TSTP Solution File: GRP127-1.004 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP127-1.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 22:26:06 EDT 2022
% Result : Unsatisfiable 0.23s 0.46s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.14 % Problem : GRP127-1.004 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.37 % Computer : n015.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Aug 31 15:10:22 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.37 Usage: tptp [options] [-file:]file
% 0.15/0.37 -h, -? prints this message.
% 0.15/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.37 -m, -model generate model.
% 0.15/0.37 -p, -proof generate proof.
% 0.15/0.37 -c, -core generate unsat core of named formulas.
% 0.15/0.37 -st, -statistics display statistics.
% 0.15/0.37 -t:timeout set timeout (in second).
% 0.15/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.37 -<param>:<value> configuration parameter and value.
% 0.15/0.37 -o:<output-file> file to place output in.
% 0.23/0.46 % SZS status Unsatisfiable
% 0.23/0.46 % SZS output start Proof
% 0.23/0.46 tff(product_type, type, (
% 0.23/0.46 product: ( $i * $i * $i ) > $o)).
% 0.23/0.46 tff(e_2_type, type, (
% 0.23/0.46 e_2: $i)).
% 0.23/0.46 tff(e_4_type, type, (
% 0.23/0.46 e_4: $i)).
% 0.23/0.46 tff(e_3_type, type, (
% 0.23/0.46 e_3: $i)).
% 0.23/0.46 tff(e_1_type, type, (
% 0.23/0.46 e_1: $i)).
% 0.23/0.46 tff(equalish_type, type, (
% 0.23/0.46 equalish: ( $i * $i ) > $o)).
% 0.23/0.46 tff(group_element_type, type, (
% 0.23/0.46 group_element: $i > $o)).
% 0.23/0.46 tff(1,plain,
% 0.23/0.46 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(2,plain,
% 0.23/0.46 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.23/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.46 tff(3,plain,
% 0.23/0.46 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(4,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_idempotence')).
% 0.23/0.46 tff(5,plain,
% 0.23/0.46 (![X: $i] : product(X, X, X)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.23/0.46 tff(6,plain,(
% 0.23/0.46 ![X: $i] : product(X, X, X)),
% 0.23/0.46 inference(skolemize,[status(sab)],[5])).
% 0.23/0.46 tff(7,plain,
% 0.23/0.46 (![X: $i] : product(X, X, X)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.23/0.46 tff(8,plain,
% 0.23/0.46 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(9,plain,
% 0.23/0.46 (product(e_4, e_4, e_4)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.23/0.46 tff(10,assumption,(product(e_1, e_4, e_4)), introduced(assumption)).
% 0.23/0.46 tff(11,plain,
% 0.23/0.46 (^[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))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(12,plain,
% 0.23/0.46 (![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)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[11])).
% 0.23/0.46 tff(13,plain,
% 0.23/0.46 (![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)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(14,plain,
% 0.23/0.46 (^[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)))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(15,plain,
% 0.23/0.46 (![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)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[14])).
% 0.23/0.46 tff(16,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')).
% 0.23/0.46 tff(17,plain,
% 0.23/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.23/0.46 tff(18,plain,
% 0.23/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.23/0.46 tff(19,plain,(
% 0.23/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.23/0.46 inference(skolemize,[status(sab)],[18])).
% 0.23/0.46 tff(20,plain,
% 0.23/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.23/0.46 tff(21,plain,
% 0.23/0.46 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(22,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.23/0.46 tff(23,plain,
% 0.23/0.46 (~equalish(e_1, e_4)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.23/0.46 tff(24,plain,
% 0.23/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(25,plain,
% 0.23/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(26,plain,
% 0.23/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.23/0.46 tff(27,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[26, 23, 20, 10, 9])).
% 0.23/0.46 tff(28,plain,(~product(e_1, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.46 tff(29,assumption,(product(e_2, e_4, e_4)), introduced(assumption)).
% 0.23/0.46 tff(30,plain,
% 0.23/0.46 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(31,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.23/0.46 tff(32,plain,
% 0.23/0.46 (~equalish(e_2, e_4)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.23/0.46 tff(33,plain,
% 0.23/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(34,plain,
% 0.23/0.46 ((equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4))) <=> (equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(35,plain,
% 0.23/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[34])).
% 0.23/0.46 tff(36,plain,
% 0.23/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.23/0.46 inference(transitivity,[status(thm)],[35, 33])).
% 0.23/0.46 tff(37,plain,
% 0.23/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(38,plain,
% 0.23/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.23/0.46 tff(39,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[38, 32, 20, 29, 9])).
% 0.23/0.46 tff(40,plain,(~product(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.46 tff(41,assumption,(product(e_3, e_4, e_2)), introduced(assumption)).
% 0.23/0.46 tff(42,plain,
% 0.23/0.46 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(43,plain,
% 0.23/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[42])).
% 0.23/0.46 tff(44,plain,
% 0.23/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(45,plain,
% 0.23/0.46 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) <=> ((~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X)) <=> (((~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) | product(Z2, Y, X)))), rewrite((((~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(46,plain,
% 0.23/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[45])).
% 0.23/0.46 tff(47,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.23/0.46 tff(48,plain,
% 0.23/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.23/0.46 tff(49,plain,
% 0.23/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.23/0.46 tff(50,plain,(
% 0.23/0.46 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.23/0.46 inference(skolemize,[status(sab)],[49])).
% 0.23/0.46 tff(51,plain,
% 0.23/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.23/0.46 tff(52,plain,
% 0.23/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_4, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_4, e_3)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(53,plain,
% 0.23/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_4, e_3)))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(54,plain,
% 0.23/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_4, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_4, e_3))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.23/0.46 tff(55,plain,
% 0.23/0.46 (~product(e_4, e_4, e_3)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[54, 51, 41, 40])).
% 0.23/0.46 tff(56,plain,
% 0.23/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_4, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_4, e_4, e_4)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(57,plain,
% 0.23/0.46 ((product(e_4, e_4, e_3) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4))) <=> ((~product(e_4, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_4, e_4, e_4)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(58,plain,
% 0.23/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_3) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_4, e_4, e_4))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[57])).
% 0.23/0.47 tff(59,plain,
% 0.23/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_3) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_4, e_4, e_4)))),
% 0.23/0.47 inference(transitivity,[status(thm)],[58, 56])).
% 0.23/0.47 tff(60,plain,
% 0.23/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_3) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(61,plain,
% 0.23/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_4, e_4, e_4))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.23/0.47 tff(62,plain,
% 0.23/0.47 (~product(e_4, e_3, e_4)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[61, 51, 9, 55])).
% 0.23/0.47 tff(63,assumption,(product(e_2, e_4, e_2)), introduced(assumption)).
% 0.23/0.47 tff(64,plain,
% 0.23/0.47 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(65,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.23/0.47 tff(66,plain,
% 0.23/0.47 (~equalish(e_2, e_3)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.23/0.47 tff(67,plain,
% 0.23/0.47 (((~![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_4, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(68,plain,
% 0.23/0.47 ((~![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_4, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(69,plain,
% 0.23/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_2))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.23/0.47 tff(70,plain,
% 0.23/0.47 ($false),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[69, 66, 20, 41, 63])).
% 0.23/0.47 tff(71,plain,((~product(e_2, e_4, e_2)) | (~product(e_3, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.47 tff(72,plain,
% 0.23/0.47 (~product(e_2, e_4, e_2)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[71, 41])).
% 0.23/0.47 tff(73,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.23/0.47 tff(74,plain,
% 0.23/0.47 (^[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))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(75,plain,
% 0.23/0.47 (![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)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[74])).
% 0.23/0.47 tff(76,plain,
% 0.23/0.47 (![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)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(77,plain,
% 0.23/0.47 (^[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)))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(78,plain,
% 0.23/0.47 (![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)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[77])).
% 0.23/0.47 tff(79,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')).
% 0.23/0.47 tff(80,plain,
% 0.23/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.23/0.47 tff(81,plain,
% 0.23/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.23/0.47 tff(82,plain,(
% 0.23/0.47 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.23/0.47 inference(skolemize,[status(sab)],[81])).
% 0.23/0.47 tff(83,plain,
% 0.23/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.23/0.47 tff(84,plain,
% 0.23/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(85,plain,
% 0.23/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(86,plain,
% 0.23/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_1, e_2))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.23/0.47 tff(87,plain,
% 0.23/0.47 ($false),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[86, 23, 83, 41, 73])).
% 0.23/0.47 tff(88,plain,((~product(e_3, e_1, e_2)) | (~product(e_3, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.47 tff(89,plain,
% 0.23/0.47 (~product(e_3, e_1, e_2)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[88, 41])).
% 0.23/0.47 tff(90,assumption,(product(e_1, e_4, e_3)), introduced(assumption)).
% 0.23/0.47 tff(91,assumption,(product(e_3, e_4, e_4)), introduced(assumption)).
% 0.23/0.47 tff(92,plain,
% 0.23/0.47 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(93,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.23/0.47 tff(94,plain,
% 0.23/0.47 (~equalish(e_3, e_4)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.23/0.47 tff(95,plain,
% 0.23/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(96,plain,
% 0.23/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(97,plain,
% 0.23/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.23/0.47 tff(98,plain,
% 0.23/0.47 ($false),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[97, 94, 20, 91, 9])).
% 0.23/0.47 tff(99,plain,(~product(e_3, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.47 tff(100,plain,
% 0.23/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(101,plain,
% 0.23/0.47 ((product(e_3, e_4, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_4, e_1))) <=> (product(e_3, e_4, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(102,plain,
% 0.23/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_3))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[101])).
% 0.23/0.47 tff(103,plain,
% 0.23/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.23/0.47 inference(transitivity,[status(thm)],[102, 100])).
% 0.23/0.47 tff(104,plain,
% 0.23/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_4, e_1)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(105,plain,
% 0.23/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_1, e_4, e_3))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.23/0.47 tff(106,plain,
% 0.23/0.47 (~product(e_4, e_4, e_1)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[105, 51, 99, 90])).
% 0.23/0.47 tff(107,plain,
% 0.23/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_4, e_4)) | product(e_4, e_4, e_1) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_4, e_4)) | product(e_4, e_4, e_1) | (~product(e_4, e_1, e_4)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(108,plain,
% 0.23/0.47 ((product(e_4, e_4, e_1) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4))) <=> ((~product(e_4, e_4, e_4)) | product(e_4, e_4, e_1) | (~product(e_4, e_1, e_4)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(109,plain,
% 0.23/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_1) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_4, e_4)) | product(e_4, e_4, e_1) | (~product(e_4, e_1, e_4))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[108])).
% 0.23/0.48 tff(110,plain,
% 0.23/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_1) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_4, e_4)) | product(e_4, e_4, e_1) | (~product(e_4, e_1, e_4)))),
% 0.23/0.48 inference(transitivity,[status(thm)],[109, 107])).
% 0.23/0.48 tff(111,plain,
% 0.23/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_1) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(112,plain,
% 0.23/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_4, e_4)) | product(e_4, e_4, e_1) | (~product(e_4, e_1, e_4))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.23/0.48 tff(113,plain,
% 0.23/0.48 (~product(e_4, e_1, e_4)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[112, 51, 9, 106])).
% 0.23/0.48 tff(114,assumption,(~product(e_3, e_1, e_2)), introduced(assumption)).
% 0.23/0.48 tff(115,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.23/0.48 tff(116,plain,
% 0.23/0.48 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(117,plain,
% 0.23/0.48 (product(e_1, e_1, e_1)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[116, 7])).
% 0.23/0.48 tff(118,plain,
% 0.23/0.48 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(119,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.23/0.48 tff(120,plain,
% 0.23/0.48 (~equalish(e_3, e_1)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.23/0.48 tff(121,plain,
% 0.23/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(122,plain,
% 0.23/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(123,plain,
% 0.23/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.23/0.48 tff(124,plain,
% 0.23/0.48 ($false),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[123, 120, 20, 117, 115])).
% 0.23/0.48 tff(125,plain,(~product(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.48 tff(126,assumption,(~product(e_3, e_1, e_4)), introduced(assumption)).
% 0.23/0.48 tff(127,plain,
% 0.23/0.48 (^[Y: $i, X: $i] : refl((product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(128,plain,
% 0.23/0.48 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[127])).
% 0.23/0.48 tff(129,plain,
% 0.23/0.48 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(130,plain,
% 0.23/0.48 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)))), rewrite(((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(131,plain,
% 0.23/0.48 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[130])).
% 0.23/0.48 tff(132,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.23/0.48 tff(133,plain,
% 0.23/0.48 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.23/0.48 tff(134,plain,
% 0.23/0.48 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.23/0.48 tff(135,plain,(
% 0.23/0.48 ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.48 inference(skolemize,[status(sab)],[134])).
% 0.23/0.48 tff(136,plain,
% 0.23/0.48 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.23/0.48 tff(137,plain,
% 0.23/0.48 (group_element(e_3) <=> group_element(e_3)),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(138,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.23/0.48 tff(139,plain,
% 0.23/0.48 (group_element(e_3)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.23/0.48 tff(140,plain,
% 0.23/0.48 (group_element(e_1) <=> group_element(e_1)),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(141,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.23/0.48 tff(142,plain,
% 0.23/0.48 (group_element(e_1)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.23/0.48 tff(143,plain,
% 0.23/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_1) | (~group_element(e_1)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_1) | (~group_element(e_1)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(144,plain,
% 0.23/0.48 ((product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_1) | (~group_element(e_1)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(145,plain,
% 0.23/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_1) | (~group_element(e_1)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3)))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[144])).
% 0.23/0.48 tff(146,plain,
% 0.23/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_1) | (~group_element(e_1)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3))),
% 0.23/0.48 inference(transitivity,[status(thm)],[145, 143])).
% 0.23/0.48 tff(147,plain,
% 0.23/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(148,plain,
% 0.23/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_1) | (~group_element(e_1)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.23/0.48 tff(149,plain,
% 0.23/0.48 (product(e_3, e_1, e_4) | product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[148, 142, 139, 136])).
% 0.23/0.48 tff(150,plain,
% 0.23/0.48 (product(e_3, e_1, e_3)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[149, 126, 125, 114])).
% 0.23/0.48 tff(151,plain,
% 0.23/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(152,plain,
% 0.23/0.48 ((product(e_3, e_1, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_4, e_3))) <=> (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(153,plain,
% 0.23/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[152])).
% 0.23/0.49 tff(154,plain,
% 0.23/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[153, 151])).
% 0.23/0.49 tff(155,plain,
% 0.23/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(156,plain,
% 0.23/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.23/0.49 tff(157,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[156, 51, 126, 150, 90])).
% 0.23/0.49 tff(158,plain,(product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | product(e_3, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.49 tff(159,plain,
% 0.23/0.49 (product(e_3, e_1, e_4)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[158, 90, 114])).
% 0.23/0.49 tff(160,plain,
% 0.23/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(161,plain,
% 0.23/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(162,plain,
% 0.23/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.23/0.49 tff(163,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[162, 51, 159, 90, 113])).
% 0.23/0.49 tff(164,plain,((~product(e_1, e_4, e_3)) | product(e_3, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.49 tff(165,plain,
% 0.23/0.49 (~product(e_1, e_4, e_3)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[164, 89])).
% 0.23/0.49 tff(166,assumption,(~product(e_2, e_4, e_2)), introduced(assumption)).
% 0.23/0.49 tff(167,assumption,(~product(e_2, e_4, e_3)), introduced(assumption)).
% 0.23/0.49 tff(168,plain,
% 0.23/0.49 (group_element(e_4) <=> group_element(e_4)),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(169,axiom,(group_element(e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_4')).
% 0.23/0.49 tff(170,plain,
% 0.23/0.49 (group_element(e_4)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.23/0.49 tff(171,plain,
% 0.23/0.49 (group_element(e_2) <=> group_element(e_2)),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(172,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.23/0.49 tff(173,plain,
% 0.23/0.49 (group_element(e_2)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.23/0.49 tff(174,plain,
% 0.23/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(175,plain,
% 0.23/0.49 ((product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2))) <=> ((~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(176,plain,
% 0.23/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3)))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[175])).
% 0.23/0.49 tff(177,plain,
% 0.23/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3))),
% 0.23/0.49 inference(transitivity,[status(thm)],[176, 174])).
% 0.23/0.49 tff(178,plain,
% 0.23/0.49 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(179,plain,
% 0.23/0.49 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.23/0.49 tff(180,plain,
% 0.23/0.49 (product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[179, 173, 170, 136])).
% 0.23/0.49 tff(181,plain,
% 0.23/0.49 (product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[180, 40])).
% 0.23/0.49 tff(182,plain,
% 0.23/0.49 (product(e_2, e_4, e_1)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[181, 167, 166])).
% 0.23/0.49 tff(183,assumption,(product(e_1, e_4, e_1)), introduced(assumption)).
% 0.23/0.49 tff(184,assumption,(product(e_2, e_4, e_1)), introduced(assumption)).
% 0.23/0.49 tff(185,plain,
% 0.23/0.49 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(186,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.23/0.49 tff(187,plain,
% 0.23/0.49 (~equalish(e_1, e_2)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.23/0.49 tff(188,plain,
% 0.23/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(189,plain,
% 0.23/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(190,plain,
% 0.23/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_1))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.23/0.49 tff(191,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[190, 187, 20, 184, 183])).
% 0.23/0.49 tff(192,plain,((~product(e_1, e_4, e_1)) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.49 tff(193,plain,
% 0.23/0.49 (~product(e_1, e_4, e_1)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[192, 182])).
% 0.23/0.49 tff(194,assumption,(~product(e_1, e_4, e_3)), introduced(assumption)).
% 0.23/0.49 tff(195,assumption,(~product(e_4, e_4, e_3)), introduced(assumption)).
% 0.23/0.49 tff(196,plain,
% 0.23/0.49 (~product(e_4, e_3, e_4)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[61, 51, 9, 195])).
% 0.23/0.49 tff(197,plain,
% 0.23/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_1)) | product(e_1, e_4, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_1)) | product(e_1, e_4, e_3))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(198,plain,
% 0.23/0.49 ((product(e_1, e_4, e_3) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_3, e_2))) <=> ((~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_1)) | product(e_1, e_4, e_3))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(199,plain,
% 0.23/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_3) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_1)) | product(e_1, e_4, e_3)))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[198])).
% 0.23/0.49 tff(200,plain,
% 0.23/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_3) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_1)) | product(e_1, e_4, e_3))),
% 0.23/0.49 inference(transitivity,[status(thm)],[199, 197])).
% 0.23/0.49 tff(201,plain,
% 0.23/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_3) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_3, e_2)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(202,plain,
% 0.23/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_1)) | product(e_1, e_4, e_3)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.23/0.49 tff(203,plain,
% 0.23/0.49 (~product(e_4, e_3, e_2)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[202, 51, 182, 194])).
% 0.23/0.49 tff(204,assumption,(product(e_4, e_3, e_3)), introduced(assumption)).
% 0.23/0.49 tff(205,plain,
% 0.23/0.49 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(206,plain,
% 0.23/0.49 (product(e_3, e_3, e_3)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[205, 7])).
% 0.23/0.49 tff(207,plain,
% 0.23/0.49 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(208,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.23/0.49 tff(209,plain,
% 0.23/0.49 (~equalish(e_4, e_3)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.23/0.49 tff(210,plain,
% 0.23/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(211,plain,
% 0.23/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(212,plain,
% 0.23/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.23/0.50 tff(213,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[212, 209, 20, 206, 204])).
% 0.23/0.50 tff(214,plain,(~product(e_4, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(215,plain,
% 0.23/0.50 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(216,plain,
% 0.23/0.50 ((product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4))) <=> ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(217,plain,
% 0.23/0.50 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2)))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[216])).
% 0.23/0.50 tff(218,plain,
% 0.23/0.50 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2))),
% 0.23/0.50 inference(transitivity,[status(thm)],[217, 215])).
% 0.23/0.50 tff(219,plain,
% 0.23/0.50 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(220,plain,
% 0.23/0.50 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2)),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.23/0.50 tff(221,plain,
% 0.23/0.50 (product(e_4, e_3, e_1) | product(e_4, e_3, e_4) | product(e_4, e_3, e_2)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[220, 139, 170, 136, 214])).
% 0.23/0.50 tff(222,plain,
% 0.23/0.50 (product(e_4, e_3, e_1)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[221, 203, 196])).
% 0.23/0.50 tff(223,assumption,(product(e_4, e_3, e_1)), introduced(assumption)).
% 0.23/0.50 tff(224,assumption,(product(e_1, e_4, e_2)), introduced(assumption)).
% 0.23/0.50 tff(225,plain,
% 0.23/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_4, e_3) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_3, e_1)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(226,plain,
% 0.23/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_3, e_1)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(227,plain,
% 0.23/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_4, e_3) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_3, e_1))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.23/0.50 tff(228,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[227, 51, 167, 224, 223])).
% 0.23/0.50 tff(229,plain,((~product(e_1, e_4, e_2)) | product(e_2, e_4, e_3) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(230,plain,
% 0.23/0.50 (~product(e_1, e_4, e_2)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[229, 222, 167])).
% 0.23/0.50 tff(231,plain,
% 0.23/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_4, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_4)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(232,plain,
% 0.23/0.50 ((product(e_4, e_4, e_3) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_3, e_1))) <=> (product(e_4, e_4, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_4)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(233,plain,
% 0.23/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_3) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_4))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[232])).
% 0.23/0.50 tff(234,plain,
% 0.23/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_3) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_4, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_4)))),
% 0.23/0.50 inference(transitivity,[status(thm)],[233, 231])).
% 0.23/0.50 tff(235,plain,
% 0.23/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_3) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_3, e_1)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(236,plain,
% 0.23/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_4, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_4))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.23/0.50 tff(237,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[236, 51, 10, 223, 195])).
% 0.23/0.50 tff(238,plain,((~product(e_1, e_4, e_4)) | (~product(e_4, e_3, e_1)) | product(e_4, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(239,plain,
% 0.23/0.50 (~product(e_1, e_4, e_4)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[238, 222, 195])).
% 0.23/0.50 tff(240,plain,
% 0.23/0.50 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(241,plain,
% 0.23/0.50 ((product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1))) <=> ((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(242,plain,
% 0.23/0.50 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1)))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[241])).
% 0.23/0.50 tff(243,plain,
% 0.23/0.50 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1))),
% 0.23/0.50 inference(transitivity,[status(thm)],[242, 240])).
% 0.23/0.50 tff(244,plain,
% 0.23/0.50 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(245,plain,
% 0.23/0.50 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1)),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.23/0.50 tff(246,plain,
% 0.23/0.50 (product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[245, 142, 170, 136])).
% 0.23/0.50 tff(247,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[246, 239, 230, 194, 193])).
% 0.23/0.50 tff(248,plain,(product(e_2, e_4, e_3) | product(e_1, e_4, e_3) | product(e_4, e_4, e_3) | product(e_2, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(249,plain,
% 0.23/0.50 (product(e_2, e_4, e_3)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[248, 165, 55, 72])).
% 0.23/0.50 tff(250,assumption,(product(e_3, e_4, e_3)), introduced(assumption)).
% 0.23/0.50 tff(251,plain,
% 0.23/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_4, 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_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(252,plain,
% 0.23/0.50 ((equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3))) <=> (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(253,plain,
% 0.23/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[252])).
% 0.23/0.51 tff(254,plain,
% 0.23/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.23/0.51 inference(transitivity,[status(thm)],[253, 251])).
% 0.23/0.51 tff(255,plain,
% 0.23/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(256,plain,
% 0.23/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.23/0.51 tff(257,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[256, 209, 83, 250, 206])).
% 0.23/0.51 tff(258,plain,(~product(e_3, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.51 tff(259,plain,
% 0.23/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_4, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_3)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(260,plain,
% 0.23/0.51 ((product(e_3, e_4, e_3) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_3, e_2))) <=> (product(e_3, e_4, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_3)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(261,plain,
% 0.23/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_3) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_3))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[260])).
% 0.23/0.51 tff(262,plain,
% 0.23/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_3) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_4, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_3)))),
% 0.23/0.51 inference(transitivity,[status(thm)],[261, 259])).
% 0.23/0.51 tff(263,plain,
% 0.23/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_3) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_3, e_2)))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(264,plain,
% 0.23/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_4, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_3))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.23/0.51 tff(265,plain,
% 0.23/0.51 (~product(e_4, e_3, e_2)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[264, 51, 258, 249])).
% 0.23/0.51 tff(266,plain,
% 0.23/0.51 (product(e_4, e_3, e_1)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[221, 265, 62])).
% 0.23/0.51 tff(267,plain,
% 0.23/0.51 (~product(e_1, e_4, e_4)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[238, 266, 55])).
% 0.23/0.51 tff(268,plain,
% 0.23/0.51 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(269,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.23/0.51 tff(270,plain,
% 0.23/0.51 (~equalish(e_1, e_3)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.23/0.51 tff(271,plain,
% 0.23/0.51 (((~![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_4, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(272,plain,
% 0.23/0.51 ((~![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_4, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(273,plain,
% 0.23/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.23/0.51 tff(274,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[273, 270, 20, 41, 224])).
% 0.23/0.51 tff(275,plain,((~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.51 tff(276,plain,
% 0.23/0.51 (~product(e_1, e_4, e_2)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[275, 41])).
% 0.23/0.51 tff(277,plain,
% 0.23/0.51 (product(e_1, e_4, e_1)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[246, 276, 165, 267])).
% 0.23/0.51 tff(278,plain,
% 0.23/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(279,plain,
% 0.23/0.51 ((product(e_1, e_4, e_3) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_3, e_1))) <=> (product(e_1, e_4, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(280,plain,
% 0.23/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_3) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_1))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[279])).
% 0.23/0.51 tff(281,plain,
% 0.23/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_3) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.23/0.51 inference(transitivity,[status(thm)],[280, 278])).
% 0.23/0.51 tff(282,plain,
% 0.23/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_3) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(283,plain,
% 0.23/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_3) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_1))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.23/0.51 tff(284,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[283, 51, 165, 277, 266])).
% 0.23/0.51 tff(285,plain,(~product(e_3, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.51 tff(286,plain,
% 0.23/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(287,plain,
% 0.23/0.51 ((product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(288,plain,
% 0.23/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[287])).
% 0.23/0.51 tff(289,plain,
% 0.23/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)))),
% 0.23/0.51 inference(transitivity,[status(thm)],[288, 286])).
% 0.23/0.51 tff(290,plain,
% 0.23/0.51 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3)))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(291,plain,
% 0.23/0.51 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.23/0.51 tff(292,plain,
% 0.23/0.51 (product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[291, 139, 170, 136])).
% 0.23/0.51 tff(293,plain,
% 0.23/0.51 (product(e_3, e_4, e_4) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[292, 258])).
% 0.23/0.51 tff(294,plain,
% 0.23/0.51 (product(e_3, e_4, e_2) | product(e_3, e_4, e_1)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[293, 99])).
% 0.23/0.51 tff(295,plain,
% 0.23/0.51 (product(e_3, e_4, e_1)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[294, 285])).
% 0.23/0.51 tff(296,plain,
% 0.23/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_4, e_3)) | product(e_1, e_4, e_4) | (~product(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_4, e_3)) | product(e_1, e_4, e_4) | (~product(e_3, e_4, e_1)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(297,plain,
% 0.23/0.51 ((product(e_1, e_4, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_4, e_3))) <=> ((~product(e_4, e_4, e_3)) | product(e_1, e_4, e_4) | (~product(e_3, e_4, e_1)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(298,plain,
% 0.23/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_4, e_3)) | product(e_1, e_4, e_4) | (~product(e_3, e_4, e_1))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[297])).
% 0.23/0.51 tff(299,plain,
% 0.23/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_4, e_3)) | product(e_1, e_4, e_4) | (~product(e_3, e_4, e_1)))),
% 0.23/0.51 inference(transitivity,[status(thm)],[298, 296])).
% 0.23/0.51 tff(300,plain,
% 0.23/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_4, e_3)))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(301,plain,
% 0.23/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_4, e_3)) | product(e_1, e_4, e_4) | (~product(e_3, e_4, e_1))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.23/0.51 tff(302,plain,
% 0.23/0.51 (~product(e_4, e_4, e_3)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[301, 51, 295, 28])).
% 0.23/0.51 tff(303,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.23/0.51 tff(304,assumption,(product(e_3, e_4, e_1)), introduced(assumption)).
% 0.23/0.51 tff(305,plain,
% 0.23/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_1)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(306,plain,
% 0.23/0.51 ((equalish(e_2, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_2, e_1))) <=> (equalish(e_2, e_4) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_1)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(307,plain,
% 0.23/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_1))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[306])).
% 0.23/0.51 tff(308,plain,
% 0.23/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_1)))),
% 0.23/0.51 inference(transitivity,[status(thm)],[307, 305])).
% 0.23/0.51 tff(309,plain,
% 0.23/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(310,plain,
% 0.23/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_1))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.23/0.51 tff(311,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[310, 32, 83, 304, 303])).
% 0.23/0.51 tff(312,plain,((~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.51 tff(313,plain,
% 0.23/0.51 (~product(e_3, e_2, e_1)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[312, 295])).
% 0.23/0.51 tff(314,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.23/0.51 tff(315,plain,
% 0.23/0.51 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(316,plain,
% 0.23/0.51 (product(e_2, e_2, e_2)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[315, 7])).
% 0.23/0.51 tff(317,plain,
% 0.23/0.51 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(318,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.23/0.51 tff(319,plain,
% 0.23/0.51 (~equalish(e_3, e_2)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.23/0.51 tff(320,plain,
% 0.23/0.51 (((~![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_2, e_2)) | (~product(e_3, 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_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(321,plain,
% 0.23/0.52 ((~![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_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.23/0.52 inference(quant_inst,[status(thm)],[])).
% 0.23/0.52 tff(322,plain,
% 0.23/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.23/0.52 tff(323,plain,
% 0.23/0.52 ($false),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[322, 319, 20, 316, 314])).
% 0.23/0.52 tff(324,plain,(~product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.52 tff(325,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.23/0.52 tff(326,plain,
% 0.23/0.52 (((~![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_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(327,plain,
% 0.23/0.52 ((~![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)))),
% 0.23/0.52 inference(quant_inst,[status(thm)],[])).
% 0.23/0.52 tff(328,plain,
% 0.23/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.23/0.52 tff(329,plain,
% 0.23/0.52 ($false),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[328, 66, 83, 206, 325])).
% 0.23/0.52 tff(330,plain,(~product(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.52 tff(331,plain,
% 0.23/0.52 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | 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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(332,plain,
% 0.23/0.52 ((product(e_3, e_2, e_4) | 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_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(333,plain,
% 0.23/0.52 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_4) | 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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[332])).
% 0.23/0.52 tff(334,plain,
% 0.23/0.52 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_4) | 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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))),
% 0.23/0.52 inference(transitivity,[status(thm)],[333, 331])).
% 0.23/0.52 tff(335,plain,
% 0.23/0.52 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_4) | 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)))),
% 0.23/0.52 inference(quant_inst,[status(thm)],[])).
% 0.23/0.52 tff(336,plain,
% 0.23/0.52 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.23/0.52 tff(337,plain,
% 0.23/0.52 (product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[336, 173, 139, 136])).
% 0.23/0.52 tff(338,plain,
% 0.23/0.52 (product(e_3, e_2, e_4) | product(e_3, e_2, e_1)),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[337, 330, 324])).
% 0.23/0.52 tff(339,plain,
% 0.23/0.52 (product(e_3, e_2, e_4)),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[338, 313])).
% 0.23/0.52 tff(340,assumption,(product(e_3, e_2, e_4)), introduced(assumption)).
% 0.23/0.52 tff(341,assumption,(product(e_4, e_3, e_2)), introduced(assumption)).
% 0.23/0.52 tff(342,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.23/0.52 tff(343,plain,
% 0.23/0.52 (((~![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)))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(344,plain,
% 0.23/0.52 ((~![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)))),
% 0.23/0.52 inference(quant_inst,[status(thm)],[])).
% 0.23/0.52 tff(345,plain,
% 0.23/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.23/0.52 tff(346,plain,
% 0.23/0.52 ($false),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[345, 319, 83, 316, 342])).
% 0.23/0.52 tff(347,plain,(~product(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.52 tff(348,plain,
% 0.23/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_2, e_4)))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(349,plain,
% 0.23/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_2, e_4)))),
% 0.40/0.52 inference(quant_inst,[status(thm)],[])).
% 0.40/0.52 tff(350,plain,
% 0.40/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_2, e_4))),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.40/0.52 tff(351,plain,
% 0.40/0.52 ($false),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[350, 51, 347, 340, 341])).
% 0.40/0.52 tff(352,plain,((~product(e_4, e_3, e_2)) | (~product(e_3, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.52 tff(353,plain,
% 0.40/0.52 (~product(e_4, e_3, e_2)),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[352, 340])).
% 0.40/0.52 tff(354,plain,
% 0.40/0.52 (product(e_4, e_3, e_1)),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[221, 353, 196])).
% 0.40/0.52 tff(355,plain,
% 0.40/0.52 (~product(e_1, e_4, e_4)),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[238, 354, 195])).
% 0.40/0.52 tff(356,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.40/0.52 tff(357,plain,
% 0.40/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_4, e_2)))),
% 0.40/0.52 inference(rewrite,[status(thm)],[])).
% 0.40/0.52 tff(358,plain,
% 0.40/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_4, e_2)))),
% 0.40/0.52 inference(quant_inst,[status(thm)],[])).
% 0.40/0.52 tff(359,plain,
% 0.40/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_4, e_2))),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.40/0.52 tff(360,plain,
% 0.40/0.52 (~product(e_4, e_4, e_2)),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[359, 51, 99, 356])).
% 0.40/0.52 tff(361,plain,
% 0.40/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_4, e_2) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.40/0.52 inference(rewrite,[status(thm)],[])).
% 0.40/0.52 tff(362,plain,
% 0.40/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.40/0.52 inference(quant_inst,[status(thm)],[])).
% 0.40/0.52 tff(363,plain,
% 0.40/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_4, e_2) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4))),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.40/0.52 tff(364,plain,
% 0.40/0.52 (~product(e_4, e_2, e_4)),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[363, 51, 9, 360])).
% 0.40/0.52 tff(365,plain,
% 0.40/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_4, e_2, e_4) | (~product(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_4, e_3)) | product(e_4, e_2, e_4) | (~product(e_3, e_2, e_4)))),
% 0.40/0.52 inference(rewrite,[status(thm)],[])).
% 0.40/0.52 tff(366,plain,
% 0.40/0.52 ((product(e_4, e_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3))) <=> ((~product(e_2, e_4, e_3)) | product(e_4, e_2, e_4) | (~product(e_3, e_2, e_4)))),
% 0.40/0.52 inference(rewrite,[status(thm)],[])).
% 0.40/0.52 tff(367,plain,
% 0.40/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_4, e_2, e_4) | (~product(e_3, e_2, e_4))))),
% 0.40/0.52 inference(monotonicity,[status(thm)],[366])).
% 0.40/0.52 tff(368,plain,
% 0.40/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_4, e_3)) | product(e_4, e_2, e_4) | (~product(e_3, e_2, e_4)))),
% 0.40/0.52 inference(transitivity,[status(thm)],[367, 365])).
% 0.40/0.52 tff(369,plain,
% 0.40/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)))),
% 0.40/0.52 inference(quant_inst,[status(thm)],[])).
% 0.40/0.52 tff(370,plain,
% 0.40/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_4, e_3)) | product(e_4, e_2, e_4) | (~product(e_3, e_2, e_4))),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.40/0.52 tff(371,plain,
% 0.40/0.52 ($false),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[370, 51, 356, 340, 364])).
% 0.40/0.52 tff(372,plain,((~product(e_2, e_4, e_3)) | (~product(e_3, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.52 tff(373,plain,
% 0.40/0.52 (~product(e_2, e_4, e_3)),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[372, 340])).
% 0.40/0.52 tff(374,plain,
% 0.40/0.52 (product(e_2, e_4, e_1)),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[181, 373, 166])).
% 0.40/0.52 tff(375,plain,
% 0.40/0.52 (~product(e_1, e_4, e_1)),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[192, 374])).
% 0.40/0.52 tff(376,plain,
% 0.40/0.52 (~product(e_1, e_4, e_2)),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[229, 354, 373])).
% 0.40/0.52 tff(377,plain,
% 0.40/0.52 (product(e_1, e_4, e_3)),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[246, 376, 375, 355])).
% 0.40/0.52 tff(378,plain,
% 0.40/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_4, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_3, e_1)))),
% 0.40/0.52 inference(rewrite,[status(thm)],[])).
% 0.40/0.52 tff(379,plain,
% 0.40/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_3, e_1)))),
% 0.40/0.52 inference(quant_inst,[status(thm)],[])).
% 0.40/0.52 tff(380,plain,
% 0.40/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_4, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_3, e_1))),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.40/0.52 tff(381,plain,
% 0.40/0.52 ($false),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[380, 51, 258, 377, 354])).
% 0.40/0.52 tff(382,plain,((~product(e_3, e_2, e_4)) | product(e_4, e_4, e_3) | product(e_2, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.52 tff(383,plain,
% 0.40/0.52 (product(e_4, e_4, e_3) | product(e_2, e_4, e_2)),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[382, 339])).
% 0.40/0.52 tff(384,plain,
% 0.40/0.52 (product(e_2, e_4, e_2)),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[383, 302])).
% 0.40/0.52 tff(385,plain,
% 0.40/0.52 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.40/0.52 inference(rewrite,[status(thm)],[])).
% 0.40/0.52 tff(386,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.40/0.52 tff(387,plain,
% 0.40/0.52 (~equalish(e_4, e_2)),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.40/0.52 tff(388,plain,
% 0.40/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.40/0.52 inference(rewrite,[status(thm)],[])).
% 0.40/0.52 tff(389,plain,
% 0.40/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.40/0.52 inference(quant_inst,[status(thm)],[])).
% 0.40/0.52 tff(390,plain,
% 0.40/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2))),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.40/0.52 tff(391,plain,
% 0.40/0.52 ($false),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[390, 387, 83, 316, 384])).
% 0.40/0.52 % SZS output end Proof
%------------------------------------------------------------------------------