TSTP Solution File: GRP125-2.005 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP125-2.005 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 22:26:03 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP125-2.005 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 14:57:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 tff(product_type, type, (
% 0.19/0.50 product: ( $i * $i * $i ) > $o)).
% 0.19/0.50 tff(e_2_type, type, (
% 0.19/0.50 e_2: $i)).
% 0.19/0.50 tff(e_3_type, type, (
% 0.19/0.50 e_3: $i)).
% 0.19/0.50 tff(e_1_type, type, (
% 0.19/0.50 e_1: $i)).
% 0.19/0.50 tff(equalish_type, type, (
% 0.19/0.50 equalish: ( $i * $i ) > $o)).
% 0.19/0.50 tff(e_5_type, type, (
% 0.19/0.50 e_5: $i)).
% 0.19/0.50 tff(next_type, type, (
% 0.19/0.50 next: ( $i * $i ) > $o)).
% 0.19/0.50 tff(greater_type, type, (
% 0.19/0.50 greater: ( $i * $i ) > $o)).
% 0.19/0.50 tff(e_4_type, type, (
% 0.19/0.50 e_4: $i)).
% 0.19/0.50 tff(group_element_type, type, (
% 0.19/0.50 group_element: $i > $o)).
% 0.19/0.50 tff(1,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.19/0.50 tff(2,plain,
% 0.19/0.50 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(3,plain,
% 0.19/0.50 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.19/0.50 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.50 tff(4,plain,
% 0.19/0.50 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(5,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.19/0.50 tff(6,plain,
% 0.19/0.50 (![X: $i] : product(X, X, X)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.50 tff(7,plain,(
% 0.19/0.50 ![X: $i] : product(X, X, X)),
% 0.19/0.50 inference(skolemize,[status(sab)],[6])).
% 0.19/0.50 tff(8,plain,
% 0.19/0.50 (![X: $i] : product(X, X, X)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.50 tff(9,plain,
% 0.19/0.50 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(10,plain,
% 0.19/0.50 (product(e_3, e_3, e_3)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.19/0.50 tff(11,plain,
% 0.19/0.50 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(12,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.50 tff(13,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(14,plain,
% 0.19/0.50 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(15,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.50 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/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.19/0.50 tff(17,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.50 tff(18,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.50 tff(19,plain,(
% 0.19/0.50 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[18])).
% 0.19/0.50 tff(20,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.50 tff(21,plain,
% 0.19/0.50 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(22,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.19/0.50 tff(23,plain,
% 0.19/0.50 (~equalish(e_1, e_3)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.50 tff(24,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(25,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(26,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.50 tff(27,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[26, 23, 20, 10, 1])).
% 0.19/0.50 tff(28,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(29,plain,
% 0.19/0.50 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(30,plain,
% 0.19/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.50 tff(31,plain,
% 0.19/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.50 tff(34,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.19/0.50 tff(35,plain,
% 0.19/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.50 tff(36,plain,
% 0.19/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.50 tff(37,plain,(
% 0.19/0.50 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[36])).
% 0.19/0.50 tff(38,plain,
% 0.19/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.50 tff(39,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(40,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(41,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.50 tff(42,plain,
% 0.19/0.50 (~product(e_3, e_3, e_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[41, 38, 10, 28])).
% 0.19/0.50 tff(43,plain,
% 0.19/0.50 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(44,plain,
% 0.19/0.50 (product(e_1, e_1, e_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[43, 8])).
% 0.19/0.50 tff(45,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.19/0.50 tff(46,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.19/0.50 tff(47,plain,
% 0.19/0.50 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(48,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.19/0.50 tff(49,plain,
% 0.19/0.50 (~equalish(e_2, e_1)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.50 tff(50,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(51,plain,
% 0.19/0.50 ((equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(52,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.50 tff(53,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.50 tff(54,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(55,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.50 tff(56,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[55, 49, 20, 46, 45])).
% 0.19/0.50 tff(57,plain,((~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(58,plain,
% 0.19/0.50 (~product(e_2, e_1, e_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[57, 44])).
% 0.19/0.50 tff(59,assumption,(~product(e_2, e_2, e_2)), introduced(assumption)).
% 0.19/0.50 tff(60,plain,
% 0.19/0.50 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(61,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[60, 8, 59])).
% 0.19/0.50 tff(62,plain,(product(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(63,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.19/0.50 tff(64,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.19/0.50 tff(65,plain,
% 0.19/0.50 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(66,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.50 tff(67,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(68,plain,
% 0.19/0.50 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, W, Y)) | (~product(X, Z, Y))) <=> ((~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)))), rewrite((((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(69,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.50 tff(70,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.19/0.50 tff(71,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.50 tff(72,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.50 tff(73,plain,(
% 0.19/0.50 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[72])).
% 0.19/0.50 tff(74,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.50 tff(75,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(76,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(77,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.50 tff(78,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[77, 49, 74, 64, 63])).
% 0.19/0.50 tff(79,plain,((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(80,plain,
% 0.19/0.50 (~product(e_2, e_1, e_2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[79, 62])).
% 0.19/0.50 tff(81,plain,
% 0.19/0.50 (^[Y: $i, X: $i, X1: $i] : refl(((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(82,plain,
% 0.19/0.50 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.50 tff(83,plain,
% 0.19/0.50 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(84,plain,
% 0.19/0.50 (^[Y: $i, X: $i, X1: $i] : trans(monotonicity(rewrite(((~product(X, e_1, Y)) | (~next(X, X1))) <=> ((~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> (((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))))), rewrite((((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(85,plain,
% 0.19/0.50 (![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.50 tff(86,axiom,(![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_redundancy')).
% 0.19/0.50 tff(87,plain,
% 0.19/0.50 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.50 tff(88,plain,
% 0.19/0.50 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.50 tff(89,plain,(
% 0.19/0.50 ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[88])).
% 0.19/0.50 tff(90,plain,
% 0.19/0.50 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.19/0.50 tff(91,plain,
% 0.19/0.50 (greater(e_5, e_3) <=> greater(e_5, e_3)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(92,axiom,(greater(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_3')).
% 0.19/0.50 tff(93,plain,
% 0.19/0.50 (greater(e_5, e_3)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.50 tff(94,plain,
% 0.19/0.50 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(95,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.19/0.50 tff(96,plain,
% 0.19/0.50 (next(e_2, e_3)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.50 tff(97,plain,
% 0.19/0.50 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(98,plain,
% 0.19/0.50 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(99,plain,
% 0.19/0.50 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.50 tff(100,plain,
% 0.19/0.50 (~product(e_2, e_1, e_5)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[99, 96, 93, 90])).
% 0.19/0.50 tff(101,plain,
% 0.19/0.50 (greater(e_4, e_3) <=> greater(e_4, e_3)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(102,axiom,(greater(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_3')).
% 0.19/0.50 tff(103,plain,
% 0.19/0.50 (greater(e_4, e_3)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.50 tff(104,plain,
% 0.19/0.50 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(105,plain,
% 0.19/0.51 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(106,plain,
% 0.19/0.51 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.51 tff(107,plain,
% 0.19/0.51 (~product(e_2, e_1, e_4)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[106, 96, 103, 90])).
% 0.19/0.51 tff(108,plain,
% 0.19/0.51 (^[Y: $i, X: $i] : refl((product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(109,plain,
% 0.19/0.51 (![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[108])).
% 0.19/0.51 tff(110,plain,
% 0.19/0.51 (![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(111,plain,
% 0.19/0.51 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)))), rewrite(((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) <=> ((product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_5)))), rewrite(((product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_5)) <=> (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) <=> (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(112,plain,
% 0.19/0.51 (![Y: $i, X: $i] : (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) <=> ![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[111])).
% 0.19/0.51 tff(113,axiom,(![Y: $i, X: $i] : (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.19/0.51 tff(114,plain,
% 0.19/0.51 (![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.51 tff(115,plain,
% 0.19/0.51 (![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.19/0.51 tff(116,plain,(
% 0.19/0.51 ![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[115])).
% 0.19/0.51 tff(117,plain,
% 0.19/0.51 (![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.19/0.51 tff(118,plain,
% 0.19/0.51 (group_element(e_2) <=> group_element(e_2)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(119,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.19/0.51 tff(120,plain,
% 0.19/0.51 (group_element(e_2)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.51 tff(121,plain,
% 0.19/0.51 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(122,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.19/0.51 tff(123,plain,
% 0.19/0.51 (group_element(e_1)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.51 tff(124,plain,
% 0.19/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(125,plain,
% 0.19/0.51 ((product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2))) <=> (product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(126,plain,
% 0.19/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[125])).
% 0.19/0.51 tff(127,plain,
% 0.19/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[126, 124])).
% 0.19/0.51 tff(128,plain,
% 0.19/0.51 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(129,plain,
% 0.19/0.51 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.51 tff(130,plain,
% 0.19/0.51 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[129, 123, 120, 117, 107, 100])).
% 0.19/0.51 tff(131,plain,
% 0.19/0.51 (product(e_2, e_1, e_3) | product(e_2, e_1, e_1)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[130, 80])).
% 0.19/0.51 tff(132,plain,
% 0.19/0.51 (product(e_2, e_1, e_3)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[131, 58])).
% 0.19/0.51 tff(133,plain,
% 0.19/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(134,plain,
% 0.19/0.51 (((~product(e_2, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3))) <=> ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(135,plain,
% 0.19/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[134])).
% 0.19/0.51 tff(136,plain,
% 0.19/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1))),
% 0.19/0.51 inference(transitivity,[status(thm)],[135, 133])).
% 0.19/0.51 tff(137,plain,
% 0.19/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(138,plain,
% 0.19/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.51 tff(139,plain,
% 0.19/0.51 (~product(e_1, e_2, e_3)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[138, 38, 132, 42])).
% 0.19/0.51 tff(140,assumption,(product(e_2, e_5, e_1)), introduced(assumption)).
% 0.19/0.51 tff(141,assumption,(product(e_5, e_1, e_5)), introduced(assumption)).
% 0.19/0.51 tff(142,plain,
% 0.19/0.51 ((~![X: $i] : product(X, X, X)) | product(e_5, e_5, e_5)),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(143,plain,
% 0.19/0.51 (product(e_5, e_5, e_5)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[142, 8])).
% 0.19/0.51 tff(144,plain,
% 0.19/0.51 ((~equalish(e_1, e_5)) <=> (~equalish(e_1, e_5))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(145,axiom,(~equalish(e_1, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_5')).
% 0.19/0.51 tff(146,plain,
% 0.19/0.51 (~equalish(e_1, e_5)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.19/0.51 tff(147,plain,
% 0.19/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(148,plain,
% 0.19/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(149,plain,
% 0.19/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.51 tff(150,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[149, 146, 74, 143, 141])).
% 0.19/0.51 tff(151,plain,(~product(e_5, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(152,assumption,(~product(e_5, e_3, e_4)), introduced(assumption)).
% 0.19/0.51 tff(153,assumption,(product(e_3, e_5, e_1)), introduced(assumption)).
% 0.19/0.51 tff(154,plain,
% 0.19/0.51 (greater(e_5, e_2) <=> greater(e_5, e_2)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(155,axiom,(greater(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_2')).
% 0.19/0.51 tff(156,plain,
% 0.19/0.51 (greater(e_5, e_2)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.19/0.51 tff(157,plain,
% 0.19/0.51 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(158,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.19/0.51 tff(159,plain,
% 0.19/0.51 (next(e_1, e_2)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.51 tff(160,plain,
% 0.19/0.51 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(161,plain,
% 0.19/0.52 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(162,plain,
% 0.19/0.52 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.19/0.52 tff(163,plain,
% 0.19/0.52 (~product(e_1, e_1, e_5)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[162, 159, 156, 90])).
% 0.19/0.52 tff(164,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_1)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(165,plain,
% 0.19/0.52 (((~product(e_3, e_5, e_1)) | product(e_1, e_1, e_5) | (~product(e_5, e_3, e_1))) <=> (product(e_1, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_1)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(166,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_1)) | product(e_1, e_1, e_5) | (~product(e_5, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_1))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[165])).
% 0.19/0.52 tff(167,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_1)) | product(e_1, e_1, e_5) | (~product(e_5, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_1)))),
% 0.19/0.52 inference(transitivity,[status(thm)],[166, 164])).
% 0.19/0.52 tff(168,plain,
% 0.19/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_1)) | product(e_1, e_1, e_5) | (~product(e_5, e_3, e_1)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(169,plain,
% 0.19/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_1))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.19/0.52 tff(170,plain,
% 0.19/0.52 (~product(e_5, e_3, e_1)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[169, 38, 163, 153])).
% 0.19/0.52 tff(171,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_2)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(172,plain,
% 0.19/0.52 (((~product(e_3, e_5, e_1)) | product(e_2, e_1, e_5) | (~product(e_5, e_3, e_2))) <=> (product(e_2, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_2)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(173,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_1)) | product(e_2, e_1, e_5) | (~product(e_5, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_2))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[172])).
% 0.19/0.52 tff(174,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_1)) | product(e_2, e_1, e_5) | (~product(e_5, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_2)))),
% 0.19/0.52 inference(transitivity,[status(thm)],[173, 171])).
% 0.19/0.52 tff(175,plain,
% 0.19/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_1)) | product(e_2, e_1, e_5) | (~product(e_5, e_3, e_2)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(176,plain,
% 0.19/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_2))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.19/0.52 tff(177,plain,
% 0.19/0.52 (~product(e_5, e_3, e_2)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[176, 38, 100, 153])).
% 0.19/0.52 tff(178,plain,
% 0.19/0.52 (greater(e_5, e_4) <=> greater(e_5, e_4)),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(179,axiom,(greater(e_5, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_4')).
% 0.19/0.52 tff(180,plain,
% 0.19/0.52 (greater(e_5, e_4)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.19/0.52 tff(181,plain,
% 0.19/0.52 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(182,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.19/0.52 tff(183,plain,
% 0.19/0.52 (next(e_3, e_4)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.19/0.52 tff(184,plain,
% 0.19/0.52 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(185,plain,
% 0.19/0.52 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(186,plain,
% 0.19/0.52 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.19/0.52 tff(187,plain,
% 0.19/0.52 (~product(e_3, e_1, e_5)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[186, 183, 180, 90])).
% 0.19/0.52 tff(188,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_3)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(189,plain,
% 0.19/0.52 (((~product(e_3, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_3, e_3))) <=> (product(e_3, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_3)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(190,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_3))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[189])).
% 0.19/0.52 tff(191,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_3)))),
% 0.19/0.52 inference(transitivity,[status(thm)],[190, 188])).
% 0.19/0.52 tff(192,plain,
% 0.19/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_3, e_3)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(193,plain,
% 0.19/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_3, e_5, e_1)) | (~product(e_5, e_3, e_3))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.19/0.52 tff(194,plain,
% 0.19/0.52 (~product(e_5, e_3, e_3)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[193, 38, 187, 153])).
% 0.19/0.52 tff(195,assumption,(product(e_5, e_3, e_5)), introduced(assumption)).
% 0.19/0.52 tff(196,plain,
% 0.19/0.52 ((~equalish(e_3, e_5)) <=> (~equalish(e_3, e_5))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(197,axiom,(~equalish(e_3, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_5')).
% 0.19/0.52 tff(198,plain,
% 0.19/0.52 (~equalish(e_3, e_5)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.19/0.52 tff(199,plain,
% 0.19/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(200,plain,
% 0.19/0.52 ((equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5))) <=> (equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(201,plain,
% 0.19/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[200])).
% 0.19/0.52 tff(202,plain,
% 0.19/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.19/0.52 inference(transitivity,[status(thm)],[201, 199])).
% 0.19/0.52 tff(203,plain,
% 0.19/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(204,plain,
% 0.19/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.19/0.52 tff(205,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[204, 198, 74, 143, 195])).
% 0.19/0.52 tff(206,plain,(~product(e_5, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(207,plain,
% 0.19/0.52 (group_element(e_5) <=> group_element(e_5)),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(208,axiom,(group_element(e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_5')).
% 0.19/0.52 tff(209,plain,
% 0.19/0.52 (group_element(e_5)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.19/0.52 tff(210,plain,
% 0.19/0.52 (group_element(e_3) <=> group_element(e_3)),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(211,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.19/0.52 tff(212,plain,
% 0.19/0.52 (group_element(e_3)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.19/0.52 tff(213,plain,
% 0.19/0.52 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_5)) | product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_5)) | product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(214,plain,
% 0.19/0.52 ((product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_5))) <=> ((~group_element(e_3)) | (~group_element(e_5)) | product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(215,plain,
% 0.19/0.52 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_5)) | product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[214])).
% 0.19/0.52 tff(216,plain,
% 0.19/0.52 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_5)) | product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4))),
% 0.19/0.52 inference(transitivity,[status(thm)],[215, 213])).
% 0.19/0.52 tff(217,plain,
% 0.19/0.52 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_5)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(218,plain,
% 0.19/0.52 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_5)) | product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.19/0.52 tff(219,plain,
% 0.19/0.52 (product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[218, 212, 209, 117, 206])).
% 0.19/0.52 tff(220,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[219, 194, 177, 152, 170])).
% 0.19/0.52 tff(221,plain,((~product(e_3, e_5, e_1)) | product(e_5, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(222,plain,
% 0.19/0.52 (~product(e_3, e_5, e_1)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[221, 152])).
% 0.19/0.52 tff(223,assumption,(product(e_5, e_1, e_4)), introduced(assumption)).
% 0.19/0.52 tff(224,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.19/0.52 tff(225,plain,
% 0.19/0.52 ((~equalish(e_5, e_3)) <=> (~equalish(e_5, e_3))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(226,axiom,(~equalish(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_3')).
% 0.19/0.52 tff(227,plain,
% 0.19/0.52 (~equalish(e_5, e_3)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.19/0.52 tff(228,plain,
% 0.19/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(229,plain,
% 0.19/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(230,plain,
% 0.19/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.19/0.52 tff(231,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[230, 227, 20, 224, 223])).
% 0.19/0.52 tff(232,plain,((~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(233,plain,
% 0.19/0.52 (~product(e_3, e_1, e_4)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[232, 223])).
% 0.19/0.52 tff(234,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.19/0.52 tff(235,plain,
% 0.19/0.52 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(236,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.19/0.52 tff(237,plain,
% 0.19/0.52 (~equalish(e_3, e_1)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.19/0.52 tff(238,plain,
% 0.19/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(239,plain,
% 0.19/0.52 ((equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))) <=> (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(240,plain,
% 0.19/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[239])).
% 0.19/0.52 tff(241,plain,
% 0.19/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.52 inference(transitivity,[status(thm)],[240, 238])).
% 0.19/0.52 tff(242,plain,
% 0.19/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(243,plain,
% 0.19/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.19/0.52 tff(244,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[243, 237, 20, 44, 234])).
% 0.19/0.52 tff(245,plain,(~product(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(246,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.19/0.53 tff(247,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.19/0.53 tff(248,plain,
% 0.19/0.53 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(249,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.19/0.53 tff(250,plain,
% 0.19/0.53 (~equalish(e_3, e_2)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.19/0.53 tff(251,plain,
% 0.19/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(252,plain,
% 0.19/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(253,plain,
% 0.19/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.19/0.53 tff(254,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[253, 250, 20, 247, 246])).
% 0.19/0.53 tff(255,plain,((~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(256,plain,
% 0.19/0.53 (~product(e_3, e_1, e_3)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[255, 132])).
% 0.19/0.53 tff(257,plain,
% 0.19/0.53 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_5) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_5) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(258,plain,
% 0.19/0.53 ((product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> (product(e_3, e_1, e_5) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(259,plain,
% 0.19/0.53 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_5) | product(e_3, e_1, e_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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_5) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[258])).
% 0.19/0.53 tff(260,plain,
% 0.19/0.53 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_5) | product(e_3, e_1, e_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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_5) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3)))),
% 0.19/0.53 inference(transitivity,[status(thm)],[259, 257])).
% 0.19/0.53 tff(261,plain,
% 0.19/0.53 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(262,plain,
% 0.19/0.53 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_5) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.19/0.53 tff(263,plain,
% 0.19/0.53 (product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[262, 123, 212, 117, 187])).
% 0.19/0.53 tff(264,plain,
% 0.19/0.53 (product(e_3, e_1, e_4) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[263, 256])).
% 0.19/0.53 tff(265,plain,
% 0.19/0.53 (product(e_3, e_1, e_4) | product(e_3, e_1, e_2)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[264, 245])).
% 0.19/0.53 tff(266,plain,
% 0.19/0.53 (product(e_3, e_1, e_2)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[265, 233])).
% 0.19/0.53 tff(267,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.19/0.53 tff(268,assumption,(product(e_5, e_1, e_2)), introduced(assumption)).
% 0.19/0.53 tff(269,plain,
% 0.19/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_5, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(270,plain,
% 0.19/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(271,plain,
% 0.19/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_5, e_1, e_2))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.19/0.53 tff(272,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[271, 227, 20, 267, 268])).
% 0.19/0.53 tff(273,plain,((~product(e_5, e_1, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(274,plain,
% 0.19/0.53 (~product(e_5, e_1, e_2)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[273, 267])).
% 0.19/0.53 tff(275,assumption,(product(e_5, e_1, e_3)), introduced(assumption)).
% 0.19/0.53 tff(276,plain,
% 0.19/0.53 ((~equalish(e_5, e_2)) <=> (~equalish(e_5, e_2))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(277,axiom,(~equalish(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_2')).
% 0.19/0.53 tff(278,plain,
% 0.19/0.53 (~equalish(e_5, e_2)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.19/0.53 tff(279,plain,
% 0.19/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(280,plain,
% 0.19/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(281,plain,
% 0.19/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.19/0.53 tff(282,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[281, 278, 20, 132, 275])).
% 0.19/0.53 tff(283,plain,(~product(e_5, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(284,assumption,(product(e_5, e_1, e_1)), introduced(assumption)).
% 0.19/0.53 tff(285,plain,
% 0.19/0.53 ((~equalish(e_5, e_1)) <=> (~equalish(e_5, e_1))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(286,axiom,(~equalish(e_5, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_1')).
% 0.19/0.53 tff(287,plain,
% 0.19/0.53 (~equalish(e_5, e_1)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.19/0.53 tff(288,plain,
% 0.19/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(289,plain,
% 0.19/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(290,plain,
% 0.19/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.19/0.53 tff(291,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[290, 287, 20, 44, 284])).
% 0.19/0.53 tff(292,plain,(~product(e_5, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(293,plain,
% 0.19/0.53 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_5)) | product(e_5, e_1, e_1) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_5)) | product(e_5, e_1, e_1) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(294,plain,
% 0.19/0.53 ((product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5))) <=> ((~group_element(e_1)) | (~group_element(e_5)) | product(e_5, e_1, e_1) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(295,plain,
% 0.19/0.53 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_5)) | product(e_5, e_1, e_1) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4)))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[294])).
% 0.19/0.53 tff(296,plain,
% 0.19/0.53 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_5)) | product(e_5, e_1, e_1) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4))),
% 0.19/0.53 inference(transitivity,[status(thm)],[295, 293])).
% 0.19/0.53 tff(297,plain,
% 0.19/0.53 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(298,plain,
% 0.19/0.53 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_5)) | product(e_5, e_1, e_1) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.19/0.53 tff(299,plain,
% 0.19/0.53 (product(e_5, e_1, e_1) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[298, 123, 209, 117])).
% 0.19/0.53 tff(300,plain,
% 0.19/0.53 (product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[299, 292])).
% 0.19/0.53 tff(301,plain,
% 0.19/0.53 (product(e_5, e_1, e_2) | product(e_5, e_1, e_4)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[300, 151, 283])).
% 0.19/0.53 tff(302,plain,
% 0.19/0.53 (product(e_5, e_1, e_4)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[301, 274])).
% 0.19/0.53 tff(303,assumption,(~product(e_3, e_5, e_4)), introduced(assumption)).
% 0.19/0.53 tff(304,assumption,(product(e_3, e_5, e_2)), introduced(assumption)).
% 0.19/0.53 tff(305,plain,
% 0.19/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_5, e_2)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(306,plain,
% 0.19/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_5, e_2)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(307,plain,
% 0.19/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_5, e_2))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.19/0.53 tff(308,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[307, 287, 74, 267, 304])).
% 0.19/0.53 tff(309,plain,((~product(e_3, e_5, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(310,plain,
% 0.19/0.53 (~product(e_3, e_5, e_2)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[309, 267])).
% 0.19/0.53 tff(311,assumption,(product(e_3, e_5, e_3)), introduced(assumption)).
% 0.19/0.53 tff(312,plain,
% 0.19/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(313,plain,
% 0.19/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(314,plain,
% 0.19/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.19/0.54 tff(315,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[314, 227, 74, 311, 10])).
% 0.19/0.54 tff(316,plain,(~product(e_3, e_5, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(317,assumption,(product(e_3, e_5, e_5)), introduced(assumption)).
% 0.19/0.54 tff(318,plain,
% 0.19/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_5) | (~product(e_3, e_5, e_5)) | (~product(e_5, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_5) | (~product(e_3, e_5, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(319,plain,
% 0.19/0.54 ((equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_3, e_5, e_5))) <=> (equalish(e_3, e_5) | (~product(e_3, e_5, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(320,plain,
% 0.19/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_3, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_5) | (~product(e_3, e_5, e_5)) | (~product(e_5, e_5, e_5))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[319])).
% 0.19/0.54 tff(321,plain,
% 0.19/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_3, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_5) | (~product(e_3, e_5, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.19/0.54 inference(transitivity,[status(thm)],[320, 318])).
% 0.19/0.54 tff(322,plain,
% 0.19/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_3, e_5, e_5)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(323,plain,
% 0.19/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_5) | (~product(e_3, e_5, e_5)) | (~product(e_5, e_5, e_5))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.19/0.54 tff(324,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[323, 198, 20, 317, 143])).
% 0.19/0.54 tff(325,plain,(~product(e_3, e_5, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(326,plain,
% 0.19/0.54 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | (~group_element(e_5)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(327,plain,
% 0.19/0.54 ((product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | (~group_element(e_5)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(328,plain,
% 0.19/0.54 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | (~group_element(e_5))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[327])).
% 0.19/0.54 tff(329,plain,
% 0.19/0.54 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | (~group_element(e_5)))),
% 0.19/0.54 inference(transitivity,[status(thm)],[328, 326])).
% 0.19/0.54 tff(330,plain,
% 0.19/0.54 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_3)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(331,plain,
% 0.19/0.54 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | (~group_element(e_5))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.19/0.54 tff(332,plain,
% 0.19/0.54 (product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[331, 212, 209, 117])).
% 0.19/0.54 tff(333,plain,
% 0.19/0.54 (product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_4)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[332, 325])).
% 0.19/0.54 tff(334,plain,
% 0.19/0.54 (product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_4)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[333, 316])).
% 0.19/0.54 tff(335,plain,
% 0.19/0.54 (product(e_3, e_5, e_1)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[334, 310, 303])).
% 0.19/0.54 tff(336,plain,
% 0.19/0.54 (product(e_5, e_3, e_4)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[221, 335])).
% 0.19/0.54 tff(337,assumption,(product(e_5, e_3, e_4)), introduced(assumption)).
% 0.19/0.54 tff(338,plain,
% 0.19/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_5, e_3, e_4)) | (~product(e_5, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_5, e_3, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(339,plain,
% 0.19/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_5, e_3, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(340,plain,
% 0.19/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_5, e_3, e_4)) | (~product(e_5, e_1, e_4))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.19/0.54 tff(341,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[340, 23, 74, 337, 223])).
% 0.19/0.54 tff(342,plain,((~product(e_5, e_1, e_4)) | (~product(e_5, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(343,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[342, 336, 302])).
% 0.19/0.54 tff(344,plain,((~product(e_3, e_1, e_2)) | product(e_3, e_5, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(345,plain,
% 0.19/0.54 (product(e_3, e_5, e_4)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[344, 266])).
% 0.19/0.54 tff(346,assumption,(product(e_2, e_5, e_4)), introduced(assumption)).
% 0.19/0.54 tff(347,assumption,(product(e_3, e_5, e_4)), introduced(assumption)).
% 0.19/0.54 tff(348,plain,
% 0.19/0.54 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(349,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.19/0.54 tff(350,plain,
% 0.19/0.54 (~equalish(e_2, e_3)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.19/0.54 tff(351,plain,
% 0.19/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_5, e_4)) | (~product(e_3, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_5, e_4)) | (~product(e_3, e_5, e_4)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(352,plain,
% 0.19/0.54 ((equalish(e_2, e_3) | (~product(e_3, e_5, e_4)) | (~product(e_2, e_5, e_4))) <=> (equalish(e_2, e_3) | (~product(e_2, e_5, e_4)) | (~product(e_3, e_5, e_4)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(353,plain,
% 0.19/0.54 (((~![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_5, e_4)) | (~product(e_2, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_5, e_4)) | (~product(e_3, e_5, e_4))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[352])).
% 0.19/0.54 tff(354,plain,
% 0.19/0.54 (((~![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_5, e_4)) | (~product(e_2, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_5, e_4)) | (~product(e_3, e_5, e_4)))),
% 0.19/0.54 inference(transitivity,[status(thm)],[353, 351])).
% 0.19/0.54 tff(355,plain,
% 0.19/0.54 ((~![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_5, e_4)) | (~product(e_2, e_5, e_4)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(356,plain,
% 0.19/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_5, e_4)) | (~product(e_3, e_5, e_4))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.19/0.54 tff(357,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[356, 350, 20, 347, 346])).
% 0.19/0.54 tff(358,plain,((~product(e_2, e_5, e_4)) | (~product(e_3, e_5, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(359,plain,
% 0.19/0.54 (~product(e_2, e_5, e_4)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[358, 345])).
% 0.19/0.54 tff(360,assumption,(product(e_2, e_5, e_3)), introduced(assumption)).
% 0.19/0.54 tff(361,plain,
% 0.19/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(362,plain,
% 0.19/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(363,plain,
% 0.19/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.19/0.54 tff(364,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[363, 287, 74, 132, 360])).
% 0.19/0.54 tff(365,plain,(~product(e_2, e_5, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(366,assumption,(product(e_2, e_5, e_2)), introduced(assumption)).
% 0.19/0.54 tff(367,plain,
% 0.19/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(368,plain,
% 0.19/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(369,plain,
% 0.19/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.19/0.54 tff(370,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[369, 278, 74, 62, 366])).
% 0.19/0.54 tff(371,plain,(~product(e_2, e_5, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(372,assumption,(product(e_2, e_5, e_5)), introduced(assumption)).
% 0.19/0.54 tff(373,plain,
% 0.19/0.54 ((~equalish(e_2, e_5)) <=> (~equalish(e_2, e_5))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(374,axiom,(~equalish(e_2, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_5')).
% 0.19/0.54 tff(375,plain,
% 0.19/0.54 (~equalish(e_2, e_5)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.19/0.54 tff(376,plain,
% 0.19/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_2, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_2, e_5, e_5)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(377,plain,
% 0.19/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_2, e_5, e_5)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(378,plain,
% 0.19/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_2, e_5, e_5))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.19/0.54 tff(379,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[378, 375, 20, 143, 372])).
% 0.19/0.54 tff(380,plain,(~product(e_2, e_5, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(381,plain,
% 0.19/0.54 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_3) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_3) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(382,plain,
% 0.19/0.54 ((product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_3) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(383,plain,
% 0.19/0.54 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_3) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1)))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[382])).
% 0.19/0.55 tff(384,plain,
% 0.19/0.55 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_3) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1))),
% 0.19/0.55 inference(transitivity,[status(thm)],[383, 381])).
% 0.19/0.55 tff(385,plain,
% 0.19/0.55 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_2)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(386,plain,
% 0.19/0.55 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_3) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.19/0.55 tff(387,plain,
% 0.19/0.55 (product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_3) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[386, 120, 209, 117])).
% 0.19/0.55 tff(388,plain,
% 0.19/0.55 (product(e_2, e_5, e_2) | product(e_2, e_5, e_3) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[387, 380])).
% 0.19/0.55 tff(389,plain,
% 0.19/0.55 (product(e_2, e_5, e_3) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[388, 371])).
% 0.19/0.55 tff(390,plain,
% 0.19/0.55 (product(e_2, e_5, e_4) | product(e_2, e_5, e_1)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[389, 365])).
% 0.19/0.55 tff(391,plain,
% 0.19/0.55 (product(e_2, e_5, e_1)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[390, 359])).
% 0.19/0.55 tff(392,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_5, e_2, e_2)) | (~product(e_2, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_5, e_2, e_2)) | (~product(e_2, e_5, e_1)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(393,plain,
% 0.19/0.55 (((~product(e_2, e_5, e_1)) | product(e_2, e_1, e_5) | (~product(e_5, e_2, e_2))) <=> (product(e_2, e_1, e_5) | (~product(e_5, e_2, e_2)) | (~product(e_2, e_5, e_1)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(394,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_2, e_1, e_5) | (~product(e_5, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_5, e_2, e_2)) | (~product(e_2, e_5, e_1))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[393])).
% 0.19/0.55 tff(395,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_2, e_1, e_5) | (~product(e_5, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_5, e_2, e_2)) | (~product(e_2, e_5, e_1)))),
% 0.19/0.55 inference(transitivity,[status(thm)],[394, 392])).
% 0.19/0.55 tff(396,plain,
% 0.19/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_2, e_1, e_5) | (~product(e_5, e_2, e_2)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(397,plain,
% 0.19/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_5, e_2, e_2)) | (~product(e_2, e_5, e_1))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.19/0.55 tff(398,plain,
% 0.19/0.55 (~product(e_5, e_2, e_2)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[397, 38, 100, 391])).
% 0.19/0.55 tff(399,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_5) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_1)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(400,plain,
% 0.19/0.55 (((~product(e_2, e_5, e_1)) | product(e_1, e_1, e_5) | (~product(e_5, e_2, e_1))) <=> (product(e_1, e_1, e_5) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_1)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(401,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_1, e_1, e_5) | (~product(e_5, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_1))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[400])).
% 0.19/0.55 tff(402,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_1, e_1, e_5) | (~product(e_5, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_5) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_1)))),
% 0.19/0.55 inference(transitivity,[status(thm)],[401, 399])).
% 0.19/0.55 tff(403,plain,
% 0.19/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_1, e_1, e_5) | (~product(e_5, e_2, e_1)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(404,plain,
% 0.19/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_5) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_1))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[403, 402])).
% 0.19/0.55 tff(405,plain,
% 0.19/0.55 (~product(e_5, e_2, e_1)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[404, 38, 163, 391])).
% 0.19/0.55 tff(406,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_5) | (~product(e_5, e_2, e_5)) | (~product(e_2, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_1, e_5) | (~product(e_5, e_2, e_5)) | (~product(e_2, e_5, e_1)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(407,plain,
% 0.19/0.55 (((~product(e_2, e_5, e_1)) | product(e_5, e_1, e_5) | (~product(e_5, e_2, e_5))) <=> (product(e_5, e_1, e_5) | (~product(e_5, e_2, e_5)) | (~product(e_2, e_5, e_1)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(408,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_5, e_1, e_5) | (~product(e_5, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_5) | (~product(e_5, e_2, e_5)) | (~product(e_2, e_5, e_1))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[407])).
% 0.19/0.55 tff(409,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_5, e_1, e_5) | (~product(e_5, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_1, e_5) | (~product(e_5, e_2, e_5)) | (~product(e_2, e_5, e_1)))),
% 0.19/0.55 inference(transitivity,[status(thm)],[408, 406])).
% 0.19/0.55 tff(410,plain,
% 0.19/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_5, e_1, e_5) | (~product(e_5, e_2, e_5)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(411,plain,
% 0.19/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_1, e_5) | (~product(e_5, e_2, e_5)) | (~product(e_2, e_5, e_1))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.19/0.55 tff(412,plain,
% 0.19/0.55 (~product(e_5, e_2, e_5)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[411, 38, 151, 391])).
% 0.19/0.55 tff(413,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_1)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(414,plain,
% 0.19/0.55 (((~product(e_2, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_2, e_3))) <=> (product(e_3, e_1, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_1)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(415,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_1))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[414])).
% 0.19/0.55 tff(416,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_1)))),
% 0.19/0.55 inference(transitivity,[status(thm)],[415, 413])).
% 0.19/0.55 tff(417,plain,
% 0.19/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_2, e_3)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(418,plain,
% 0.19/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_1))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.19/0.55 tff(419,plain,
% 0.19/0.55 (~product(e_5, e_2, e_3)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[418, 38, 187, 391])).
% 0.19/0.55 tff(420,plain,
% 0.19/0.55 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_5)) | product(e_5, e_2, e_3) | product(e_5, e_2, e_5) | product(e_5, e_2, e_4) | product(e_5, e_2, e_2) | product(e_5, e_2, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_5)) | product(e_5, e_2, e_3) | product(e_5, e_2, e_5) | product(e_5, e_2, e_4) | product(e_5, e_2, e_2) | product(e_5, e_2, e_1))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(421,plain,
% 0.19/0.55 ((product(e_5, e_2, e_5) | product(e_5, e_2, e_4) | product(e_5, e_2, e_3) | product(e_5, e_2, e_2) | product(e_5, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_5))) <=> ((~group_element(e_2)) | (~group_element(e_5)) | product(e_5, e_2, e_3) | product(e_5, e_2, e_5) | product(e_5, e_2, e_4) | product(e_5, e_2, e_2) | product(e_5, e_2, e_1))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(422,plain,
% 0.19/0.55 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_2, e_5) | product(e_5, e_2, e_4) | product(e_5, e_2, e_3) | product(e_5, e_2, e_2) | product(e_5, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_5)) | product(e_5, e_2, e_3) | product(e_5, e_2, e_5) | product(e_5, e_2, e_4) | product(e_5, e_2, e_2) | product(e_5, e_2, e_1)))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[421])).
% 0.19/0.55 tff(423,plain,
% 0.19/0.55 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_2, e_5) | product(e_5, e_2, e_4) | product(e_5, e_2, e_3) | product(e_5, e_2, e_2) | product(e_5, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_5)) | product(e_5, e_2, e_3) | product(e_5, e_2, e_5) | product(e_5, e_2, e_4) | product(e_5, e_2, e_2) | product(e_5, e_2, e_1))),
% 0.19/0.55 inference(transitivity,[status(thm)],[422, 420])).
% 0.19/0.55 tff(424,plain,
% 0.19/0.55 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_2, e_5) | product(e_5, e_2, e_4) | product(e_5, e_2, e_3) | product(e_5, e_2, e_2) | product(e_5, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_5)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(425,plain,
% 0.19/0.55 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_5)) | product(e_5, e_2, e_3) | product(e_5, e_2, e_5) | product(e_5, e_2, e_4) | product(e_5, e_2, e_2) | product(e_5, e_2, e_1)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[424, 423])).
% 0.19/0.55 tff(426,plain,
% 0.19/0.55 (product(e_5, e_2, e_3) | product(e_5, e_2, e_5) | product(e_5, e_2, e_4) | product(e_5, e_2, e_2) | product(e_5, e_2, e_1)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[425, 120, 209, 117])).
% 0.19/0.55 tff(427,plain,
% 0.19/0.55 (product(e_5, e_2, e_4)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[426, 419, 412, 405, 398])).
% 0.19/0.55 tff(428,plain,
% 0.19/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_5, e_2, e_4)) | (~product(e_5, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_5, e_2, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(429,plain,
% 0.19/0.55 ((equalish(e_2, e_1) | (~product(e_5, e_1, e_4)) | (~product(e_5, e_2, e_4))) <=> (equalish(e_2, e_1) | (~product(e_5, e_2, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(430,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_5, e_1, e_4)) | (~product(e_5, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_5, e_2, e_4)) | (~product(e_5, e_1, e_4))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[429])).
% 0.19/0.56 tff(431,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_5, e_1, e_4)) | (~product(e_5, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_5, e_2, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.19/0.56 inference(transitivity,[status(thm)],[430, 428])).
% 0.19/0.56 tff(432,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_5, e_1, e_4)) | (~product(e_5, e_2, e_4)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(433,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_5, e_2, e_4)) | (~product(e_5, e_1, e_4))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[432, 431])).
% 0.19/0.56 tff(434,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[433, 49, 74, 427, 223])).
% 0.19/0.56 tff(435,plain,(~product(e_5, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(436,plain,
% 0.19/0.56 (product(e_5, e_1, e_2)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[301, 435])).
% 0.19/0.56 tff(437,plain,
% 0.19/0.56 (~product(e_3, e_1, e_2)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[273, 436])).
% 0.19/0.56 tff(438,plain,
% 0.19/0.56 (product(e_3, e_1, e_4)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[265, 437])).
% 0.19/0.56 tff(439,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_5, e_4)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(440,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_5, e_4)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(441,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_5, e_4))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.19/0.56 tff(442,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[441, 287, 74, 224, 347])).
% 0.19/0.56 tff(443,plain,((~product(e_3, e_5, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(444,plain,
% 0.19/0.56 (~product(e_3, e_5, e_4)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[443, 438])).
% 0.19/0.56 tff(445,plain,
% 0.19/0.56 (product(e_3, e_5, e_2) | product(e_3, e_5, e_1)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[334, 444])).
% 0.19/0.56 tff(446,plain,
% 0.19/0.56 (product(e_3, e_5, e_2)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[445, 222])).
% 0.19/0.56 tff(447,assumption,(product(e_5, e_5, e_2)), introduced(assumption)).
% 0.19/0.56 tff(448,plain,
% 0.19/0.56 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(449,plain,
% 0.19/0.56 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[448])).
% 0.19/0.56 tff(450,plain,
% 0.19/0.56 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(451,plain,
% 0.19/0.56 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, Y, W)) | (~product(X, Y, Z))) <=> ((~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)))), rewrite((((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(452,plain,
% 0.19/0.56 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[451])).
% 0.19/0.56 tff(453,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function2')).
% 0.19/0.56 tff(454,plain,
% 0.19/0.56 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.19/0.56 tff(455,plain,
% 0.19/0.56 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[454, 450])).
% 0.19/0.56 tff(456,plain,(
% 0.19/0.56 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.56 inference(skolemize,[status(sab)],[455])).
% 0.19/0.56 tff(457,plain,
% 0.19/0.56 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[456, 449])).
% 0.19/0.56 tff(458,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_5, e_2)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(459,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_5, e_2)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(460,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_5, e_2))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.19/0.56 tff(461,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[460, 375, 457, 143, 447])).
% 0.19/0.56 tff(462,plain,(~product(e_5, e_5, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(463,assumption,(~product(e_5, e_5, e_2)), introduced(assumption)).
% 0.19/0.56 tff(464,assumption,(product(e_2, e_2, e_5)), introduced(assumption)).
% 0.19/0.56 tff(465,plain,
% 0.19/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_2) | (~product(e_2, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_2) | (~product(e_2, e_2, e_5)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(466,plain,
% 0.19/0.56 (((~product(e_2, e_2, e_5)) | product(e_5, e_5, e_2) | (~product(e_2, e_2, e_5))) <=> (product(e_5, e_5, e_2) | (~product(e_2, e_2, e_5)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(467,plain,
% 0.19/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_5)) | product(e_5, e_5, e_2) | (~product(e_2, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_2) | (~product(e_2, e_2, e_5))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[466])).
% 0.19/0.56 tff(468,plain,
% 0.19/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_5)) | product(e_5, e_5, e_2) | (~product(e_2, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_2) | (~product(e_2, e_2, e_5)))),
% 0.19/0.56 inference(transitivity,[status(thm)],[467, 465])).
% 0.19/0.56 tff(469,plain,
% 0.19/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_5)) | product(e_5, e_5, e_2) | (~product(e_2, e_2, e_5)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(470,plain,
% 0.19/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_2) | (~product(e_2, e_2, e_5))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.19/0.56 tff(471,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[470, 38, 464, 463])).
% 0.19/0.56 tff(472,plain,(product(e_5, e_5, e_2) | (~product(e_2, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(473,plain,
% 0.19/0.56 (~product(e_2, e_2, e_5)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[472, 462])).
% 0.19/0.56 tff(474,plain,
% 0.19/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_5) | (~product(e_5, e_3, e_2)) | (~product(e_3, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_5) | (~product(e_5, e_3, e_2)) | (~product(e_3, e_5, e_2)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(475,plain,
% 0.19/0.56 (((~product(e_3, e_5, e_2)) | product(e_2, e_2, e_5) | (~product(e_5, e_3, e_2))) <=> (product(e_2, e_2, e_5) | (~product(e_5, e_3, e_2)) | (~product(e_3, e_5, e_2)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(476,plain,
% 0.19/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_2)) | product(e_2, e_2, e_5) | (~product(e_5, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_5) | (~product(e_5, e_3, e_2)) | (~product(e_3, e_5, e_2))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[475])).
% 0.19/0.56 tff(477,plain,
% 0.19/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_2)) | product(e_2, e_2, e_5) | (~product(e_5, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_5) | (~product(e_5, e_3, e_2)) | (~product(e_3, e_5, e_2)))),
% 0.19/0.56 inference(transitivity,[status(thm)],[476, 474])).
% 0.19/0.56 tff(478,plain,
% 0.19/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_2)) | product(e_2, e_2, e_5) | (~product(e_5, e_3, e_2)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(479,plain,
% 0.19/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_5) | (~product(e_5, e_3, e_2)) | (~product(e_3, e_5, e_2))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.19/0.56 tff(480,plain,
% 0.19/0.56 ((~product(e_5, e_3, e_2)) | (~product(e_3, e_5, e_2))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[479, 38, 473])).
% 0.19/0.56 tff(481,plain,
% 0.19/0.56 (~product(e_5, e_3, e_2)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[480, 446])).
% 0.19/0.56 tff(482,assumption,(product(e_5, e_3, e_3)), introduced(assumption)).
% 0.19/0.56 tff(483,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(484,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(485,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.19/0.56 tff(486,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[485, 227, 20, 10, 482])).
% 0.19/0.56 tff(487,plain,(~product(e_5, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(488,plain,
% 0.19/0.56 (product(e_5, e_3, e_1) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[219, 487])).
% 0.19/0.56 tff(489,plain,
% 0.19/0.56 (product(e_5, e_3, e_1)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[488, 481, 152])).
% 0.19/0.56 tff(490,assumption,(product(e_5, e_4, e_1)), introduced(assumption)).
% 0.19/0.56 tff(491,assumption,(product(e_5, e_3, e_1)), introduced(assumption)).
% 0.19/0.56 tff(492,plain,
% 0.19/0.56 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(493,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.19/0.56 tff(494,plain,
% 0.19/0.56 (~equalish(e_4, e_3)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[493, 492])).
% 0.19/0.56 tff(495,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_5, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_5, e_4, e_1)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(496,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_5, e_4, e_1)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(497,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_5, e_4, e_1))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.19/0.56 tff(498,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[497, 494, 74, 491, 490])).
% 0.19/0.56 tff(499,plain,((~product(e_5, e_4, e_1)) | (~product(e_5, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(500,plain,
% 0.19/0.56 (~product(e_5, e_4, e_1)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[499, 489])).
% 0.19/0.56 tff(501,assumption,(product(e_5, e_4, e_5)), introduced(assumption)).
% 0.19/0.56 tff(502,plain,
% 0.19/0.56 ((~equalish(e_4, e_5)) <=> (~equalish(e_4, e_5))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(503,axiom,(~equalish(e_4, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_5')).
% 0.19/0.56 tff(504,plain,
% 0.19/0.56 (~equalish(e_4, e_5)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.19/0.56 tff(505,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_4, e_5)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(506,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_4, e_5)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(507,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_4, e_5))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.19/0.56 tff(508,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[507, 504, 74, 143, 501])).
% 0.19/0.56 tff(509,plain,(~product(e_5, e_4, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(510,assumption,(product(e_5, e_4, e_2)), introduced(assumption)).
% 0.19/0.56 tff(511,plain,
% 0.19/0.56 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(512,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.19/0.57 tff(513,plain,
% 0.19/0.57 (~equalish(e_4, e_1)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.19/0.57 tff(514,plain,
% 0.19/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_5, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_5, e_4, e_2)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(515,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_5, e_4, e_2)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(516,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_5, e_4, e_2))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.19/0.57 tff(517,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[516, 513, 74, 436, 510])).
% 0.19/0.57 tff(518,plain,(~product(e_5, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(519,assumption,(product(e_5, e_4, e_4)), introduced(assumption)).
% 0.19/0.57 tff(520,plain,
% 0.19/0.57 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(521,plain,
% 0.19/0.57 (product(e_4, e_4, e_4)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[520, 8])).
% 0.19/0.57 tff(522,plain,
% 0.19/0.57 ((~equalish(e_5, e_4)) <=> (~equalish(e_5, e_4))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(523,axiom,(~equalish(e_5, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_4')).
% 0.19/0.57 tff(524,plain,
% 0.19/0.57 (~equalish(e_5, e_4)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.19/0.57 tff(525,plain,
% 0.19/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(526,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(527,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.19/0.57 tff(528,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[527, 524, 20, 521, 519])).
% 0.19/0.57 tff(529,plain,(~product(e_5, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(530,plain,
% 0.19/0.57 (group_element(e_4) <=> group_element(e_4)),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(531,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.19/0.57 tff(532,plain,
% 0.19/0.57 (group_element(e_4)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.19/0.57 tff(533,plain,
% 0.19/0.57 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5)) | product(e_5, e_4, e_5) | (~group_element(e_4)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_3) | product(e_5, e_4, e_4) | product(e_5, e_4, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5)) | product(e_5, e_4, e_5) | (~group_element(e_4)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_3) | product(e_5, e_4, e_4) | product(e_5, e_4, e_1))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(534,plain,
% 0.19/0.57 ((product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_5))) <=> ((~group_element(e_5)) | product(e_5, e_4, e_5) | (~group_element(e_4)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_3) | product(e_5, e_4, e_4) | product(e_5, e_4, e_1))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(535,plain,
% 0.19/0.57 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5)) | product(e_5, e_4, e_5) | (~group_element(e_4)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_3) | product(e_5, e_4, e_4) | product(e_5, e_4, e_1)))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[534])).
% 0.19/0.57 tff(536,plain,
% 0.19/0.57 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5)) | product(e_5, e_4, e_5) | (~group_element(e_4)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_3) | product(e_5, e_4, e_4) | product(e_5, e_4, e_1))),
% 0.19/0.57 inference(transitivity,[status(thm)],[535, 533])).
% 0.19/0.57 tff(537,plain,
% 0.19/0.57 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_5)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(538,plain,
% 0.19/0.57 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5)) | product(e_5, e_4, e_5) | (~group_element(e_4)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_3) | product(e_5, e_4, e_4) | product(e_5, e_4, e_1)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.19/0.57 tff(539,plain,
% 0.19/0.57 (product(e_5, e_4, e_5) | product(e_5, e_4, e_2) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[538, 532, 209, 117, 529])).
% 0.19/0.57 tff(540,plain,
% 0.19/0.57 (product(e_5, e_4, e_3) | product(e_5, e_4, e_1)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[539, 518, 509])).
% 0.19/0.57 tff(541,plain,
% 0.19/0.57 (product(e_5, e_4, e_3)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[540, 500])).
% 0.19/0.57 tff(542,assumption,(product(e_5, e_4, e_3)), introduced(assumption)).
% 0.19/0.57 tff(543,plain,
% 0.19/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_5)) | product(e_5, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_5)) | product(e_5, e_3, e_3))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(544,plain,
% 0.19/0.57 (((~product(e_3, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5))) <=> ((~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_5)) | product(e_5, e_3, e_3))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(545,plain,
% 0.19/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_5)) | product(e_5, e_3, e_3)))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[544])).
% 0.19/0.57 tff(546,plain,
% 0.19/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_5)) | product(e_5, e_3, e_3))),
% 0.19/0.57 inference(transitivity,[status(thm)],[545, 543])).
% 0.19/0.57 tff(547,plain,
% 0.19/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(548,plain,
% 0.19/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_5)) | product(e_5, e_3, e_3)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.19/0.57 tff(549,plain,
% 0.19/0.57 (~product(e_3, e_3, e_5)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[548, 38, 10, 487])).
% 0.19/0.57 tff(550,assumption,(product(e_4, e_5, e_3)), introduced(assumption)).
% 0.19/0.57 tff(551,plain,
% 0.19/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(552,plain,
% 0.19/0.57 (((~product(e_4, e_5, e_3)) | product(e_3, e_3, e_5) | (~product(e_5, e_4, e_3))) <=> (product(e_3, e_3, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(553,plain,
% 0.19/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_3)) | product(e_3, e_3, e_5) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[552])).
% 0.19/0.57 tff(554,plain,
% 0.19/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_3)) | product(e_3, e_3, e_5) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3)))),
% 0.19/0.57 inference(transitivity,[status(thm)],[553, 551])).
% 0.19/0.57 tff(555,plain,
% 0.19/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_3)) | product(e_3, e_3, e_5) | (~product(e_5, e_4, e_3)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(556,plain,
% 0.19/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.19/0.57 tff(557,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[556, 38, 550, 549, 542])).
% 0.19/0.57 tff(558,plain,((~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(559,plain,
% 0.19/0.57 (~product(e_4, e_5, e_3)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[558, 541])).
% 0.19/0.57 tff(560,assumption,(product(e_4, e_5, e_4)), introduced(assumption)).
% 0.19/0.57 tff(561,plain,
% 0.19/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_5, e_4)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(562,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_5, e_4)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(563,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_5, e_4))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[562, 561])).
% 0.19/0.57 tff(564,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[563, 524, 74, 521, 560])).
% 0.19/0.57 tff(565,plain,(~product(e_4, e_5, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(566,assumption,(product(e_4, e_5, e_2)), introduced(assumption)).
% 0.19/0.57 tff(567,plain,
% 0.19/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_5, e_2)) | (~product(e_4, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_5, e_2)) | (~product(e_4, e_5, e_2)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(568,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_5, e_2)) | (~product(e_4, e_5, e_2)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(569,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_5, e_2)) | (~product(e_4, e_5, e_2))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.19/0.57 tff(570,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[569, 494, 20, 304, 566])).
% 0.19/0.57 tff(571,plain,((~product(e_4, e_5, e_2)) | (~product(e_3, e_5, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(572,plain,
% 0.19/0.57 (~product(e_4, e_5, e_2)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[571, 446])).
% 0.19/0.57 tff(573,assumption,(product(e_4, e_5, e_5)), introduced(assumption)).
% 0.19/0.57 tff(574,plain,
% 0.19/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_4, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_4, e_5, e_5)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(575,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_4, e_5, e_5)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(576,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_4, e_5, e_5))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.19/0.57 tff(577,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[576, 504, 20, 143, 573])).
% 0.19/0.57 tff(578,plain,(~product(e_4, e_5, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(579,plain,
% 0.19/0.57 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5)) | (~group_element(e_4)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5)) | (~group_element(e_4)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(580,plain,
% 0.19/0.58 ((product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_4))) <=> ((~group_element(e_5)) | (~group_element(e_4)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(581,plain,
% 0.19/0.58 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5)) | (~group_element(e_4)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1)))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[580])).
% 0.19/0.58 tff(582,plain,
% 0.19/0.58 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5)) | (~group_element(e_4)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1))),
% 0.19/0.58 inference(transitivity,[status(thm)],[581, 579])).
% 0.19/0.58 tff(583,plain,
% 0.19/0.58 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_4)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(584,plain,
% 0.19/0.58 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, 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_5)) | (~group_element(e_4)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[583, 582])).
% 0.19/0.58 tff(585,plain,
% 0.19/0.58 (product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[584, 532, 209, 117])).
% 0.19/0.58 tff(586,plain,
% 0.19/0.58 (product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[585, 578])).
% 0.19/0.58 tff(587,plain,
% 0.19/0.58 (product(e_4, e_5, e_1)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[586, 572, 565, 559])).
% 0.19/0.58 tff(588,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3)) | (~product(e_4, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3)) | (~product(e_4, e_5, e_1)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(589,plain,
% 0.19/0.58 (((~product(e_4, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3))) <=> (product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3)) | (~product(e_4, e_5, e_1)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(590,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3)) | (~product(e_4, e_5, e_1))))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[589])).
% 0.19/0.58 tff(591,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3)) | (~product(e_4, e_5, e_1)))),
% 0.19/0.58 inference(transitivity,[status(thm)],[590, 588])).
% 0.19/0.58 tff(592,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(593,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3)) | (~product(e_4, e_5, e_1))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.19/0.58 tff(594,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[593, 38, 187, 587, 541])).
% 0.19/0.58 tff(595,plain,(product(e_5, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(596,assumption,(product(e_5, e_2, e_4)), introduced(assumption)).
% 0.19/0.58 tff(597,plain,
% 0.19/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_5, e_3, e_4)) | (~product(e_5, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_5, e_3, e_4)) | (~product(e_5, e_2, e_4)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(598,plain,
% 0.19/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_5, e_3, e_4)) | (~product(e_5, e_2, e_4)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(599,plain,
% 0.19/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_5, e_3, e_4)) | (~product(e_5, e_2, e_4))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[598, 597])).
% 0.19/0.58 tff(600,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[599, 350, 74, 596, 595])).
% 0.19/0.58 tff(601,plain,(~product(e_5, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(602,plain,
% 0.19/0.58 (~product(e_5, e_2, e_2)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[397, 38, 100, 140])).
% 0.19/0.58 tff(603,assumption,(~product(e_5, e_2, e_4)), introduced(assumption)).
% 0.19/0.58 tff(604,assumption,(~product(e_5, e_2, e_5)), introduced(assumption)).
% 0.19/0.58 tff(605,plain,
% 0.19/0.58 (~product(e_5, e_2, e_1)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[404, 38, 163, 140])).
% 0.19/0.58 tff(606,plain,
% 0.19/0.58 (~product(e_5, e_2, e_3)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[418, 38, 187, 140])).
% 0.19/0.58 tff(607,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[426, 606, 605, 604, 603, 602])).
% 0.19/0.58 tff(608,plain,((~product(e_2, e_5, e_1)) | product(e_5, e_2, e_5) | product(e_5, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(609,plain,
% 0.19/0.58 (product(e_5, e_2, e_5)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[608, 140, 601])).
% 0.19/0.58 tff(610,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[411, 38, 609, 151, 140])).
% 0.19/0.58 tff(611,plain,(~product(e_2, e_5, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(612,plain,
% 0.19/0.58 (product(e_2, e_5, e_4)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[390, 611])).
% 0.19/0.58 tff(613,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.19/0.58 tff(614,plain,
% 0.19/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(615,plain,
% 0.19/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(616,plain,
% 0.19/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_2))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.19/0.58 tff(617,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[616, 504, 20, 436, 613])).
% 0.19/0.58 tff(618,plain,(~product(e_4, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(619,assumption,(product(e_5, e_2, e_1)), introduced(assumption)).
% 0.19/0.58 tff(620,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_4)) | (~product(e_5, e_2, e_1)) | product(e_4, e_1, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_5, e_4)) | (~product(e_5, e_2, e_1)) | product(e_4, e_1, e_2))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(621,plain,
% 0.19/0.58 (((~product(e_5, e_2, e_1)) | product(e_4, e_1, e_2) | (~product(e_2, e_5, e_4))) <=> ((~product(e_2, e_5, e_4)) | (~product(e_5, e_2, e_1)) | product(e_4, e_1, e_2))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(622,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_2, e_1)) | product(e_4, e_1, e_2) | (~product(e_2, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_4)) | (~product(e_5, e_2, e_1)) | product(e_4, e_1, e_2)))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[621])).
% 0.19/0.58 tff(623,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_2, e_1)) | product(e_4, e_1, e_2) | (~product(e_2, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_5, e_4)) | (~product(e_5, e_2, e_1)) | product(e_4, e_1, e_2))),
% 0.19/0.58 inference(transitivity,[status(thm)],[622, 620])).
% 0.19/0.58 tff(624,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_2, e_1)) | product(e_4, e_1, e_2) | (~product(e_2, e_5, e_4)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(625,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_5, e_4)) | (~product(e_5, e_2, e_1)) | product(e_4, e_1, e_2)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.19/0.58 tff(626,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[625, 38, 619, 346, 618])).
% 0.19/0.58 tff(627,plain,((~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(628,plain,
% 0.19/0.58 (~product(e_5, e_2, e_1)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[627, 612])).
% 0.19/0.58 tff(629,assumption,(product(e_5, e_2, e_2)), introduced(assumption)).
% 0.19/0.58 tff(630,plain,
% 0.19/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_5, 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_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_5, e_2, e_2)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(631,plain,
% 0.19/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_5, e_2, e_2)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(632,plain,
% 0.19/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_5, e_2, e_2))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[631, 630])).
% 0.19/0.58 tff(633,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[632, 278, 20, 62, 629])).
% 0.19/0.58 tff(634,plain,(~product(e_5, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(635,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_4)) | product(e_5, e_4, e_5) | (~product(e_5, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_5, e_4)) | product(e_5, e_4, e_5) | (~product(e_5, e_2, e_5)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(636,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_4)) | product(e_5, e_4, e_5) | (~product(e_5, e_2, e_5)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(637,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_5, e_4)) | product(e_5, e_4, e_5) | (~product(e_5, e_2, e_5))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[636, 635])).
% 0.19/0.58 tff(638,plain,
% 0.19/0.58 (~product(e_5, e_2, e_5)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[637, 38, 612, 509])).
% 0.19/0.58 tff(639,plain,
% 0.19/0.58 (product(e_5, e_2, e_3)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[426, 638, 634, 601, 628])).
% 0.19/0.58 tff(640,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_4)) | product(e_4, e_3, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_4)) | product(e_4, e_3, e_2))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(641,plain,
% 0.19/0.58 (((~product(e_5, e_2, e_3)) | product(e_4, e_3, e_2) | (~product(e_2, e_5, e_4))) <=> ((~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_4)) | product(e_4, e_3, e_2))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(642,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_2, e_3)) | product(e_4, e_3, e_2) | (~product(e_2, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_4)) | product(e_4, e_3, e_2)))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[641])).
% 0.19/0.58 tff(643,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_2, e_3)) | product(e_4, e_3, e_2) | (~product(e_2, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_4)) | product(e_4, e_3, e_2))),
% 0.19/0.58 inference(transitivity,[status(thm)],[642, 640])).
% 0.19/0.58 tff(644,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_2, e_3)) | product(e_4, e_3, e_2) | (~product(e_2, e_5, e_4)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(645,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_4)) | product(e_4, e_3, e_2)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[644, 643])).
% 0.19/0.58 tff(646,plain,
% 0.19/0.58 ((~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_4)) | product(e_4, e_3, e_2)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[645, 38])).
% 0.19/0.58 tff(647,plain,
% 0.19/0.58 (product(e_4, e_3, e_2)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[646, 639, 612])).
% 0.19/0.58 tff(648,assumption,(product(e_4, e_3, e_1)), introduced(assumption)).
% 0.19/0.58 tff(649,plain,
% 0.19/0.58 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(650,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.19/0.58 tff(651,plain,
% 0.19/0.58 (~equalish(e_1, e_2)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[650, 649])).
% 0.19/0.58 tff(652,plain,
% 0.19/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_3, e_2)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(653,plain,
% 0.19/0.58 ((equalish(e_1, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_3, e_1))) <=> (equalish(e_1, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_3, e_2)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(654,plain,
% 0.19/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_3, e_2))))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[653])).
% 0.19/0.58 tff(655,plain,
% 0.19/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_3, e_2)))),
% 0.19/0.58 inference(transitivity,[status(thm)],[654, 652])).
% 0.19/0.58 tff(656,plain,
% 0.19/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_3, e_1)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(657,plain,
% 0.19/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_3, e_2))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.19/0.58 tff(658,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[657, 651, 457, 648, 647])).
% 0.19/0.58 tff(659,plain,(~product(e_4, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(660,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_4, e_3, e_1) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_4, e_3, e_1) | (~product(e_1, e_2, e_4)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(661,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_4, e_3, e_1) | (~product(e_1, e_2, e_4)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(662,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_4, e_3, e_1) | (~product(e_1, e_2, e_4))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.19/0.58 tff(663,plain,
% 0.19/0.58 (product(e_4, e_3, e_1) | (~product(e_1, e_2, e_4))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[662, 38, 132])).
% 0.19/0.58 tff(664,plain,
% 0.19/0.58 (~product(e_1, e_2, e_4)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[663, 659])).
% 0.19/0.58 tff(665,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.19/0.58 tff(666,plain,
% 0.19/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(667,plain,
% 0.19/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(668,plain,
% 0.19/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[667, 666])).
% 0.19/0.59 tff(669,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[668, 651, 20, 62, 665])).
% 0.19/0.59 tff(670,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(671,assumption,(product(e_1, e_4, e_1)), introduced(assumption)).
% 0.19/0.59 tff(672,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.19/0.59 tff(673,plain,
% 0.19/0.59 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(674,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.19/0.59 tff(675,plain,
% 0.19/0.59 (~equalish(e_4, e_2)),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.19/0.59 tff(676,plain,
% 0.19/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(677,plain,
% 0.19/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(678,plain,
% 0.19/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[677, 676])).
% 0.19/0.59 tff(679,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[678, 675, 20, 132, 672])).
% 0.19/0.59 tff(680,plain,(~product(e_4, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(681,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.19/0.59 tff(682,plain,
% 0.19/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(683,plain,
% 0.19/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(684,plain,
% 0.19/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.19/0.59 tff(685,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[684, 513, 20, 44, 681])).
% 0.19/0.59 tff(686,plain,(~product(e_4, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(687,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.19/0.59 tff(688,plain,
% 0.19/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(689,plain,
% 0.19/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(690,plain,
% 0.19/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.19/0.59 tff(691,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[690, 494, 20, 438, 687])).
% 0.19/0.59 tff(692,plain,(~product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(693,plain,
% 0.19/0.59 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(694,plain,
% 0.19/0.59 ((product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4))) <=> ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(695,plain,
% 0.19/0.59 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[694])).
% 0.19/0.59 tff(696,plain,
% 0.19/0.59 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))),
% 0.19/0.59 inference(transitivity,[status(thm)],[695, 693])).
% 0.19/0.59 tff(697,plain,
% 0.19/0.59 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(698,plain,
% 0.19/0.59 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[697, 696])).
% 0.19/0.59 tff(699,plain,
% 0.19/0.59 (product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[698, 123, 532, 117])).
% 0.19/0.59 tff(700,plain,
% 0.19/0.59 (product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1)),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[699, 618])).
% 0.19/0.59 tff(701,plain,
% 0.19/0.59 (product(e_4, e_1, e_5) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1)),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[700, 692])).
% 0.19/0.59 tff(702,plain,
% 0.19/0.59 (product(e_4, e_1, e_5) | product(e_4, e_1, e_3)),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[701, 686])).
% 0.19/0.59 tff(703,plain,
% 0.19/0.59 (product(e_4, e_1, e_5)),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[702, 680])).
% 0.19/0.59 tff(704,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_1, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_4, e_1)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(705,plain,
% 0.19/0.59 (((~product(e_1, e_4, e_1)) | product(e_5, e_1, e_4) | (~product(e_4, e_1, e_5))) <=> (product(e_5, e_1, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_4, e_1)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(706,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_1)) | product(e_5, e_1, e_4) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_4, e_1))))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[705])).
% 0.19/0.59 tff(707,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_1)) | product(e_5, e_1, e_4) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_1, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_4, e_1)))),
% 0.19/0.59 inference(transitivity,[status(thm)],[706, 704])).
% 0.19/0.59 tff(708,plain,
% 0.19/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_1)) | product(e_5, e_1, e_4) | (~product(e_4, e_1, e_5)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(709,plain,
% 0.19/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_1, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_4, e_1))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.19/0.59 tff(710,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[709, 38, 435, 703, 671])).
% 0.19/0.59 tff(711,plain,(~product(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(712,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_1, e_4, e_1) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_1, e_4, e_1) | (~product(e_1, e_3, e_1)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(713,plain,
% 0.19/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_1, e_4, e_1) | (~product(e_1, e_3, e_1)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(714,plain,
% 0.19/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_1, e_4, e_1) | (~product(e_1, e_3, e_1))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[713, 712])).
% 0.19/0.59 tff(715,plain,
% 0.19/0.59 (~product(e_1, e_3, e_1)),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[714, 38, 438, 711])).
% 0.19/0.59 tff(716,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(717,plain,
% 0.19/0.59 (((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1))) <=> (product(e_1, e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(718,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1))))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[717])).
% 0.19/0.59 tff(719,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.59 inference(transitivity,[status(thm)],[718, 716])).
% 0.19/0.59 tff(720,plain,
% 0.19/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(721,plain,
% 0.19/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[720, 719])).
% 0.19/0.60 tff(722,plain,
% 0.19/0.60 (~product(e_1, e_2, e_1)),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[721, 38, 132, 715])).
% 0.19/0.60 tff(723,plain,
% 0.19/0.60 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(724,plain,
% 0.19/0.60 ((product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(725,plain,
% 0.19/0.60 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4)))),
% 0.19/0.60 inference(monotonicity,[status(thm)],[724])).
% 0.19/0.60 tff(726,plain,
% 0.19/0.60 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4))),
% 0.19/0.60 inference(transitivity,[status(thm)],[725, 723])).
% 0.19/0.60 tff(727,plain,
% 0.19/0.60 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.19/0.60 inference(quant_inst,[status(thm)],[])).
% 0.19/0.60 tff(728,plain,
% 0.19/0.60 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4)),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[727, 726])).
% 0.19/0.60 tff(729,plain,
% 0.19/0.60 (product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_2) | product(e_1, e_2, e_4)),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[728, 123, 120, 117, 722])).
% 0.19/0.60 tff(730,plain,
% 0.19/0.60 (product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4)),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[729, 670])).
% 0.19/0.60 tff(731,plain,
% 0.19/0.60 (product(e_1, e_2, e_5)),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[730, 664, 139])).
% 0.19/0.60 tff(732,assumption,(product(e_1, e_2, e_5)), introduced(assumption)).
% 0.19/0.60 tff(733,assumption,(product(e_1, e_3, e_5)), introduced(assumption)).
% 0.19/0.60 tff(734,plain,
% 0.19/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(735,plain,
% 0.19/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.19/0.60 inference(quant_inst,[status(thm)],[])).
% 0.19/0.60 tff(736,plain,
% 0.19/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_3, e_5))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[735, 734])).
% 0.19/0.60 tff(737,plain,
% 0.19/0.60 ($false),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[736, 250, 74, 733, 732])).
% 0.19/0.60 tff(738,plain,((~product(e_1, e_3, e_5)) | (~product(e_1, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.60 tff(739,plain,
% 0.19/0.60 (~product(e_1, e_3, e_5)),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[738, 731])).
% 0.19/0.60 tff(740,assumption,(product(e_1, e_4, e_4)), introduced(assumption)).
% 0.19/0.60 tff(741,plain,
% 0.19/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_4)) | product(e_5, e_4, e_4) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_4, e_4)) | product(e_5, e_4, e_4) | (~product(e_4, e_1, e_5)))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(742,plain,
% 0.19/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_4)) | product(e_5, e_4, e_4) | (~product(e_4, e_1, e_5)))),
% 0.19/0.60 inference(quant_inst,[status(thm)],[])).
% 0.19/0.60 tff(743,plain,
% 0.19/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_4, e_4)) | product(e_5, e_4, e_4) | (~product(e_4, e_1, e_5))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[742, 741])).
% 0.19/0.60 tff(744,plain,
% 0.19/0.60 ($false),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[743, 38, 529, 703, 740])).
% 0.19/0.60 tff(745,plain,(~product(e_1, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.60 tff(746,plain,
% 0.19/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_4)) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_4)) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_1)))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(747,plain,
% 0.19/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_4)) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_1)))),
% 0.19/0.60 inference(quant_inst,[status(thm)],[])).
% 0.19/0.60 tff(748,plain,
% 0.19/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_4)) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_1))),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[747, 746])).
% 0.19/0.60 tff(749,plain,
% 0.19/0.60 (~product(e_4, e_4, e_1)),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[748, 38, 521, 745])).
% 0.19/0.60 tff(750,plain,
% 0.19/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(751,plain,
% 0.19/0.60 (((~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1) | (~product(e_1, e_3, e_4))) <=> ((~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(752,plain,
% 0.19/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1)))),
% 0.19/0.60 inference(monotonicity,[status(thm)],[751])).
% 0.19/0.60 tff(753,plain,
% 0.19/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1))),
% 0.19/0.60 inference(transitivity,[status(thm)],[752, 750])).
% 0.19/0.60 tff(754,plain,
% 0.19/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1) | (~product(e_1, e_3, e_4)))),
% 0.19/0.60 inference(quant_inst,[status(thm)],[])).
% 0.19/0.60 tff(755,plain,
% 0.19/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1)),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[754, 753])).
% 0.19/0.60 tff(756,plain,
% 0.19/0.60 (~product(e_1, e_3, e_4)),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[755, 38, 438, 749])).
% 0.19/0.60 tff(757,plain,
% 0.19/0.60 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(758,plain,
% 0.19/0.60 ((product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(759,plain,
% 0.19/0.60 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1)))),
% 0.19/0.60 inference(monotonicity,[status(thm)],[758])).
% 0.19/0.60 tff(760,plain,
% 0.19/0.60 (((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))),
% 0.19/0.60 inference(transitivity,[status(thm)],[759, 757])).
% 0.19/0.60 tff(761,plain,
% 0.19/0.60 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))),
% 0.19/0.60 inference(quant_inst,[status(thm)],[])).
% 0.19/0.60 tff(762,plain,
% 0.19/0.60 ((~![Y: $i, X: $i] : (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1)),
% 0.19/0.60 inference(modus_ponens,[status(thm)],[761, 760])).
% 0.19/0.60 tff(763,plain,
% 0.19/0.60 (product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3)),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[762, 123, 212, 117, 715])).
% 0.19/0.60 tff(764,plain,
% 0.19/0.60 (product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_3)),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[763, 756])).
% 0.19/0.60 tff(765,plain,
% 0.19/0.60 (product(e_1, e_3, e_2)),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[764, 739, 28])).
% 0.19/0.60 tff(766,plain,
% 0.19/0.60 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.19/0.60 inference(rewrite,[status(thm)],[])).
% 0.19/0.60 tff(767,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.19/0.61 tff(768,plain,
% 0.19/0.61 (~equalish(e_1, e_4)),
% 0.19/0.61 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.19/0.61 tff(769,plain,
% 0.19/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.19/0.61 inference(rewrite,[status(thm)],[])).
% 0.19/0.61 tff(770,plain,
% 0.19/0.61 ((equalish(e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_1, e_3, e_2))) <=> (equalish(e_1, e_4) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.19/0.61 inference(rewrite,[status(thm)],[])).
% 0.19/0.61 tff(771,plain,
% 0.19/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_2))))),
% 0.19/0.61 inference(monotonicity,[status(thm)],[770])).
% 0.19/0.61 tff(772,plain,
% 0.19/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.19/0.61 inference(transitivity,[status(thm)],[771, 769])).
% 0.19/0.61 tff(773,plain,
% 0.19/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.61 inference(quant_inst,[status(thm)],[])).
% 0.19/0.61 tff(774,plain,
% 0.19/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_2))),
% 0.19/0.61 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.19/0.61 tff(775,plain,
% 0.19/0.61 ($false),
% 0.19/0.61 inference(unit_resolution,[status(thm)],[774, 768, 20, 647, 765])).
% 0.19/0.61 % SZS output end Proof
%------------------------------------------------------------------------------