TSTP Solution File: GRP134-1.003 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP134-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:26:18 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP134-1.003 : 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 : n009.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 15:06:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(product_type, type, (
% 0.20/0.43 product: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(e_3_type, type, (
% 0.20/0.43 e_3: $i)).
% 0.20/0.43 tff(e_2_type, type, (
% 0.20/0.43 e_2: $i)).
% 0.20/0.43 tff(e_1_type, type, (
% 0.20/0.43 e_1: $i)).
% 0.20/0.43 tff(equalish_type, type, (
% 0.20/0.43 equalish: ( $i * $i ) > $o)).
% 0.20/0.43 tff(group_element_type, type, (
% 0.20/0.43 group_element: $i > $o)).
% 0.20/0.43 tff(1,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.20/0.43 tff(2,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(6,plain,
% 0.20/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.43 tff(8,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.43 tff(11,plain,(
% 0.20/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[10])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(14,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 (~equalish(e_2, e_3)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 ((equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_2, e_3))) <=> (equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[17])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[18, 16])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[21, 15, 12, 2, 1])).
% 0.20/0.43 tff(23,plain,((~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (~product(e_3, e_2, e_3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[23, 1])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.43 tff(30,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg4')).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.43 tff(33,plain,(
% 0.20/0.43 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[32])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (((~product(e_2, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3))) <=> (product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[37, 35])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[40, 34])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (product(e_3, e_3, e_2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[41, 1])).
% 0.20/0.44 tff(43,assumption,(product(e_3, e_3, e_2)), introduced(assumption)).
% 0.20/0.44 tff(44,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, W, Y)) | (~product(X, Z, Y))) <=> ((~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)))), rewrite((((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.44 tff(50,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.44 tff(53,plain,(
% 0.20/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[52])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(56,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (~equalish(e_3, e_2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 ((equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2))) <=> (equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, 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_3, e_3, e_2)) | (~product(e_3, e_2, e_2))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, 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_3, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[60, 58])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[63, 57, 54, 44, 43])).
% 0.20/0.44 tff(65,plain,((~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (~product(e_3, e_2, e_2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[65, 42])).
% 0.20/0.44 tff(67,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.20/0.44 tff(68,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(70,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (~equalish(e_1, e_3)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[74, 71, 12, 67, 68])).
% 0.20/0.44 tff(76,plain,((~product(e_1, e_2, e_1)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (~product(e_1, e_2, e_1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[76, 67])).
% 0.20/0.44 tff(78,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 ((equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1))) <=> (equalish(e_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[81, 79])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[84, 15, 12, 67, 78])).
% 0.20/0.44 tff(86,plain,((~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (~product(e_2, e_2, e_1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[86, 67])).
% 0.20/0.44 tff(88,assumption,(~product(e_2, e_2, e_3)), introduced(assumption)).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (^[Y: $i, X: $i] : refl((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.45 tff(94,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.45 tff(97,plain,(
% 0.20/0.45 ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[96])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(100,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 (group_element(e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 ((product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.45 inference(transitivity,[status(thm)],[104, 102])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(107,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[107, 101, 98])).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 (product(e_2, e_2, e_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[108, 88, 87])).
% 0.20/0.45 tff(110,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.20/0.45 tff(111,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (((~![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_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 ((~![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)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[114, 57, 54, 111, 110])).
% 0.20/0.45 tff(116,plain,((~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 (~product(e_2, e_3, e_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[116, 109])).
% 0.20/0.45 tff(118,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(120,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (~equalish(e_1, e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[124, 121, 12, 111, 118])).
% 0.20/0.45 tff(126,plain,((~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 (~product(e_1, e_2, e_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[126, 109])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(129,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 (group_element(e_1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 ((product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1))) <=> (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[132])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[133, 131])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[136, 130, 101, 98])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (product(e_1, e_2, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[137, 127, 77])).
% 0.20/0.45 tff(139,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.20/0.45 tff(140,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.46 tff(144,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[143, 57, 54, 140, 139])).
% 0.20/0.46 tff(145,plain,((~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(146,plain,
% 0.20/0.46 (~product(e_1, e_3, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[145, 138])).
% 0.20/0.46 tff(147,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.20/0.46 tff(148,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(149,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[150, 121, 54, 147, 67])).
% 0.20/0.46 tff(152,plain,((~product(e_3, e_1, e_1)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(153,plain,
% 0.20/0.46 (~product(e_3, e_1, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[152, 67])).
% 0.20/0.46 tff(154,assumption,(~product(e_3, e_1, e_2)), introduced(assumption)).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(156,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 (group_element(e_3)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.20/0.46 tff(158,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 ((product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> (product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[159])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[160, 158])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[163, 130, 157, 98])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 (product(e_3, e_1, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[164, 154, 153])).
% 0.20/0.46 tff(166,assumption,(product(e_1, e_1, e_3)), introduced(assumption)).
% 0.20/0.46 tff(167,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_1, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[170, 71, 12, 167, 166])).
% 0.20/0.46 tff(172,plain,((~product(e_1, e_1, e_3)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (~product(e_1, e_1, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[172, 165])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 (((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_3, e_1))) <=> (product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[175])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[176, 174])).
% 0.20/0.47 tff(178,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_3, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.20/0.47 tff(180,plain,
% 0.20/0.47 (~product(e_2, e_3, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[179, 34, 67, 173])).
% 0.20/0.47 tff(181,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 (((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(183,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[182])).
% 0.20/0.47 tff(184,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[183, 181])).
% 0.20/0.47 tff(185,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(186,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.20/0.47 tff(187,plain,
% 0.20/0.47 (~product(e_2, e_1, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[186, 34, 140, 180])).
% 0.20/0.47 tff(188,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.47 tff(189,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(190,plain,
% 0.20/0.47 (((~product(e_2, e_1, e_1)) | product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3))) <=> (product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(191,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_1)) | product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[190])).
% 0.20/0.47 tff(192,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_1)) | product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[191, 189])).
% 0.20/0.47 tff(193,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_1)) | product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(194,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.20/0.47 tff(195,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[194, 34, 154, 140, 188])).
% 0.20/0.47 tff(196,plain,((~product(e_2, e_1, e_1)) | product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(197,plain,
% 0.20/0.47 (~product(e_2, e_1, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[196, 154, 140])).
% 0.20/0.47 tff(198,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(199,plain,
% 0.20/0.47 ((product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(200,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[199])).
% 0.20/0.47 tff(201,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1))),
% 0.20/0.47 inference(transitivity,[status(thm)],[200, 198])).
% 0.20/0.47 tff(202,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_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)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(203,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.47 tff(204,plain,
% 0.20/0.47 (product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[203, 130, 101, 98])).
% 0.20/0.47 tff(205,plain,
% 0.20/0.47 (product(e_2, e_1, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[204, 197, 187])).
% 0.20/0.47 tff(206,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(207,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(208,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.20/0.47 tff(209,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[208, 15, 12, 165, 205])).
% 0.20/0.47 tff(210,plain,(product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(211,plain,
% 0.20/0.47 (product(e_3, e_1, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[210, 138, 67])).
% 0.20/0.47 tff(212,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.47 tff(213,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.20/0.47 tff(214,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(215,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(216,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.20/0.47 tff(217,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[216, 34, 213, 88, 212])).
% 0.20/0.47 tff(218,plain,((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(219,plain,
% 0.20/0.47 (~product(e_1, e_3, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[218, 211, 88])).
% 0.20/0.47 tff(220,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | product(e_1, e_3, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | product(e_1, e_3, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(221,plain,
% 0.20/0.47 ((product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1))) <=> ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | product(e_1, e_3, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(222,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | product(e_1, e_3, e_3)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[221])).
% 0.20/0.47 tff(223,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | product(e_1, e_3, e_3))),
% 0.20/0.47 inference(transitivity,[status(thm)],[222, 220])).
% 0.20/0.47 tff(224,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(225,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | product(e_1, e_3, e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.20/0.47 tff(226,plain,
% 0.20/0.47 (product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | product(e_1, e_3, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[225, 130, 157, 98])).
% 0.20/0.47 tff(227,plain,
% 0.20/0.47 (product(e_1, e_3, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[226, 219, 146])).
% 0.20/0.47 tff(228,assumption,(product(e_2, e_3, e_1)), introduced(assumption)).
% 0.20/0.47 tff(229,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.47 tff(230,plain,
% 0.20/0.47 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(231,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.47 tff(232,plain,
% 0.20/0.47 (~equalish(e_2, e_1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.20/0.47 tff(233,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_2, 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_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(234,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(235,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.20/0.47 tff(236,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[235, 232, 12, 229, 228])).
% 0.20/0.47 tff(237,plain,((~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(238,plain,
% 0.20/0.47 (~product(e_2, e_3, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[237, 227])).
% 0.20/0.47 tff(239,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(240,plain,
% 0.20/0.48 ((product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2))) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(241,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[240])).
% 0.20/0.48 tff(242,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))),
% 0.20/0.48 inference(transitivity,[status(thm)],[241, 239])).
% 0.20/0.48 tff(243,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(244,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.20/0.48 tff(245,plain,
% 0.20/0.48 (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[244, 101, 157, 98])).
% 0.20/0.48 tff(246,plain,
% 0.20/0.48 (product(e_2, e_3, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[245, 238, 117])).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 (((~product(e_2, e_3, e_3)) | product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1))) <=> (product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(249,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_3)) | product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[248])).
% 0.20/0.48 tff(250,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_3)) | product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[249, 247])).
% 0.20/0.48 tff(251,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_3)) | product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(252,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.48 tff(253,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[252, 34, 67, 219, 246])).
% 0.20/0.48 tff(254,plain,(product(e_2, e_2, e_3) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(255,plain,
% 0.20/0.48 (product(e_2, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[254, 67])).
% 0.20/0.48 tff(256,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.20/0.48 tff(257,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(258,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(259,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.20/0.48 tff(260,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[259, 121, 54, 1, 256])).
% 0.20/0.48 tff(261,plain,((~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(262,plain,
% 0.20/0.48 (~product(e_2, e_1, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[261, 255])).
% 0.20/0.48 tff(263,assumption,(~product(e_2, e_1, e_3)), introduced(assumption)).
% 0.20/0.48 tff(264,assumption,(~product(e_2, e_2, e_1)), introduced(assumption)).
% 0.20/0.48 tff(265,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(266,plain,
% 0.20/0.48 (((~product(e_1, e_2, e_2)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(267,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[266])).
% 0.20/0.48 tff(268,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[267, 265])).
% 0.20/0.48 tff(269,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(270,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.20/0.48 tff(271,plain,
% 0.20/0.48 (~product(e_2, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[270, 34, 264, 118])).
% 0.20/0.48 tff(272,assumption,(~product(e_1, e_2, e_1)), introduced(assumption)).
% 0.20/0.48 tff(273,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(274,plain,
% 0.20/0.48 (((~product(e_1, e_2, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1))) <=> (product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(275,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, 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(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_2))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[274])).
% 0.20/0.48 tff(276,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, 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(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[275, 273])).
% 0.20/0.48 tff(277,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(278,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.20/0.48 tff(279,plain,
% 0.20/0.48 (~product(e_2, e_1, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[278, 34, 118, 272])).
% 0.20/0.48 tff(280,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[204, 279, 271, 263])).
% 0.20/0.48 tff(281,plain,((~product(e_1, e_2, e_2)) | product(e_2, e_1, e_3) | product(e_1, e_2, e_1) | product(e_2, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(282,plain,
% 0.20/0.48 (~product(e_1, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[281, 262, 77, 87])).
% 0.20/0.48 tff(283,plain,
% 0.20/0.48 (product(e_1, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[137, 282, 77])).
% 0.20/0.48 tff(284,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(285,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(286,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.20/0.48 tff(287,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[286, 121, 12, 255, 283])).
% 0.20/0.48 tff(288,plain,(~product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(289,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(290,plain,
% 0.20/0.48 ((product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(291,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[290])).
% 0.20/0.48 tff(292,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))),
% 0.20/0.48 inference(transitivity,[status(thm)],[291, 289])).
% 0.20/0.48 tff(293,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(294,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.20/0.48 tff(295,plain,
% 0.20/0.48 (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[294, 101, 157, 98])).
% 0.20/0.48 tff(296,plain,
% 0.20/0.48 (product(e_3, e_2, e_3) | product(e_3, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[295, 288])).
% 0.20/0.48 tff(297,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[296, 66, 24])).
% 0.20/0.48 tff(298,plain,(~product(e_2, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(299,assumption,(product(e_2, e_3, e_3)), introduced(assumption)).
% 0.20/0.48 tff(300,assumption,(~product(e_3, e_2, e_3)), introduced(assumption)).
% 0.20/0.48 tff(301,plain,
% 0.20/0.48 (product(e_3, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[296, 300])).
% 0.20/0.48 tff(302,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(303,plain,
% 0.20/0.49 (((~product(e_3, e_2, e_2)) | product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3))) <=> (product(e_3, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(304,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_3))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[303])).
% 0.20/0.49 tff(305,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[304, 302])).
% 0.20/0.49 tff(306,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(307,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.20/0.49 tff(308,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[307, 34, 300, 301, 299])).
% 0.20/0.49 tff(309,plain,(product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(310,plain,
% 0.20/0.49 (product(e_3, e_2, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[309, 299])).
% 0.20/0.49 tff(311,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(312,plain,
% 0.20/0.49 (((~product(e_3, e_2, e_3)) | product(e_3, e_3, e_3) | (~product(e_2, e_3, e_3))) <=> (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(313,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_3, e_3, e_3) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_3))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[312])).
% 0.20/0.49 tff(314,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_3, e_3, e_3) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[313, 311])).
% 0.20/0.49 tff(315,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_3, e_3, e_3) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(316,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.20/0.49 tff(317,plain,
% 0.20/0.49 (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[316, 34])).
% 0.20/0.49 tff(318,plain,
% 0.20/0.49 (product(e_3, e_3, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[317, 310, 299])).
% 0.20/0.49 tff(319,plain,
% 0.20/0.49 (((~![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_3, e_2, 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_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(320,plain,
% 0.20/0.49 ((equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))) <=> (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(321,plain,
% 0.20/0.49 (((~![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_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[320])).
% 0.20/0.49 tff(322,plain,
% 0.20/0.49 (((~![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_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[321, 319])).
% 0.20/0.49 tff(323,plain,
% 0.20/0.49 ((~![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_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(324,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.20/0.49 tff(325,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[324, 15, 54, 310, 318])).
% 0.20/0.49 tff(326,plain,(~product(e_2, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(327,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(328,plain,
% 0.20/0.49 (((~product(e_3, e_2, e_2)) | product(e_2, e_2, e_3) | (~product(e_2, e_3, e_2))) <=> (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(329,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_2, e_2, e_3) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[328])).
% 0.20/0.49 tff(330,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_2, e_2, e_3) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[329, 327])).
% 0.20/0.49 tff(331,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_2, e_2, e_3) | (~product(e_2, e_3, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(332,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.20/0.49 tff(333,plain,
% 0.20/0.49 (~product(e_2, e_3, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[332, 34, 44, 88])).
% 0.20/0.49 tff(334,plain,
% 0.20/0.49 (product(e_2, e_3, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[245, 333, 326])).
% 0.20/0.49 tff(335,plain,
% 0.20/0.49 (~product(e_3, e_3, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[65, 44])).
% 0.20/0.49 tff(336,plain,
% 0.20/0.49 (~product(e_2, e_2, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[41, 335])).
% 0.20/0.49 tff(337,plain,
% 0.20/0.49 (product(e_2, e_2, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[108, 336, 264])).
% 0.20/0.49 tff(338,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(339,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(340,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.20/0.49 tff(341,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[340, 15, 12, 44, 337])).
% 0.20/0.49 tff(342,plain,((~product(e_3, e_2, e_2)) | product(e_2, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(343,plain,
% 0.20/0.49 (product(e_2, e_2, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[342, 44])).
% 0.20/0.49 tff(344,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(345,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(346,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.20/0.49 tff(347,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[346, 57, 54, 343, 334])).
% 0.20/0.49 tff(348,plain,((~product(e_3, e_2, e_2)) | product(e_2, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(349,plain,
% 0.20/0.49 (~product(e_3, e_2, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[348, 88])).
% 0.20/0.49 tff(350,plain,
% 0.20/0.49 (product(e_3, e_2, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[296, 349])).
% 0.20/0.49 tff(351,assumption,(~product(e_3, e_2, e_2)), introduced(assumption)).
% 0.20/0.49 tff(352,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(353,plain,
% 0.20/0.49 (((~product(e_2, e_3, e_2)) | product(e_3, e_2, e_2) | (~product(e_3, e_2, e_3))) <=> (product(e_3, e_2, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(354,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_2)) | product(e_3, e_2, e_2) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_2))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[353])).
% 0.20/0.49 tff(355,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_2)) | product(e_3, e_2, e_2) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_2)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[354, 352])).
% 0.20/0.49 tff(356,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_2)) | product(e_3, e_2, e_2) | (~product(e_3, e_2, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(357,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.20/0.49 tff(358,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[357, 34, 2, 351, 110])).
% 0.20/0.49 tff(359,plain,((~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_3)) | product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(360,plain,
% 0.20/0.49 (~product(e_2, e_3, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[359, 350, 349])).
% 0.20/0.49 tff(361,plain,
% 0.20/0.49 (product(e_2, e_3, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[245, 360, 326])).
% 0.20/0.49 tff(362,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(363,plain,
% 0.20/0.49 ((equalish(e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_1, e_3) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(364,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[363])).
% 0.20/0.49 tff(365,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[364, 362])).
% 0.20/0.49 tff(366,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(367,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_3, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.20/0.50 tff(368,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[367, 71, 54, 228, 188])).
% 0.20/0.50 tff(369,plain,((~product(e_2, e_1, e_1)) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(370,plain,
% 0.20/0.50 (~product(e_2, e_1, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[369, 361])).
% 0.20/0.50 tff(371,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(372,plain,
% 0.20/0.50 ((equalish(e_2, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_2, e_1))) <=> (equalish(e_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(373,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, 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_2, e_2, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[372])).
% 0.20/0.50 tff(374,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, 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_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[373, 371])).
% 0.20/0.50 tff(375,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(376,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.20/0.50 tff(377,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[376, 15, 54, 78, 228])).
% 0.20/0.50 tff(378,plain,((~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(379,plain,
% 0.20/0.50 (~product(e_2, e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[378, 361])).
% 0.20/0.50 tff(380,plain,
% 0.20/0.50 (product(e_2, e_2, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[108, 379, 88])).
% 0.20/0.50 tff(381,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.20/0.50 tff(382,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_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_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(383,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(384,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.20/0.50 tff(385,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[384, 121, 54, 111, 381])).
% 0.20/0.50 tff(386,plain,((~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(387,plain,
% 0.20/0.50 (~product(e_2, e_1, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[386, 380])).
% 0.20/0.50 tff(388,plain,
% 0.20/0.50 (product(e_2, e_1, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[204, 387, 370])).
% 0.20/0.50 tff(389,assumption,(product(e_3, e_3, e_1)), introduced(assumption)).
% 0.20/0.50 tff(390,plain,
% 0.20/0.50 (((~![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_3, e_1)) | (~product(e_2, 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_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(391,plain,
% 0.20/0.50 ((equalish(e_3, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_3, e_1))) <=> (equalish(e_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(392,plain,
% 0.20/0.50 (((~![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_3, e_1)) | (~product(e_3, 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_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[391])).
% 0.20/0.50 tff(393,plain,
% 0.20/0.50 (((~![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_3, e_1)) | (~product(e_3, 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_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[392, 390])).
% 0.20/0.50 tff(394,plain,
% 0.20/0.50 ((~![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_3, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(395,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.20/0.50 tff(396,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[395, 57, 12, 228, 389])).
% 0.20/0.50 tff(397,plain,((~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(398,plain,
% 0.20/0.50 (~product(e_3, e_3, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[397, 361])).
% 0.20/0.50 tff(399,assumption,(~product(e_1, e_3, e_3)), introduced(assumption)).
% 0.20/0.50 tff(400,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(401,plain,
% 0.20/0.50 (((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1))) <=> (product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(402,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[401])).
% 0.20/0.50 tff(403,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[402, 400])).
% 0.20/0.50 tff(404,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(405,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.20/0.50 tff(406,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[405, 34, 2, 399, 228])).
% 0.20/0.50 tff(407,plain,(product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(408,plain,
% 0.20/0.50 (product(e_1, e_3, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[407, 350, 361])).
% 0.20/0.50 tff(409,assumption,(~product(e_3, e_3, e_1)), introduced(assumption)).
% 0.20/0.50 tff(410,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(411,plain,
% 0.20/0.50 (((~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_3, e_1, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(412,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_3))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[411])).
% 0.20/0.50 tff(413,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[412, 410])).
% 0.20/0.50 tff(414,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(415,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.20/0.50 tff(416,plain,
% 0.20/0.50 (~product(e_3, e_1, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[415, 34, 139, 409])).
% 0.20/0.50 tff(417,plain,
% 0.20/0.50 (product(e_3, e_1, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[164, 416, 154])).
% 0.20/0.50 tff(418,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(419,plain,
% 0.20/0.50 (((~product(e_3, e_1, e_1)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3))) <=> (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(420,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[419])).
% 0.20/0.50 tff(421,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[420, 418])).
% 0.20/0.50 tff(422,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(423,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.20/0.50 tff(424,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[423, 34, 416, 417, 139])).
% 0.20/0.50 tff(425,plain,((~product(e_1, e_3, e_3)) | product(e_3, e_1, e_2) | product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(426,plain,
% 0.20/0.50 (product(e_3, e_1, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[425, 408, 398])).
% 0.20/0.50 tff(427,plain,
% 0.20/0.50 (~product(e_1, e_3, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[218, 426, 88])).
% 0.20/0.50 tff(428,assumption,(~product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.50 tff(429,plain,
% 0.20/0.50 (~product(e_1, e_2, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[126, 380])).
% 0.20/0.50 tff(430,plain,
% 0.20/0.50 (product(e_1, e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[137, 429, 428])).
% 0.20/0.50 tff(431,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(432,plain,
% 0.20/0.50 (((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1))) <=> (product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(433,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_3))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[432])).
% 0.20/0.50 tff(434,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[433, 431])).
% 0.20/0.50 tff(435,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(436,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.20/0.51 tff(437,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[436, 34, 430, 427, 388])).
% 0.20/0.51 tff(438,plain,(product(e_2, e_2, e_3) | product(e_1, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(439,plain,
% 0.20/0.51 (product(e_1, e_2, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[438, 298])).
% 0.20/0.51 tff(440,plain,
% 0.20/0.51 (~product(e_3, e_2, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[348, 298])).
% 0.20/0.51 tff(441,plain,
% 0.20/0.51 (product(e_3, e_2, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[296, 440])).
% 0.20/0.51 tff(442,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(443,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(444,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.20/0.51 tff(445,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[444, 71, 12, 2, 140])).
% 0.20/0.51 tff(446,plain,((~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(447,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[446, 441, 439])).
% 0.20/0.51 % SZS output end Proof
%------------------------------------------------------------------------------