 1.11/1.04 (~product(e_5, e_1, e_6)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[800, 2233, 518])).
% 1.11/1.04 tff(2235,plain,
% 1.11/1.04 (product(e_5, e_1, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[629, 2234, 2225, 2216, 2215, 2214])).
% 1.11/1.04 tff(2236,plain,
% 1.11/1.04 ($false),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1153, 636, 87, 2235, 2213])).
% 1.11/1.04 tff(2237,plain,((~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_5)) | product(e_6, e_1, e_6) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.04 tff(2238,plain,
% 1.11/1.04 (~product(e_1, e_1, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2237, 661, 518, 818, 373, 363, 268])).
% 1.11/1.04 tff(2239,plain,
% 1.11/1.04 (product(e_1, e_1, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[154, 2238])).
% 1.11/1.04 tff(2240,plain,
% 1.11/1.04 (product(e_3, e_1, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[310, 2239, 2207])).
% 1.11/1.04 tff(2241,plain,
% 1.11/1.04 (product(e_2, e_3, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[328, 2240, 363])).
% 1.11/1.04 tff(2242,plain,
% 1.11/1.04 (~product(e_4, e_3, e_3)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[380, 2241, 373])).
% 1.11/1.04 tff(2243,plain,
% 1.11/1.04 (~product(e_4, e_3, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1477, 2241])).
% 1.11/1.04 tff(2244,plain,
% 1.11/1.04 (~product(e_4, e_3, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[360, 2241])).
% 1.11/1.04 tff(2245,plain,
% 1.11/1.04 (~product(e_4, e_3, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1487, 2241, 818])).
% 1.11/1.04 tff(2246,plain,
% 1.11/1.04 (product(e_4, e_3, e_6)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[534, 2245, 2230, 2244, 2243, 2242])).
% 1.11/1.04 tff(2247,plain,
% 1.11/1.04 (~product(e_4, e_5, e_6)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1941, 2246])).
% 1.11/1.04 tff(2248,plain,
% 1.11/1.04 (~product(e_5, e_1, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[602, 2240])).
% 1.11/1.04 tff(2249,plain,
% 1.11/1.04 (~product(e_5, e_1, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1188, 2239])).
% 1.11/1.04 tff(2250,plain,
% 1.11/1.04 (~product(e_6, e_1, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[729, 2239])).
% 1.11/1.04 tff(2251,plain,
% 1.11/1.04 (~product(e_6, e_1, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[689, 2240])).
% 1.11/1.04 tff(2252,plain,
% 1.11/1.04 (product(e_6, e_1, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[700, 2251, 661, 1715, 2209, 2250])).
% 1.11/1.04 tff(2253,plain,
% 1.11/1.04 (~product(e_5, e_1, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1168, 2252])).
% 1.11/1.04 tff(2254,plain,
% 1.11/1.04 (product(e_5, e_1, e_6)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[629, 2253, 2225, 2249, 2248, 2214])).
% 1.11/1.04 tff(2255,plain,
% 1.11/1.04 ($false),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[800, 2254, 2247, 518])).
% 1.11/1.04 tff(2256,plain,(product(e_6, e_1, e_6) | (~product(e_4, e_1, e_5)) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.04 tff(2257,plain,
% 1.11/1.04 (product(e_6, e_1, e_6) | (~product(e_4, e_1, e_5)) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | (~product(e_2, e_1, e_3))),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2256, 266])).
% 1.11/1.04 tff(2258,plain,
% 1.11/1.04 (product(e_6, e_1, e_6) | (~product(e_4, e_1, e_5)) | product(e_2, e_4, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2257, 207, 372])).
% 1.11/1.04 tff(2259,plain,
% 1.11/1.04 (product(e_2, e_4, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2258, 2173, 661])).
% 1.11/1.04 tff(2260,plain,
% 1.11/1.04 (~product(e_4, e_4, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1437, 2259])).
% 1.11/1.04 tff(2261,plain,
% 1.11/1.04 (~product(e_5, e_4, e_3)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1342, 2176, 1333])).
% 1.11/1.04 tff(2262,plain,
% 1.11/1.04 (product(e_3, e_4, e_5)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[771, 518])).
% 1.11/1.04 tff(2263,plain,
% 1.11/1.04 (~product(e_5, e_4, e_5)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1323, 2262])).
% 1.11/1.04 tff(2264,plain,
% 1.11/1.04 (~product(e_4, e_4, e_3)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1894, 1382, 2263, 1026, 1747, 1891])).
% 1.11/1.04 tff(2265,plain,
% 1.11/1.04 (product(e_4, e_5, e_6)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[800, 1, 518])).
% 1.11/1.04 tff(2266,plain,
% 1.11/1.04 (~product(e_4, e_4, e_6)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[876, 2265])).
% 1.11/1.04 tff(2267,plain,
% 1.11/1.04 (product(e_4, e_4, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[903, 2266, 1561, 1560, 1750, 1659])).
% 1.11/1.04 tff(2268,plain,
% 1.11/1.04 (~product(e_5, e_4, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1573, 2267])).
% 1.11/1.04 tff(2269,plain,
% 1.11/1.04 (product(e_5, e_4, e_6)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1558, 2268, 1747, 1891, 1382, 1689])).
% 1.11/1.04 tff(2270,plain,
% 1.11/1.04 (((~![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_5, e_1, e_6)) | (~product(e_5, 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_1, e_4) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_4, e_6)))),
% 1.11/1.04 inference(rewrite,[status(thm)],[])).
% 1.11/1.04 tff(2271,plain,
% 1.11/1.04 ((equalish(e_1, e_4) | (~product(e_5, e_4, e_6)) | (~product(e_5, e_1, e_6))) <=> (equalish(e_1, e_4) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_4, e_6)))),
% 1.11/1.04 inference(rewrite,[status(thm)],[])).
% 1.11/1.04 tff(2272,plain,
% 1.11/1.04 (((~![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_5, e_4, e_6)) | (~product(e_5, 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_4) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_4, e_6))))),
% 1.11/1.04 inference(monotonicity,[status(thm)],[2271])).
% 1.11/1.04 tff(2273,plain,
% 1.11/1.04 (((~![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_5, e_4, e_6)) | (~product(e_5, 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_4) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_4, e_6)))),
% 1.11/1.04 inference(transitivity,[status(thm)],[2272, 2270])).
% 1.11/1.04 tff(2274,plain,
% 1.11/1.04 ((~![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_5, e_4, e_6)) | (~product(e_5, e_1, e_6)))),
% 1.11/1.04 inference(quant_inst,[status(thm)],[])).
% 1.11/1.04 tff(2275,plain,
% 1.11/1.04 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_4, e_6))),
% 1.11/1.04 inference(modus_ponens,[status(thm)],[2274, 2273])).
% 1.11/1.04 tff(2276,plain,
% 1.11/1.04 ($false),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2275, 1673, 12, 2269, 1])).
% 1.11/1.04 tff(2277,plain,((~product(e_5, e_1, e_6)) | product(e_5, e_4, e_1) | product(e_5, e_4, e_2) | product(e_5, e_4, e_3) | product(e_4, e_4, e_1) | product(e_4, e_4, e_2) | product(e_4, e_4, e_3) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.04 tff(2278,plain,
% 1.11/1.04 ($false),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2277, 2264, 1382, 1, 1747, 1561, 1560, 1891, 518])).
% 1.11/1.04 tff(2279,plain,(product(e_5, e_4, e_3) | (~product(e_5, e_1, e_6)) | product(e_5, e_4, e_1) | product(e_4, e_4, e_1) | product(e_4, e_4, e_2) | product(e_5, e_4, e_2) | (~product(e_4, e_1, e_5)) | product(e_5, e_4, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.04 tff(2280,plain,
% 1.11/1.04 (product(e_4, e_4, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2279, 2261, 2173, 2260, 2172, 2206, 2200, 2191])).
% 1.11/1.04 tff(2281,plain,
% 1.11/1.04 ($false),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1373, 2280, 2181, 2177, 2175])).
% 1.11/1.04 tff(2282,plain,(product(e_6, e_1, e_5) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_4, e_3, e_6) | product(e_6, e_1, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.04 tff(2283,plain,
% 1.11/1.04 (product(e_6, e_1, e_5)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2282, 2171, 2164, 2144, 2054, 2039])).
% 1.11/1.04 tff(2284,plain,
% 1.11/1.04 (~product(e_4, e_1, e_5)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1146, 2283])).
% 1.11/1.04 tff(2285,plain,
% 1.11/1.04 (~product(e_1, e_1, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[515, 2284])).
% 1.11/1.04 tff(2286,plain,
% 1.11/1.04 (product(e_1, e_1, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[154, 2285])).
% 1.11/1.04 tff(2287,plain,
% 1.11/1.04 (~product(e_4, e_1, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[548, 2286])).
% 1.11/1.04 tff(2288,plain,
% 1.11/1.04 (product(e_4, e_1, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[550, 2287, 2284])).
% 1.11/1.04 tff(2289,plain,
% 1.11/1.04 (~product(e_5, e_1, e_6)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2086, 2283, 2061])).
% 1.11/1.04 tff(2290,plain,
% 1.11/1.04 (~product(e_5, e_1, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[582, 2286])).
% 1.11/1.04 tff(2291,plain,
% 1.11/1.04 (product(e_5, e_1, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[631, 2290, 2289])).
% 1.11/1.04 tff(2292,plain,
% 1.11/1.04 ($false),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[569, 2291, 2288])).
% 1.11/1.04 tff(2293,plain,((~product(e_6, e_3, e_6)) | product(e_3, e_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.04 tff(2294,plain,
% 1.11/1.04 (~product(e_6, e_3, e_6)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2293, 1985, 1986, 1025])).
% 1.11/1.04 tff(2295,plain,
% 1.11/1.04 (~product(e_1, e_3, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1032, 374])).
% 1.11/1.04 tff(2296,plain,
% 1.11/1.04 (product(e_1, e_3, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1083, 54, 1025, 2295, 1024, 1027])).
% 1.11/1.04 tff(2297,plain,
% 1.11/1.04 (product(e_1, e_2, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1301, 2296, 374])).
% 1.11/1.04 tff(2298,plain,
% 1.11/1.04 (~product(e_5, e_3, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1982, 374])).
% 1.11/1.04 tff(2299,plain,
% 1.11/1.04 (~product(e_6, e_3, e_4)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1260, 374])).
% 1.11/1.04 tff(2300,plain,
% 1.11/1.04 (product(e_1, e_3, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1083, 54, 1025, 1035, 1024, 1027])).
% 1.11/1.04 tff(2301,plain,
% 1.11/1.04 (~product(e_6, e_3, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1097, 2300])).
% 1.11/1.04 tff(2302,plain,
% 1.11/1.04 (~product(e_3, e_3, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1243, 54, 1027, 1225, 1035])).
% 1.11/1.04 tff(2303,plain,
% 1.11/1.04 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_5, 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_5, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_5, e_3, e_2)))),
% 1.11/1.04 inference(rewrite,[status(thm)],[])).
% 1.11/1.04 tff(2304,plain,
% 1.11/1.04 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_5, e_3, e_2)))),
% 1.11/1.04 inference(quant_inst,[status(thm)],[])).
% 1.11/1.04 tff(2305,plain,
% 1.11/1.04 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_5, e_3, e_2))),
% 1.11/1.04 inference(modus_ponens,[status(thm)],[2304, 2303])).
% 1.11/1.04 tff(2306,plain,
% 1.11/1.04 ($false),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2305, 577, 87, 464, 2003])).
% 1.11/1.04 tff(2307,plain,((~product(e_5, e_3, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.04 tff(2308,plain,
% 1.11/1.04 (~product(e_5, e_3, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2307, 2300])).
% 1.11/1.04 tff(2309,plain,
% 1.11/1.04 (product(e_5, e_3, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2123, 2308, 1986, 1985, 1994, 1025, 2302])).
% 1.11/1.04 tff(2310,assumption,(product(e_5, e_3, e_1)), introduced(assumption)).
% 1.11/1.04 tff(2311,plain,
% 1.11/1.04 (((~![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_3, e_1)) | (~product(e_6, e_3, e_1)))) <=> ((~![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_3, e_1)) | (~product(e_6, e_3, e_1)))),
% 1.11/1.04 inference(rewrite,[status(thm)],[])).
% 1.11/1.04 tff(2312,plain,
% 1.11/1.04 ((equalish(e_5, e_6) | (~product(e_6, e_3, e_1)) | (~product(e_5, e_3, e_1))) <=> (equalish(e_5, e_6) | (~product(e_5, e_3, e_1)) | (~product(e_6, e_3, e_1)))),
% 1.11/1.04 inference(rewrite,[status(thm)],[])).
% 1.11/1.04 tff(2313,plain,
% 1.11/1.04 (((~![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_3, e_1)) | (~product(e_5, e_3, e_1)))) <=> ((~![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_3, e_1)) | (~product(e_6, e_3, e_1))))),
% 1.11/1.04 inference(monotonicity,[status(thm)],[2312])).
% 1.11/1.04 tff(2314,plain,
% 1.11/1.04 (((~![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_3, e_1)) | (~product(e_5, e_3, e_1)))) <=> ((~![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_3, e_1)) | (~product(e_6, e_3, e_1)))),
% 1.11/1.04 inference(transitivity,[status(thm)],[2313, 2311])).
% 1.11/1.04 tff(2315,plain,
% 1.11/1.04 ((~![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_3, e_1)) | (~product(e_5, e_3, e_1)))),
% 1.11/1.04 inference(quant_inst,[status(thm)],[])).
% 1.11/1.04 tff(2316,plain,
% 1.11/1.04 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_5, e_3, e_1)) | (~product(e_6, e_3, e_1))),
% 1.11/1.04 inference(modus_ponens,[status(thm)],[2315, 2314])).
% 1.11/1.04 tff(2317,plain,
% 1.11/1.04 ($false),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2316, 45, 87, 1352, 2310])).
% 1.11/1.04 tff(2318,plain,((~product(e_5, e_3, e_1)) | (~product(e_6, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.04 tff(2319,plain,
% 1.11/1.04 (~product(e_6, e_3, e_1)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2318, 2309])).
% 1.11/1.04 tff(2320,plain,
% 1.11/1.04 (product(e_6, e_3, e_3)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1275, 2319, 1262, 1265, 1267, 2301])).
% 1.11/1.04 tff(2321,plain,
% 1.11/1.04 (~product(e_3, e_3, e_3)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1253, 2320])).
% 1.11/1.04 tff(2322,plain,
% 1.11/1.04 (~product(e_3, e_3, e_2)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1211, 2300])).
% 1.11/1.04 tff(2323,plain,
% 1.11/1.04 (product(e_3, e_3, e_5)),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[1246, 2322, 1025, 2321, 2302])).
% 1.11/1.04 tff(2324,plain,
% 1.11/1.04 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_5)) | product(e_6, e_3, e_5) | (~product(e_6, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_5)) | product(e_6, e_3, e_5) | (~product(e_6, e_3, e_3)))),
% 1.11/1.04 inference(rewrite,[status(thm)],[])).
% 1.11/1.04 tff(2325,plain,
% 1.11/1.04 ((product(e_6, e_3, e_5) | (~product(e_3, e_3, e_5)) | (~product(e_6, e_3, e_3))) <=> ((~product(e_3, e_3, e_5)) | product(e_6, e_3, e_5) | (~product(e_6, e_3, e_3)))),
% 1.11/1.04 inference(rewrite,[status(thm)],[])).
% 1.11/1.04 tff(2326,plain,
% 1.11/1.04 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_3, e_5) | (~product(e_3, e_3, e_5)) | (~product(e_6, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_5)) | product(e_6, e_3, e_5) | (~product(e_6, e_3, e_3))))),
% 1.11/1.04 inference(monotonicity,[status(thm)],[2325])).
% 1.11/1.04 tff(2327,plain,
% 1.11/1.04 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_3, e_5) | (~product(e_3, e_3, e_5)) | (~product(e_6, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_5)) | product(e_6, e_3, e_5) | (~product(e_6, e_3, e_3)))),
% 1.11/1.04 inference(transitivity,[status(thm)],[2326, 2324])).
% 1.11/1.04 tff(2328,plain,
% 1.11/1.04 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_3, e_5) | (~product(e_3, e_3, e_5)) | (~product(e_6, e_3, e_3)))),
% 1.11/1.04 inference(quant_inst,[status(thm)],[])).
% 1.11/1.04 tff(2329,plain,
% 1.11/1.04 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_5)) | product(e_6, e_3, e_5) | (~product(e_6, e_3, e_3))),
% 1.11/1.04 inference(modus_ponens,[status(thm)],[2328, 2327])).
% 1.11/1.04 tff(2330,plain,
% 1.11/1.04 ($false),
% 1.11/1.04 inference(unit_resolution,[status(thm)],[2329, 33, 2323, 1267, 2320])).
% 1.11/1.05 tff(2331,plain,(product(e_1, e_3, e_5) | product(e_6, e_3, e_5) | product(e_3, e_3, e_6) | product(e_6, e_3, e_4) | product(e_6, e_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_5, e_3, e_4) | product(e_1, e_3, e_1) | product(e_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2332,plain,
% 1.11/1.05 (product(e_1, e_3, e_3)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2331, 54, 1025, 2299, 1265, 1986, 1985, 2298, 1027, 1267, 2295, 1024])).
% 1.11/1.05 tff(2333,plain,
% 1.11/1.05 (((~![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_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_3, e_3)))),
% 1.11/1.05 inference(rewrite,[status(thm)],[])).
% 1.11/1.05 tff(2334,plain,
% 1.11/1.05 ((~![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_3)) | (~product(e_1, e_3, e_3)))),
% 1.11/1.05 inference(quant_inst,[status(thm)],[])).
% 1.11/1.05 tff(2335,plain,
% 1.11/1.05 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_3, e_3))),
% 1.11/1.05 inference(modus_ponens,[status(thm)],[2334, 2333])).
% 1.11/1.05 tff(2336,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2335, 974, 12, 453, 1415])).
% 1.11/1.05 tff(2337,plain,((~product(e_1, e_3, e_3)) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2338,plain,
% 1.11/1.05 (~product(e_1, e_4, e_3)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2337, 2332])).
% 1.11/1.05 tff(2339,assumption,(~product(e_1, e_4, e_3)), introduced(assumption)).
% 1.11/1.05 tff(2340,plain,
% 1.11/1.05 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_4, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_4, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_1, e_2, e_4)))),
% 1.11/1.05 inference(rewrite,[status(thm)],[])).
% 1.11/1.05 tff(2341,plain,
% 1.11/1.05 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_4, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_1, e_2, e_4)))),
% 1.11/1.05 inference(quant_inst,[status(thm)],[])).
% 1.11/1.05 tff(2342,plain,
% 1.11/1.05 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_4, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_1, e_2, e_4))),
% 1.11/1.05 inference(modus_ponens,[status(thm)],[2341, 2340])).
% 1.11/1.05 tff(2343,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2342, 33, 889, 2339, 1304])).
% 1.11/1.05 tff(2344,plain,(product(e_1, e_4, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2345,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2344, 2338, 2297, 889])).
% 1.11/1.05 tff(2346,plain,(product(e_1, e_3, e_5) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_4)) | product(e_3, e_3, e_6) | product(e_6, e_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_1, e_3, e_1) | product(e_6, e_3, e_5) | product(e_1, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2347,plain,
% 1.11/1.05 (product(e_1, e_3, e_5) | (~product(e_4, e_2, e_3)) | product(e_3, e_3, e_6) | product(e_6, e_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_1, e_3, e_1) | product(e_6, e_3, e_5) | product(e_1, e_3, e_6)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2346, 330])).
% 1.11/1.05 tff(2348,plain,
% 1.11/1.05 (~product(e_4, e_2, e_3)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2347, 54, 1025, 1265, 1986, 1985, 1027, 1267, 1024])).
% 1.11/1.05 tff(2349,plain,
% 1.11/1.05 (product(e_4, e_2, e_3) | (~product(e_4, e_1, e_2))),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[887, 207])).
% 1.11/1.05 tff(2350,plain,
% 1.11/1.05 (~product(e_4, e_1, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2349, 2348])).
% 1.11/1.05 tff(2351,plain,
% 1.11/1.05 (~product(e_1, e_1, e_1)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[548, 540])).
% 1.11/1.05 tff(2352,plain,
% 1.11/1.05 (~product(e_1, e_1, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[394, 540, 463])).
% 1.11/1.05 tff(2353,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[154, 2352, 2351])).
% 1.11/1.05 tff(2354,plain,((~product(e_4, e_1, e_1)) | product(e_4, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2355,plain,
% 1.11/1.05 (~product(e_4, e_1, e_1)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2354, 2350])).
% 1.11/1.05 tff(2356,plain,
% 1.11/1.05 (product(e_1, e_3, e_3)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2331, 54, 1025, 1024, 1262, 1986, 1985, 1994, 1027, 1267, 1035, 1265])).
% 1.11/1.05 tff(2357,plain,
% 1.11/1.05 (product(e_1, e_3, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1083, 54, 1024, 1035, 1025, 1027])).
% 1.11/1.05 tff(2358,plain,
% 1.11/1.05 (~product(e_3, e_3, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1211, 2357])).
% 1.11/1.05 tff(2359,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1077, 2358, 2356, 1025, 1053])).
% 1.11/1.05 tff(2360,plain,(product(e_1, e_3, e_5) | product(e_3, e_3, e_6) | product(e_3, e_3, e_5) | product(e_1, e_3, e_6) | product(e_6, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_5, e_3, e_4) | product(e_1, e_3, e_1) | product(e_6, e_3, e_5) | product(e_1, e_3, e_4) | product(e_6, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2361,plain,
% 1.11/1.05 (product(e_1, e_3, e_5) | product(e_3, e_3, e_6) | product(e_3, e_3, e_5) | product(e_1, e_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_1, e_3, e_1) | product(e_6, e_3, e_5) | product(e_6, e_3, e_6)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2360, 1261, 1983, 1033])).
% 1.11/1.05 tff(2362,plain,
% 1.11/1.05 (product(e_3, e_3, e_5)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2361, 54, 1265, 1024, 1986, 1985, 1027, 1267, 1025])).
% 1.11/1.05 tff(2363,plain,
% 1.11/1.05 (~product(e_3, e_4, e_5)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1221, 2362])).
% 1.11/1.05 tff(2364,plain,
% 1.11/1.05 (~product(e_4, e_1, e_5)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[771, 2363])).
% 1.11/1.05 tff(2365,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[550, 2364, 2355, 2350])).
% 1.11/1.05 tff(2366,plain,(product(e_1, e_3, e_5) | product(e_6, e_3, e_6) | product(e_1, e_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_1, e_3, e_1) | product(e_6, e_3, e_5) | product(e_3, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2367,plain,
% 1.11/1.05 (product(e_1, e_3, e_5)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2366, 1265, 1024, 1986, 1985, 1027, 1267, 1025])).
% 1.11/1.05 tff(2368,plain,
% 1.11/1.05 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3)))),
% 1.11/1.05 inference(rewrite,[status(thm)],[])).
% 1.11/1.05 tff(2369,plain,
% 1.11/1.05 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3)))),
% 1.11/1.05 inference(quant_inst,[status(thm)],[])).
% 1.11/1.05 tff(2370,plain,
% 1.11/1.05 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3))),
% 1.11/1.05 inference(modus_ponens,[status(thm)],[2369, 2368])).
% 1.11/1.05 tff(2371,plain,
% 1.11/1.05 (~product(e_1, e_3, e_3)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2370, 33, 1027, 1224])).
% 1.11/1.05 tff(2372,plain,
% 1.11/1.05 (product(e_1, e_3, e_5)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2331, 2371, 1025, 1262, 1265, 1986, 1985, 1994, 1027, 1267, 1035, 1024])).
% 1.11/1.05 tff(2373,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2093, 33, 286, 2372, 1224])).
% 1.11/1.05 tff(2374,plain,((~product(e_3, e_3, e_1)) | product(e_3, e_3, e_6) | product(e_6, e_3, e_4) | product(e_6, e_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_5, e_3, e_4) | product(e_1, e_3, e_1) | product(e_6, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2375,plain,
% 1.11/1.05 ((~product(e_3, e_3, e_1)) | product(e_3, e_3, e_6) | product(e_6, e_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_1, e_3, e_1) | product(e_6, e_3, e_5) | product(e_1, e_3, e_6)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2374, 1261, 1983, 1033])).
% 1.11/1.05 tff(2376,plain,
% 1.11/1.05 (~product(e_3, e_3, e_1)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2375, 1265, 1025, 1986, 1985, 1027, 1267, 1024])).
% 1.11/1.05 tff(2377,plain,
% 1.11/1.05 (~product(e_5, e_3, e_1)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1965, 33, 2367, 619])).
% 1.11/1.05 tff(2378,plain,
% 1.11/1.05 (product(e_5, e_3, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2124, 2377, 1025, 1986, 1985, 2376])).
% 1.11/1.05 tff(2379,plain,
% 1.11/1.05 (product(e_1, e_5, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2132, 2378, 2367])).
% 1.11/1.05 tff(2380,plain,
% 1.11/1.05 (((~![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_2)) | (~product(e_1, 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_4) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_5, e_2)))),
% 1.11/1.05 inference(rewrite,[status(thm)],[])).
% 1.11/1.05 tff(2381,plain,
% 1.11/1.05 ((~![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_2)) | (~product(e_1, e_5, e_2)))),
% 1.11/1.05 inference(quant_inst,[status(thm)],[])).
% 1.11/1.05 tff(2382,plain,
% 1.11/1.05 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_5, e_2))),
% 1.11/1.05 inference(modus_ponens,[status(thm)],[2381, 2380])).
% 1.11/1.05 tff(2383,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2382, 561, 12, 1278, 2134])).
% 1.11/1.05 tff(2384,plain,((~product(e_1, e_5, e_2)) | (~product(e_1, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2385,plain,
% 1.11/1.05 (~product(e_1, e_4, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2384, 2379])).
% 1.11/1.05 tff(2386,plain,
% 1.11/1.05 (~product(e_3, e_3, e_5)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2155, 2367])).
% 1.11/1.05 tff(2387,plain,
% 1.11/1.05 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_5, e_3, e_4) | (~product(e_5, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_5, e_3, e_4) | (~product(e_5, e_1, e_3)))),
% 1.11/1.05 inference(rewrite,[status(thm)],[])).
% 1.11/1.05 tff(2388,plain,
% 1.11/1.05 ((product(e_5, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_3))) <=> ((~product(e_3, e_1, e_4)) | product(e_5, e_3, e_4) | (~product(e_5, e_1, e_3)))),
% 1.11/1.05 inference(rewrite,[status(thm)],[])).
% 1.11/1.05 tff(2389,plain,
% 1.11/1.05 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_5, e_3, e_4) | (~product(e_5, e_1, e_3))))),
% 1.11/1.05 inference(monotonicity,[status(thm)],[2388])).
% 1.11/1.05 tff(2390,plain,
% 1.11/1.05 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_5, e_3, e_4) | (~product(e_5, e_1, e_3)))),
% 1.11/1.05 inference(transitivity,[status(thm)],[2389, 2387])).
% 1.11/1.05 tff(2391,plain,
% 1.11/1.05 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_3)))),
% 1.11/1.05 inference(quant_inst,[status(thm)],[])).
% 1.11/1.05 tff(2392,plain,
% 1.11/1.05 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_5, e_3, e_4) | (~product(e_5, e_1, e_3))),
% 1.11/1.05 inference(modus_ponens,[status(thm)],[2391, 2390])).
% 1.11/1.05 tff(2393,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2392, 33, 324, 584, 1994])).
% 1.11/1.05 tff(2394,plain,(product(e_5, e_3, e_4) | (~product(e_5, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2395,plain,
% 1.11/1.05 (~product(e_5, e_1, e_3)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2394, 1994])).
% 1.11/1.05 tff(2396,plain,
% 1.11/1.05 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_3)) | product(e_6, e_3, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_3)) | product(e_6, e_3, e_4))),
% 1.11/1.05 inference(rewrite,[status(thm)],[])).
% 1.11/1.05 tff(2397,plain,
% 1.11/1.05 ((product(e_6, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_3))) <=> ((~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_3)) | product(e_6, e_3, e_4))),
% 1.11/1.05 inference(rewrite,[status(thm)],[])).
% 1.11/1.05 tff(2398,plain,
% 1.11/1.05 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_3)) | product(e_6, e_3, e_4)))),
% 1.11/1.05 inference(monotonicity,[status(thm)],[2397])).
% 1.11/1.05 tff(2399,plain,
% 1.11/1.05 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_3)) | product(e_6, e_3, e_4))),
% 1.11/1.05 inference(transitivity,[status(thm)],[2398, 2396])).
% 1.11/1.05 tff(2400,plain,
% 1.11/1.05 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_3)))),
% 1.11/1.05 inference(quant_inst,[status(thm)],[])).
% 1.11/1.05 tff(2401,plain,
% 1.11/1.05 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_3)) | product(e_6, e_3, e_4)),
% 1.11/1.05 inference(modus_ponens,[status(thm)],[2400, 2399])).
% 1.11/1.05 tff(2402,plain,
% 1.11/1.05 (~product(e_6, e_1, e_3)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2401, 33, 324, 1262])).
% 1.11/1.05 tff(2403,plain,
% 1.11/1.05 (~product(e_5, e_1, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1180, 56])).
% 1.11/1.05 tff(2404,plain,
% 1.11/1.05 (product(e_6, e_1, e_6)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[713, 56, 663, 662])).
% 1.11/1.05 tff(2405,plain,
% 1.11/1.05 (~product(e_5, e_1, e_6)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[641, 2404])).
% 1.11/1.05 tff(2406,plain,
% 1.11/1.05 (~product(e_5, e_1, e_1)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[582, 673])).
% 1.11/1.05 tff(2407,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[630, 2406, 2405, 1148, 2403])).
% 1.11/1.05 tff(2408,plain,((~product(e_2, e_1, e_2)) | product(e_5, e_1, e_3) | product(e_6, e_1, e_3) | product(e_6, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2409,plain,
% 1.11/1.05 (~product(e_2, e_1, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2408, 2402, 2395, 662])).
% 1.11/1.05 tff(2410,plain,
% 1.11/1.05 (product(e_2, e_1, e_3)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[206, 2409])).
% 1.11/1.05 tff(2411,plain,
% 1.11/1.05 (product(e_2, e_3, e_4)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[329, 2410])).
% 1.11/1.05 tff(2412,plain,
% 1.11/1.05 (~product(e_1, e_3, e_4)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1032, 2411])).
% 1.11/1.05 tff(2413,plain,
% 1.11/1.05 (~product(e_3, e_3, e_1)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2374, 1265, 1025, 1262, 1986, 1985, 1994, 1027, 1267, 2412, 1024])).
% 1.11/1.05 tff(2414,plain,
% 1.11/1.05 (product(e_1, e_3, e_5)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2360, 1265, 1053, 1024, 1262, 1986, 1985, 1994, 1027, 1267, 2412, 1025])).
% 1.11/1.05 tff(2415,plain,
% 1.11/1.05 (~product(e_5, e_3, e_1)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1965, 33, 2414, 619])).
% 1.11/1.05 tff(2416,plain,
% 1.11/1.05 (product(e_5, e_3, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2123, 2415, 1025, 1986, 1985, 1994, 2413])).
% 1.11/1.05 tff(2417,plain,
% 1.11/1.05 (~product(e_1, e_3, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2307, 2416])).
% 1.11/1.05 tff(2418,plain,
% 1.11/1.05 (~product(e_3, e_3, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2149, 2416])).
% 1.11/1.05 tff(2419,plain,
% 1.11/1.05 (~product(e_6, e_3, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2008, 2416])).
% 1.11/1.05 tff(2420,plain,
% 1.11/1.05 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_4)) | product(e_6, e_3, e_4) | (~product(e_6, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_4)) | product(e_6, e_3, e_4) | (~product(e_6, e_3, e_3)))),
% 1.11/1.05 inference(rewrite,[status(thm)],[])).
% 1.11/1.05 tff(2421,plain,
% 1.11/1.05 ((product(e_6, e_3, e_4) | (~product(e_3, e_3, e_4)) | (~product(e_6, e_3, e_3))) <=> ((~product(e_3, e_3, e_4)) | product(e_6, e_3, e_4) | (~product(e_6, e_3, e_3)))),
% 1.11/1.05 inference(rewrite,[status(thm)],[])).
% 1.11/1.05 tff(2422,plain,
% 1.11/1.05 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_3, e_4) | (~product(e_3, e_3, e_4)) | (~product(e_6, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_4)) | product(e_6, e_3, e_4) | (~product(e_6, e_3, e_3))))),
% 1.11/1.05 inference(monotonicity,[status(thm)],[2421])).
% 1.11/1.05 tff(2423,plain,
% 1.11/1.05 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_3, e_4) | (~product(e_3, e_3, e_4)) | (~product(e_6, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_4)) | product(e_6, e_3, e_4) | (~product(e_6, e_3, e_3)))),
% 1.11/1.05 inference(transitivity,[status(thm)],[2422, 2420])).
% 1.11/1.05 tff(2424,plain,
% 1.11/1.05 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_3, e_4) | (~product(e_3, e_3, e_4)) | (~product(e_6, e_3, e_3)))),
% 1.11/1.05 inference(quant_inst,[status(thm)],[])).
% 1.11/1.05 tff(2425,plain,
% 1.11/1.05 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_4)) | product(e_6, e_3, e_4) | (~product(e_6, e_3, e_3))),
% 1.11/1.05 inference(modus_ponens,[status(thm)],[2424, 2423])).
% 1.11/1.05 tff(2426,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2425, 33, 1047, 1262, 1248])).
% 1.11/1.05 tff(2427,plain,((~product(e_3, e_3, e_4)) | product(e_6, e_3, e_4) | (~product(e_6, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2428,plain,
% 1.11/1.05 (~product(e_3, e_3, e_4)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2427, 1248, 1262])).
% 1.11/1.05 tff(2429,plain,
% 1.11/1.05 (~product(e_3, e_3, e_3)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1253, 1248])).
% 1.11/1.05 tff(2430,plain,
% 1.11/1.05 (~product(e_1, e_3, e_5)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2161, 2429, 1025, 2428, 1054])).
% 1.11/1.05 tff(2431,plain,
% 1.11/1.05 (~product(e_1, e_3, e_3)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1075, 2428, 1053, 1054, 1025, 223])).
% 1.11/1.05 tff(2432,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[480, 2431, 2430, 1035, 1024, 1027, 1034])).
% 1.11/1.05 tff(2433,plain,((~product(e_6, e_3, e_3)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_6) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2) | product(e_3, e_3, e_5) | product(e_3, e_3, e_2) | product(e_3, e_3, e_6) | product(e_6, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2434,plain,
% 1.11/1.05 (~product(e_6, e_3, e_3)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2433, 1025, 1024, 1027, 1034, 1053, 1054, 1035, 1262])).
% 1.11/1.05 tff(2435,plain,
% 1.11/1.05 (product(e_6, e_3, e_1)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1275, 2434, 1265, 1264, 1267, 1262])).
% 1.11/1.05 tff(2436,plain,
% 1.11/1.05 (~product(e_1, e_3, e_5)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1975, 2435, 662])).
% 1.11/1.05 tff(2437,plain,
% 1.11/1.05 (product(e_1, e_3, e_3)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[480, 2436, 1035, 1024, 1027, 1034])).
% 1.11/1.05 tff(2438,plain,
% 1.11/1.05 (product(e_3, e_3, e_4)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1075, 2437, 1053, 1054, 1025, 223])).
% 1.11/1.05 tff(2439,plain,
% 1.11/1.05 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_4) | (~product(e_3, e_3, e_4)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_4) | (~product(e_3, e_3, e_4)) | (~product(e_1, e_3, e_3)))),
% 1.11/1.05 inference(rewrite,[status(thm)],[])).
% 1.11/1.05 tff(2440,plain,
% 1.11/1.05 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_4) | (~product(e_3, e_3, e_4)) | (~product(e_1, e_3, e_3)))),
% 1.11/1.05 inference(quant_inst,[status(thm)],[])).
% 1.11/1.05 tff(2441,plain,
% 1.11/1.05 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_4) | (~product(e_3, e_3, e_4)) | (~product(e_1, e_3, e_3))),
% 1.11/1.05 inference(modus_ponens,[status(thm)],[2440, 2439])).
% 1.11/1.05 tff(2442,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2441, 33, 1035, 2437, 2438])).
% 1.11/1.05 tff(2443,plain,(product(e_3, e_3, e_6) | product(e_1, e_3, e_4) | product(e_3, e_3, e_5) | product(e_3, e_3, e_2) | product(e_1, e_3, e_6) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2) | product(e_6, e_1, e_5) | product(e_6, e_3, e_6) | product(e_6, e_3, e_2) | product(e_6, e_3, e_5) | product(e_6, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2444,plain,
% 1.11/1.05 ($false),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2443, 2419, 2418, 662, 1262, 1024, 1025, 1265, 1053, 1027, 2417, 1267, 2412])).
% 1.11/1.05 tff(2445,plain,(product(e_6, e_3, e_6) | product(e_6, e_1, e_5) | product(e_6, e_3, e_4) | product(e_1, e_3, e_6) | product(e_3, e_3, e_6) | product(e_3, e_3, e_5) | product(e_1, e_3, e_1) | product(e_6, e_3, e_5) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_5, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.05 tff(2446,plain,
% 1.11/1.05 (product(e_6, e_3, e_6) | product(e_6, e_1, e_5) | product(e_1, e_3, e_6) | product(e_3, e_3, e_6) | product(e_3, e_3, e_5) | product(e_1, e_3, e_1) | product(e_6, e_3, e_5) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2445, 1261, 1983])).
% 1.11/1.05 tff(2447,plain,
% 1.11/1.05 (product(e_6, e_1, e_5)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[2446, 2386, 1024, 1025, 1265, 1027, 1267, 1986, 1985])).
% 1.11/1.05 tff(2448,plain,
% 1.11/1.05 (~product(e_4, e_1, e_5)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1146, 2447])).
% 1.11/1.05 tff(2449,plain,
% 1.11/1.05 (~product(e_1, e_1, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[515, 2448])).
% 1.11/1.05 tff(2450,plain,
% 1.11/1.05 (product(e_1, e_1, e_1)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[154, 2449])).
% 1.11/1.05 tff(2451,plain,
% 1.11/1.05 (~product(e_1, e_4, e_1)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[1393, 2450])).
% 1.11/1.05 tff(2452,plain,
% 1.11/1.05 (~product(e_4, e_1, e_1)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[548, 2450])).
% 1.11/1.05 tff(2453,plain,
% 1.11/1.05 (product(e_4, e_1, e_2)),
% 1.11/1.05 inference(unit_resolution,[status(thm)],[550, 2452, 2448])).
% 1.11/1.05 tff(2454,plain,
% 1.11/1.05 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, 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_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_4, e_2)))),
% 1.11/1.05 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2455,plain,
% 1.11/1.06 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_4, e_2)))),
% 1.11/1.06 inference(quant_inst,[status(thm)],[])).
% 1.11/1.06 tff(2456,plain,
% 1.11/1.06 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_4, e_2))),
% 1.11/1.06 inference(modus_ponens,[status(thm)],[2455, 2454])).
% 1.11/1.06 tff(2457,plain,
% 1.11/1.06 ($false),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2456, 366, 12, 384, 814])).
% 1.11/1.06 tff(2458,plain,((~product(e_4, e_4, e_2)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.06 tff(2459,plain,
% 1.11/1.06 (~product(e_4, e_4, e_2)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2458, 2453])).
% 1.11/1.06 tff(2460,plain,
% 1.11/1.06 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_4, e_3, e_1)))),
% 1.11/1.06 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2461,plain,
% 1.11/1.06 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_4, e_3, e_1)))),
% 1.11/1.06 inference(quant_inst,[status(thm)],[])).
% 1.11/1.06 tff(2462,plain,
% 1.11/1.06 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_4, e_3, e_1))),
% 1.11/1.06 inference(modus_ponens,[status(thm)],[2461, 2460])).
% 1.11/1.06 tff(2463,plain,
% 1.11/1.06 (~product(e_4, e_3, e_1)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2462, 33, 2448, 2367])).
% 1.11/1.06 tff(2464,plain,
% 1.11/1.06 (~product(e_5, e_1, e_1)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[582, 2450])).
% 1.11/1.06 tff(2465,plain,
% 1.11/1.06 (~product(e_5, e_1, e_2)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[569, 2453])).
% 1.11/1.06 tff(2466,plain,
% 1.11/1.06 (product(e_5, e_1, e_6)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[631, 2465, 2464])).
% 1.11/1.06 tff(2467,plain,
% 1.11/1.06 (product(e_6, e_5, e_6)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2086, 2466, 2447])).
% 1.11/1.06 tff(2468,assumption,(product(e_2, e_5, e_6)), introduced(assumption)).
% 1.11/1.06 tff(2469,plain,
% 1.11/1.06 (((~![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_5, e_6)) | (~product(e_6, 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_6, e_2) | (~product(e_2, e_5, e_6)) | (~product(e_6, e_5, e_6)))),
% 1.11/1.06 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2470,plain,
% 1.11/1.06 ((~![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_5, e_6)) | (~product(e_6, e_5, e_6)))),
% 1.11/1.06 inference(quant_inst,[status(thm)],[])).
% 1.11/1.06 tff(2471,plain,
% 1.11/1.06 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_2) | (~product(e_2, e_5, e_6)) | (~product(e_6, e_5, e_6))),
% 1.11/1.06 inference(modus_ponens,[status(thm)],[2470, 2469])).
% 1.11/1.06 tff(2472,plain,
% 1.11/1.06 ($false),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2471, 654, 87, 2468, 2055])).
% 1.11/1.06 tff(2473,plain,((~product(e_6, e_5, e_6)) | (~product(e_2, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.06 tff(2474,plain,
% 1.11/1.06 (~product(e_2, e_5, e_6)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2473, 2467])).
% 1.11/1.06 tff(2475,plain,
% 1.11/1.06 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_2, e_5, e_1)) | (~product(e_1, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_2, e_5, e_1)) | (~product(e_1, e_5, e_2)))),
% 1.11/1.06 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2476,plain,
% 1.11/1.06 ((product(e_2, e_1, e_2) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_5, e_1))) <=> (product(e_2, e_1, e_2) | (~product(e_2, e_5, e_1)) | (~product(e_1, e_5, e_2)))),
% 1.11/1.06 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2477,plain,
% 1.11/1.06 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_2, e_5, e_1)) | (~product(e_1, e_5, e_2))))),
% 1.11/1.06 inference(monotonicity,[status(thm)],[2476])).
% 1.11/1.06 tff(2478,plain,
% 1.11/1.06 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_2, e_5, e_1)) | (~product(e_1, e_5, e_2)))),
% 1.11/1.06 inference(transitivity,[status(thm)],[2477, 2475])).
% 1.11/1.06 tff(2479,plain,
% 1.11/1.06 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_5, e_1)))),
% 1.11/1.06 inference(quant_inst,[status(thm)],[])).
% 1.11/1.06 tff(2480,plain,
% 1.11/1.06 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_2, e_5, e_1)) | (~product(e_1, e_5, e_2))),
% 1.11/1.06 inference(modus_ponens,[status(thm)],[2479, 2478])).
% 1.11/1.06 tff(2481,plain,
% 1.11/1.06 (~product(e_2, e_5, e_1)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2480, 33, 75, 2379])).
% 1.11/1.06 tff(2482,assumption,(product(e_2, e_5, e_3)), introduced(assumption)).
% 1.11/1.06 tff(2483,plain,
% 1.11/1.06 (((~![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_2, e_1, e_3)) | (~product(e_2, 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_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))),
% 1.11/1.06 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2484,plain,
% 1.11/1.06 ((~![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_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))),
% 1.11/1.06 inference(quant_inst,[status(thm)],[])).
% 1.11/1.06 tff(2485,plain,
% 1.11/1.06 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3))),
% 1.11/1.06 inference(modus_ponens,[status(thm)],[2484, 2483])).
% 1.11/1.06 tff(2486,plain,
% 1.11/1.06 ($false),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2485, 577, 12, 363, 2482])).
% 1.11/1.06 tff(2487,plain,((~product(e_2, e_5, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.06 tff(2488,plain,
% 1.11/1.06 (~product(e_2, e_5, e_3)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2487, 207])).
% 1.11/1.06 tff(2489,assumption,(product(e_2, e_5, e_2)), introduced(assumption)).
% 1.11/1.06 tff(2490,plain,
% 1.11/1.06 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2)))),
% 1.11/1.06 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2491,plain,
% 1.11/1.06 ((product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_5, e_2))) <=> (product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2)))),
% 1.11/1.06 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2492,plain,
% 1.11/1.06 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2))))),
% 1.11/1.06 inference(monotonicity,[status(thm)],[2491])).
% 1.11/1.06 tff(2493,plain,
% 1.11/1.06 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2)))),
% 1.11/1.06 inference(transitivity,[status(thm)],[2492, 2490])).
% 1.11/1.06 tff(2494,plain,
% 1.11/1.06 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_5, e_2)))),
% 1.11/1.06 inference(quant_inst,[status(thm)],[])).
% 1.11/1.06 tff(2495,plain,
% 1.11/1.06 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2))),
% 1.11/1.06 inference(modus_ponens,[status(thm)],[2494, 2493])).
% 1.11/1.06 tff(2496,plain,
% 1.11/1.06 (product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2))),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2495, 33])).
% 1.11/1.06 tff(2497,plain,
% 1.11/1.06 (product(e_2, e_2, e_2)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2496, 2489])).
% 1.11/1.06 tff(2498,plain,
% 1.11/1.06 (((~![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_2, e_5, 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_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2)))),
% 1.11/1.06 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2499,plain,
% 1.11/1.06 ((equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2))) <=> (equalish(e_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2)))),
% 1.11/1.06 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2500,plain,
% 1.11/1.06 (((~![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_2, e_2, e_2)) | (~product(e_2, 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_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2))))),
% 1.11/1.06 inference(monotonicity,[status(thm)],[2499])).
% 1.11/1.06 tff(2501,plain,
% 1.11/1.06 (((~![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_2, e_2, e_2)) | (~product(e_2, 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_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2)))),
% 1.11/1.06 inference(transitivity,[status(thm)],[2500, 2498])).
% 1.11/1.06 tff(2502,plain,
% 1.11/1.06 ((~![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_2, e_2, e_2)) | (~product(e_2, e_5, e_2)))),
% 1.11/1.06 inference(quant_inst,[status(thm)],[])).
% 1.11/1.06 tff(2503,plain,
% 1.11/1.06 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2))),
% 1.11/1.06 inference(modus_ponens,[status(thm)],[2502, 2501])).
% 1.11/1.06 tff(2504,plain,
% 1.11/1.06 ($false),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2503, 587, 12, 2489, 2497])).
% 1.11/1.06 tff(2505,plain,(~product(e_2, e_5, e_2)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.06 tff(2506,plain,
% 1.11/1.06 (((~![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_5)) | product(e_2, e_5, e_1) | product(e_2, e_5, e_4) | product(e_2, e_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, 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_2)) | (~group_element(e_5)) | product(e_2, e_5, e_1) | product(e_2, e_5, e_4) | product(e_2, e_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2))),
% 1.11/1.06 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2507,plain,
% 1.11/1.06 ((product(e_2, e_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_1) | product(e_2, e_5, e_4) | product(e_2, e_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2))),
% 1.11/1.06 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2508,plain,
% 1.11/1.06 (((~![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_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)) | (~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)))) | ((~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_1) | product(e_2, e_5, e_4) | product(e_2, e_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2)))),
% 1.11/1.06 inference(monotonicity,[status(thm)],[2507])).
% 1.11/1.06 tff(2509,plain,
% 1.11/1.06 (((~![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_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)) | (~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)))) | (~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_1) | product(e_2, e_5, e_4) | product(e_2, e_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2))),
% 1.11/1.06 inference(transitivity,[status(thm)],[2508, 2506])).
% 1.11/1.06 tff(2510,plain,
% 1.11/1.06 ((~![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_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_2)))),
% 1.11/1.06 inference(quant_inst,[status(thm)],[])).
% 1.11/1.06 tff(2511,plain,
% 1.11/1.06 ((~![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_5)) | product(e_2, e_5, e_1) | product(e_2, e_5, e_4) | product(e_2, e_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2)),
% 1.11/1.06 inference(modus_ponens,[status(thm)],[2510, 2509])).
% 1.11/1.06 tff(2512,plain,
% 1.11/1.06 (product(e_2, e_5, e_1) | product(e_2, e_5, e_4) | product(e_2, e_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2511, 198, 622, 144])).
% 1.11/1.06 tff(2513,plain,
% 1.11/1.06 (product(e_2, e_5, e_1) | product(e_2, e_5, e_4) | product(e_2, e_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2512, 2505])).
% 1.11/1.06 tff(2514,plain,
% 1.11/1.06 (product(e_2, e_5, e_1) | product(e_2, e_5, e_6) | product(e_2, e_5, e_5)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2513, 2488, 1656])).
% 1.11/1.06 tff(2515,plain,
% 1.11/1.06 (product(e_2, e_5, e_5)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2514, 2481, 2474])).
% 1.11/1.06 tff(2516,assumption,(product(e_2, e_5, e_5)), introduced(assumption)).
% 1.11/1.06 tff(2517,plain,
% 1.11/1.06 (((~![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_2, e_4, e_5)) | (~product(e_2, 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_4, e_5) | (~product(e_2, e_4, e_5)) | (~product(e_2, e_5, e_5)))),
% 1.11/1.06 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2518,plain,
% 1.11/1.06 ((equalish(e_4, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_2, e_4, e_5))) <=> (equalish(e_4, e_5) | (~product(e_2, e_4, e_5)) | (~product(e_2, e_5, e_5)))),
% 1.11/1.06 inference(rewrite,[status(thm)],[])).
% 1.11/1.06 tff(2519,plain,
% 1.11/1.06 (((~![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_2, e_5, e_5)) | (~product(e_2, 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_5) | (~product(e_2, e_4, e_5)) | (~product(e_2, e_5, e_5))))),
% 1.11/1.06 inference(monotonicity,[status(thm)],[2518])).
% 1.11/1.06 tff(2520,plain,
% 1.11/1.06 (((~![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_2, e_5, e_5)) | (~product(e_2, 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_5) | (~product(e_2, e_4, e_5)) | (~product(e_2, e_5, e_5)))),
% 1.11/1.06 inference(transitivity,[status(thm)],[2519, 2517])).
% 1.11/1.06 tff(2521,plain,
% 1.11/1.06 ((~![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_2, e_5, e_5)) | (~product(e_2, e_4, e_5)))),
% 1.11/1.06 inference(quant_inst,[status(thm)],[])).
% 1.11/1.06 tff(2522,plain,
% 1.11/1.06 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_2, e_4, e_5)) | (~product(e_2, e_5, e_5))),
% 1.11/1.06 inference(modus_ponens,[status(thm)],[2521, 2520])).
% 1.11/1.06 tff(2523,plain,
% 1.11/1.06 ($false),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2522, 871, 12, 2516, 774])).
% 1.11/1.06 tff(2524,plain,((~product(e_2, e_4, e_5)) | (~product(e_2, e_5, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.06 tff(2525,plain,
% 1.11/1.06 (~product(e_2, e_4, e_5)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2524, 2515])).
% 1.11/1.06 tff(2526,plain,
% 1.11/1.06 ($false),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[1493, 33, 517, 374, 816])).
% 1.11/1.06 tff(2527,plain,(product(e_2, e_4, e_5) | (~product(e_4, e_3, e_5)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.06 tff(2528,plain,
% 1.11/1.06 (product(e_2, e_4, e_5) | (~product(e_4, e_3, e_5))),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2527, 330])).
% 1.11/1.06 tff(2529,plain,
% 1.11/1.06 (~product(e_4, e_3, e_5)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2528, 2525])).
% 1.11/1.06 tff(2530,plain,
% 1.11/1.06 (product(e_4, e_3, e_6)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2179, 2529, 2463])).
% 1.11/1.06 tff(2531,plain,
% 1.11/1.06 (~product(e_4, e_4, e_6)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[1379, 2530])).
% 1.11/1.06 tff(2532,plain,
% 1.11/1.06 (~product(e_2, e_1, e_2)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[2073, 1004])).
% 1.11/1.06 tff(2533,plain,
% 1.11/1.06 (product(e_2, e_1, e_3)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[206, 2532])).
% 1.11/1.06 tff(2534,plain,
% 1.11/1.06 (~product(e_6, e_1, e_3)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[659, 2533])).
% 1.11/1.06 tff(2535,plain,
% 1.11/1.06 (~product(e_5, e_1, e_2)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[569, 1004])).
% 1.11/1.06 tff(2536,plain,
% 1.11/1.06 (~product(e_5, e_1, e_3)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[592, 2533])).
% 1.11/1.06 tff(2537,plain,
% 1.11/1.06 (product(e_5, e_1, e_6)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[630, 2536, 2535, 1005])).
% 1.11/1.06 tff(2538,plain,
% 1.11/1.06 (~product(e_6, e_1, e_6)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[641, 2537])).
% 1.11/1.06 tff(2539,plain,
% 1.11/1.06 (product(e_6, e_1, e_5)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[701, 2538, 2534, 1108, 1107])).
% 1.11/1.06 tff(2540,plain,
% 1.11/1.06 (~product(e_6, e_3, e_5)),
% 1.11/1.06 inference(unit_resolution,[status(thm)],[1105, 2539])).
% 1.11/1.06 tff(2541,plain,
% 1.11/1.06 (product(e_4, e_2, e_3)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[887, 2533, 1004])).
% 1.11/1.07 tff(2542,plain,
% 1.11/1.07 (product(e_2, e_3, e_4)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[329, 2533])).
% 1.11/1.07 tff(2543,plain,
% 1.11/1.07 (~product(e_4, e_4, e_3)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[895, 2541])).
% 1.11/1.07 tff(2544,plain,
% 1.11/1.07 (~product(e_2, e_5, e_4)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[1655, 2542])).
% 1.11/1.07 tff(2545,plain,
% 1.11/1.07 (~product(e_2, e_5, e_3)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2487, 2533])).
% 1.11/1.07 tff(2546,plain,
% 1.11/1.07 (~product(e_6, e_1, e_6)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[641, 1])).
% 1.11/1.07 tff(2547,plain,
% 1.11/1.07 (~product(e_6, e_1, e_5)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2086, 1, 2062])).
% 1.11/1.07 tff(2548,plain,
% 1.11/1.07 ($false),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[700, 2547, 2546, 1870, 1745, 663, 1160])).
% 1.11/1.07 tff(2549,plain,((~product(e_5, e_1, e_6)) | product(e_6, e_1, e_4) | product(e_6, e_1, e_1) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_5, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.07 tff(2550,plain,
% 1.11/1.07 ((~product(e_5, e_1, e_6)) | product(e_6, e_1, e_1) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_5, e_6)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2549, 690])).
% 1.11/1.07 tff(2551,plain,
% 1.11/1.07 (product(e_6, e_5, e_6)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2550, 2534, 2537, 1108, 1107])).
% 1.11/1.07 tff(2552,plain,
% 1.11/1.07 (~product(e_2, e_5, e_6)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2473, 2551])).
% 1.11/1.07 tff(2553,plain,
% 1.11/1.07 (~product(e_4, e_3, e_3)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[380, 2542, 373])).
% 1.11/1.07 tff(2554,plain,
% 1.11/1.07 (~product(e_4, e_3, e_1)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[1487, 2542, 818])).
% 1.11/1.07 tff(2555,plain,
% 1.11/1.07 (~product(e_4, e_3, e_2)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[360, 2542])).
% 1.11/1.07 tff(2556,plain,
% 1.11/1.07 (product(e_4, e_3, e_5)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[535, 2555, 55, 2554, 2553])).
% 1.11/1.07 tff(2557,plain,
% 1.11/1.07 (product(e_2, e_4, e_5)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2527, 2556, 2542])).
% 1.11/1.07 tff(2558,plain,
% 1.11/1.07 (~product(e_2, e_5, e_5)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2524, 2557])).
% 1.11/1.07 tff(2559,assumption,(product(e_4, e_5, e_2)), introduced(assumption)).
% 1.11/1.07 tff(2560,plain,
% 1.11/1.07 (((~![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)))),
% 1.11/1.07 inference(rewrite,[status(thm)],[])).
% 1.11/1.07 tff(2561,plain,
% 1.11/1.07 ((~![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)))),
% 1.11/1.07 inference(quant_inst,[status(thm)],[])).
% 1.11/1.07 tff(2562,plain,
% 1.11/1.07 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_5, e_2))),
% 1.11/1.07 inference(modus_ponens,[status(thm)],[2561, 2560])).
% 1.11/1.07 tff(2563,plain,
% 1.11/1.07 ($false),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2562, 577, 12, 384, 2559])).
% 1.11/1.07 tff(2564,plain,((~product(e_4, e_5, e_2)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.07 tff(2565,plain,
% 1.11/1.07 (~product(e_4, e_5, e_2)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2564, 1004])).
% 1.11/1.07 tff(2566,plain,
% 1.11/1.07 (((~![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_5, e_6)) | (~product(e_6, 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_6, e_4) | (~product(e_4, e_5, e_6)) | (~product(e_6, e_5, e_6)))),
% 1.11/1.07 inference(rewrite,[status(thm)],[])).
% 1.11/1.07 tff(2567,plain,
% 1.11/1.07 ((~![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_5, e_6)) | (~product(e_6, e_5, e_6)))),
% 1.11/1.07 inference(quant_inst,[status(thm)],[])).
% 1.11/1.07 tff(2568,plain,
% 1.11/1.07 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_5, e_6)) | (~product(e_6, e_5, e_6))),
% 1.11/1.07 inference(modus_ponens,[status(thm)],[2567, 2566])).
% 1.11/1.07 tff(2569,plain,
% 1.11/1.07 ($false),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2568, 738, 87, 803, 2055])).
% 1.11/1.07 tff(2570,plain,((~product(e_6, e_5, e_6)) | (~product(e_4, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.07 tff(2571,plain,
% 1.11/1.07 (~product(e_4, e_5, e_6)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2570, 2551])).
% 1.11/1.07 tff(2572,assumption,(~product(e_4, e_5, e_4)), introduced(assumption)).
% 1.11/1.07 tff(2573,assumption,(product(e_4, e_5, e_3)), introduced(assumption)).
% 1.11/1.07 tff(2574,plain,
% 1.11/1.07 (((~![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_2, e_3)) | (~product(e_4, 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_2, e_5) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_5, e_3)))),
% 1.11/1.07 inference(rewrite,[status(thm)],[])).
% 1.11/1.07 tff(2575,plain,
% 1.11/1.07 ((equalish(e_2, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_4, e_2, e_3))) <=> (equalish(e_2, e_5) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_5, e_3)))),
% 1.11/1.07 inference(rewrite,[status(thm)],[])).
% 1.11/1.07 tff(2576,plain,
% 1.11/1.07 (((~![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_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_5) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_5, e_3))))),
% 1.11/1.07 inference(monotonicity,[status(thm)],[2575])).
% 1.11/1.07 tff(2577,plain,
% 1.11/1.07 (((~![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_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_5) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_5, e_3)))),
% 1.11/1.07 inference(transitivity,[status(thm)],[2576, 2574])).
% 1.11/1.07 tff(2578,plain,
% 1.11/1.07 ((~![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_3)) | (~product(e_4, e_2, e_3)))),
% 1.11/1.07 inference(quant_inst,[status(thm)],[])).
% 1.11/1.07 tff(2579,plain,
% 1.11/1.07 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_5, e_3))),
% 1.11/1.07 inference(modus_ponens,[status(thm)],[2578, 2577])).
% 1.11/1.07 tff(2580,plain,
% 1.11/1.07 ($false),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2579, 1642, 12, 2573, 889])).
% 1.11/1.07 tff(2581,plain,((~product(e_4, e_2, e_3)) | (~product(e_4, e_5, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.07 tff(2582,plain,
% 1.11/1.07 (~product(e_4, e_5, e_3)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2581, 2541])).
% 1.11/1.07 tff(2583,assumption,(product(e_4, e_5, e_5)), introduced(assumption)).
% 1.11/1.07 tff(2584,plain,
% 1.11/1.07 (((~![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_5)) | (~product(e_4, 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_3) | (~product(e_4, e_3, e_5)) | (~product(e_4, e_5, e_5)))),
% 1.11/1.07 inference(rewrite,[status(thm)],[])).
% 1.11/1.07 tff(2585,plain,
% 1.11/1.07 ((~![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_5)) | (~product(e_4, e_5, e_5)))),
% 1.11/1.07 inference(quant_inst,[status(thm)],[])).
% 1.11/1.07 tff(2586,plain,
% 1.11/1.07 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_3) | (~product(e_4, e_3, e_5)) | (~product(e_4, e_5, e_5))),
% 1.11/1.07 inference(modus_ponens,[status(thm)],[2585, 2584])).
% 1.11/1.07 tff(2587,plain,
% 1.11/1.07 ($false),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2586, 597, 12, 517, 2583])).
% 1.11/1.07 tff(2588,plain,((~product(e_4, e_5, e_5)) | (~product(e_4, e_3, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.07 tff(2589,plain,
% 1.11/1.07 (~product(e_4, e_5, e_5)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2588, 2556])).
% 1.11/1.07 tff(2590,plain,
% 1.11/1.07 (((~![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_1) | product(e_4, e_5, e_2) | 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))) <=> ((~![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_1) | product(e_4, e_5, e_2) | 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))),
% 1.11/1.07 inference(rewrite,[status(thm)],[])).
% 1.11/1.07 tff(2591,plain,
% 1.11/1.07 ((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_1) | product(e_4, e_5, e_2) | 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))),
% 1.11/1.07 inference(rewrite,[status(thm)],[])).
% 1.11/1.07 tff(2592,plain,
% 1.11/1.07 (((~![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_1) | product(e_4, e_5, e_2) | 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)))),
% 1.11/1.07 inference(monotonicity,[status(thm)],[2591])).
% 1.11/1.07 tff(2593,plain,
% 1.11/1.07 (((~![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_1) | product(e_4, e_5, e_2) | 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))),
% 1.11/1.07 inference(transitivity,[status(thm)],[2592, 2590])).
% 1.11/1.07 tff(2594,plain,
% 1.11/1.07 ((~![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)))),
% 1.11/1.07 inference(quant_inst,[status(thm)],[])).
% 1.11/1.07 tff(2595,plain,
% 1.11/1.07 ((~![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_1) | product(e_4, e_5, e_2) | 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)),
% 1.11/1.07 inference(modus_ponens,[status(thm)],[2594, 2593])).
% 1.11/1.07 tff(2596,plain,
% 1.11/1.07 (product(e_4, e_5, e_1) | product(e_4, e_5, e_2) | 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)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2595, 505, 622, 144])).
% 1.11/1.07 tff(2597,plain,
% 1.11/1.07 (product(e_4, e_5, e_1)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2596, 2589, 2582, 2572, 2571, 2565])).
% 1.11/1.07 tff(2598,assumption,(product(e_2, e_5, e_1)), introduced(assumption)).
% 1.11/1.07 tff(2599,plain,
% 1.11/1.07 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_2, e_5, e_1)) | (~product(e_4, e_5, 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_4) | (~product(e_2, e_5, e_1)) | (~product(e_4, e_5, e_1)))),
% 1.11/1.07 inference(rewrite,[status(thm)],[])).
% 1.11/1.07 tff(2600,plain,
% 1.11/1.07 ((equalish(e_2, e_4) | (~product(e_4, e_5, e_1)) | (~product(e_2, e_5, e_1))) <=> (equalish(e_2, e_4) | (~product(e_2, e_5, e_1)) | (~product(e_4, e_5, e_1)))),
% 1.11/1.07 inference(rewrite,[status(thm)],[])).
% 1.11/1.07 tff(2601,plain,
% 1.11/1.07 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_5, e_1)) | (~product(e_2, e_5, 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_4) | (~product(e_2, e_5, e_1)) | (~product(e_4, e_5, e_1))))),
% 1.11/1.07 inference(monotonicity,[status(thm)],[2600])).
% 1.11/1.07 tff(2602,plain,
% 1.11/1.07 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_5, e_1)) | (~product(e_2, e_5, 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_4) | (~product(e_2, e_5, e_1)) | (~product(e_4, e_5, e_1)))),
% 1.11/1.07 inference(transitivity,[status(thm)],[2601, 2599])).
% 1.11/1.07 tff(2603,plain,
% 1.11/1.07 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_5, e_1)) | (~product(e_2, e_5, e_1)))),
% 1.11/1.07 inference(quant_inst,[status(thm)],[])).
% 1.11/1.07 tff(2604,plain,
% 1.11/1.07 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_5, e_1)) | (~product(e_4, e_5, e_1))),
% 1.11/1.07 inference(modus_ponens,[status(thm)],[2603, 2602])).
% 1.11/1.07 tff(2605,plain,
% 1.11/1.07 ($false),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2604, 822, 87, 2598, 1591])).
% 1.11/1.07 tff(2606,plain,((~product(e_2, e_5, e_1)) | (~product(e_4, e_5, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.07 tff(2607,plain,
% 1.11/1.07 (~product(e_2, e_5, e_1)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2606, 2597])).
% 1.11/1.07 tff(2608,plain,
% 1.11/1.07 ($false),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2513, 2607, 2558, 2552, 2545, 2544])).
% 1.11/1.07 tff(2609,plain,(product(e_4, e_1, e_5) | product(e_4, e_5, e_4) | product(e_4, e_3, e_6) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.07 tff(2610,plain,
% 1.11/1.07 (product(e_4, e_5, e_4)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2609, 55, 502, 818, 373])).
% 1.11/1.07 tff(2611,assumption,(product(e_4, e_5, e_4)), introduced(assumption)).
% 1.11/1.07 tff(2612,plain,
% 1.11/1.07 (((~![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)))),
% 1.11/1.07 inference(rewrite,[status(thm)],[])).
% 1.11/1.07 tff(2613,plain,
% 1.11/1.07 ((~![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)))),
% 1.11/1.07 inference(quant_inst,[status(thm)],[])).
% 1.11/1.07 tff(2614,plain,
% 1.11/1.07 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_5, e_4))),
% 1.11/1.07 inference(modus_ponens,[status(thm)],[2613, 2612])).
% 1.11/1.07 tff(2615,plain,
% 1.11/1.07 ($false),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2614, 561, 12, 2611, 332])).
% 1.11/1.07 tff(2616,plain,((~product(e_4, e_5, e_4)) | (~product(e_4, e_4, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.07 tff(2617,plain,
% 1.11/1.07 (~product(e_4, e_4, e_4)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2616, 2610])).
% 1.11/1.07 tff(2618,plain,
% 1.11/1.07 (~product(e_4, e_3, e_3)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[380, 374, 373])).
% 1.11/1.07 tff(2619,plain,
% 1.11/1.07 (~product(e_4, e_3, e_5)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2527, 374, 816])).
% 1.11/1.07 tff(2620,plain,
% 1.11/1.07 (~product(e_4, e_3, e_2)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[360, 374])).
% 1.11/1.07 tff(2621,plain,
% 1.11/1.07 (~product(e_4, e_3, e_1)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[1487, 374, 818])).
% 1.11/1.07 tff(2622,plain,
% 1.11/1.07 ($false),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[535, 2621, 2620, 55, 2619, 2618])).
% 1.11/1.07 tff(2623,plain,((~product(e_2, e_3, e_4)) | product(e_4, e_3, e_6) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5) | product(e_2, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.07 tff(2624,plain,
% 1.11/1.07 (product(e_2, e_4, e_5)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2623, 55, 2542, 818, 373])).
% 1.11/1.07 tff(2625,plain,
% 1.11/1.07 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_2, e_4, e_5)) | (~product(e_4, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_5)) | (~product(e_4, e_4, e_5)))),
% 1.11/1.07 inference(rewrite,[status(thm)],[])).
% 1.11/1.07 tff(2626,plain,
% 1.11/1.07 ((equalish(e_2, e_4) | (~product(e_4, e_4, e_5)) | (~product(e_2, e_4, e_5))) <=> (equalish(e_2, e_4) | (~product(e_2, e_4, e_5)) | (~product(e_4, e_4, e_5)))),
% 1.11/1.07 inference(rewrite,[status(thm)],[])).
% 1.11/1.07 tff(2627,plain,
% 1.11/1.07 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_5)) | (~product(e_2, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_2, e_4, e_5)) | (~product(e_4, e_4, e_5))))),
% 1.11/1.07 inference(monotonicity,[status(thm)],[2626])).
% 1.11/1.07 tff(2628,plain,
% 1.11/1.07 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_5)) | (~product(e_2, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_5)) | (~product(e_4, e_4, e_5)))),
% 1.11/1.07 inference(transitivity,[status(thm)],[2627, 2625])).
% 1.11/1.07 tff(2629,plain,
% 1.11/1.07 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_5)) | (~product(e_2, e_4, e_5)))),
% 1.11/1.07 inference(quant_inst,[status(thm)],[])).
% 1.11/1.07 tff(2630,plain,
% 1.11/1.07 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_5)) | (~product(e_4, e_4, e_5))),
% 1.11/1.07 inference(modus_ponens,[status(thm)],[2629, 2628])).
% 1.11/1.07 tff(2631,plain,
% 1.11/1.07 ($false),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2630, 822, 87, 774, 746])).
% 1.11/1.07 tff(2632,plain,((~product(e_2, e_4, e_5)) | (~product(e_4, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.07 tff(2633,plain,
% 1.11/1.07 (~product(e_4, e_4, e_5)),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[2632, 2624])).
% 1.11/1.07 tff(2634,plain,
% 1.11/1.07 ($false),
% 1.11/1.07 inference(unit_resolution,[status(thm)],[903, 2633, 2617, 2543, 1561, 1562, 1560])).
% 1.11/1.07 tff(2635,plain,(product(e_4, e_3, e_6) | product(e_4, e_4, e_1) | product(e_4, e_4, e_6) | product(e_4, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_4, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.08 tff(2636,plain,
% 1.11/1.08 (product(e_4, e_3, e_6)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2635, 818, 1562, 1560, 1561, 373, 502])).
% 1.11/1.08 tff(2637,plain,
% 1.11/1.08 (~product(e_1, e_3, e_6)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[969, 2636])).
% 1.11/1.08 tff(2638,plain,
% 1.11/1.08 (~product(e_1, e_3, e_1)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1617, 1002])).
% 1.11/1.08 tff(2639,plain,
% 1.11/1.08 (~product(e_5, e_3, e_6)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[20, 2537])).
% 1.11/1.08 tff(2640,plain,
% 1.11/1.08 (product(e_5, e_6, e_5)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[649, 2539, 2537])).
% 1.11/1.08 tff(2641,plain,
% 1.11/1.08 ((~equalish(e_3, e_6)) <=> (~equalish(e_3, e_6))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2642,axiom,(~equalish(e_3, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_6')).
% 1.11/1.08 tff(2643,plain,
% 1.11/1.08 (~equalish(e_3, e_6)),
% 1.11/1.08 inference(modus_ponens,[status(thm)],[2642, 2641])).
% 1.11/1.08 tff(2644,plain,
% 1.11/1.08 (((~![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_5, e_6, e_5)) | (~product(e_5, 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_6) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_3, e_5)))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2645,plain,
% 1.11/1.08 ((~![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_5, e_6, e_5)) | (~product(e_5, e_3, e_5)))),
% 1.11/1.08 inference(quant_inst,[status(thm)],[])).
% 1.11/1.08 tff(2646,plain,
% 1.11/1.08 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_6) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_3, e_5))),
% 1.11/1.08 inference(modus_ponens,[status(thm)],[2645, 2644])).
% 1.11/1.08 tff(2647,plain,
% 1.11/1.08 ($false),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2646, 2643, 12, 22, 1946])).
% 1.11/1.08 tff(2648,plain,((~product(e_5, e_3, e_5)) | (~product(e_5, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.08 tff(2649,plain,
% 1.11/1.08 (~product(e_5, e_3, e_5)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2648, 2640])).
% 1.11/1.08 tff(2650,plain,
% 1.11/1.08 (~product(e_6, e_3, e_6)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2060, 2551])).
% 1.11/1.08 tff(2651,plain,
% 1.11/1.08 (~product(e_3, e_3, e_6)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[979, 2636])).
% 1.11/1.08 tff(2652,plain,
% 1.11/1.08 (product(e_1, e_3, e_5)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2346, 2651, 2542, 2541, 2650, 2649, 2639, 2638, 2540, 2637])).
% 1.11/1.08 tff(2653,plain,
% 1.11/1.08 (~product(e_1, e_3, e_4)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1032, 2542])).
% 1.11/1.08 tff(2654,plain,
% 1.11/1.08 (~product(e_5, e_3, e_4)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1982, 2542])).
% 1.11/1.08 tff(2655,plain,
% 1.11/1.08 (~product(e_6, e_3, e_4)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1260, 2542])).
% 1.11/1.08 tff(2656,plain,
% 1.11/1.08 (~product(e_3, e_3, e_1)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2374, 2651, 2655, 2650, 2649, 2639, 2654, 2638, 2540, 2653, 2637])).
% 1.11/1.08 tff(2657,plain,
% 1.11/1.08 (~product(e_5, e_3, e_1)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1965, 33, 2652, 619])).
% 1.11/1.08 tff(2658,plain,
% 1.11/1.08 (product(e_5, e_3, e_2)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2123, 2657, 2649, 2639, 2654, 2651, 2656])).
% 1.11/1.08 tff(2659,plain,
% 1.11/1.08 (product(e_1, e_5, e_2)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2132, 2658, 2652])).
% 1.11/1.08 tff(2660,plain,
% 1.11/1.08 (~product(e_3, e_5, e_2)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2143, 2659])).
% 1.11/1.08 tff(2661,plain,
% 1.11/1.08 (~product(e_3, e_5, e_1)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2170, 33, 266, 2659])).
% 1.11/1.08 tff(2662,plain,
% 1.11/1.08 (~product(e_3, e_3, e_5)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2155, 2652])).
% 1.11/1.08 tff(2663,plain,
% 1.11/1.08 (~product(e_3, e_3, e_2)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2149, 2658])).
% 1.11/1.08 tff(2664,plain,
% 1.11/1.08 (product(e_3, e_3, e_3)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1246, 2663, 2651, 2662, 2656])).
% 1.11/1.08 tff(2665,plain,
% 1.11/1.08 (~product(e_3, e_5, e_3)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1331, 2664])).
% 1.11/1.08 tff(2666,assumption,(product(e_3, e_5, e_6)), introduced(assumption)).
% 1.11/1.08 tff(2667,plain,
% 1.11/1.08 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_6) | (~product(e_6, e_5, e_6)) | (~product(e_3, 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_3, e_6) | (~product(e_6, e_5, e_6)) | (~product(e_3, e_5, e_6)))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2668,plain,
% 1.11/1.08 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_6) | (~product(e_6, e_5, e_6)) | (~product(e_3, e_5, e_6)))),
% 1.11/1.08 inference(quant_inst,[status(thm)],[])).
% 1.11/1.08 tff(2669,plain,
% 1.11/1.08 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_6) | (~product(e_6, e_5, e_6)) | (~product(e_3, e_5, e_6))),
% 1.11/1.08 inference(modus_ponens,[status(thm)],[2668, 2667])).
% 1.11/1.08 tff(2670,plain,
% 1.11/1.08 ($false),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2669, 2643, 87, 2055, 2666])).
% 1.11/1.08 tff(2671,plain,((~product(e_3, e_5, e_6)) | (~product(e_6, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.08 tff(2672,plain,
% 1.11/1.08 (~product(e_3, e_5, e_6)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2671, 2551])).
% 1.11/1.08 tff(2673,plain,
% 1.11/1.08 (~product(e_2, e_5, e_1)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2480, 33, 2532, 2659])).
% 1.11/1.08 tff(2674,plain,
% 1.11/1.08 (product(e_2, e_5, e_5)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2513, 2673, 2552, 2545, 2544])).
% 1.11/1.08 tff(2675,assumption,(product(e_3, e_5, e_5)), introduced(assumption)).
% 1.11/1.08 tff(2676,plain,
% 1.11/1.08 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_5, e_5)) | (~product(e_3, 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_3, e_2) | (~product(e_2, e_5, e_5)) | (~product(e_3, e_5, e_5)))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2677,plain,
% 1.11/1.08 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_5, e_5)) | (~product(e_3, e_5, e_5)))),
% 1.11/1.08 inference(quant_inst,[status(thm)],[])).
% 1.11/1.08 tff(2678,plain,
% 1.11/1.08 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_5, e_5)) | (~product(e_3, e_5, e_5))),
% 1.11/1.08 inference(modus_ponens,[status(thm)],[2677, 2676])).
% 1.11/1.08 tff(2679,plain,
% 1.11/1.08 ($false),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2678, 248, 87, 2516, 2675])).
% 1.11/1.08 tff(2680,plain,((~product(e_3, e_5, e_5)) | (~product(e_2, e_5, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.08 tff(2681,plain,
% 1.11/1.08 (~product(e_3, e_5, e_5)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2680, 2674])).
% 1.11/1.08 tff(2682,plain,
% 1.11/1.08 (((~![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_5)) | product(e_3, e_5, e_4) | product(e_3, e_5, e_6) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_5) | product(e_3, 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_3)) | (~group_element(e_5)) | product(e_3, e_5, e_4) | product(e_3, e_5, e_6) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_5) | product(e_3, e_5, e_2))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2683,plain,
% 1.11/1.08 ((product(e_3, e_5, e_6) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | (~group_element(e_5)) | product(e_3, e_5, e_4) | product(e_3, e_5, e_6) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_5) | product(e_3, e_5, e_2))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2684,plain,
% 1.11/1.08 (((~![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_5, e_6) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | (~group_element(e_5)) | (~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)))) | ((~group_element(e_3)) | (~group_element(e_5)) | product(e_3, e_5, e_4) | product(e_3, e_5, e_6) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_5) | product(e_3, e_5, e_2)))),
% 1.11/1.08 inference(monotonicity,[status(thm)],[2683])).
% 1.11/1.08 tff(2685,plain,
% 1.11/1.08 (((~![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_5, e_6) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | (~group_element(e_5)) | (~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)))) | (~group_element(e_3)) | (~group_element(e_5)) | product(e_3, e_5, e_4) | product(e_3, e_5, e_6) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_5) | product(e_3, e_5, e_2))),
% 1.11/1.08 inference(transitivity,[status(thm)],[2684, 2682])).
% 1.11/1.08 tff(2686,plain,
% 1.11/1.08 ((~![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_5, e_6) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_3)))),
% 1.11/1.08 inference(quant_inst,[status(thm)],[])).
% 1.11/1.08 tff(2687,plain,
% 1.11/1.08 ((~![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_5)) | product(e_3, e_5, e_4) | product(e_3, e_5, e_6) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_5) | product(e_3, e_5, e_2)),
% 1.11/1.08 inference(modus_ponens,[status(thm)],[2686, 2685])).
% 1.11/1.08 tff(2688,plain,
% 1.11/1.08 (product(e_3, e_5, e_4) | product(e_3, e_5, e_6) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_5) | product(e_3, e_5, e_2)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2687, 289, 622, 144])).
% 1.11/1.08 tff(2689,plain,
% 1.11/1.08 (product(e_3, e_5, e_4)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2688, 2681, 2672, 2665, 2661, 2660])).
% 1.11/1.08 tff(2690,plain,
% 1.11/1.08 (((~![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_6, e_4, e_6)) | (~product(e_6, 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_6, e_4, e_6)) | (~product(e_6, e_5, e_6)))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2691,plain,
% 1.11/1.08 ((~![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_6, e_4, e_6)) | (~product(e_6, e_5, e_6)))),
% 1.11/1.08 inference(quant_inst,[status(thm)],[])).
% 1.11/1.08 tff(2692,plain,
% 1.11/1.08 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_6, e_4, e_6)) | (~product(e_6, e_5, e_6))),
% 1.11/1.08 inference(modus_ponens,[status(thm)],[2691, 2690])).
% 1.11/1.08 tff(2693,plain,
% 1.11/1.08 ($false),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2692, 561, 12, 1497, 2055])).
% 1.11/1.08 tff(2694,plain,((~product(e_6, e_5, e_6)) | (~product(e_6, e_4, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.08 tff(2695,plain,
% 1.11/1.08 (~product(e_6, e_4, e_6)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2694, 2551])).
% 1.11/1.08 tff(2696,plain,
% 1.11/1.08 (~product(e_1, e_4, e_1)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1393, 1002])).
% 1.11/1.08 tff(2697,plain,
% 1.11/1.08 (~product(e_1, e_3, e_6)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[969, 961])).
% 1.11/1.08 tff(2698,assumption,(~product(e_2, e_1, e_2)), introduced(assumption)).
% 1.11/1.08 tff(2699,plain,
% 1.11/1.08 (product(e_2, e_1, e_3)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[206, 2698])).
% 1.11/1.08 tff(2700,plain,
% 1.11/1.08 (product(e_2, e_3, e_4)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[329, 2699])).
% 1.11/1.08 tff(2701,plain,
% 1.11/1.08 (~product(e_1, e_3, e_4)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1032, 2700])).
% 1.11/1.08 tff(2702,plain,
% 1.11/1.08 (~product(e_3, e_3, e_6)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[979, 961])).
% 1.11/1.08 tff(2703,assumption,(~product(e_5, e_1, e_2)), introduced(assumption)).
% 1.11/1.08 tff(2704,plain,
% 1.11/1.08 (~product(e_5, e_1, e_3)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[592, 2699])).
% 1.11/1.08 tff(2705,plain,
% 1.11/1.08 (product(e_5, e_1, e_6)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[630, 2704, 2703, 1182])).
% 1.11/1.08 tff(2706,plain,
% 1.11/1.08 (product(e_5, e_6, e_5)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[649, 1100, 2705])).
% 1.11/1.08 tff(2707,plain,
% 1.11/1.08 (~product(e_5, e_3, e_5)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2648, 2706])).
% 1.11/1.08 tff(2708,plain,
% 1.11/1.08 (((~![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_6, e_1, e_5)) | (~product(e_6, 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_1, e_4) | (~product(e_6, e_1, e_5)) | (~product(e_6, e_4, e_5)))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2709,plain,
% 1.11/1.08 ((equalish(e_1, e_4) | (~product(e_6, e_4, e_5)) | (~product(e_6, e_1, e_5))) <=> (equalish(e_1, e_4) | (~product(e_6, e_1, e_5)) | (~product(e_6, e_4, e_5)))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2710,plain,
% 1.11/1.08 (((~![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_6, e_4, e_5)) | (~product(e_6, e_1, e_5)))) <=> ((~![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_6, e_1, e_5)) | (~product(e_6, e_4, e_5))))),
% 1.11/1.08 inference(monotonicity,[status(thm)],[2709])).
% 1.11/1.08 tff(2711,plain,
% 1.11/1.08 (((~![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_6, e_4, e_5)) | (~product(e_6, e_1, e_5)))) <=> ((~![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_6, e_1, e_5)) | (~product(e_6, e_4, e_5)))),
% 1.11/1.08 inference(transitivity,[status(thm)],[2710, 2708])).
% 1.11/1.08 tff(2712,plain,
% 1.11/1.08 ((~![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_6, e_4, e_5)) | (~product(e_6, e_1, e_5)))),
% 1.11/1.08 inference(quant_inst,[status(thm)],[])).
% 1.11/1.08 tff(2713,plain,
% 1.11/1.08 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_6, e_1, e_5)) | (~product(e_6, e_4, e_5))),
% 1.11/1.08 inference(modus_ponens,[status(thm)],[2712, 2711])).
% 1.11/1.08 tff(2714,plain,
% 1.11/1.08 ($false),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2713, 1673, 12, 1100, 1286])).
% 1.11/1.08 tff(2715,plain,((~product(e_6, e_1, e_5)) | (~product(e_6, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.08 tff(2716,plain,
% 1.11/1.08 (~product(e_6, e_4, e_5)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2715, 1100])).
% 1.11/1.08 tff(2717,plain,
% 1.11/1.08 (~product(e_6, e_1, e_3)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[659, 2699])).
% 1.11/1.08 tff(2718,plain,
% 1.11/1.08 (~product(e_5, e_4, e_6)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2205, 2705])).
% 1.11/1.08 tff(2719,plain,
% 1.11/1.08 ((~equalish(e_4, e_6)) <=> (~equalish(e_4, e_6))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2720,axiom,(~equalish(e_4, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_6')).
% 1.11/1.08 tff(2721,plain,
% 1.11/1.08 (~equalish(e_4, e_6)),
% 1.11/1.08 inference(modus_ponens,[status(thm)],[2720, 2719])).
% 1.11/1.08 tff(2722,plain,
% 1.11/1.08 (((~![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_5, e_4, e_5)) | (~product(e_5, 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_4, e_6) | (~product(e_5, e_4, e_5)) | (~product(e_5, e_6, e_5)))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2723,plain,
% 1.11/1.08 ((equalish(e_4, e_6) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_4, e_5))) <=> (equalish(e_4, e_6) | (~product(e_5, e_4, e_5)) | (~product(e_5, e_6, e_5)))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2724,plain,
% 1.11/1.08 (((~![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_5, e_6, e_5)) | (~product(e_5, 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_5, e_4, e_5)) | (~product(e_5, e_6, e_5))))),
% 1.11/1.08 inference(monotonicity,[status(thm)],[2723])).
% 1.11/1.08 tff(2725,plain,
% 1.11/1.08 (((~![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_5, e_6, e_5)) | (~product(e_5, 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_5, e_4, e_5)) | (~product(e_5, e_6, e_5)))),
% 1.11/1.08 inference(transitivity,[status(thm)],[2724, 2722])).
% 1.11/1.08 tff(2726,plain,
% 1.11/1.08 ((~![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_5, e_6, e_5)) | (~product(e_5, e_4, e_5)))),
% 1.11/1.08 inference(quant_inst,[status(thm)],[])).
% 1.11/1.08 tff(2727,plain,
% 1.11/1.08 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_5, e_4, e_5)) | (~product(e_5, e_6, e_5))),
% 1.11/1.08 inference(modus_ponens,[status(thm)],[2726, 2725])).
% 1.11/1.08 tff(2728,plain,
% 1.11/1.08 ($false),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2727, 2721, 12, 1315, 22])).
% 1.11/1.08 tff(2729,plain,((~product(e_5, e_4, e_5)) | (~product(e_5, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.08 tff(2730,plain,
% 1.11/1.08 (~product(e_5, e_4, e_5)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2729, 2706])).
% 1.11/1.08 tff(2731,plain,
% 1.11/1.08 (~product(e_6, e_3, e_5)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1105, 1100])).
% 1.11/1.08 tff(2732,plain,
% 1.11/1.08 (~product(e_6, e_3, e_4)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1260, 2700])).
% 1.11/1.08 tff(2733,plain,
% 1.11/1.08 (~product(e_5, e_3, e_4)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1982, 2700])).
% 1.11/1.08 tff(2734,plain,
% 1.11/1.08 (~product(e_5, e_3, e_6)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[20, 2705])).
% 1.11/1.08 tff(2735,plain,
% 1.11/1.08 (~product(e_1, e_3, e_3)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2337, 1415])).
% 1.11/1.08 tff(2736,plain,
% 1.11/1.08 (product(e_1, e_3, e_5)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2331, 2735, 1025, 1262, 1265, 1986, 1985, 1994, 1027, 1267, 1035, 1024])).
% 1.11/1.08 tff(2737,plain,
% 1.11/1.08 (~product(e_3, e_3, e_1)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2093, 33, 286, 2736])).
% 1.11/1.08 tff(2738,plain,
% 1.11/1.08 (~product(e_3, e_3, e_5)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2155, 2736])).
% 1.11/1.08 tff(2739,plain,
% 1.11/1.08 (~product(e_5, e_3, e_1)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1965, 33, 2736, 619])).
% 1.11/1.08 tff(2740,plain,
% 1.11/1.08 (product(e_5, e_3, e_2)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2114, 2739, 1986, 1025, 2738, 1985, 1994, 2737])).
% 1.11/1.08 tff(2741,plain,
% 1.11/1.08 (product(e_6, e_4, e_4)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1911, 1415, 663, 1395, 1707, 1907])).
% 1.11/1.08 tff(2742,plain,
% 1.11/1.08 (((~![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_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_5, e_6) | (~product(e_5, e_4, e_4)) | (~product(e_6, e_4, e_4)))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2743,plain,
% 1.11/1.08 ((equalish(e_5, e_6) | (~product(e_6, e_4, e_4)) | (~product(e_5, e_4, e_4))) <=> (equalish(e_5, e_6) | (~product(e_5, e_4, e_4)) | (~product(e_6, e_4, e_4)))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2744,plain,
% 1.11/1.08 (((~![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_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_6) | (~product(e_5, e_4, e_4)) | (~product(e_6, e_4, e_4))))),
% 1.11/1.08 inference(monotonicity,[status(thm)],[2743])).
% 1.11/1.08 tff(2745,plain,
% 1.11/1.08 (((~![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_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_6) | (~product(e_5, e_4, e_4)) | (~product(e_6, e_4, e_4)))),
% 1.11/1.08 inference(transitivity,[status(thm)],[2744, 2742])).
% 1.11/1.08 tff(2746,plain,
% 1.11/1.08 ((~![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_4)) | (~product(e_5, e_4, e_4)))),
% 1.11/1.08 inference(quant_inst,[status(thm)],[])).
% 1.11/1.08 tff(2747,plain,
% 1.11/1.08 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_5, e_4, e_4)) | (~product(e_6, e_4, e_4))),
% 1.11/1.08 inference(modus_ponens,[status(thm)],[2746, 2745])).
% 1.11/1.08 tff(2748,plain,
% 1.11/1.08 ($false),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2747, 45, 87, 1563, 1728])).
% 1.11/1.08 tff(2749,plain,((~product(e_5, e_4, e_4)) | (~product(e_6, e_4, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.08 tff(2750,plain,
% 1.11/1.08 (~product(e_5, e_4, e_4)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2749, 2741])).
% 1.11/1.08 tff(2751,plain,
% 1.11/1.08 (product(e_5, e_4, e_2)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1558, 1913, 1545, 1026, 1922, 2750])).
% 1.11/1.08 tff(2752,plain,
% 1.11/1.08 (((~![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_5, e_4, e_2)) | (~product(e_5, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_5, e_4, e_2)) | (~product(e_5, e_3, e_2)))),
% 1.11/1.08 inference(rewrite,[status(thm)],[])).
% 1.11/1.08 tff(2753,plain,
% 1.11/1.08 ((~![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_5, e_4, e_2)) | (~product(e_5, e_3, e_2)))),
% 1.11/1.08 inference(quant_inst,[status(thm)],[])).
% 1.11/1.08 tff(2754,plain,
% 1.11/1.08 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_5, e_4, e_2)) | (~product(e_5, e_3, e_2))),
% 1.11/1.08 inference(modus_ponens,[status(thm)],[2753, 2752])).
% 1.11/1.08 tff(2755,plain,
% 1.11/1.08 ($false),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2754, 974, 12, 2751, 2740])).
% 1.11/1.08 tff(2756,plain,((~product(e_1, e_4, e_3)) | product(e_5, e_3, e_5) | product(e_3, e_3, e_6) | product(e_5, e_3, e_6) | product(e_5, e_3, e_4) | product(e_6, e_3, e_4) | product(e_6, e_3, e_6) | product(e_1, e_3, e_1) | product(e_6, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_6) | product(e_5, e_1, e_3) | product(e_6, e_1, e_3) | product(e_6, e_4, e_5) | product(e_6, e_4, e_6) | product(e_6, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.08 tff(2757,plain,
% 1.11/1.08 (~product(e_1, e_4, e_3)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2756, 1907, 2702, 2734, 2733, 2732, 1265, 1027, 2731, 2701, 2697, 2730, 2718, 2704, 2717, 2716, 1707, 2707])).
% 1.11/1.08 tff(2758,plain,
% 1.11/1.08 (~product(e_1, e_2, e_4)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[2344, 2757, 889])).
% 1.11/1.08 tff(2759,plain,
% 1.11/1.08 (~product(e_1, e_3, e_2)),
% 1.11/1.08 inference(unit_resolution,[status(thm)],[1301, 2758, 2700])).
% 1.11/1.09 tff(2760,plain,
% 1.11/1.09 (product(e_1, e_3, e_5)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[1083, 2759, 2702, 2701, 2697, 1027])).
% 1.11/1.09 tff(2761,assumption,(~product(e_4, e_5, e_6)), introduced(assumption)).
% 1.11/1.09 tff(2762,assumption,(~product(e_2, e_5, e_6)), introduced(assumption)).
% 1.11/1.09 tff(2763,assumption,(~product(e_3, e_5, e_6)), introduced(assumption)).
% 1.11/1.09 tff(2764,assumption,(~product(e_4, e_5, e_2)), introduced(assumption)).
% 1.11/1.09 tff(2765,plain,
% 1.11/1.09 (~product(e_1, e_2, e_4)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2344, 2339, 889])).
% 1.11/1.09 tff(2766,plain,
% 1.11/1.09 (~product(e_1, e_3, e_2)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[1301, 2765, 2700])).
% 1.11/1.09 tff(2767,plain,
% 1.11/1.09 (product(e_1, e_3, e_5)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[1083, 2766, 1025, 2701, 2697, 1027])).
% 1.11/1.09 tff(2768,plain,
% 1.11/1.09 (~product(e_5, e_3, e_1)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[1965, 33, 2767, 619])).
% 1.11/1.09 tff(2769,plain,
% 1.11/1.09 (~product(e_5, e_3, e_5)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[1952, 2767])).
% 1.11/1.09 tff(2770,plain,
% 1.11/1.09 (~product(e_3, e_3, e_5)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2155, 2767])).
% 1.11/1.09 tff(2771,plain,
% 1.11/1.09 (~product(e_3, e_3, e_1)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2093, 33, 286, 2767])).
% 1.11/1.09 tff(2772,plain,
% 1.11/1.09 (product(e_5, e_3, e_2)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2114, 2771, 1025, 2770, 2769, 2734, 2733, 2768])).
% 1.11/1.09 tff(2773,plain,
% 1.11/1.09 (product(e_1, e_5, e_2)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2132, 2772, 2767])).
% 1.11/1.09 tff(2774,plain,
% 1.11/1.09 (~product(e_3, e_5, e_2)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2143, 2773])).
% 1.11/1.09 tff(2775,plain,
% 1.11/1.09 (~product(e_3, e_5, e_1)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2170, 33, 266, 2773])).
% 1.11/1.09 tff(2776,plain,
% 1.11/1.09 (~product(e_3, e_3, e_2)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2149, 2772])).
% 1.11/1.09 tff(2777,plain,
% 1.11/1.09 (product(e_3, e_3, e_3)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2162, 2776, 1025, 2767])).
% 1.11/1.09 tff(2778,plain,
% 1.11/1.09 (~product(e_3, e_5, e_3)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[1331, 2777])).
% 1.11/1.09 tff(2779,plain,
% 1.11/1.09 (~product(e_2, e_5, e_4)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[1655, 2700])).
% 1.11/1.09 tff(2780,plain,
% 1.11/1.09 (~product(e_2, e_5, e_3)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2487, 2699])).
% 1.11/1.09 tff(2781,plain,
% 1.11/1.09 (~product(e_2, e_5, e_1)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2480, 33, 2698, 2773])).
% 1.11/1.09 tff(2782,plain,
% 1.11/1.09 (product(e_2, e_5, e_5)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2513, 2781, 2762, 2780, 2779])).
% 1.11/1.09 tff(2783,plain,
% 1.11/1.09 (~product(e_3, e_5, e_5)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2680, 2782])).
% 1.11/1.09 tff(2784,plain,
% 1.11/1.09 (product(e_3, e_5, e_4)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2688, 2783, 2763, 2778, 2775, 2774])).
% 1.11/1.09 tff(2785,plain,
% 1.11/1.09 (~product(e_6, e_3, e_5)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[1958, 2767])).
% 1.11/1.09 tff(2786,plain,
% 1.11/1.09 (product(e_6, e_4, e_6)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[1518, 2716, 1751, 1907, 1504, 1746])).
% 1.11/1.09 tff(2787,assumption,(~product(e_5, e_1, e_4)), introduced(assumption)).
% 1.11/1.09 tff(2788,plain,
% 1.11/1.09 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, 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_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_5)))),
% 1.11/1.09 inference(rewrite,[status(thm)],[])).
% 1.11/1.09 tff(2789,plain,
% 1.11/1.09 ((equalish(e_6, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_6, e_1, e_5))) <=> (equalish(e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_5)))),
% 1.11/1.09 inference(rewrite,[status(thm)],[])).
% 1.11/1.09 tff(2790,plain,
% 1.11/1.09 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, 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_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_5))))),
% 1.11/1.09 inference(monotonicity,[status(thm)],[2789])).
% 1.11/1.09 tff(2791,plain,
% 1.11/1.09 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, 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_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_5)))),
% 1.11/1.09 inference(transitivity,[status(thm)],[2790, 2788])).
% 1.11/1.09 tff(2792,plain,
% 1.11/1.09 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_6, e_1, e_5)))),
% 1.11/1.09 inference(quant_inst,[status(thm)],[])).
% 1.11/1.09 tff(2793,plain,
% 1.11/1.09 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_5))),
% 1.11/1.09 inference(modus_ponens,[status(thm)],[2792, 2791])).
% 1.11/1.09 tff(2794,plain,
% 1.11/1.09 ($false),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2793, 636, 87, 604, 1100])).
% 1.11/1.09 tff(2795,plain,((~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.09 tff(2796,plain,
% 1.11/1.09 (~product(e_5, e_1, e_5)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2795, 1100])).
% 1.11/1.09 tff(2797,plain,
% 1.11/1.09 (product(e_5, e_1, e_6)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[629, 2796, 1182, 2703, 2787, 1148])).
% 1.11/1.09 tff(2798,plain,
% 1.11/1.09 (product(e_6, e_5, e_6)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2086, 2797, 1100])).
% 1.11/1.09 tff(2799,plain,
% 1.11/1.09 ($false),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2694, 2798, 2786])).
% 1.11/1.09 tff(2800,plain,((~product(e_6, e_1, e_5)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_2) | product(e_6, e_4, e_3) | product(e_6, e_4, e_4) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.09 tff(2801,plain,
% 1.11/1.09 ((~product(e_6, e_1, e_5)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_2) | product(e_6, e_4, e_3) | product(e_6, e_4, e_4) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2800, 603])).
% 1.11/1.09 tff(2802,plain,
% 1.11/1.09 (product(e_6, e_4, e_4)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2801, 1504, 1100, 1907, 1148, 1182, 2703, 1751])).
% 1.11/1.09 tff(2803,plain,
% 1.11/1.09 (product(e_4, e_4, e_5)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[1743, 2802, 1560, 1504, 1562, 1561])).
% 1.11/1.09 tff(2804,plain,
% 1.11/1.09 (~product(e_2, e_4, e_5)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2632, 2803])).
% 1.11/1.09 tff(2805,plain,
% 1.11/1.09 (product(e_4, e_3, e_6)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[2623, 2804, 374, 818, 373])).
% 1.11/1.09 tff(2806,plain,
% 1.11/1.09 (~product(e_1, e_3, e_6)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[969, 2805])).
% 1.11/1.09 tff(2807,plain,
% 1.11/1.09 (product(e_1, e_3, e_5)),
% 1.11/1.09 inference(unit_resolution,[status(thm)],[1083, 2806, 1025, 2295, 1034, 1027])).
% 1.11/1.09 tff(2808,plain,
% 1.11/1.09 (((~![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_5)) | (~product(e_4, e_4, 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_4) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_4, e_5)))),
% 1.11/1.09 inference(rewrite,[status(thm)],[])).
% 1.11/1.09 tff(2809,plain,
% 1.11/1.09 ((equalish(e_1, e_4) | (~product(e_4, e_4, e_5)) | (~product(e_1, e_4, e_5))) <=> (equalish(e_1, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_4, e_5)))),
% 1.11/1.09 inference(rewrite,[status(thm)],[])).
% 1.11/1.09 tff(2810,plain,
% 1.11/1.09 (((~![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_5)) | (~product(e_1, e_4, 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_4) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_4, e_5))))),
% 1.11/1.09 inference(monotonicity,[status(thm)],[2809])).
% 1.11/1.09 tff(2811,plain,
% 1.11/1.09 (((~![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_5)) | (~product(e_1, e_4, 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_4) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_4, e_5)))),
% 1.18/1.09 inference(transitivity,[status(thm)],[2810, 2808])).
% 1.18/1.09 tff(2812,plain,
% 1.18/1.09 ((~![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_5)) | (~product(e_1, e_4, e_5)))),
% 1.18/1.09 inference(quant_inst,[status(thm)],[])).
% 1.18/1.09 tff(2813,plain,
% 1.18/1.09 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_4, e_5))),
% 1.18/1.09 inference(modus_ponens,[status(thm)],[2812, 2811])).
% 1.18/1.09 tff(2814,plain,
% 1.18/1.09 ($false),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2813, 1673, 87, 1011, 746])).
% 1.18/1.09 tff(2815,plain,((~product(e_1, e_4, e_5)) | (~product(e_4, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.09 tff(2816,plain,
% 1.18/1.09 (~product(e_1, e_4, e_5)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2815, 2803])).
% 1.18/1.09 tff(2817,plain,
% 1.18/1.09 (((~![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_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_1, e_6) | (~product(e_1, e_4, e_4)) | (~product(e_6, e_4, e_4)))),
% 1.18/1.09 inference(rewrite,[status(thm)],[])).
% 1.18/1.09 tff(2818,plain,
% 1.18/1.09 ((equalish(e_1, e_6) | (~product(e_6, e_4, e_4)) | (~product(e_1, e_4, e_4))) <=> (equalish(e_1, e_6) | (~product(e_1, e_4, e_4)) | (~product(e_6, e_4, e_4)))),
% 1.18/1.09 inference(rewrite,[status(thm)],[])).
% 1.18/1.09 tff(2819,plain,
% 1.18/1.09 (((~![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_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_6) | (~product(e_1, e_4, e_4)) | (~product(e_6, e_4, e_4))))),
% 1.18/1.09 inference(monotonicity,[status(thm)],[2818])).
% 1.18/1.09 tff(2820,plain,
% 1.18/1.09 (((~![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_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_6) | (~product(e_1, e_4, e_4)) | (~product(e_6, e_4, e_4)))),
% 1.18/1.09 inference(transitivity,[status(thm)],[2819, 2817])).
% 1.18/1.09 tff(2821,plain,
% 1.18/1.09 ((~![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_4, e_4)) | (~product(e_1, e_4, e_4)))),
% 1.18/1.09 inference(quant_inst,[status(thm)],[])).
% 1.18/1.09 tff(2822,plain,
% 1.18/1.09 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_6) | (~product(e_1, e_4, e_4)) | (~product(e_6, e_4, e_4))),
% 1.18/1.09 inference(modus_ponens,[status(thm)],[2821, 2820])).
% 1.18/1.09 tff(2823,plain,
% 1.18/1.09 ($false),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2822, 1089, 87, 1305, 1728])).
% 1.18/1.09 tff(2824,plain,((~product(e_1, e_4, e_4)) | (~product(e_6, e_4, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.09 tff(2825,plain,
% 1.18/1.09 (~product(e_1, e_4, e_4)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2824, 2802])).
% 1.18/1.09 tff(2826,plain,
% 1.18/1.09 (~product(e_2, e_4, e_4)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[792, 374])).
% 1.18/1.09 tff(2827,plain,
% 1.18/1.09 (product(e_2, e_4, e_6)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[1495, 2804, 2826, 373, 818])).
% 1.18/1.09 tff(2828,plain,
% 1.18/1.09 (~product(e_1, e_4, e_6)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[1402, 2827])).
% 1.18/1.09 tff(2829,plain,
% 1.18/1.09 (product(e_1, e_4, e_2)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[1413, 2828, 2339, 2825, 1424, 2816])).
% 1.18/1.09 tff(2830,plain,
% 1.18/1.09 (~product(e_1, e_5, e_2)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2384, 2829])).
% 1.18/1.09 tff(2831,plain,
% 1.18/1.09 (~product(e_5, e_3, e_2)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2132, 2830, 2807])).
% 1.18/1.09 tff(2832,plain,
% 1.18/1.09 (~product(e_5, e_3, e_1)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[1965, 33, 2807, 619])).
% 1.18/1.09 tff(2833,plain,
% 1.18/1.09 (product(e_5, e_1, e_6)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[630, 1148, 2703, 1182])).
% 1.18/1.09 tff(2834,plain,
% 1.18/1.09 (~product(e_5, e_3, e_6)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[20, 2833])).
% 1.18/1.09 tff(2835,plain,
% 1.18/1.09 (~product(e_5, e_3, e_5)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[1952, 2807])).
% 1.18/1.09 tff(2836,plain,
% 1.18/1.09 (product(e_5, e_3, e_3) | product(e_5, e_3, e_2)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2000, 289, 622, 144, 2835, 2834, 2298, 2832])).
% 1.18/1.09 tff(2837,plain,
% 1.18/1.09 (product(e_5, e_3, e_3)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2836, 2831])).
% 1.18/1.09 tff(2838,plain,
% 1.18/1.09 (~product(e_3, e_3, e_1)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2093, 33, 286, 2807])).
% 1.18/1.09 tff(2839,plain,
% 1.18/1.09 (~product(e_3, e_3, e_5)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2155, 2807])).
% 1.18/1.09 tff(2840,plain,
% 1.18/1.09 (~product(e_3, e_3, e_3)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2107, 2837])).
% 1.18/1.09 tff(2841,plain,
% 1.18/1.09 (product(e_3, e_3, e_2)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[1246, 2840, 1025, 2839, 2838])).
% 1.18/1.09 tff(2842,plain,
% 1.18/1.09 ($false),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2112, 33, 2841, 2831, 2837])).
% 1.18/1.09 tff(2843,plain,(product(e_6, e_4, e_3) | product(e_3, e_3, e_6) | product(e_1, e_4, e_3) | product(e_1, e_4, e_1) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | (~product(e_2, e_3, e_4)) | product(e_4, e_4, e_2) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | (~product(e_6, e_1, e_5)) | product(e_6, e_4, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_6, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.09 tff(2844,plain,
% 1.18/1.09 (product(e_6, e_4, e_3)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2843, 2766, 1025, 1424, 2339, 1027, 373, 818, 2700, 1560, 1562, 1561, 1100, 1907, 2704, 1182, 2703, 1751])).
% 1.18/1.09 tff(2845,plain,
% 1.18/1.09 (((~![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_3)) | (~product(e_6, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_6, e_4, e_3)) | (~product(e_6, e_3, e_3)))),
% 1.18/1.09 inference(rewrite,[status(thm)],[])).
% 1.18/1.09 tff(2846,plain,
% 1.18/1.09 ((~![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_3)) | (~product(e_6, e_3, e_3)))),
% 1.18/1.09 inference(quant_inst,[status(thm)],[])).
% 1.18/1.09 tff(2847,plain,
% 1.18/1.09 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_6, e_4, e_3)) | (~product(e_6, e_3, e_3))),
% 1.18/1.09 inference(modus_ponens,[status(thm)],[2846, 2845])).
% 1.18/1.09 tff(2848,plain,
% 1.18/1.09 ($false),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2847, 974, 12, 1416, 1248])).
% 1.18/1.09 tff(2849,plain,((~product(e_6, e_3, e_3)) | (~product(e_6, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.09 tff(2850,plain,
% 1.18/1.09 (~product(e_6, e_3, e_3)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2849, 2844])).
% 1.18/1.09 tff(2851,plain,
% 1.18/1.09 (~product(e_6, e_3, e_2)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2008, 2772])).
% 1.18/1.09 tff(2852,plain,
% 1.18/1.09 (product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | product(e_6, e_3, e_5) | product(e_6, e_3, e_1)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[1273, 289, 693, 144, 1265, 2732])).
% 1.18/1.09 tff(2853,plain,
% 1.18/1.09 (product(e_6, e_3, e_1)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2852, 2851, 2850, 2785])).
% 1.18/1.09 tff(2854,plain,
% 1.18/1.09 (product(e_4, e_6, e_1)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[1361, 2853, 961])).
% 1.18/1.09 tff(2855,plain,
% 1.18/1.09 (~product(e_4, e_5, e_1)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[1599, 2854])).
% 1.18/1.09 tff(2856,plain,
% 1.18/1.09 (~product(e_4, e_5, e_3)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2581, 889])).
% 1.18/1.09 tff(2857,plain,
% 1.18/1.09 (((~![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_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_2) | (~product(e_2, e_5, e_5)) | (~product(e_4, e_5, e_5)))),
% 1.18/1.09 inference(rewrite,[status(thm)],[])).
% 1.18/1.09 tff(2858,plain,
% 1.18/1.09 ((~![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_5, e_5)) | (~product(e_4, e_5, e_5)))),
% 1.18/1.09 inference(quant_inst,[status(thm)],[])).
% 1.18/1.09 tff(2859,plain,
% 1.18/1.09 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_5, e_5)) | (~product(e_4, e_5, e_5))),
% 1.18/1.09 inference(modus_ponens,[status(thm)],[2858, 2857])).
% 1.18/1.09 tff(2860,plain,
% 1.18/1.09 ($false),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2859, 335, 87, 2516, 2583])).
% 1.18/1.09 tff(2861,plain,((~product(e_4, e_5, e_5)) | (~product(e_2, e_5, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.09 tff(2862,plain,
% 1.18/1.09 (~product(e_4, e_5, e_5)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2861, 2782])).
% 1.18/1.09 tff(2863,plain,
% 1.18/1.09 (product(e_4, e_5, e_4)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2596, 2862, 2856, 2761, 2855, 2764])).
% 1.18/1.09 tff(2864,plain,
% 1.18/1.09 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_5, e_4)) | (~product(e_3, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_5, e_4)) | (~product(e_3, e_5, e_4)))),
% 1.18/1.09 inference(rewrite,[status(thm)],[])).
% 1.18/1.09 tff(2865,plain,
% 1.18/1.09 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_5, e_4)) | (~product(e_3, e_5, e_4)))),
% 1.18/1.09 inference(quant_inst,[status(thm)],[])).
% 1.18/1.09 tff(2866,plain,
% 1.18/1.09 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_5, e_4)) | (~product(e_3, e_5, e_4))),
% 1.18/1.09 inference(modus_ponens,[status(thm)],[2865, 2864])).
% 1.18/1.09 tff(2867,plain,
% 1.18/1.09 ($false),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2866, 974, 87, 2863, 2784])).
% 1.18/1.09 tff(2868,plain,(product(e_1, e_4, e_3) | product(e_4, e_5, e_6) | product(e_4, e_5, e_2) | product(e_3, e_5, e_6) | product(e_2, e_5, e_6) | product(e_2, e_1, e_2) | (~product(e_4, e_3, e_6)) | product(e_6, e_3, e_6) | product(e_3, e_3, e_6) | product(e_1, e_4, e_1) | product(e_1, e_3, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_4, e_4, e_2) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | (~product(e_6, e_1, e_5)) | product(e_6, e_4, e_2) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_6, e_4, e_1) | (~product(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.09 tff(2869,plain,
% 1.18/1.09 (product(e_6, e_4, e_1)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2868, 2757, 2764, 2763, 2762, 2698, 2761, 1265, 2702, 1424, 1027, 373, 818, 1560, 1562, 1561, 1100, 961, 1182, 2703, 1907, 889])).
% 1.18/1.09 tff(2870,plain,
% 1.18/1.09 ((~product(e_1, e_4, e_4)) | (~product(e_6, e_4, e_1))),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[1875, 690])).
% 1.18/1.09 tff(2871,plain,
% 1.18/1.09 (~product(e_1, e_4, e_4)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[2870, 2869])).
% 1.18/1.09 tff(2872,plain,
% 1.18/1.09 (product(e_2, e_4, e_6)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[989, 961, 2700])).
% 1.18/1.09 tff(2873,plain,
% 1.18/1.09 (~product(e_1, e_4, e_6)),
% 1.18/1.09 inference(unit_resolution,[status(thm)],[1402, 2872])).
% 1.18/1.09 tff(2874,plain,
% 1.18/1.09 (((~![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_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_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_3, e_5)))),
% 1.18/1.09 inference(rewrite,[status(thm)],[])).
% 1.18/1.09 tff(2875,plain,
% 1.18/1.10 ((~![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_5)) | (~product(e_1, e_3, e_5)))),
% 1.18/1.10 inference(quant_inst,[status(thm)],[])).
% 1.18/1.10 tff(2876,plain,
% 1.18/1.10 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_3, e_5))),
% 1.18/1.10 inference(modus_ponens,[status(thm)],[2875, 2874])).
% 1.18/1.10 tff(2877,plain,
% 1.18/1.10 ($false),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2876, 974, 12, 1947, 1011])).
% 1.18/1.10 tff(2878,plain,((~product(e_1, e_3, e_5)) | (~product(e_1, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.10 tff(2879,plain,
% 1.18/1.10 (~product(e_1, e_4, e_5)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2878, 2760])).
% 1.18/1.10 tff(2880,plain,
% 1.18/1.10 (product(e_1, e_4, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[1413, 2879, 2757, 2873, 1424, 2871])).
% 1.18/1.10 tff(2881,plain,
% 1.18/1.10 (~product(e_1, e_5, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2384, 2880])).
% 1.18/1.10 tff(2882,plain,
% 1.18/1.10 (~product(e_5, e_3, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2132, 2881, 2760])).
% 1.18/1.10 tff(2883,plain,
% 1.18/1.10 (~product(e_3, e_3, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2093, 33, 286, 2760])).
% 1.18/1.10 tff(2884,plain,
% 1.18/1.10 (~product(e_5, e_3, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[1965, 33, 2760, 619])).
% 1.18/1.10 tff(2885,plain,
% 1.18/1.10 ($false),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2123, 2884, 2883, 2707, 2734, 2733, 2702, 2882])).
% 1.18/1.10 tff(2886,plain,(product(e_6, e_4, e_2) | product(e_1, e_4, e_1) | product(e_1, e_3, e_1) | product(e_4, e_5, e_2) | product(e_3, e_5, e_6) | product(e_2, e_5, e_6) | product(e_2, e_1, e_2) | product(e_4, e_5, e_6) | product(e_6, e_3, e_6) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_4, e_4, e_2) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | (~product(e_6, e_1, e_5)) | (~product(e_4, e_3, e_6)) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | (~product(e_4, e_2, e_3)) | product(e_6, e_4, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.10 tff(2887,plain,
% 1.18/1.10 (product(e_6, e_4, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2886, 818, 2638, 2565, 2672, 2552, 2532, 2571, 2650, 373, 2696, 1560, 1562, 1561, 2539, 2636, 1005, 2535, 2541, 2695])).
% 1.18/1.10 tff(2888,plain,
% 1.18/1.10 (((~![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_2)) | (~product(e_6, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_6, e_4, e_2)) | (~product(e_6, e_3, e_2)))),
% 1.18/1.10 inference(rewrite,[status(thm)],[])).
% 1.18/1.10 tff(2889,plain,
% 1.18/1.10 ((~![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_2)) | (~product(e_6, e_3, e_2)))),
% 1.18/1.10 inference(quant_inst,[status(thm)],[])).
% 1.18/1.10 tff(2890,plain,
% 1.18/1.10 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_6, e_4, e_2)) | (~product(e_6, e_3, e_2))),
% 1.18/1.10 inference(modus_ponens,[status(thm)],[2889, 2888])).
% 1.18/1.10 tff(2891,plain,
% 1.18/1.10 ($false),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2890, 974, 12, 1520, 1086])).
% 1.18/1.10 tff(2892,plain,((~product(e_6, e_3, e_2)) | (~product(e_6, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.10 tff(2893,plain,
% 1.18/1.10 (~product(e_6, e_3, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2892, 2887])).
% 1.18/1.10 tff(2894,plain,
% 1.18/1.10 (~product(e_1, e_3, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2307, 2658])).
% 1.18/1.10 tff(2895,plain,
% 1.18/1.10 (~product(e_6, e_3, e_3)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2433, 2894, 2651, 2638, 2663, 2662, 2637, 2653, 2655])).
% 1.18/1.10 tff(2896,plain,
% 1.18/1.10 (product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | product(e_6, e_3, e_5) | product(e_6, e_3, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[1273, 289, 693, 144, 2650, 2655])).
% 1.18/1.10 tff(2897,plain,
% 1.18/1.10 (product(e_6, e_3, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2896, 2895, 2540, 2893])).
% 1.18/1.10 tff(2898,plain,
% 1.18/1.10 (product(e_4, e_6, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[1361, 2897, 2636])).
% 1.18/1.10 tff(2899,plain,
% 1.18/1.10 (~product(e_4, e_5, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[1599, 2898])).
% 1.18/1.10 tff(2900,plain,
% 1.18/1.10 (~product(e_4, e_5, e_5)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2861, 2674])).
% 1.18/1.10 tff(2901,plain,
% 1.18/1.10 (product(e_4, e_5, e_4)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2596, 2900, 2582, 2571, 2899, 2565])).
% 1.18/1.10 tff(2902,plain,
% 1.18/1.10 ($false),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2866, 974, 87, 2901, 2689])).
% 1.18/1.10 tff(2903,plain,(product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.10 tff(2904,plain,
% 1.18/1.10 (product(e_2, e_4, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2903, 502, 1560, 1562, 1561, 373])).
% 1.18/1.10 tff(2905,plain,
% 1.18/1.10 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_4, e_5)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_4, e_5)) | (~product(e_2, e_4, e_1)))),
% 1.18/1.10 inference(rewrite,[status(thm)],[])).
% 1.18/1.10 tff(2906,plain,
% 1.18/1.10 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_4, e_5)) | (~product(e_2, e_4, e_1)))),
% 1.18/1.10 inference(quant_inst,[status(thm)],[])).
% 1.18/1.10 tff(2907,plain,
% 1.18/1.10 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_4, e_5)) | (~product(e_2, e_4, e_1))),
% 1.18/1.10 inference(modus_ponens,[status(thm)],[2906, 2905])).
% 1.18/1.10 tff(2908,plain,
% 1.18/1.10 ($false),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2907, 33, 188, 1011, 1432])).
% 1.18/1.10 tff(2909,plain,((~product(e_1, e_4, e_5)) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.10 tff(2910,plain,
% 1.18/1.10 (~product(e_1, e_4, e_5)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2909, 2904])).
% 1.18/1.10 tff(2911,plain,
% 1.18/1.10 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_6) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_6)))),
% 1.18/1.10 inference(rewrite,[status(thm)],[])).
% 1.18/1.10 tff(2912,plain,
% 1.18/1.10 ((product(e_2, e_1, e_6) | (~product(e_1, e_4, e_6)) | (~product(e_2, e_4, e_1))) <=> (product(e_2, e_1, e_6) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_6)))),
% 1.18/1.10 inference(rewrite,[status(thm)],[])).
% 1.18/1.10 tff(2913,plain,
% 1.18/1.10 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_4, e_6)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_6))))),
% 1.18/1.10 inference(monotonicity,[status(thm)],[2912])).
% 1.18/1.10 tff(2914,plain,
% 1.18/1.10 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_4, e_6)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_6) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_6)))),
% 1.18/1.10 inference(transitivity,[status(thm)],[2913, 2911])).
% 1.18/1.10 tff(2915,plain,
% 1.18/1.10 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_4, e_6)) | (~product(e_2, e_4, e_1)))),
% 1.18/1.10 inference(quant_inst,[status(thm)],[])).
% 1.18/1.10 tff(2916,plain,
% 1.18/1.10 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_6) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_6))),
% 1.18/1.10 inference(modus_ponens,[status(thm)],[2915, 2914])).
% 1.18/1.10 tff(2917,plain,
% 1.18/1.10 ($false),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2916, 33, 181, 1432, 1397])).
% 1.18/1.10 tff(2918,plain,((~product(e_1, e_4, e_6)) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.10 tff(2919,plain,
% 1.18/1.10 (~product(e_1, e_4, e_6)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2918, 2904])).
% 1.18/1.10 tff(2920,plain,
% 1.18/1.10 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_4)))),
% 1.18/1.10 inference(rewrite,[status(thm)],[])).
% 1.18/1.10 tff(2921,plain,
% 1.18/1.10 ((product(e_2, e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_2, e_4, e_1))) <=> (product(e_2, e_1, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_4)))),
% 1.18/1.10 inference(rewrite,[status(thm)],[])).
% 1.18/1.10 tff(2922,plain,
% 1.18/1.10 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_4))))),
% 1.18/1.10 inference(monotonicity,[status(thm)],[2921])).
% 1.18/1.10 tff(2923,plain,
% 1.18/1.10 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_4)))),
% 1.18/1.10 inference(transitivity,[status(thm)],[2922, 2920])).
% 1.18/1.10 tff(2924,plain,
% 1.18/1.10 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_2, e_4, e_1)))),
% 1.18/1.10 inference(quant_inst,[status(thm)],[])).
% 1.18/1.10 tff(2925,plain,
% 1.18/1.10 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_4))),
% 1.18/1.10 inference(modus_ponens,[status(thm)],[2924, 2923])).
% 1.18/1.10 tff(2926,plain,
% 1.18/1.10 ($false),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2925, 33, 195, 1305, 1432])).
% 1.18/1.10 tff(2927,plain,((~product(e_1, e_4, e_4)) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.10 tff(2928,plain,
% 1.18/1.10 (~product(e_1, e_4, e_4)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2927, 2904])).
% 1.18/1.10 tff(2929,plain,
% 1.18/1.10 (~product(e_6, e_4, e_5)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2715, 2539])).
% 1.18/1.10 tff(2930,plain,
% 1.18/1.10 (((~![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_2, e_4, e_1)) | (~product(e_2, e_5, e_1)))) <=> ((~![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_2, e_4, e_1)) | (~product(e_2, e_5, e_1)))),
% 1.18/1.10 inference(rewrite,[status(thm)],[])).
% 1.18/1.10 tff(2931,plain,
% 1.18/1.10 ((~![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_2, e_4, e_1)) | (~product(e_2, e_5, e_1)))),
% 1.18/1.10 inference(quant_inst,[status(thm)],[])).
% 1.18/1.10 tff(2932,plain,
% 1.18/1.10 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_5, e_1))),
% 1.18/1.10 inference(modus_ponens,[status(thm)],[2931, 2930])).
% 1.18/1.10 tff(2933,plain,
% 1.18/1.10 ($false),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2932, 561, 12, 2598, 1432])).
% 1.18/1.10 tff(2934,plain,((~product(e_2, e_5, e_1)) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.10 tff(2935,plain,
% 1.18/1.10 (~product(e_2, e_5, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2934, 2904])).
% 1.18/1.10 tff(2936,plain,
% 1.18/1.10 (product(e_2, e_5, e_5)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2513, 2935, 2552, 2545, 2544])).
% 1.18/1.10 tff(2937,plain,
% 1.18/1.10 (~product(e_2, e_4, e_5)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2524, 2936])).
% 1.18/1.10 tff(2938,plain,
% 1.18/1.10 (~product(e_4, e_3, e_5)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2527, 2937, 2542])).
% 1.18/1.10 tff(2939,plain,
% 1.18/1.10 (~product(e_1, e_3, e_6)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2036, 2555, 2553, 2938])).
% 1.18/1.10 tff(2940,plain,
% 1.18/1.10 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_5, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_5, e_4, e_1)))),
% 1.18/1.10 inference(rewrite,[status(thm)],[])).
% 1.18/1.10 tff(2941,plain,
% 1.18/1.10 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_5, e_4, e_1)))),
% 1.18/1.10 inference(quant_inst,[status(thm)],[])).
% 1.18/1.10 tff(2942,plain,
% 1.18/1.10 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_5, e_4, e_1))),
% 1.18/1.10 inference(modus_ponens,[status(thm)],[2941, 2940])).
% 1.18/1.10 tff(2943,plain,
% 1.18/1.10 ($false),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2942, 587, 87, 1690, 1432])).
% 1.18/1.10 tff(2944,plain,((~product(e_5, e_4, e_1)) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.10 tff(2945,plain,
% 1.18/1.10 (~product(e_5, e_4, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2944, 2904])).
% 1.18/1.10 tff(2946,plain,
% 1.18/1.10 (~product(e_5, e_4, e_6)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2205, 2537])).
% 1.18/1.10 tff(2947,plain,
% 1.18/1.10 (~product(e_5, e_4, e_5)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2729, 2640])).
% 1.18/1.10 tff(2948,plain,
% 1.18/1.10 (product(e_1, e_3, e_5)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2346, 1025, 374, 889, 1265, 1986, 1985, 1027, 1267, 1024])).
% 1.18/1.10 tff(2949,plain,
% 1.18/1.10 (~product(e_3, e_3, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2374, 1025, 2299, 1265, 1986, 1985, 2298, 1027, 1267, 2295, 1024])).
% 1.18/1.10 tff(2950,plain,
% 1.18/1.10 (~product(e_5, e_3, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[1965, 33, 2948, 619])).
% 1.18/1.10 tff(2951,plain,
% 1.18/1.10 (product(e_5, e_3, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2123, 2950, 1986, 1985, 2298, 1025, 2949])).
% 1.18/1.10 tff(2952,plain,
% 1.18/1.10 (product(e_1, e_5, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2132, 2951, 2948])).
% 1.18/1.10 tff(2953,plain,
% 1.18/1.10 (~product(e_1, e_4, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2384, 2952])).
% 1.18/1.10 tff(2954,plain,
% 1.18/1.10 (product(e_1, e_4, e_3)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[1413, 2953, 1405, 1423, 1424, 1404])).
% 1.18/1.10 tff(2955,plain,
% 1.18/1.10 (~product(e_5, e_4, e_3)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[1921, 2954])).
% 1.18/1.10 tff(2956,plain,
% 1.18/1.10 (product(e_6, e_4, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2756, 2954, 1024, 1985, 2298, 2299, 1265, 1027, 1267, 2295, 1025, 1545, 1026, 1148, 663, 1395, 1707, 1986])).
% 1.18/1.10 tff(2957,plain,
% 1.18/1.10 (~product(e_5, e_4, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[1861, 2956])).
% 1.18/1.10 tff(2958,plain,
% 1.18/1.10 (product(e_5, e_4, e_4)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[1558, 2957, 1545, 1026, 1747, 2955])).
% 1.18/1.10 tff(2959,plain,
% 1.18/1.10 (product(e_4, e_4, e_5)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[1576, 2958, 1562, 2955, 1561, 1560])).
% 1.18/1.10 tff(2960,plain,
% 1.18/1.10 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_5) | (~product(e_4, e_4, e_5)) | (~product(e_5, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_5) | (~product(e_4, e_4, e_5)) | (~product(e_5, e_4, e_4)))),
% 1.18/1.10 inference(rewrite,[status(thm)],[])).
% 1.18/1.10 tff(2961,plain,
% 1.18/1.10 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_5) | (~product(e_4, e_4, e_5)) | (~product(e_5, e_4, e_4)))),
% 1.18/1.10 inference(quant_inst,[status(thm)],[])).
% 1.18/1.10 tff(2962,plain,
% 1.18/1.10 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_5) | (~product(e_4, e_4, e_5)) | (~product(e_5, e_4, e_4))),
% 1.18/1.10 inference(modus_ponens,[status(thm)],[2961, 2960])).
% 1.18/1.10 tff(2963,plain,
% 1.18/1.10 ($false),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2962, 33, 2958, 1545, 2959])).
% 1.18/1.10 tff(2964,plain,(product(e_3, e_3, e_6) | product(e_5, e_4, e_5) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_4, e_2) | product(e_5, e_4, e_6) | product(e_5, e_4, e_1) | product(e_1, e_3, e_6) | product(e_5, e_3, e_6) | product(e_6, e_3, e_6) | product(e_1, e_3, e_1) | product(e_6, e_3, e_5) | product(e_5, e_1, e_3) | product(e_6, e_1, e_3) | product(e_6, e_4, e_5) | product(e_6, e_4, e_6) | product(e_5, e_3, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_6) | product(e_1, e_4, e_1) | product(e_1, e_4, e_5) | (~product(e_2, e_3, e_4)) | (~product(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.10 tff(2965,plain,
% 1.18/1.10 (product(e_3, e_3, e_6)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2964, 2947, 1562, 1561, 1560, 2946, 2945, 2939, 2639, 2650, 2638, 2540, 2536, 2534, 2929, 2695, 2649, 2928, 2919, 2696, 2910, 2542, 2541])).
% 1.18/1.10 tff(2966,plain,
% 1.18/1.10 (~product(e_4, e_3, e_6)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[979, 2965])).
% 1.18/1.10 tff(2967,plain,
% 1.18/1.10 (product(e_4, e_3, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[535, 2966, 2555, 2553, 2938])).
% 1.18/1.10 tff(2968,plain,
% 1.18/1.10 ((~product(e_1, e_3, e_3)) | (~product(e_4, e_3, e_1))),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[461, 417])).
% 1.18/1.10 tff(2969,plain,
% 1.18/1.10 (~product(e_1, e_3, e_3)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2968, 2967])).
% 1.18/1.10 tff(2970,plain,
% 1.18/1.10 (product(e_1, e_3, e_6)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[480, 451, 1027, 1225, 1034, 54])).
% 1.18/1.10 tff(2971,plain,
% 1.18/1.10 ($false),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[497, 33, 491, 430, 2970])).
% 1.18/1.10 tff(2972,plain,((~product(e_4, e_3, e_1)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.10 tff(2973,plain,
% 1.18/1.10 (product(e_1, e_3, e_5)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2972, 430, 1225, 1027, 1034, 441])).
% 1.18/1.10 tff(2974,plain,
% 1.18/1.10 ($false),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2462, 33, 502, 430, 2973])).
% 1.18/1.10 tff(2975,plain,((~product(e_4, e_3, e_1)) | product(e_4, e_1, 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_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.10 tff(2976,plain,
% 1.18/1.10 ((~product(e_4, e_3, e_1)) | product(e_4, e_1, e_5) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2975, 428])).
% 1.18/1.10 tff(2977,plain,
% 1.18/1.10 (product(e_1, e_3, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2976, 2967, 502, 2638, 2969])).
% 1.18/1.10 tff(2978,plain,
% 1.18/1.10 (~product(e_6, e_3, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[1097, 2977])).
% 1.18/1.10 tff(2979,plain,
% 1.18/1.10 (product(e_6, e_3, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2021, 2978, 2655, 2650, 2965, 2540])).
% 1.18/1.10 tff(2980,plain,
% 1.18/1.10 (((~![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_3, e_1)) | (~product(e_6, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_6) | (~product(e_4, e_3, e_1)) | (~product(e_6, e_3, e_1)))),
% 1.18/1.10 inference(rewrite,[status(thm)],[])).
% 1.18/1.10 tff(2981,plain,
% 1.18/1.10 ((equalish(e_4, e_6) | (~product(e_6, e_3, e_1)) | (~product(e_4, e_3, e_1))) <=> (equalish(e_4, e_6) | (~product(e_4, e_3, e_1)) | (~product(e_6, e_3, e_1)))),
% 1.18/1.10 inference(rewrite,[status(thm)],[])).
% 1.18/1.10 tff(2982,plain,
% 1.18/1.10 (((~![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_3, e_1)) | (~product(e_4, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_6) | (~product(e_4, e_3, e_1)) | (~product(e_6, e_3, e_1))))),
% 1.18/1.10 inference(monotonicity,[status(thm)],[2981])).
% 1.18/1.10 tff(2983,plain,
% 1.18/1.10 (((~![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_3, e_1)) | (~product(e_4, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_6) | (~product(e_4, e_3, e_1)) | (~product(e_6, e_3, e_1)))),
% 1.18/1.10 inference(transitivity,[status(thm)],[2982, 2980])).
% 1.18/1.10 tff(2984,plain,
% 1.18/1.10 ((~![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_3, e_1)) | (~product(e_4, e_3, e_1)))),
% 1.18/1.10 inference(quant_inst,[status(thm)],[])).
% 1.18/1.10 tff(2985,plain,
% 1.18/1.10 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_6) | (~product(e_4, e_3, e_1)) | (~product(e_6, e_3, e_1))),
% 1.18/1.10 inference(modus_ponens,[status(thm)],[2984, 2983])).
% 1.18/1.10 tff(2986,plain,
% 1.18/1.10 ($false),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2985, 2721, 87, 2967, 2979])).
% 1.18/1.10 tff(2987,plain,(product(e_4, e_1, e_5) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_4, e_2) | product(e_2, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.10 tff(2988,plain,
% 1.18/1.10 (product(e_4, e_1, e_5) | product(e_4, e_4, e_6) | product(e_4, e_4, e_1) | product(e_4, e_4, e_2)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2987, 372])).
% 1.18/1.10 tff(2989,plain,
% 1.18/1.10 (product(e_4, e_4, e_1)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[2988, 2531, 2448, 2459])).
% 1.18/1.10 tff(2990,plain,
% 1.18/1.10 (product(e_2, e_4, e_6)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[990, 2530])).
% 1.18/1.10 tff(2991,plain,
% 1.18/1.10 (~product(e_1, e_4, e_6)),
% 1.18/1.10 inference(unit_resolution,[status(thm)],[1402, 2990])).
% 1.18/1.10 tff(2992,plain,
% 1.18/1.10 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_1)) | product(e_1, e_4, e_1) | (~product(e_1, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_1)) | product(e_1, e_4, e_1) | (~product(e_1, e_4, e_4)))),
% 1.18/1.10 inference(rewrite,[status(thm)],[])).
% 1.18/1.10 tff(2993,plain,
% 1.18/1.10 ((product(e_1, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_4))) <=> ((~product(e_4, e_4, e_1)) | product(e_1, e_4, e_1) | (~product(e_1, e_4, e_4)))),
% 1.18/1.10 inference(rewrite,[status(thm)],[])).
% 1.18/1.10 tff(2994,plain,
% 1.18/1.10 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_1)) | product(e_1, e_4, e_1) | (~product(e_1, e_4, e_4))))),
% 1.18/1.10 inference(monotonicity,[status(thm)],[2993])).
% 1.18/1.10 tff(2995,plain,
% 1.18/1.10 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_1)) | product(e_1, e_4, e_1) | (~product(e_1, e_4, e_4)))),
% 1.18/1.10 inference(transitivity,[status(thm)],[2994, 2992])).
% 1.18/1.10 tff(2996,plain,
% 1.18/1.10 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_4)))),
% 1.18/1.10 inference(quant_inst,[status(thm)],[])).
% 1.18/1.10 tff(2997,plain,
% 1.18/1.10 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_1)) | product(e_1, e_4, e_1) | (~product(e_1, e_4, e_4))),
% 1.18/1.11 inference(modus_ponens,[status(thm)],[2996, 2995])).
% 1.18/1.11 tff(2998,plain,
% 1.18/1.11 ($false),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[2997, 33, 1424, 1305, 858])).
% 1.18/1.11 tff(2999,plain,((~product(e_4, e_4, e_1)) | product(e_1, e_4, e_1) | (~product(e_1, e_4, e_4))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.11 tff(3000,plain,
% 1.18/1.11 (~product(e_1, e_4, e_4)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[2999, 858, 1424])).
% 1.18/1.11 tff(3001,plain,
% 1.18/1.11 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_5) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_5)))),
% 1.18/1.11 inference(rewrite,[status(thm)],[])).
% 1.18/1.11 tff(3002,plain,
% 1.18/1.11 ((product(e_4, e_1, e_5) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_4, e_1))) <=> (product(e_4, e_1, e_5) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_5)))),
% 1.18/1.11 inference(rewrite,[status(thm)],[])).
% 1.18/1.11 tff(3003,plain,
% 1.18/1.11 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_5))))),
% 1.18/1.11 inference(monotonicity,[status(thm)],[3002])).
% 1.18/1.11 tff(3004,plain,
% 1.18/1.11 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_5) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_5)))),
% 1.18/1.11 inference(transitivity,[status(thm)],[3003, 3001])).
% 1.18/1.11 tff(3005,plain,
% 1.18/1.11 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_4, e_1)))),
% 1.18/1.11 inference(quant_inst,[status(thm)],[])).
% 1.18/1.11 tff(3006,plain,
% 1.18/1.11 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_5) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_5))),
% 1.18/1.11 inference(modus_ponens,[status(thm)],[3005, 3004])).
% 1.18/1.11 tff(3007,plain,
% 1.18/1.11 ($false),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3006, 33, 502, 1011, 858])).
% 1.18/1.11 tff(3008,plain,((~product(e_1, e_4, e_5)) | product(e_4, e_1, e_5) | (~product(e_4, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.11 tff(3009,plain,
% 1.18/1.11 (~product(e_1, e_4, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3008, 858, 502])).
% 1.18/1.11 tff(3010,plain,
% 1.18/1.11 (product(e_1, e_4, e_3)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1413, 3009, 1406, 1423, 3000, 1424])).
% 1.18/1.11 tff(3011,plain,
% 1.18/1.11 ($false),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1533, 33, 452, 858, 3010])).
% 1.18/1.11 tff(3012,plain,((~product(e_4, e_4, e_1)) | product(e_4, e_1, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_6) | product(e_1, e_4, e_1) | product(e_4, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.11 tff(3013,plain,
% 1.18/1.11 ((~product(e_4, e_4, e_1)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_6) | product(e_1, e_4, e_1) | product(e_4, e_1, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3012, 417])).
% 1.18/1.11 tff(3014,plain,
% 1.18/1.11 ($false),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3013, 2991, 2989, 2448, 2451, 2385])).
% 1.18/1.11 tff(3015,plain,(product(e_6, e_3, e_6) | product(e_3, e_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_1, e_3, e_6) | product(e_1, e_3, e_1) | product(e_6, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.11 tff(3016,plain,
% 1.18/1.11 (product(e_1, e_3, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3015, 1138, 1986, 1985, 1024, 2294, 1025])).
% 1.18/1.11 tff(3017,plain,
% 1.18/1.11 (~product(e_1, e_1, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1617, 3016])).
% 1.18/1.11 tff(3018,plain,
% 1.18/1.11 (product(e_1, e_1, e_2)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[154, 3017])).
% 1.18/1.11 tff(3019,plain,
% 1.18/1.11 (product(e_4, e_1, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[515, 3018])).
% 1.18/1.11 tff(3020,plain,
% 1.18/1.11 (product(e_3, e_4, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[771, 3019])).
% 1.18/1.11 tff(3021,plain,
% 1.18/1.11 (~product(e_1, e_4, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1022, 3020])).
% 1.18/1.11 tff(3022,plain,
% 1.18/1.11 (~product(e_1, e_4, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1611, 3016])).
% 1.18/1.11 tff(3023,plain,
% 1.18/1.11 (product(e_4, e_3, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[571, 3018, 54])).
% 1.18/1.11 tff(3024,plain,
% 1.18/1.11 (product(e_2, e_4, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[990, 3023])).
% 1.18/1.11 tff(3025,plain,
% 1.18/1.11 (~product(e_1, e_4, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1402, 3024])).
% 1.18/1.11 tff(3026,plain,
% 1.18/1.11 (~product(e_1, e_4, e_2)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1624, 3018])).
% 1.18/1.11 tff(3027,plain,
% 1.18/1.11 (~product(e_4, e_5, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1941, 3023])).
% 1.18/1.11 tff(3028,plain,
% 1.18/1.11 (~product(e_5, e_1, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[800, 3027, 3019])).
% 1.18/1.11 tff(3029,plain,
% 1.18/1.11 (~product(e_4, e_2, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1350, 3023])).
% 1.18/1.11 tff(3030,plain,
% 1.18/1.11 (~product(e_6, e_4, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1502, 3024])).
% 1.18/1.11 tff(3031,plain,
% 1.18/1.11 (~product(e_5, e_4, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[998, 3024])).
% 1.18/1.11 tff(3032,plain,
% 1.18/1.11 (~product(e_4, e_4, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1379, 3023])).
% 1.18/1.11 tff(3033,plain,
% 1.18/1.11 (~product(e_2, e_4, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[782, 3020])).
% 1.18/1.11 tff(3034,plain,
% 1.18/1.11 (~product(e_5, e_1, e_2)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1188, 3018])).
% 1.18/1.11 tff(3035,plain,
% 1.18/1.11 (product(e_5, e_1, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[631, 3028, 3034])).
% 1.18/1.11 tff(3036,plain,
% 1.18/1.11 (product(e_4, e_5, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1589, 3035, 3019])).
% 1.18/1.11 tff(3037,plain,
% 1.18/1.11 (~product(e_4, e_2, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1647, 3036])).
% 1.18/1.11 tff(3038,plain,
% 1.18/1.11 (~product(e_4, e_4, e_2)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1373, 3037, 3033, 3029])).
% 1.18/1.11 tff(3039,plain,
% 1.18/1.11 (product(e_4, e_4, e_4)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1901, 3038, 3018, 3025, 3032, 3031, 3030, 3029, 3019, 3028])).
% 1.18/1.11 tff(3040,plain,
% 1.18/1.11 (~product(e_1, e_4, e_4)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1801, 3039])).
% 1.18/1.11 tff(3041,plain,
% 1.18/1.11 (product(e_1, e_4, e_3)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1413, 3040, 3026, 3025, 3022, 3021])).
% 1.18/1.11 tff(3042,plain,
% 1.18/1.11 (~product(e_6, e_4, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1291, 3020])).
% 1.18/1.11 tff(3043,plain,
% 1.18/1.11 (~product(e_5, e_4, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1323, 3020])).
% 1.18/1.11 tff(3044,plain,
% 1.18/1.11 (~product(e_6, e_4, e_4)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1733, 3039])).
% 1.18/1.11 tff(3045,plain,
% 1.18/1.11 (~product(e_5, e_4, e_4)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1573, 3039])).
% 1.18/1.11 tff(3046,plain,
% 1.18/1.11 ($false),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1926, 3045, 3044, 3043, 3031, 3042, 3030, 3041])).
% 1.18/1.11 tff(3047,plain,(product(e_1, e_3, e_5) | product(e_5, e_3, e_5) | product(e_5, e_3, e_6) | product(e_1, e_3, e_6) | product(e_3, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.11 tff(3048,plain,
% 1.18/1.11 (product(e_1, e_3, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3047, 1985, 1986, 1024, 1025])).
% 1.18/1.11 tff(3049,plain,
% 1.18/1.11 (~product(e_1, e_4, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[2878, 3048])).
% 1.18/1.11 tff(3050,plain,
% 1.18/1.11 (~product(e_6, e_3, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1958, 3048])).
% 1.18/1.11 tff(3051,plain,
% 1.18/1.11 (product(e_1, e_3, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3015, 3050, 1986, 1985, 1024, 2294, 1025])).
% 1.18/1.11 tff(3052,plain,
% 1.18/1.11 (~product(e_1, e_4, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1611, 3051])).
% 1.18/1.11 tff(3053,plain,
% 1.18/1.11 (~product(e_1, e_1, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1617, 3051])).
% 1.18/1.11 tff(3054,plain,
% 1.18/1.11 (product(e_1, e_1, e_2)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[154, 3053])).
% 1.18/1.11 tff(3055,plain,
% 1.18/1.11 (product(e_4, e_1, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[515, 3054])).
% 1.18/1.11 tff(3056,plain,
% 1.18/1.11 (~product(e_4, e_3, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[526, 3055])).
% 1.18/1.11 tff(3057,plain,
% 1.18/1.11 (~product(e_4, e_1, e_2)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[389, 3054])).
% 1.18/1.11 tff(3058,plain,
% 1.18/1.11 (~product(e_4, e_1, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[394, 3054, 3057])).
% 1.18/1.11 tff(3059,plain,
% 1.18/1.11 (~product(e_4, e_3, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[439, 3058, 3051])).
% 1.18/1.11 tff(3060,plain,
% 1.18/1.11 (product(e_4, e_3, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[2179, 3059, 3056])).
% 1.18/1.11 tff(3061,plain,
% 1.18/1.11 (product(e_2, e_4, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[990, 3060])).
% 1.18/1.11 tff(3062,plain,
% 1.18/1.11 (~product(e_1, e_4, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1402, 3061])).
% 1.18/1.11 tff(3063,plain,
% 1.18/1.11 (~product(e_1, e_4, e_2)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1624, 3054])).
% 1.18/1.11 tff(3064,plain,
% 1.18/1.11 (~product(e_4, e_5, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1941, 3060])).
% 1.18/1.11 tff(3065,plain,
% 1.18/1.11 (~product(e_5, e_1, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[800, 3064, 3055])).
% 1.18/1.11 tff(3066,plain,
% 1.18/1.11 (~product(e_4, e_2, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1350, 3060])).
% 1.18/1.11 tff(3067,plain,
% 1.18/1.11 (~product(e_6, e_4, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1502, 3061])).
% 1.18/1.11 tff(3068,plain,
% 1.18/1.11 (~product(e_5, e_4, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[998, 3061])).
% 1.18/1.11 tff(3069,plain,
% 1.18/1.11 (~product(e_4, e_4, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1379, 3060])).
% 1.18/1.11 tff(3070,plain,
% 1.18/1.11 (product(e_3, e_4, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[771, 3055])).
% 1.18/1.11 tff(3071,plain,
% 1.18/1.11 (~product(e_2, e_4, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[782, 3070])).
% 1.18/1.11 tff(3072,plain,
% 1.18/1.11 (~product(e_5, e_1, e_2)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1188, 3054])).
% 1.18/1.11 tff(3073,plain,
% 1.18/1.11 (product(e_5, e_1, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[631, 3065, 3072])).
% 1.18/1.11 tff(3074,plain,
% 1.18/1.11 (product(e_4, e_5, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1589, 3073, 3055])).
% 1.18/1.11 tff(3075,plain,
% 1.18/1.11 (~product(e_4, e_2, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1647, 3074])).
% 1.18/1.11 tff(3076,plain,
% 1.18/1.11 (~product(e_4, e_4, e_2)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1373, 3075, 3071, 3066])).
% 1.18/1.11 tff(3077,plain,
% 1.18/1.11 (product(e_4, e_4, e_4)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1901, 3076, 3054, 3062, 3069, 3068, 3067, 3066, 3055, 3065])).
% 1.18/1.11 tff(3078,plain,
% 1.18/1.11 (~product(e_1, e_4, e_4)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1801, 3077])).
% 1.18/1.11 tff(3079,plain,
% 1.18/1.11 (product(e_1, e_4, e_3)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1413, 3078, 3063, 3062, 3052, 3049])).
% 1.18/1.11 tff(3080,plain,
% 1.18/1.11 (~product(e_6, e_4, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1291, 3070])).
% 1.18/1.11 tff(3081,plain,
% 1.18/1.11 (~product(e_5, e_4, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1323, 3070])).
% 1.18/1.11 tff(3082,plain,
% 1.18/1.11 (~product(e_6, e_4, e_4)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1733, 3077])).
% 1.18/1.11 tff(3083,plain,
% 1.18/1.11 (~product(e_5, e_4, e_4)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1573, 3077])).
% 1.18/1.11 tff(3084,plain,
% 1.18/1.11 ($false),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1926, 3083, 3082, 3081, 3068, 3080, 3067, 3079])).
% 1.18/1.11 tff(3085,plain,(product(e_5, e_3, e_6) | product(e_5, e_3, e_5) | product(e_1, e_3, e_6) | product(e_3, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.11 tff(3086,plain,
% 1.18/1.11 ($false),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3085, 2038, 2029, 1953, 21])).
% 1.18/1.11 tff(3087,plain,(~product(e_5, e_1, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.11 tff(3088,plain,
% 1.18/1.11 (~product(e_6, e_3, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1975, 1147, 1945])).
% 1.18/1.11 tff(3089,plain,
% 1.18/1.11 (~product(e_4, e_3, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[526, 1009])).
% 1.18/1.11 tff(3090,plain,
% 1.18/1.11 (product(e_4, e_3, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[2179, 3089, 55])).
% 1.18/1.11 tff(3091,plain,
% 1.18/1.11 (((~![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_4, e_3, e_1)) | (~product(e_4, e_5, 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_5) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_5, e_1)))),
% 1.18/1.11 inference(rewrite,[status(thm)],[])).
% 1.18/1.11 tff(3092,plain,
% 1.18/1.11 ((equalish(e_3, e_5) | (~product(e_4, e_5, e_1)) | (~product(e_4, e_3, e_1))) <=> (equalish(e_3, e_5) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_5, e_1)))),
% 1.18/1.11 inference(rewrite,[status(thm)],[])).
% 1.18/1.11 tff(3093,plain,
% 1.18/1.11 (((~![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_4, e_5, e_1)) | (~product(e_4, 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_5) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_5, e_1))))),
% 1.18/1.11 inference(monotonicity,[status(thm)],[3092])).
% 1.18/1.11 tff(3094,plain,
% 1.18/1.11 (((~![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_4, e_5, e_1)) | (~product(e_4, 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_5) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_5, e_1)))),
% 1.18/1.11 inference(transitivity,[status(thm)],[3093, 3091])).
% 1.18/1.11 tff(3095,plain,
% 1.18/1.11 ((~![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_4, e_5, e_1)) | (~product(e_4, e_3, e_1)))),
% 1.18/1.11 inference(quant_inst,[status(thm)],[])).
% 1.18/1.11 tff(3096,plain,
% 1.18/1.11 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_5, e_1))),
% 1.18/1.11 inference(modus_ponens,[status(thm)],[3095, 3094])).
% 1.18/1.11 tff(3097,plain,
% 1.18/1.11 ($false),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3096, 1933, 12, 430, 1591])).
% 1.18/1.11 tff(3098,plain,((~product(e_4, e_3, e_1)) | (~product(e_4, e_5, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.11 tff(3099,plain,
% 1.18/1.11 (~product(e_4, e_5, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3098, 3090])).
% 1.18/1.11 tff(3100,plain,
% 1.18/1.11 (~product(e_5, e_1, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1589, 3099, 1009])).
% 1.18/1.11 tff(3101,plain,
% 1.18/1.11 (product(e_5, e_1, e_2)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[631, 3100, 1000])).
% 1.18/1.11 tff(3102,plain,
% 1.18/1.11 (~product(e_5, e_4, e_2)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1543, 3101])).
% 1.18/1.11 tff(3103,assumption,(product(e_3, e_5, e_4)), introduced(assumption)).
% 1.18/1.11 tff(3104,plain,
% 1.18/1.11 (((~![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_3, e_1, e_4)) | (~product(e_3, 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_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_5, e_4)))),
% 1.18/1.11 inference(rewrite,[status(thm)],[])).
% 1.18/1.11 tff(3105,plain,
% 1.18/1.11 ((~![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_3, e_1, e_4)) | (~product(e_3, e_5, e_4)))),
% 1.18/1.11 inference(quant_inst,[status(thm)],[])).
% 1.18/1.11 tff(3106,plain,
% 1.18/1.11 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_5, e_4))),
% 1.18/1.11 inference(modus_ponens,[status(thm)],[3105, 3104])).
% 1.18/1.11 tff(3107,plain,
% 1.18/1.11 ($false),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3106, 577, 12, 324, 3103])).
% 1.18/1.11 tff(3108,plain,(~product(e_3, e_5, e_4)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.11 tff(3109,assumption,(~product(e_3, e_5, e_4)), introduced(assumption)).
% 1.18/1.11 tff(3110,plain,
% 1.18/1.11 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_4) | (~product(e_5, e_4, e_4)) | (~product(e_3, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_5, e_4) | (~product(e_5, e_4, e_4)) | (~product(e_3, e_4, e_5)))),
% 1.18/1.11 inference(rewrite,[status(thm)],[])).
% 1.18/1.11 tff(3111,plain,
% 1.18/1.11 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_4) | (~product(e_5, e_4, e_4)) | (~product(e_3, e_4, e_5)))),
% 1.18/1.11 inference(quant_inst,[status(thm)],[])).
% 1.18/1.11 tff(3112,plain,
% 1.18/1.11 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_5, e_4) | (~product(e_5, e_4, e_4)) | (~product(e_3, e_4, e_5))),
% 1.18/1.11 inference(modus_ponens,[status(thm)],[3111, 3110])).
% 1.18/1.11 tff(3113,plain,
% 1.18/1.11 ($false),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3112, 33, 1563, 773, 3109])).
% 1.18/1.11 tff(3114,plain,((~product(e_5, e_4, e_4)) | (~product(e_3, e_4, e_5)) | product(e_3, e_5, e_4)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.11 tff(3115,plain,
% 1.18/1.11 (~product(e_5, e_4, e_4)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3114, 1010, 3108])).
% 1.18/1.11 tff(3116,plain,
% 1.18/1.11 ((~product(e_4, e_3, e_1)) | product(e_2, e_4, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1487, 330])).
% 1.18/1.11 tff(3117,plain,
% 1.18/1.11 (product(e_2, e_4, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3116, 3090])).
% 1.18/1.11 tff(3118,plain,
% 1.18/1.11 (~product(e_5, e_4, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[2944, 3117])).
% 1.18/1.11 tff(3119,plain,
% 1.18/1.11 (~product(e_1, e_4, e_4)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[2927, 3117])).
% 1.18/1.11 tff(3120,plain,
% 1.18/1.11 (~product(e_1, e_4, e_5)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[2878, 1945])).
% 1.18/1.11 tff(3121,plain,
% 1.18/1.11 (~product(e_1, e_4, e_1)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1889, 3117])).
% 1.18/1.11 tff(3122,plain,
% 1.18/1.11 (~product(e_1, e_4, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[2918, 3117])).
% 1.18/1.11 tff(3123,plain,
% 1.18/1.11 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_2)))),
% 1.18/1.11 inference(rewrite,[status(thm)],[])).
% 1.18/1.11 tff(3124,plain,
% 1.18/1.11 ((product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_1))) <=> (product(e_2, e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_2)))),
% 1.18/1.11 inference(rewrite,[status(thm)],[])).
% 1.18/1.11 tff(3125,plain,
% 1.18/1.11 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_2))))),
% 1.18/1.11 inference(monotonicity,[status(thm)],[3124])).
% 1.18/1.11 tff(3126,plain,
% 1.18/1.11 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_2)))),
% 1.18/1.11 inference(transitivity,[status(thm)],[3125, 3123])).
% 1.18/1.11 tff(3127,plain,
% 1.18/1.11 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_1)))),
% 1.18/1.11 inference(quant_inst,[status(thm)],[])).
% 1.18/1.11 tff(3128,plain,
% 1.18/1.11 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_2))),
% 1.18/1.11 inference(modus_ponens,[status(thm)],[3127, 3126])).
% 1.18/1.11 tff(3129,plain,
% 1.18/1.11 ($false),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3128, 33, 75, 1432, 1278])).
% 1.18/1.11 tff(3130,plain,((~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.11 tff(3131,plain,
% 1.18/1.11 (~product(e_1, e_4, e_2)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3130, 3117])).
% 1.18/1.11 tff(3132,plain,
% 1.18/1.11 (product(e_1, e_4, e_3)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1413, 3131, 3122, 3121, 3120, 3119])).
% 1.18/1.11 tff(3133,plain,
% 1.18/1.11 (~product(e_5, e_4, e_3)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1921, 3132])).
% 1.18/1.11 tff(3134,plain,
% 1.18/1.11 (product(e_5, e_4, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[1558, 3133, 1324, 3118, 3115, 3102])).
% 1.18/1.11 tff(3135,plain,
% 1.18/1.11 (((~![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_5, e_4, e_6)) | (~product(e_5, 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_5, e_4, e_6)) | (~product(e_5, e_3, e_6)))),
% 1.18/1.11 inference(rewrite,[status(thm)],[])).
% 1.18/1.11 tff(3136,plain,
% 1.18/1.11 ((~![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_5, e_4, e_6)) | (~product(e_5, e_3, e_6)))),
% 1.18/1.11 inference(quant_inst,[status(thm)],[])).
% 1.18/1.11 tff(3137,plain,
% 1.18/1.11 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_5, e_4, e_6)) | (~product(e_5, e_3, e_6))),
% 1.18/1.11 inference(modus_ponens,[status(thm)],[3136, 3135])).
% 1.18/1.11 tff(3138,plain,
% 1.18/1.11 ($false),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3137, 974, 12, 993, 2])).
% 1.18/1.11 tff(3139,plain,((~product(e_5, e_3, e_6)) | (~product(e_5, e_4, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.11 tff(3140,plain,
% 1.18/1.11 (~product(e_5, e_3, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3139, 3134])).
% 1.18/1.11 tff(3141,plain,
% 1.18/1.11 (~product(e_1, e_3, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[2037, 3089])).
% 1.18/1.11 tff(3142,plain,
% 1.18/1.11 (product(e_3, e_3, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3085, 3140, 1953, 3141])).
% 1.18/1.11 tff(3143,plain,
% 1.18/1.11 ($false),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[2028, 3142, 3140, 1953, 1966, 3088, 1959])).
% 1.18/1.11 tff(3144,plain,(product(e_5, e_1, e_6) | product(e_4, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.11 tff(3145,plain,
% 1.18/1.11 (product(e_4, e_3, e_6)),
% 1.18/1.11 inference(unit_resolution,[status(thm)],[3144, 3087])).
% 1.18/1.11 tff(3146,plain,
% 1.18/1.11 (((~![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_3, e_6)) | (~product(e_5, 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_5) | (~product(e_4, e_3, e_6)) | (~product(e_5, e_3, e_6)))),
% 1.18/1.11 inference(rewrite,[status(thm)],[])).
% 1.18/1.11 tff(3147,plain,
% 1.18/1.11 ((equalish(e_4, e_5) | (~product(e_5, e_3, e_6)) | (~product(e_4, e_3, e_6))) <=> (equalish(e_4, e_5) | (~product(e_4, e_3, e_6)) | (~product(e_5, e_3, e_6)))),
% 1.18/1.11 inference(rewrite,[status(thm)],[])).
% 1.18/1.11 tff(3148,plain,
% 1.18/1.11 (((~![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_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_5) | (~product(e_4, e_3, e_6)) | (~product(e_5, e_3, e_6))))),
% 1.18/1.11 inference(monotonicity,[status(thm)],[3147])).
% 1.18/1.11 tff(3149,plain,
% 1.18/1.11 (((~![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_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_5) | (~product(e_4, e_3, e_6)) | (~product(e_5, e_3, e_6)))),
% 1.18/1.11 inference(transitivity,[status(thm)],[3148, 3146])).
% 1.18/1.12 tff(3150,plain,
% 1.18/1.12 ((~![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_3, e_6)) | (~product(e_4, e_3, e_6)))),
% 1.18/1.12 inference(quant_inst,[status(thm)],[])).
% 1.18/1.12 tff(3151,plain,
% 1.18/1.12 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_4, e_3, e_6)) | (~product(e_5, e_3, e_6))),
% 1.18/1.12 inference(modus_ponens,[status(thm)],[3150, 3149])).
% 1.18/1.12 tff(3152,plain,
% 1.18/1.12 ($false),
% 1.18/1.12 inference(unit_resolution,[status(thm)],[3151, 871, 87, 961, 2])).
% 1.18/1.12 tff(3153,plain,((~product(e_4, e_3, e_6)) | (~product(e_5, e_3, e_6))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.12 tff(3154,plain,
% 1.18/1.12 (~product(e_5, e_3, e_6)),
% 1.18/1.12 inference(unit_resolution,[status(thm)],[3153, 3145])).
% 1.18/1.12 tff(3155,plain,
% 1.18/1.12 (~product(e_1, e_3, e_6)),
% 1.18/1.12 inference(unit_resolution,[status(thm)],[969, 3145])).
% 1.18/1.12 tff(3156,plain,
% 1.18/1.12 (~product(e_3, e_3, e_6)),
% 1.18/1.12 inference(unit_resolution,[status(thm)],[979, 3145])).
% 1.18/1.12 tff(3157,plain,
% 1.18/1.12 ($false),
% 1.18/1.12 inference(unit_resolution,[status(thm)],[3085, 3156, 3155, 1953, 3154])).
% 1.18/1.12 % SZS output end Proof
%------------------------------------------------------------------------------