TSTP Solution File: GRP125-3.005 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP125-3.005 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 0.67s 0.72s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : GRP125-3.005 : TPTP v8.1.0. Released v1.2.0.
% 0.14/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.37 % Computer : n005.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Aug 31 14:57:03 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.38 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.38 Usage: tptp [options] [-file:]file
% 0.15/0.38 -h, -? prints this message.
% 0.15/0.38 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.38 -m, -model generate model.
% 0.15/0.38 -p, -proof generate proof.
% 0.15/0.38 -c, -core generate unsat core of named formulas.
% 0.15/0.38 -st, -statistics display statistics.
% 0.15/0.38 -t:timeout set timeout (in second).
% 0.15/0.38 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.38 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.38 -<param>:<value> configuration parameter and value.
% 0.15/0.38 -o:<output-file> file to place output in.
% 0.67/0.72 % SZS status Unsatisfiable
% 0.67/0.72 % SZS output start Proof
% 0.67/0.72 tff(product_type, type, (
% 0.67/0.72 product: ( $i * $i * $i ) > $o)).
% 0.67/0.72 tff(e_1_type, type, (
% 0.67/0.72 e_1: $i)).
% 0.67/0.72 tff(e_5_type, type, (
% 0.67/0.72 e_5: $i)).
% 0.67/0.72 tff(e_2_type, type, (
% 0.67/0.72 e_2: $i)).
% 0.67/0.72 tff(e_4_type, type, (
% 0.67/0.72 e_4: $i)).
% 0.67/0.72 tff(e_3_type, type, (
% 0.67/0.72 e_3: $i)).
% 0.67/0.72 tff(equalish_type, type, (
% 0.67/0.72 equalish: ( $i * $i ) > $o)).
% 0.67/0.72 tff(cycle_type, type, (
% 0.67/0.72 cycle: ( $i * $i ) > $o)).
% 0.67/0.72 tff(next_type, type, (
% 0.67/0.72 next: ( $i * $i ) > $o)).
% 0.67/0.72 tff(greater_type, type, (
% 0.67/0.72 greater: ( $i * $i ) > $o)).
% 0.67/0.72 tff(e_0_type, type, (
% 0.67/0.72 e_0: $i)).
% 0.67/0.72 tff(group_element_type, type, (
% 0.67/0.72 group_element: $i > $o)).
% 0.67/0.72 tff(1,assumption,(product(e_4, e_2, e_1)), introduced(assumption)).
% 0.67/0.72 tff(2,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.67/0.72 tff(3,plain,
% 0.67/0.72 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.67/0.72 inference(bind,[status(th)],[])).
% 0.67/0.72 tff(4,plain,
% 0.67/0.72 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.67/0.72 inference(quant_intro,[status(thm)],[3])).
% 0.67/0.72 tff(5,plain,
% 0.67/0.72 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(6,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_idempotence')).
% 0.67/0.72 tff(7,plain,
% 0.67/0.72 (![X: $i] : product(X, X, X)),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.67/0.72 tff(8,plain,(
% 0.67/0.72 ![X: $i] : product(X, X, X)),
% 0.67/0.72 inference(skolemize,[status(sab)],[7])).
% 0.67/0.72 tff(9,plain,
% 0.67/0.72 (![X: $i] : product(X, X, X)),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.67/0.72 tff(10,plain,
% 0.67/0.72 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(11,plain,
% 0.67/0.72 ($false),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.67/0.72 tff(12,plain,(product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.72 tff(13,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.67/0.72 tff(14,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.67/0.72 tff(15,plain,
% 0.67/0.72 (^[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))))),
% 0.67/0.72 inference(bind,[status(th)],[])).
% 0.67/0.72 tff(16,plain,
% 0.67/0.72 (![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)))),
% 0.67/0.72 inference(quant_intro,[status(thm)],[15])).
% 0.67/0.72 tff(17,plain,
% 0.67/0.72 (![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)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(18,plain,
% 0.67/0.72 (^[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)))))),
% 0.67/0.72 inference(bind,[status(th)],[])).
% 0.67/0.72 tff(19,plain,
% 0.67/0.72 (![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)))),
% 0.67/0.72 inference(quant_intro,[status(thm)],[18])).
% 0.67/0.72 tff(20,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.67/0.72 tff(21,plain,
% 0.67/0.72 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.67/0.72 tff(22,plain,
% 0.67/0.72 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.67/0.72 tff(23,plain,(
% 0.67/0.72 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.67/0.72 inference(skolemize,[status(sab)],[22])).
% 0.67/0.72 tff(24,plain,
% 0.67/0.72 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.67/0.72 tff(25,plain,
% 0.67/0.72 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(26,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.67/0.72 tff(27,plain,
% 0.67/0.72 (~equalish(e_2, e_1)),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.67/0.72 tff(28,plain,
% 0.67/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(29,plain,
% 0.67/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(30,plain,
% 0.67/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.67/0.72 tff(31,plain,
% 0.67/0.72 ($false),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[30, 27, 24, 14, 13])).
% 0.67/0.72 tff(32,plain,((~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.72 tff(33,plain,
% 0.67/0.72 (~product(e_2, e_1, e_1)),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[32, 12])).
% 0.67/0.72 tff(34,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.67/0.72 tff(35,plain,
% 0.67/0.72 (^[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))))),
% 0.67/0.72 inference(bind,[status(th)],[])).
% 0.67/0.72 tff(36,plain,
% 0.67/0.72 (![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)))),
% 0.67/0.72 inference(quant_intro,[status(thm)],[35])).
% 0.67/0.72 tff(37,plain,
% 0.67/0.72 (![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)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(38,plain,
% 0.67/0.72 (^[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))))),
% 0.67/0.72 inference(bind,[status(th)],[])).
% 0.67/0.72 tff(39,plain,
% 0.67/0.72 (![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)))),
% 0.67/0.72 inference(quant_intro,[status(thm)],[38])).
% 0.67/0.72 tff(40,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.67/0.72 tff(41,plain,
% 0.67/0.72 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.67/0.72 tff(42,plain,
% 0.67/0.72 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.67/0.72 tff(43,plain,(
% 0.67/0.72 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.67/0.72 inference(skolemize,[status(sab)],[42])).
% 0.67/0.72 tff(44,plain,
% 0.67/0.72 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.67/0.72 tff(45,plain,
% 0.67/0.72 (((~![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_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, 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_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(46,plain,
% 0.67/0.72 (((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(47,plain,
% 0.67/0.72 (((~![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_1)) | product(e_2, e_1, e_1) | (~product(e_1, 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_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1))))),
% 0.67/0.72 inference(monotonicity,[status(thm)],[46])).
% 0.67/0.72 tff(48,plain,
% 0.67/0.72 (((~![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_1)) | product(e_2, e_1, e_1) | (~product(e_1, 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_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1)))),
% 0.67/0.72 inference(transitivity,[status(thm)],[47, 45])).
% 0.67/0.72 tff(49,plain,
% 0.67/0.72 ((~![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_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)))),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(50,plain,
% 0.67/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.67/0.72 tff(51,plain,
% 0.67/0.72 ($false),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[50, 44, 34, 33, 12])).
% 0.67/0.72 tff(52,plain,(~product(e_1, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.72 tff(53,plain,
% 0.67/0.72 (((~![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_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, 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_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(54,plain,
% 0.67/0.72 (((~product(e_4, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_4, e_1))) <=> (product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(55,plain,
% 0.67/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, 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_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1))))),
% 0.67/0.72 inference(monotonicity,[status(thm)],[54])).
% 0.67/0.72 tff(56,plain,
% 0.67/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, 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_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.67/0.72 inference(transitivity,[status(thm)],[55, 53])).
% 0.67/0.72 tff(57,plain,
% 0.67/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_4, e_1)))),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(58,plain,
% 0.67/0.72 ((~![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_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.67/0.72 tff(59,plain,
% 0.67/0.72 (~product(e_2, e_4, e_1)),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[58, 44, 52, 1])).
% 0.67/0.72 tff(60,plain,
% 0.67/0.72 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(61,plain,
% 0.67/0.72 (product(e_2, e_2, e_2)),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[60, 9])).
% 0.67/0.72 tff(62,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.67/0.72 tff(63,plain,
% 0.67/0.72 (^[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))))),
% 0.67/0.72 inference(bind,[status(th)],[])).
% 0.67/0.72 tff(64,plain,
% 0.67/0.72 (![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)))),
% 0.67/0.72 inference(quant_intro,[status(thm)],[63])).
% 0.67/0.72 tff(65,plain,
% 0.67/0.72 (![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)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(66,plain,
% 0.67/0.72 (^[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)))))),
% 0.67/0.72 inference(bind,[status(th)],[])).
% 0.67/0.72 tff(67,plain,
% 0.67/0.72 (![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)))),
% 0.67/0.72 inference(quant_intro,[status(thm)],[66])).
% 0.67/0.72 tff(68,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.67/0.72 tff(69,plain,
% 0.67/0.72 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.67/0.72 tff(70,plain,
% 0.67/0.72 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.67/0.72 tff(71,plain,(
% 0.67/0.72 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.67/0.72 inference(skolemize,[status(sab)],[70])).
% 0.67/0.72 tff(72,plain,
% 0.67/0.72 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.67/0.72 tff(73,plain,
% 0.67/0.72 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(74,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.67/0.72 tff(75,plain,
% 0.67/0.72 (~equalish(e_1, e_2)),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.67/0.72 tff(76,plain,
% 0.67/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(77,plain,
% 0.67/0.72 ((equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))) <=> (equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(78,plain,
% 0.67/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.67/0.73 inference(monotonicity,[status(thm)],[77])).
% 0.67/0.73 tff(79,plain,
% 0.67/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.67/0.73 inference(transitivity,[status(thm)],[78, 76])).
% 0.67/0.73 tff(80,plain,
% 0.67/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.67/0.73 inference(quant_inst,[status(thm)],[])).
% 0.67/0.73 tff(81,plain,
% 0.67/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.67/0.73 tff(82,plain,
% 0.67/0.73 ($false),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[81, 75, 72, 62, 61])).
% 0.67/0.73 tff(83,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.73 tff(84,plain,
% 0.67/0.73 (((~![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_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, 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_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2)))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(85,plain,
% 0.67/0.73 (((~product(e_4, e_2, e_1)) | product(e_2, e_1, e_2) | (~product(e_2, e_4, e_2))) <=> (product(e_2, e_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2)))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(86,plain,
% 0.67/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_2, e_1, e_2) | (~product(e_2, e_4, 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_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2))))),
% 0.67/0.73 inference(monotonicity,[status(thm)],[85])).
% 0.67/0.73 tff(87,plain,
% 0.67/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_2, e_1, e_2) | (~product(e_2, e_4, 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_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2)))),
% 0.67/0.73 inference(transitivity,[status(thm)],[86, 84])).
% 0.67/0.73 tff(88,plain,
% 0.67/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_2, e_1, e_2) | (~product(e_2, e_4, e_2)))),
% 0.67/0.73 inference(quant_inst,[status(thm)],[])).
% 0.67/0.73 tff(89,plain,
% 0.67/0.73 ((~![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_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.67/0.73 tff(90,plain,
% 0.67/0.73 (~product(e_2, e_4, e_2)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[89, 44, 83, 1])).
% 0.67/0.73 tff(91,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.67/0.73 tff(92,assumption,(cycle(e_4, e_3)), introduced(assumption)).
% 0.67/0.73 tff(93,plain,
% 0.67/0.73 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(94,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.67/0.73 tff(95,plain,
% 0.67/0.73 (~equalish(e_3, e_1)),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.67/0.73 tff(96,plain,
% 0.67/0.73 (^[W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : refl(((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))),
% 0.67/0.73 inference(bind,[status(th)],[])).
% 0.67/0.73 tff(97,plain,
% 0.67/0.73 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.67/0.73 inference(quant_intro,[status(thm)],[96])).
% 0.67/0.73 tff(98,plain,
% 0.67/0.73 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(99,plain,
% 0.67/0.73 (^[W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) <=> ((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z)))), (((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) <=> (((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z))) | (~greater(Y, e_0))))), rewrite((((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z))) | (~greater(Y, e_0))) <=> ((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), (((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) <=> ((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))), ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) <=> (((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | (~next(Z, Z1))))), rewrite((((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | (~next(Z, Z1))) <=> ((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) <=> ((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))), (((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> (((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | equalish(Y, Z1)))), rewrite((((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | equalish(Y, Z1)) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), (((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))))),
% 0.67/0.73 inference(bind,[status(th)],[])).
% 0.67/0.73 tff(100,plain,
% 0.67/0.73 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.67/0.73 inference(quant_intro,[status(thm)],[99])).
% 0.67/0.73 tff(101,axiom,(![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle4')).
% 0.67/0.73 tff(102,plain,
% 0.67/0.73 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.67/0.73 tff(103,plain,
% 0.67/0.73 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.76/0.73 tff(104,plain,(
% 0.76/0.73 ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.76/0.73 inference(skolemize,[status(sab)],[103])).
% 0.76/0.73 tff(105,plain,
% 0.76/0.73 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.76/0.73 tff(106,plain,
% 0.76/0.73 (cycle(e_5, e_0) <=> cycle(e_5, e_0)),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(107,axiom,(cycle(e_5, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle3')).
% 0.76/0.73 tff(108,plain,
% 0.76/0.73 (cycle(e_5, e_0)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.76/0.73 tff(109,plain,
% 0.76/0.73 (greater(e_3, e_0) <=> greater(e_3, e_0)),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(110,axiom,(greater(e_3, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_0')).
% 0.76/0.73 tff(111,plain,
% 0.76/0.73 (greater(e_3, e_0)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.76/0.73 tff(112,plain,
% 0.76/0.73 (next(e_4, e_5) <=> next(e_4, e_5)),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(113,axiom,(next(e_4, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_then_e_5')).
% 0.76/0.73 tff(114,plain,
% 0.76/0.73 (next(e_4, e_5)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.76/0.73 tff(115,plain,
% 0.76/0.73 (next(e_0, e_1) <=> next(e_0, e_1)),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(116,axiom,(next(e_0, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_0_then_e_1')).
% 0.76/0.73 tff(117,plain,
% 0.76/0.73 (next(e_0, e_1)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.76/0.73 tff(118,plain,
% 0.76/0.73 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(119,plain,
% 0.76/0.73 (((~cycle(e_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0))) <=> (equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(120,plain,
% 0.76/0.73 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1))))),
% 0.76/0.73 inference(monotonicity,[status(thm)],[119])).
% 0.76/0.73 tff(121,plain,
% 0.76/0.73 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))),
% 0.76/0.73 inference(transitivity,[status(thm)],[120, 118])).
% 0.76/0.73 tff(122,plain,
% 0.76/0.73 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))),
% 0.76/0.73 inference(quant_inst,[status(thm)],[])).
% 0.76/0.73 tff(123,plain,
% 0.76/0.73 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.76/0.73 tff(124,plain,
% 0.76/0.73 ($false),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[123, 117, 114, 111, 108, 105, 95, 92])).
% 0.76/0.73 tff(125,plain,(~cycle(e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.73 tff(126,assumption,(cycle(e_4, e_0)), introduced(assumption)).
% 0.76/0.73 tff(127,plain,
% 0.76/0.73 (^[W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(128,plain,
% 0.76/0.73 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[127])).
% 0.76/0.73 tff(129,plain,
% 0.76/0.73 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(130,plain,
% 0.76/0.73 (^[W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) <=> ((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) <=> (((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~next(Y, W))))), rewrite((((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~next(Y, W))) <=> ((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) <=> ((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))), ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) <=> (((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Y, X))))), rewrite((((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))), (((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> (((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Z1, Z2))))), rewrite((((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Z1, Z2))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(131,plain,
% 0.76/0.73 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[130])).
% 0.76/0.73 tff(132,axiom,(![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle5')).
% 0.76/0.73 tff(133,plain,
% 0.76/0.73 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.76/0.73 tff(134,plain,
% 0.76/0.73 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.76/0.73 tff(135,plain,(
% 0.76/0.73 ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.76/0.73 inference(skolemize,[status(sab)],[134])).
% 0.76/0.73 tff(136,plain,
% 0.76/0.73 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.76/0.73 tff(137,plain,
% 0.76/0.73 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(138,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.76/0.73 tff(139,plain,
% 0.76/0.73 (greater(e_4, e_2)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.76/0.73 tff(140,plain,
% 0.76/0.73 (greater(e_4, e_0) <=> greater(e_4, e_0)),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(141,axiom,(greater(e_4, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_0')).
% 0.76/0.73 tff(142,plain,
% 0.76/0.73 (greater(e_4, e_0)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.76/0.73 tff(143,plain,
% 0.76/0.73 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(144,plain,
% 0.76/0.73 (((~greater(e_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4))) <=> ((~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(145,plain,
% 0.76/0.73 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4))))),
% 0.76/0.73 inference(monotonicity,[status(thm)],[144])).
% 0.76/0.73 tff(146,plain,
% 0.76/0.73 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))),
% 0.76/0.74 inference(transitivity,[status(thm)],[145, 143])).
% 0.76/0.74 tff(147,plain,
% 0.76/0.74 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4)))),
% 0.76/0.74 inference(quant_inst,[status(thm)],[])).
% 0.76/0.74 tff(148,plain,
% 0.76/0.74 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.76/0.74 tff(149,plain,
% 0.76/0.74 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_4))),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[148, 114, 142, 139, 108, 136])).
% 0.76/0.74 tff(150,plain,
% 0.76/0.74 (~cycle(e_2, e_4)),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[149, 126])).
% 0.76/0.74 tff(151,plain,
% 0.76/0.74 (greater(e_2, e_0) <=> greater(e_2, e_0)),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(152,axiom,(greater(e_2, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_greater_e_0')).
% 0.76/0.74 tff(153,plain,
% 0.76/0.74 (greater(e_2, e_0)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.76/0.74 tff(154,plain,
% 0.76/0.74 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(155,plain,
% 0.76/0.74 (((~greater(e_2, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_2))) <=> ((~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(156,plain,
% 0.76/0.74 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2))))),
% 0.76/0.74 inference(monotonicity,[status(thm)],[155])).
% 0.76/0.74 tff(157,plain,
% 0.76/0.74 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))),
% 0.76/0.74 inference(transitivity,[status(thm)],[156, 154])).
% 0.76/0.74 tff(158,plain,
% 0.76/0.74 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_2)))),
% 0.76/0.74 inference(quant_inst,[status(thm)],[])).
% 0.76/0.74 tff(159,plain,
% 0.76/0.74 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.76/0.74 tff(160,plain,
% 0.76/0.74 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_2))),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[159, 114, 153, 139, 108, 136])).
% 0.76/0.74 tff(161,plain,
% 0.76/0.74 (~cycle(e_2, e_2)),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[160, 126])).
% 0.76/0.74 tff(162,assumption,(cycle(e_2, e_0)), introduced(assumption)).
% 0.76/0.74 tff(163,plain,
% 0.76/0.74 (^[Y: $i, X: $i] : refl(((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))) <=> ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))))),
% 0.76/0.74 inference(bind,[status(th)],[])).
% 0.76/0.74 tff(164,plain,
% 0.76/0.74 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.76/0.74 inference(quant_intro,[status(thm)],[163])).
% 0.76/0.74 tff(165,plain,
% 0.76/0.74 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(166,plain,
% 0.76/0.74 (^[Y: $i, X: $i] : rewrite((((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))))),
% 0.76/0.74 inference(bind,[status(th)],[])).
% 0.76/0.74 tff(167,plain,
% 0.76/0.74 (![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.76/0.74 inference(quant_intro,[status(thm)],[166])).
% 0.76/0.74 tff(168,axiom,(![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle6')).
% 0.76/0.74 tff(169,plain,
% 0.76/0.74 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.76/0.74 tff(170,plain,
% 0.76/0.74 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.76/0.74 tff(171,plain,(
% 0.76/0.74 ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.76/0.74 inference(skolemize,[status(sab)],[170])).
% 0.76/0.74 tff(172,plain,
% 0.76/0.74 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.76/0.74 tff(173,plain,
% 0.76/0.74 (greater(e_5, e_2) <=> greater(e_5, e_2)),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(174,axiom,(greater(e_5, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_greater_e_2')).
% 0.76/0.74 tff(175,plain,
% 0.76/0.74 (greater(e_5, e_2)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.76/0.74 tff(176,plain,
% 0.76/0.74 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(177,plain,
% 0.76/0.74 (((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(178,plain,
% 0.76/0.74 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5))))),
% 0.76/0.74 inference(monotonicity,[status(thm)],[177])).
% 0.76/0.74 tff(179,plain,
% 0.76/0.74 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.76/0.74 inference(transitivity,[status(thm)],[178, 176])).
% 0.76/0.74 tff(180,plain,
% 0.76/0.74 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0)))),
% 0.76/0.74 inference(quant_inst,[status(thm)],[])).
% 0.76/0.74 tff(181,plain,
% 0.76/0.74 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.76/0.74 tff(182,plain,
% 0.76/0.74 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_5))),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[181, 175, 172])).
% 0.76/0.74 tff(183,plain,
% 0.76/0.74 (~product(e_2, e_1, e_5)),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[182, 162])).
% 0.76/0.74 tff(184,plain,
% 0.76/0.74 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(185,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.76/0.74 tff(186,plain,
% 0.76/0.74 (greater(e_3, e_2)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.76/0.74 tff(187,plain,
% 0.76/0.74 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(188,plain,
% 0.76/0.74 (((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(189,plain,
% 0.76/0.74 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.76/0.74 inference(monotonicity,[status(thm)],[188])).
% 0.76/0.74 tff(190,plain,
% 0.76/0.74 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.76/0.74 inference(transitivity,[status(thm)],[189, 187])).
% 0.76/0.74 tff(191,plain,
% 0.76/0.74 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0)))),
% 0.76/0.74 inference(quant_inst,[status(thm)],[])).
% 0.76/0.74 tff(192,plain,
% 0.76/0.74 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.76/0.74 tff(193,plain,
% 0.76/0.74 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_3))),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[192, 186, 172])).
% 0.76/0.74 tff(194,plain,
% 0.76/0.74 (~product(e_2, e_1, e_3)),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[193, 162])).
% 0.76/0.74 tff(195,plain,
% 0.76/0.74 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(196,plain,
% 0.76/0.74 (((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(197,plain,
% 0.76/0.74 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))))),
% 0.76/0.74 inference(monotonicity,[status(thm)],[196])).
% 0.76/0.74 tff(198,plain,
% 0.76/0.74 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.76/0.74 inference(transitivity,[status(thm)],[197, 195])).
% 0.76/0.74 tff(199,plain,
% 0.76/0.74 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0)))),
% 0.76/0.74 inference(quant_inst,[status(thm)],[])).
% 0.76/0.74 tff(200,plain,
% 0.76/0.74 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.76/0.74 tff(201,plain,
% 0.76/0.74 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_4))),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[200, 139, 172])).
% 0.76/0.74 tff(202,plain,
% 0.76/0.74 (~product(e_2, e_1, e_4)),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[201, 162])).
% 0.76/0.74 tff(203,plain,
% 0.76/0.74 (^[Y: $i, X: $i] : refl(((~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)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))),
% 0.76/0.74 inference(bind,[status(th)],[])).
% 0.76/0.74 tff(204,plain,
% 0.76/0.74 (![Y: $i, X: $i] : ((~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))) <=> ![Y: $i, X: $i] : ((~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)))),
% 0.76/0.74 inference(quant_intro,[status(thm)],[203])).
% 0.76/0.74 tff(205,plain,
% 0.76/0.74 (![Y: $i, X: $i] : ((~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))) <=> ![Y: $i, X: $i] : ((~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)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(206,plain,
% 0.76/0.74 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> ((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)))), rewrite((((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)))), rewrite((((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), (((((((~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)) <=> (((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_4)))), rewrite((((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_4)) <=> ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), ((((((((~group_element(X)) | (~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)) <=> (((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_5)))), rewrite((((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_5)) <=> ((~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)) | (~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)) <=> ((~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)))))),
% 0.76/0.74 inference(bind,[status(th)],[])).
% 0.76/0.74 tff(207,plain,
% 0.76/0.74 (![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] : ((~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)))),
% 0.76/0.74 inference(quant_intro,[status(thm)],[206])).
% 0.76/0.74 tff(208,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/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.76/0.74 tff(209,plain,
% 0.76/0.74 (![Y: $i, X: $i] : ((~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)))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.76/0.74 tff(210,plain,
% 0.76/0.74 (![Y: $i, X: $i] : ((~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)))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.76/0.74 tff(211,plain,(
% 0.76/0.74 ![Y: $i, X: $i] : ((~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)))),
% 0.76/0.74 inference(skolemize,[status(sab)],[210])).
% 0.76/0.74 tff(212,plain,
% 0.76/0.74 (![Y: $i, X: $i] : ((~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)))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[211, 204])).
% 0.76/0.74 tff(213,plain,
% 0.76/0.74 (group_element(e_2) <=> group_element(e_2)),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(214,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.76/0.74 tff(215,plain,
% 0.76/0.74 (group_element(e_2)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.76/0.74 tff(216,plain,
% 0.76/0.74 (group_element(e_1) <=> group_element(e_1)),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(217,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.76/0.74 tff(218,plain,
% 0.76/0.74 (group_element(e_1)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.76/0.74 tff(219,plain,
% 0.76/0.74 (((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(220,plain,
% 0.76/0.75 (((~group_element(e_2)) | 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_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(221,plain,
% 0.76/0.75 (((~![Y: $i, X: $i] : ((~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(e_2)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)))),
% 0.76/0.75 inference(monotonicity,[status(thm)],[220])).
% 0.76/0.75 tff(222,plain,
% 0.76/0.75 (((~![Y: $i, X: $i] : ((~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(e_2)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.76/0.75 inference(transitivity,[status(thm)],[221, 219])).
% 0.76/0.75 tff(223,plain,
% 0.76/0.75 ((~![Y: $i, X: $i] : ((~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(e_2)) | 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)))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(224,plain,
% 0.76/0.75 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.76/0.75 tff(225,plain,
% 0.76/0.75 (product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[224, 218, 215, 212, 33, 83])).
% 0.76/0.75 tff(226,plain,
% 0.76/0.75 ($false),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[225, 202, 194, 183])).
% 0.76/0.75 tff(227,plain,(~cycle(e_2, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.75 tff(228,plain,
% 0.76/0.75 (greater(e_1, e_0) <=> greater(e_1, e_0)),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(229,axiom,(greater(e_1, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_greater_e_0')).
% 0.76/0.75 tff(230,plain,
% 0.76/0.75 (greater(e_1, e_0)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.76/0.75 tff(231,plain,
% 0.76/0.75 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(232,plain,
% 0.76/0.75 (((~greater(e_1, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_1))) <=> ((~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(233,plain,
% 0.76/0.75 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2))))),
% 0.76/0.75 inference(monotonicity,[status(thm)],[232])).
% 0.76/0.75 tff(234,plain,
% 0.76/0.75 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))),
% 0.76/0.75 inference(transitivity,[status(thm)],[233, 231])).
% 0.76/0.75 tff(235,plain,
% 0.76/0.75 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_1)))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(236,plain,
% 0.76/0.75 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.76/0.75 tff(237,plain,
% 0.76/0.75 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_1))),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[236, 114, 230, 139, 108, 136])).
% 0.76/0.75 tff(238,plain,
% 0.76/0.75 (~cycle(e_2, e_1)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[237, 126])).
% 0.76/0.75 tff(239,plain,
% 0.76/0.75 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(240,plain,
% 0.76/0.75 (((~greater(e_3, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_3))) <=> ((~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(241,plain,
% 0.76/0.75 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3))))),
% 0.76/0.75 inference(monotonicity,[status(thm)],[240])).
% 0.76/0.75 tff(242,plain,
% 0.76/0.75 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))),
% 0.76/0.75 inference(transitivity,[status(thm)],[241, 239])).
% 0.76/0.75 tff(243,plain,
% 0.76/0.75 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_3)))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(244,plain,
% 0.76/0.75 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.76/0.75 tff(245,plain,
% 0.76/0.75 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_3))),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[244, 114, 111, 139, 108, 136])).
% 0.76/0.75 tff(246,plain,
% 0.76/0.75 (~cycle(e_2, e_3)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[245, 126])).
% 0.76/0.75 tff(247,plain,
% 0.76/0.75 (^[X: $i] : refl((cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(248,plain,
% 0.76/0.75 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[247])).
% 0.76/0.75 tff(249,plain,
% 0.76/0.75 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(250,plain,
% 0.76/0.75 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) <=> (cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> ((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)))), rewrite(((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))), ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> ((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_3)))), rewrite(((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_3)) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))), (((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4)) <=> ((cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_4)))), rewrite(((cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_4)) <=> (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4)) <=> (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(251,plain,
% 0.76/0.75 (![X: $i] : ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4)) <=> ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[250])).
% 0.76/0.75 tff(252,axiom,(![X: $i] : ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle2')).
% 0.76/0.75 tff(253,plain,
% 0.76/0.75 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.76/0.75 tff(254,plain,
% 0.76/0.75 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.76/0.75 tff(255,plain,(
% 0.76/0.75 ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.76/0.75 inference(skolemize,[status(sab)],[254])).
% 0.76/0.75 tff(256,plain,
% 0.76/0.75 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[255, 248])).
% 0.76/0.75 tff(257,plain,
% 0.76/0.75 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))) <=> ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(258,plain,
% 0.76/0.75 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(259,plain,
% 0.76/0.75 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.76/0.75 tff(260,plain,
% 0.76/0.75 (cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[259, 256, 215])).
% 0.76/0.75 tff(261,plain,
% 0.76/0.75 ($false),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[260, 246, 238, 227, 161, 150])).
% 0.76/0.75 tff(262,plain,(~cycle(e_4, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.75 tff(263,assumption,(cycle(e_4, e_2)), introduced(assumption)).
% 0.76/0.75 tff(264,plain,
% 0.76/0.75 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(265,plain,
% 0.76/0.76 (((~cycle(e_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0))) <=> (equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(266,plain,
% 0.76/0.76 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1))))),
% 0.76/0.76 inference(monotonicity,[status(thm)],[265])).
% 0.76/0.76 tff(267,plain,
% 0.76/0.76 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))),
% 0.76/0.76 inference(transitivity,[status(thm)],[266, 264])).
% 0.76/0.76 tff(268,plain,
% 0.76/0.76 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))),
% 0.76/0.76 inference(quant_inst,[status(thm)],[])).
% 0.76/0.76 tff(269,plain,
% 0.76/0.76 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.76/0.76 tff(270,plain,
% 0.76/0.76 ($false),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[269, 117, 114, 153, 108, 105, 27, 263])).
% 0.76/0.76 tff(271,plain,(~cycle(e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.76 tff(272,assumption,(cycle(e_4, e_4)), introduced(assumption)).
% 0.76/0.76 tff(273,plain,
% 0.76/0.76 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(274,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.76/0.76 tff(275,plain,
% 0.76/0.76 (~equalish(e_4, e_1)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.76/0.76 tff(276,plain,
% 0.76/0.76 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(277,plain,
% 0.76/0.76 (((~cycle(e_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0))) <=> (equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(278,plain,
% 0.76/0.76 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1))))),
% 0.76/0.76 inference(monotonicity,[status(thm)],[277])).
% 0.76/0.76 tff(279,plain,
% 0.76/0.76 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))),
% 0.76/0.76 inference(transitivity,[status(thm)],[278, 276])).
% 0.76/0.76 tff(280,plain,
% 0.76/0.76 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))),
% 0.76/0.76 inference(quant_inst,[status(thm)],[])).
% 0.76/0.76 tff(281,plain,
% 0.76/0.76 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.76/0.76 tff(282,plain,
% 0.76/0.76 ($false),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[281, 117, 114, 142, 108, 105, 275, 272])).
% 0.76/0.76 tff(283,plain,(~cycle(e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.76 tff(284,plain,
% 0.76/0.76 (group_element(e_4) <=> group_element(e_4)),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(285,axiom,(group_element(e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_4')).
% 0.76/0.76 tff(286,plain,
% 0.76/0.76 (group_element(e_4)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.76/0.76 tff(287,plain,
% 0.76/0.76 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4)))) <=> ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(288,plain,
% 0.76/0.76 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4)))),
% 0.76/0.76 inference(quant_inst,[status(thm)],[])).
% 0.76/0.76 tff(289,plain,
% 0.76/0.76 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.76/0.76 tff(290,plain,
% 0.76/0.76 (cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0)),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[289, 256, 286])).
% 0.76/0.76 tff(291,plain,
% 0.76/0.76 (cycle(e_4, e_3) | cycle(e_4, e_1) | cycle(e_4, e_0)),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[290, 283, 271])).
% 0.76/0.76 tff(292,plain,
% 0.76/0.76 (cycle(e_4, e_1)),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[291, 262, 125])).
% 0.76/0.76 tff(293,plain,
% 0.76/0.76 ((~equalish(e_2, e_5)) <=> (~equalish(e_2, e_5))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(294,axiom,(~equalish(e_2, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_5')).
% 0.76/0.76 tff(295,plain,
% 0.76/0.76 (~equalish(e_2, e_5)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.76/0.76 tff(296,plain,
% 0.76/0.76 (^[Z: $i, Y: $i, X: $i, X1: $i] : refl(((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(297,plain,
% 0.76/0.76 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[296])).
% 0.76/0.76 tff(298,plain,
% 0.76/0.76 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(299,plain,
% 0.76/0.76 (^[Z: $i, Y: $i, X: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z)))), (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) <=> (((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z))) | (~next(X, X1))))), rewrite((((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z))) | (~next(X, X1))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z)))), (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))))), ((((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> (((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))) | equalish(Z, X1)))), rewrite((((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))) | equalish(Z, X1)) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))), ((((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(300,plain,
% 0.76/0.76 (![Z: $i, Y: $i, X: $i, X1: $i] : (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[299])).
% 0.76/0.76 tff(301,axiom,(![Z: $i, Y: $i, X: $i, X1: $i] : (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle7')).
% 0.76/0.76 tff(302,plain,
% 0.76/0.76 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.76/0.76 tff(303,plain,
% 0.76/0.76 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.76/0.76 tff(304,plain,(
% 0.76/0.76 ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.76/0.76 inference(skolemize,[status(sab)],[303])).
% 0.76/0.76 tff(305,plain,
% 0.76/0.76 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[304, 297])).
% 0.76/0.76 tff(306,plain,
% 0.76/0.76 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(307,plain,
% 0.76/0.76 (((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_2))) <=> (equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(308,plain,
% 0.76/0.76 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2))))),
% 0.76/0.76 inference(monotonicity,[status(thm)],[307])).
% 0.76/0.76 tff(309,plain,
% 0.76/0.76 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.76/0.76 inference(transitivity,[status(thm)],[308, 306])).
% 0.76/0.76 tff(310,plain,
% 0.76/0.76 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_2)))),
% 0.76/0.76 inference(quant_inst,[status(thm)],[])).
% 0.76/0.76 tff(311,plain,
% 0.76/0.76 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.76/0.76 tff(312,plain,
% 0.76/0.76 (~product(e_4, e_1, e_2)),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[311, 114, 230, 305, 295, 292])).
% 0.76/0.76 tff(313,plain,
% 0.76/0.76 ((~equalish(e_3, e_5)) <=> (~equalish(e_3, e_5))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(314,axiom,(~equalish(e_3, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_5')).
% 0.76/0.76 tff(315,plain,
% 0.76/0.76 (~equalish(e_3, e_5)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.76/0.76 tff(316,plain,
% 0.76/0.76 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(317,plain,
% 0.76/0.76 (((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_3))) <=> (equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(318,plain,
% 0.76/0.76 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3))))),
% 0.80/0.76 inference(monotonicity,[status(thm)],[317])).
% 0.80/0.76 tff(319,plain,
% 0.80/0.76 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.80/0.76 inference(transitivity,[status(thm)],[318, 316])).
% 0.80/0.76 tff(320,plain,
% 0.80/0.76 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_3)))),
% 0.80/0.76 inference(quant_inst,[status(thm)],[])).
% 0.80/0.76 tff(321,plain,
% 0.80/0.76 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3))),
% 0.80/0.76 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.80/0.76 tff(322,plain,
% 0.80/0.76 (~product(e_4, e_1, e_3)),
% 0.80/0.76 inference(unit_resolution,[status(thm)],[321, 114, 230, 305, 315, 292])).
% 0.80/0.76 tff(323,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.80/0.76 tff(324,plain,
% 0.80/0.76 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_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)))),
% 0.80/0.76 inference(rewrite,[status(thm)],[])).
% 0.80/0.76 tff(325,plain,
% 0.80/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.80/0.76 inference(quant_inst,[status(thm)],[])).
% 0.80/0.76 tff(326,plain,
% 0.80/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))),
% 0.80/0.76 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.80/0.76 tff(327,plain,
% 0.80/0.76 ($false),
% 0.80/0.76 inference(unit_resolution,[status(thm)],[326, 275, 24, 14, 323])).
% 0.80/0.76 tff(328,plain,((~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.76 tff(329,plain,
% 0.80/0.76 (~product(e_4, e_1, e_1)),
% 0.80/0.76 inference(unit_resolution,[status(thm)],[328, 12])).
% 0.80/0.76 tff(330,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.80/0.77 tff(331,plain,
% 0.80/0.77 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.77 tff(332,plain,
% 0.80/0.77 (product(e_4, e_4, e_4)),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[331, 9])).
% 0.80/0.77 tff(333,plain,
% 0.80/0.77 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(334,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.80/0.77 tff(335,plain,
% 0.80/0.77 (~equalish(e_1, e_4)),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.80/0.77 tff(336,plain,
% 0.80/0.77 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(337,plain,
% 0.80/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.77 tff(338,plain,
% 0.80/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.80/0.77 tff(339,plain,
% 0.80/0.77 ($false),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[338, 335, 72, 332, 330])).
% 0.80/0.77 tff(340,plain,(~product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.77 tff(341,plain,
% 0.80/0.77 (((~![Y: $i, X: $i] : ((~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(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] : ((~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(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))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(342,plain,
% 0.80/0.77 (((~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) | (~group_element(e_1))) <=> ((~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))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(343,plain,
% 0.80/0.77 (((~![Y: $i, X: $i] : ((~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(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) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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(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)))),
% 0.80/0.77 inference(monotonicity,[status(thm)],[342])).
% 0.80/0.77 tff(344,plain,
% 0.80/0.77 (((~![Y: $i, X: $i] : ((~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(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) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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(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))),
% 0.80/0.77 inference(transitivity,[status(thm)],[343, 341])).
% 0.80/0.77 tff(345,plain,
% 0.80/0.77 ((~![Y: $i, X: $i] : ((~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(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) | (~group_element(e_1)))),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.77 tff(346,plain,
% 0.80/0.77 ((~![Y: $i, X: $i] : ((~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(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)),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.80/0.77 tff(347,plain,
% 0.80/0.77 (product(e_4, e_1, e_5) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[346, 218, 286, 212, 340])).
% 0.80/0.77 tff(348,plain,
% 0.80/0.77 (product(e_4, e_1, e_5) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2)),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[347, 329])).
% 0.80/0.77 tff(349,plain,
% 0.80/0.77 (product(e_4, e_1, e_5)),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[348, 322, 312])).
% 0.80/0.77 tff(350,assumption,(product(e_4, e_1, e_5)), introduced(assumption)).
% 0.80/0.77 tff(351,assumption,(product(e_2, e_1, e_5)), introduced(assumption)).
% 0.80/0.77 tff(352,plain,
% 0.80/0.77 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(353,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.80/0.77 tff(354,plain,
% 0.80/0.77 (~equalish(e_2, e_4)),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.80/0.77 tff(355,plain,
% 0.80/0.77 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_2, e_1, e_5)) | (~product(e_4, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(356,plain,
% 0.80/0.77 ((equalish(e_2, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_2, e_1, e_5))) <=> (equalish(e_2, e_4) | (~product(e_2, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(357,plain,
% 0.80/0.77 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_2, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_2, e_1, e_5)) | (~product(e_4, e_1, e_5))))),
% 0.80/0.77 inference(monotonicity,[status(thm)],[356])).
% 0.80/0.77 tff(358,plain,
% 0.80/0.77 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_2, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.80/0.77 inference(transitivity,[status(thm)],[357, 355])).
% 0.80/0.77 tff(359,plain,
% 0.80/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_2, e_1, e_5)))),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.77 tff(360,plain,
% 0.80/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_1, e_5)) | (~product(e_4, e_1, e_5))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.80/0.77 tff(361,plain,
% 0.80/0.77 ($false),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[360, 354, 24, 351, 350])).
% 0.80/0.77 tff(362,plain,((~product(e_2, e_1, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.77 tff(363,plain,
% 0.80/0.77 (~product(e_2, e_1, e_5)),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[362, 349])).
% 0.80/0.77 tff(364,assumption,(cycle(e_4, e_1)), introduced(assumption)).
% 0.80/0.77 tff(365,assumption,(cycle(e_3, e_1)), introduced(assumption)).
% 0.80/0.77 tff(366,plain,
% 0.80/0.77 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(367,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.80/0.77 tff(368,plain,
% 0.80/0.77 (next(e_3, e_4)),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.80/0.77 tff(369,plain,
% 0.80/0.77 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(370,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.80/0.77 tff(371,plain,
% 0.80/0.77 (next(e_1, e_2)),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.80/0.77 tff(372,plain,
% 0.80/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(373,plain,
% 0.80/0.77 (((~cycle(e_3, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1))) <=> (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(374,plain,
% 0.80/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1))))),
% 0.80/0.77 inference(monotonicity,[status(thm)],[373])).
% 0.80/0.77 tff(375,plain,
% 0.80/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1)))),
% 0.80/0.77 inference(transitivity,[status(thm)],[374, 372])).
% 0.80/0.77 tff(376,plain,
% 0.80/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.77 tff(377,plain,
% 0.80/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.80/0.77 tff(378,plain,
% 0.80/0.77 ($false),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[377, 371, 368, 230, 105, 75, 365, 364])).
% 0.80/0.77 tff(379,plain,((~cycle(e_3, e_1)) | (~cycle(e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.77 tff(380,plain,
% 0.80/0.77 (~cycle(e_3, e_1)),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[379, 292])).
% 0.80/0.77 tff(381,assumption,(cycle(e_3, e_3)), introduced(assumption)).
% 0.80/0.77 tff(382,plain,
% 0.80/0.77 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(383,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.80/0.77 tff(384,plain,
% 0.80/0.77 (~equalish(e_3, e_2)),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.80/0.77 tff(385,plain,
% 0.80/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(386,plain,
% 0.80/0.77 (((~cycle(e_3, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1))) <=> (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(387,plain,
% 0.80/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1))))),
% 0.80/0.77 inference(monotonicity,[status(thm)],[386])).
% 0.80/0.77 tff(388,plain,
% 0.80/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))),
% 0.80/0.77 inference(transitivity,[status(thm)],[387, 385])).
% 0.80/0.77 tff(389,plain,
% 0.80/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.80/0.77 inference(quant_inst,[status(thm)],[])).
% 0.80/0.77 tff(390,plain,
% 0.80/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1))),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.80/0.77 tff(391,plain,
% 0.80/0.77 ($false),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[390, 371, 368, 111, 105, 384, 381, 364])).
% 0.80/0.77 tff(392,plain,((~cycle(e_3, e_3)) | (~cycle(e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.77 tff(393,plain,
% 0.80/0.77 (~cycle(e_3, e_3)),
% 0.80/0.77 inference(unit_resolution,[status(thm)],[392, 292])).
% 0.80/0.77 tff(394,assumption,(cycle(e_3, e_4)), introduced(assumption)).
% 0.80/0.77 tff(395,plain,
% 0.80/0.77 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(396,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.80/0.77 tff(397,plain,
% 0.80/0.77 (~equalish(e_4, e_2)),
% 0.80/0.77 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.80/0.77 tff(398,plain,
% 0.80/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(399,plain,
% 0.80/0.77 (((~cycle(e_3, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1))) <=> (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.80/0.77 inference(rewrite,[status(thm)],[])).
% 0.80/0.77 tff(400,plain,
% 0.80/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1))))),
% 0.80/0.78 inference(monotonicity,[status(thm)],[399])).
% 0.80/0.78 tff(401,plain,
% 0.80/0.78 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.80/0.78 inference(transitivity,[status(thm)],[400, 398])).
% 0.80/0.78 tff(402,plain,
% 0.80/0.78 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.80/0.78 inference(quant_inst,[status(thm)],[])).
% 0.80/0.78 tff(403,plain,
% 0.80/0.78 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.80/0.78 tff(404,plain,
% 0.80/0.78 ($false),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[403, 371, 368, 142, 105, 397, 394, 364])).
% 0.80/0.78 tff(405,plain,((~cycle(e_3, e_4)) | (~cycle(e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.78 tff(406,plain,
% 0.80/0.78 (~cycle(e_3, e_4)),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[405, 292])).
% 0.80/0.78 tff(407,assumption,(product(e_2, e_1, e_4)), introduced(assumption)).
% 0.80/0.78 tff(408,assumption,(cycle(e_2, e_1)), introduced(assumption)).
% 0.80/0.78 tff(409,plain,
% 0.80/0.78 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(410,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.80/0.78 tff(411,plain,
% 0.80/0.78 (~equalish(e_4, e_3)),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.80/0.78 tff(412,plain,
% 0.80/0.78 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(413,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.80/0.78 tff(414,plain,
% 0.80/0.78 (next(e_2, e_3)),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.80/0.78 tff(415,plain,
% 0.80/0.78 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(416,plain,
% 0.80/0.78 (((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))) <=> (equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(417,plain,
% 0.80/0.78 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4))))),
% 0.80/0.78 inference(monotonicity,[status(thm)],[416])).
% 0.80/0.78 tff(418,plain,
% 0.80/0.78 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))),
% 0.80/0.78 inference(transitivity,[status(thm)],[417, 415])).
% 0.80/0.78 tff(419,plain,
% 0.80/0.78 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.80/0.78 inference(quant_inst,[status(thm)],[])).
% 0.80/0.78 tff(420,plain,
% 0.80/0.78 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[419, 418])).
% 0.80/0.78 tff(421,plain,
% 0.80/0.78 ($false),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[420, 414, 230, 305, 411, 408, 407])).
% 0.80/0.78 tff(422,plain,((~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.78 tff(423,plain,
% 0.80/0.78 (~cycle(e_2, e_1)),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[422, 407])).
% 0.80/0.78 tff(424,assumption,(~cycle(e_2, e_1)), introduced(assumption)).
% 0.80/0.78 tff(425,assumption,(cycle(e_2, e_2)), introduced(assumption)).
% 0.80/0.78 tff(426,plain,
% 0.80/0.78 (greater(e_2, e_1) <=> greater(e_2, e_1)),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(427,axiom,(greater(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_greater_e_1')).
% 0.80/0.78 tff(428,plain,
% 0.80/0.78 (greater(e_2, e_1)),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.80/0.78 tff(429,plain,
% 0.80/0.78 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(430,plain,
% 0.80/0.78 (((~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(431,plain,
% 0.80/0.78 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1))))),
% 0.80/0.78 inference(monotonicity,[status(thm)],[430])).
% 0.80/0.78 tff(432,plain,
% 0.80/0.78 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1)))),
% 0.80/0.78 inference(transitivity,[status(thm)],[431, 429])).
% 0.80/0.78 tff(433,plain,
% 0.80/0.78 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))),
% 0.80/0.78 inference(quant_inst,[status(thm)],[])).
% 0.80/0.78 tff(434,plain,
% 0.80/0.78 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.80/0.78 tff(435,plain,
% 0.80/0.78 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1))),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[434, 368, 428, 186, 136])).
% 0.80/0.78 tff(436,plain,
% 0.80/0.78 (~cycle(e_3, e_0)),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[435, 425, 292])).
% 0.80/0.78 tff(437,plain,
% 0.80/0.78 (group_element(e_3) <=> group_element(e_3)),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(438,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.80/0.78 tff(439,plain,
% 0.80/0.78 (group_element(e_3)),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.80/0.78 tff(440,plain,
% 0.80/0.78 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))) <=> ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(441,plain,
% 0.80/0.78 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.80/0.78 inference(quant_inst,[status(thm)],[])).
% 0.80/0.78 tff(442,plain,
% 0.80/0.78 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.80/0.78 tff(443,plain,
% 0.80/0.78 (cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[442, 256, 439])).
% 0.80/0.78 tff(444,plain,
% 0.80/0.78 (cycle(e_3, e_2)),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[443, 436, 406, 393, 380])).
% 0.80/0.78 tff(445,plain,
% 0.80/0.78 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(446,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.80/0.78 tff(447,plain,
% 0.80/0.78 (~equalish(e_2, e_3)),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.80/0.78 tff(448,plain,
% 0.80/0.78 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(449,plain,
% 0.80/0.78 (((~cycle(e_2, e_2)) | equalish(e_2, e_3) | (~next(e_2, e_3)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2))) <=> (equalish(e_2, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(450,plain,
% 0.80/0.78 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_2)) | equalish(e_2, e_3) | (~next(e_2, e_3)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2))))),
% 0.80/0.78 inference(monotonicity,[status(thm)],[449])).
% 0.80/0.78 tff(451,plain,
% 0.80/0.78 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_2)) | equalish(e_2, e_3) | (~next(e_2, e_3)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2)))),
% 0.80/0.78 inference(transitivity,[status(thm)],[450, 448])).
% 0.80/0.78 tff(452,plain,
% 0.80/0.78 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_2)) | equalish(e_2, e_3) | (~next(e_2, e_3)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))),
% 0.80/0.78 inference(quant_inst,[status(thm)],[])).
% 0.80/0.78 tff(453,plain,
% 0.80/0.78 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2))),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.80/0.78 tff(454,plain,
% 0.80/0.78 ($false),
% 0.80/0.78 inference(unit_resolution,[status(thm)],[453, 414, 153, 105, 447, 425, 444])).
% 0.80/0.78 tff(455,plain,(~cycle(e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.78 tff(456,assumption,(cycle(e_3, e_0)), introduced(assumption)).
% 0.80/0.78 tff(457,plain,
% 0.80/0.78 (greater(e_3, e_1) <=> greater(e_3, e_1)),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(458,axiom,(greater(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_1')).
% 0.80/0.78 tff(459,plain,
% 0.80/0.78 (greater(e_3, e_1)),
% 0.80/0.78 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.80/0.78 tff(460,plain,
% 0.80/0.78 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(461,plain,
% 0.80/0.78 (((~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1)))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(462,plain,
% 0.80/0.78 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1))))),
% 0.80/0.79 inference(monotonicity,[status(thm)],[461])).
% 0.80/0.79 tff(463,plain,
% 0.80/0.79 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1)))),
% 0.80/0.79 inference(transitivity,[status(thm)],[462, 460])).
% 0.80/0.79 tff(464,plain,
% 0.80/0.79 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))),
% 0.80/0.79 inference(quant_inst,[status(thm)],[])).
% 0.80/0.79 tff(465,plain,
% 0.80/0.79 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1))),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.80/0.79 tff(466,plain,
% 0.80/0.79 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[465, 368, 459, 186, 136])).
% 0.80/0.79 tff(467,plain,
% 0.80/0.79 (~cycle(e_2, e_3)),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[466, 456, 292])).
% 0.80/0.79 tff(468,plain,
% 0.80/0.79 (greater(e_4, e_1) <=> greater(e_4, e_1)),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(469,axiom,(greater(e_4, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_1')).
% 0.80/0.79 tff(470,plain,
% 0.80/0.79 (greater(e_4, e_1)),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.80/0.79 tff(471,plain,
% 0.80/0.79 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1)))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(472,plain,
% 0.80/0.79 (((~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_4))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1)))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(473,plain,
% 0.80/0.79 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1))))),
% 0.80/0.79 inference(monotonicity,[status(thm)],[472])).
% 0.80/0.79 tff(474,plain,
% 0.80/0.79 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1)))),
% 0.80/0.79 inference(transitivity,[status(thm)],[473, 471])).
% 0.80/0.79 tff(475,plain,
% 0.80/0.79 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_4)))),
% 0.80/0.79 inference(quant_inst,[status(thm)],[])).
% 0.80/0.79 tff(476,plain,
% 0.80/0.79 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1))),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.80/0.79 tff(477,plain,
% 0.80/0.79 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1))),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[476, 368, 470, 186, 136])).
% 0.80/0.79 tff(478,plain,
% 0.80/0.79 (~cycle(e_2, e_4)),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[477, 456, 292])).
% 0.80/0.79 tff(479,plain,
% 0.80/0.79 ($false),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[260, 478, 467, 227, 455, 424])).
% 0.80/0.79 tff(480,plain,((~cycle(e_3, e_0)) | cycle(e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.79 tff(481,plain,
% 0.80/0.79 (~cycle(e_3, e_0)),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[480, 423])).
% 0.80/0.79 tff(482,plain,
% 0.80/0.79 (cycle(e_3, e_2)),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[443, 481, 406, 393, 380])).
% 0.80/0.79 tff(483,plain,
% 0.80/0.79 ((~equalish(e_5, e_4)) <=> (~equalish(e_5, e_4))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(484,axiom,(~equalish(e_5, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_is_not_e_4')).
% 0.80/0.79 tff(485,plain,
% 0.80/0.79 (~equalish(e_5, e_4)),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.80/0.79 tff(486,plain,
% 0.80/0.79 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(487,plain,
% 0.80/0.79 (((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5))) <=> (equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(488,plain,
% 0.80/0.79 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5))))),
% 0.80/0.79 inference(monotonicity,[status(thm)],[487])).
% 0.80/0.79 tff(489,plain,
% 0.80/0.79 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))),
% 0.80/0.79 inference(transitivity,[status(thm)],[488, 486])).
% 0.80/0.79 tff(490,plain,
% 0.80/0.79 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.80/0.79 inference(quant_inst,[status(thm)],[])).
% 0.80/0.79 tff(491,plain,
% 0.80/0.79 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5))),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.80/0.79 tff(492,plain,
% 0.80/0.79 (~product(e_3, e_1, e_5)),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[491, 368, 153, 305, 485, 482])).
% 0.80/0.79 tff(493,assumption,(cycle(e_3, e_2)), introduced(assumption)).
% 0.80/0.79 tff(494,plain,
% 0.80/0.79 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(495,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.80/0.79 tff(496,plain,
% 0.80/0.79 (~equalish(e_3, e_4)),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.80/0.79 tff(497,plain,
% 0.80/0.79 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_3, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(498,plain,
% 0.80/0.79 (((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_3, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(499,plain,
% 0.80/0.79 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_3, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3))))),
% 0.80/0.79 inference(monotonicity,[status(thm)],[498])).
% 0.80/0.79 tff(500,plain,
% 0.80/0.79 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.80/0.79 inference(transitivity,[status(thm)],[499, 497])).
% 0.80/0.79 tff(501,plain,
% 0.80/0.79 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))),
% 0.80/0.79 inference(quant_inst,[status(thm)],[])).
% 0.80/0.79 tff(502,plain,
% 0.80/0.79 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3))),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.80/0.79 tff(503,plain,
% 0.80/0.79 (~product(e_3, e_1, e_3)),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[502, 368, 153, 305, 496, 493])).
% 0.80/0.79 tff(504,plain,
% 0.80/0.79 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(505,plain,
% 0.80/0.79 (((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(506,plain,
% 0.80/0.79 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2))))),
% 0.80/0.79 inference(monotonicity,[status(thm)],[505])).
% 0.80/0.79 tff(507,plain,
% 0.80/0.79 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.80/0.79 inference(transitivity,[status(thm)],[506, 504])).
% 0.80/0.79 tff(508,plain,
% 0.80/0.79 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.80/0.79 inference(quant_inst,[status(thm)],[])).
% 0.80/0.79 tff(509,plain,
% 0.80/0.79 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2))),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[508, 507])).
% 0.80/0.79 tff(510,plain,
% 0.80/0.79 (~product(e_3, e_1, e_2)),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[509, 368, 153, 305, 354, 493])).
% 0.80/0.79 tff(511,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.80/0.79 tff(512,plain,
% 0.80/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.80/0.79 inference(rewrite,[status(thm)],[])).
% 0.80/0.79 tff(513,plain,
% 0.80/0.79 ((~![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)))),
% 0.80/0.79 inference(quant_inst,[status(thm)],[])).
% 0.80/0.79 tff(514,plain,
% 0.80/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.80/0.79 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.80/0.79 tff(515,plain,
% 0.80/0.79 ($false),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[514, 95, 24, 14, 511])).
% 0.80/0.79 tff(516,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.79 tff(517,plain,
% 0.80/0.79 (~product(e_3, e_1, e_1)),
% 0.80/0.79 inference(unit_resolution,[status(thm)],[516, 12])).
% 0.80/0.79 tff(518,assumption,(~product(e_3, e_1, e_5)), introduced(assumption)).
% 0.80/0.79 tff(519,assumption,(~product(e_3, e_1, e_4)), introduced(assumption)).
% 0.80/0.79 tff(520,plain,
% 0.80/0.79 (((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(521,plain,
% 0.80/0.80 (((~group_element(e_3)) | 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_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(522,plain,
% 0.80/0.80 (((~![Y: $i, X: $i] : ((~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(e_3)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3)))),
% 0.80/0.80 inference(monotonicity,[status(thm)],[521])).
% 0.80/0.80 tff(523,plain,
% 0.80/0.80 (((~![Y: $i, X: $i] : ((~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(e_3)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))),
% 0.80/0.80 inference(transitivity,[status(thm)],[522, 520])).
% 0.80/0.80 tff(524,plain,
% 0.80/0.80 ((~![Y: $i, X: $i] : ((~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(e_3)) | 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)))),
% 0.80/0.80 inference(quant_inst,[status(thm)],[])).
% 0.80/0.80 tff(525,plain,
% 0.80/0.80 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3)),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.80/0.80 tff(526,plain,
% 0.80/0.80 ($false),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[525, 218, 439, 212, 519, 518, 517, 510, 503])).
% 0.80/0.80 tff(527,plain,((~cycle(e_3, e_2)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.80 tff(528,plain,
% 0.80/0.80 (product(e_3, e_1, e_4)),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[527, 492, 482])).
% 0.80/0.80 tff(529,plain,
% 0.80/0.80 (((~![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_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(530,plain,
% 0.80/0.80 ((~![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_4)) | (~product(e_3, e_1, e_4)))),
% 0.80/0.80 inference(quant_inst,[status(thm)],[])).
% 0.80/0.80 tff(531,plain,
% 0.80/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_4)) | (~product(e_3, e_1, e_4))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.80/0.80 tff(532,plain,
% 0.80/0.80 ($false),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[531, 384, 24, 407, 528])).
% 0.80/0.80 tff(533,plain,(~product(e_2, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.80 tff(534,plain,
% 0.80/0.80 (product(e_2, e_1, e_3)),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[225, 533, 363])).
% 0.80/0.80 tff(535,plain,
% 0.80/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(536,plain,
% 0.80/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.80/0.80 inference(quant_inst,[status(thm)],[])).
% 0.80/0.80 tff(537,plain,
% 0.80/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.80/0.80 tff(538,plain,
% 0.80/0.80 ($false),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[537, 275, 72, 534, 91])).
% 0.80/0.80 tff(539,plain,(~product(e_2, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.80 tff(540,assumption,(product(e_2, e_4, e_4)), introduced(assumption)).
% 0.80/0.80 tff(541,plain,
% 0.80/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(542,plain,
% 0.80/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.80/0.80 inference(quant_inst,[status(thm)],[])).
% 0.80/0.80 tff(543,plain,
% 0.80/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[542, 541])).
% 0.80/0.80 tff(544,plain,
% 0.80/0.80 ($false),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[543, 354, 24, 332, 540])).
% 0.80/0.80 tff(545,plain,(~product(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.80 tff(546,plain,
% 0.80/0.80 (((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(547,plain,
% 0.80/0.80 (((~group_element(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4))) <=> ((~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(548,plain,
% 0.80/0.80 (((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5)))),
% 0.80/0.80 inference(monotonicity,[status(thm)],[547])).
% 0.80/0.80 tff(549,plain,
% 0.80/0.80 (((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5))),
% 0.80/0.80 inference(transitivity,[status(thm)],[548, 546])).
% 0.80/0.80 tff(550,plain,
% 0.80/0.80 ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)))),
% 0.80/0.80 inference(quant_inst,[status(thm)],[])).
% 0.80/0.80 tff(551,plain,
% 0.80/0.80 ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5)),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.80/0.80 tff(552,plain,
% 0.80/0.80 (product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5)),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[551, 215, 286, 212])).
% 0.80/0.80 tff(553,plain,
% 0.80/0.80 (product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5)),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[552, 545])).
% 0.80/0.80 tff(554,plain,
% 0.80/0.80 (product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5)),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[553, 539])).
% 0.80/0.80 tff(555,plain,
% 0.80/0.80 (product(e_2, e_4, e_5)),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[554, 90, 59])).
% 0.80/0.80 tff(556,plain,
% 0.80/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_5)) | product(e_1, e_5, e_4) | (~product(e_4, 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_2, e_4, e_5)) | product(e_1, e_5, e_4) | (~product(e_4, e_2, e_1)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(557,plain,
% 0.80/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_5)) | product(e_1, e_5, e_4) | (~product(e_4, e_2, e_1)))),
% 0.80/0.80 inference(quant_inst,[status(thm)],[])).
% 0.80/0.80 tff(558,plain,
% 0.80/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_5)) | product(e_1, e_5, e_4) | (~product(e_4, e_2, e_1))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[557, 556])).
% 0.80/0.80 tff(559,plain,
% 0.80/0.80 ((~product(e_2, e_4, e_5)) | product(e_1, e_5, e_4) | (~product(e_4, e_2, e_1))),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[558, 44])).
% 0.80/0.80 tff(560,plain,
% 0.80/0.80 (product(e_1, e_5, e_4)),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[559, 555, 1])).
% 0.80/0.80 tff(561,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.80/0.80 tff(562,plain,
% 0.80/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(563,plain,
% 0.80/0.80 ((equalish(e_3, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_2, e_1))) <=> (equalish(e_3, e_4) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(564,plain,
% 0.80/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1))))),
% 0.80/0.80 inference(monotonicity,[status(thm)],[563])).
% 0.80/0.80 tff(565,plain,
% 0.80/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.80/0.80 inference(transitivity,[status(thm)],[564, 562])).
% 0.80/0.80 tff(566,plain,
% 0.80/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.80/0.80 inference(quant_inst,[status(thm)],[])).
% 0.80/0.80 tff(567,plain,
% 0.80/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[566, 565])).
% 0.80/0.80 tff(568,plain,
% 0.80/0.80 ($false),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[567, 496, 24, 561, 1])).
% 0.80/0.80 tff(569,plain,((~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.80 tff(570,plain,
% 0.80/0.80 (~product(e_3, e_2, e_1)),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[569, 1])).
% 0.80/0.80 tff(571,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.80/0.80 tff(572,assumption,(~product(e_3, e_2, e_1)), introduced(assumption)).
% 0.80/0.80 tff(573,plain,
% 0.80/0.80 (((~![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_2)) | product(e_3, e_2, e_1) | (~product(e_1, 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_2)) | product(e_3, e_2, e_1) | (~product(e_1, e_3, e_3)))),
% 0.80/0.80 inference(rewrite,[status(thm)],[])).
% 0.80/0.80 tff(574,plain,
% 0.80/0.80 ((~![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_2)) | product(e_3, e_2, e_1) | (~product(e_1, e_3, e_3)))),
% 0.80/0.80 inference(quant_inst,[status(thm)],[])).
% 0.80/0.80 tff(575,plain,
% 0.80/0.80 ((~![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_2)) | product(e_3, e_2, e_1) | (~product(e_1, e_3, e_3))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[574, 573])).
% 0.80/0.80 tff(576,plain,
% 0.80/0.80 (~product(e_1, e_3, e_3)),
% 0.80/0.80 inference(unit_resolution,[status(thm)],[575, 44, 572, 571])).
% 0.80/0.80 tff(577,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.80/0.81 tff(578,plain,
% 0.80/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_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)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(579,plain,
% 0.80/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.80/0.81 inference(quant_inst,[status(thm)],[])).
% 0.80/0.81 tff(580,plain,
% 0.80/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[579, 578])).
% 0.80/0.81 tff(581,plain,
% 0.80/0.81 ($false),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[580, 75, 24, 61, 577])).
% 0.80/0.81 tff(582,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.81 tff(583,plain,
% 0.80/0.81 (((~![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_1)) | (~product(e_2, e_2, e_2)) | product(e_1, 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_2, e_1)) | (~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(584,plain,
% 0.80/0.81 (((~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1))) <=> ((~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(585,plain,
% 0.80/0.81 (((~![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_2)) | product(e_1, e_2, e_2) | (~product(e_2, 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_2, e_2, e_1)) | (~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2)))),
% 0.80/0.81 inference(monotonicity,[status(thm)],[584])).
% 0.80/0.81 tff(586,plain,
% 0.80/0.81 (((~![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_2)) | product(e_1, e_2, e_2) | (~product(e_2, 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_2, e_2, e_1)) | (~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2))),
% 0.80/0.81 inference(transitivity,[status(thm)],[585, 583])).
% 0.80/0.81 tff(587,plain,
% 0.80/0.81 ((~![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_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1)))),
% 0.80/0.81 inference(quant_inst,[status(thm)],[])).
% 0.80/0.81 tff(588,plain,
% 0.80/0.81 ((~![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_1)) | (~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2)),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.80/0.81 tff(589,plain,
% 0.80/0.81 (~product(e_2, e_2, e_1)),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[588, 44, 61, 582])).
% 0.80/0.81 tff(590,plain,
% 0.80/0.81 (((~![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_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, 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_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(591,plain,
% 0.80/0.81 (((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_3, e_2))) <=> (product(e_2, e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(592,plain,
% 0.80/0.81 (((~![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_2)) | product(e_2, e_2, e_1) | (~product(e_1, 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_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_2))))),
% 0.80/0.81 inference(monotonicity,[status(thm)],[591])).
% 0.80/0.81 tff(593,plain,
% 0.80/0.81 (((~![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_2)) | product(e_2, e_2, e_1) | (~product(e_1, 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_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.80/0.81 inference(transitivity,[status(thm)],[592, 590])).
% 0.80/0.81 tff(594,plain,
% 0.80/0.81 ((~![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_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_3, e_2)))),
% 0.80/0.81 inference(quant_inst,[status(thm)],[])).
% 0.80/0.81 tff(595,plain,
% 0.80/0.81 ((~![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_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_2))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[594, 593])).
% 0.80/0.81 tff(596,plain,
% 0.80/0.81 (~product(e_1, e_3, e_2)),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[595, 44, 589, 571])).
% 0.80/0.81 tff(597,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.80/0.81 tff(598,plain,
% 0.80/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_3, e_1, e_2)) | (~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_2, e_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_4)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(599,plain,
% 0.80/0.81 (((~product(e_1, e_3, e_4)) | product(e_2, e_4, e_3) | (~product(e_3, e_1, e_2))) <=> (product(e_2, e_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_4)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(600,plain,
% 0.80/0.81 (((~![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_2, e_4, e_3) | (~product(e_3, 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_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_4))))),
% 0.80/0.81 inference(monotonicity,[status(thm)],[599])).
% 0.80/0.81 tff(601,plain,
% 0.80/0.81 (((~![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_2, e_4, e_3) | (~product(e_3, 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_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_4)))),
% 0.80/0.81 inference(transitivity,[status(thm)],[600, 598])).
% 0.80/0.81 tff(602,plain,
% 0.80/0.81 ((~![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_2, e_4, e_3) | (~product(e_3, e_1, e_2)))),
% 0.80/0.81 inference(quant_inst,[status(thm)],[])).
% 0.80/0.81 tff(603,plain,
% 0.80/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_4))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.80/0.81 tff(604,plain,
% 0.80/0.81 ($false),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[603, 44, 539, 597, 571])).
% 0.80/0.81 tff(605,plain,((~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.81 tff(606,plain,
% 0.80/0.81 (~product(e_1, e_3, e_4)),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[605, 571])).
% 0.80/0.81 tff(607,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.80/0.81 tff(608,plain,
% 0.80/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(609,plain,
% 0.80/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.80/0.81 inference(quant_inst,[status(thm)],[])).
% 0.80/0.81 tff(610,plain,
% 0.80/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[609, 608])).
% 0.80/0.81 tff(611,plain,
% 0.80/0.81 ($false),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[610, 95, 72, 12, 607])).
% 0.80/0.81 tff(612,plain,(~product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.81 tff(613,plain,
% 0.80/0.81 (((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | 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))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | 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))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(614,plain,
% 0.80/0.81 (((~group_element(e_1)) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | 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))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(615,plain,
% 0.80/0.81 (((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | 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)))),
% 0.80/0.81 inference(monotonicity,[status(thm)],[614])).
% 0.80/0.81 tff(616,plain,
% 0.80/0.81 (((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | 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))),
% 0.80/0.81 inference(transitivity,[status(thm)],[615, 613])).
% 0.80/0.81 tff(617,plain,
% 0.80/0.81 ((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))),
% 0.80/0.81 inference(quant_inst,[status(thm)],[])).
% 0.80/0.81 tff(618,plain,
% 0.80/0.81 ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | 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)),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[617, 616])).
% 0.80/0.81 tff(619,plain,
% 0.80/0.81 (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)),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[618, 218, 439, 212, 612])).
% 0.80/0.81 tff(620,plain,
% 0.80/0.81 (product(e_1, e_3, e_5)),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[619, 606, 596, 576])).
% 0.80/0.81 tff(621,assumption,(product(e_2, e_5, e_3)), introduced(assumption)).
% 0.80/0.81 tff(622,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.80/0.81 tff(623,plain,
% 0.80/0.81 ((~equalish(e_5, e_1)) <=> (~equalish(e_5, e_1))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(624,axiom,(~equalish(e_5, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_is_not_e_1')).
% 0.80/0.81 tff(625,plain,
% 0.80/0.81 (~equalish(e_5, e_1)),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.80/0.81 tff(626,plain,
% 0.80/0.81 (((~![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)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(627,plain,
% 0.80/0.81 ((~![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)))),
% 0.80/0.81 inference(quant_inst,[status(thm)],[])).
% 0.80/0.81 tff(628,plain,
% 0.80/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[627, 626])).
% 0.80/0.81 tff(629,plain,
% 0.80/0.81 ($false),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[628, 625, 72, 622, 621])).
% 0.80/0.81 tff(630,plain,((~product(e_2, e_5, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.81 tff(631,plain,
% 0.80/0.81 (~product(e_2, e_5, e_3)),
% 0.80/0.81 inference(unit_resolution,[status(thm)],[630, 534])).
% 0.80/0.81 tff(632,plain,
% 0.80/0.81 (((~![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_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, 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_2, e_5, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_5)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(633,plain,
% 0.80/0.81 (((~product(e_1, e_3, e_5)) | product(e_2, e_5, e_3) | (~product(e_3, e_1, e_2))) <=> (product(e_2, e_5, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_5)))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(634,plain,
% 0.80/0.81 (((~![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_5)) | product(e_2, e_5, e_3) | (~product(e_3, 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_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_5))))),
% 0.80/0.81 inference(monotonicity,[status(thm)],[633])).
% 0.80/0.81 tff(635,plain,
% 0.80/0.81 (((~![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_5)) | product(e_2, e_5, e_3) | (~product(e_3, 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_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_5)))),
% 0.80/0.81 inference(transitivity,[status(thm)],[634, 632])).
% 0.80/0.81 tff(636,plain,
% 0.80/0.81 ((~![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_5)) | product(e_2, e_5, e_3) | (~product(e_3, e_1, e_2)))),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(637,plain,
% 0.80/0.82 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_5, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_5))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[636, 635])).
% 0.80/0.82 tff(638,plain,
% 0.80/0.82 ($false),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[637, 44, 631, 620, 571])).
% 0.80/0.82 tff(639,plain,((~product(e_3, e_1, e_2)) | product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.82 tff(640,plain,
% 0.80/0.82 (~product(e_3, e_1, e_2)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[639, 570])).
% 0.80/0.82 tff(641,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.80/0.82 tff(642,plain,
% 0.80/0.82 (((~![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)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(643,plain,
% 0.80/0.82 ((~![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)))),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(644,plain,
% 0.80/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[643, 642])).
% 0.80/0.82 tff(645,plain,
% 0.80/0.82 ($false),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[644, 384, 24, 622, 641])).
% 0.80/0.82 tff(646,plain,((~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.82 tff(647,plain,
% 0.80/0.82 (~product(e_3, e_1, e_3)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[646, 534])).
% 0.80/0.82 tff(648,assumption,(product(e_3, e_1, e_5)), introduced(assumption)).
% 0.80/0.82 tff(649,plain,
% 0.80/0.82 (greater(e_5, e_3) <=> greater(e_5, e_3)),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(650,axiom,(greater(e_5, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_greater_e_3')).
% 0.80/0.82 tff(651,plain,
% 0.80/0.82 (greater(e_5, e_3)),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[650, 649])).
% 0.80/0.82 tff(652,plain,
% 0.80/0.82 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(653,plain,
% 0.80/0.82 (((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0))) <=> ((~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(654,plain,
% 0.80/0.82 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5))))),
% 0.80/0.82 inference(monotonicity,[status(thm)],[653])).
% 0.80/0.82 tff(655,plain,
% 0.80/0.82 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.80/0.82 inference(transitivity,[status(thm)],[654, 652])).
% 0.80/0.82 tff(656,plain,
% 0.80/0.82 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0)))),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(657,plain,
% 0.80/0.82 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.80/0.82 tff(658,plain,
% 0.80/0.82 ((~cycle(e_3, e_0)) | (~product(e_3, e_1, e_5))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[657, 651, 172])).
% 0.80/0.82 tff(659,plain,
% 0.80/0.82 (~cycle(e_3, e_0)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[658, 648])).
% 0.80/0.82 tff(660,plain,
% 0.80/0.82 (cycle(e_3, e_2) | cycle(e_3, e_0)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[443, 406, 393, 380])).
% 0.80/0.82 tff(661,plain,
% 0.80/0.82 (cycle(e_3, e_2)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[660, 659])).
% 0.80/0.82 tff(662,plain,
% 0.80/0.82 ($false),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[491, 368, 153, 305, 485, 661, 648])).
% 0.80/0.82 tff(663,plain,(~product(e_3, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.82 tff(664,plain,
% 0.80/0.82 (product(e_3, e_1, e_4) | product(e_3, e_1, e_2)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[525, 218, 439, 212, 663, 517, 647])).
% 0.80/0.82 tff(665,plain,
% 0.80/0.82 (product(e_3, e_1, e_4)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[664, 640])).
% 0.80/0.82 tff(666,assumption,(product(e_1, e_5, e_4)), introduced(assumption)).
% 0.80/0.82 tff(667,assumption,(product(e_2, e_5, e_4)), introduced(assumption)).
% 0.80/0.82 tff(668,plain,
% 0.80/0.82 (((~![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_5, e_4)) | (~product(e_1, 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_1) | (~product(e_2, e_5, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(669,plain,
% 0.80/0.82 ((equalish(e_2, e_1) | (~product(e_1, e_5, e_4)) | (~product(e_2, e_5, e_4))) <=> (equalish(e_2, e_1) | (~product(e_2, e_5, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(670,plain,
% 0.80/0.82 (((~![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_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_1) | (~product(e_2, e_5, e_4)) | (~product(e_1, e_5, e_4))))),
% 0.80/0.82 inference(monotonicity,[status(thm)],[669])).
% 0.80/0.82 tff(671,plain,
% 0.80/0.82 (((~![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_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_1) | (~product(e_2, e_5, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.80/0.82 inference(transitivity,[status(thm)],[670, 668])).
% 0.80/0.82 tff(672,plain,
% 0.80/0.82 ((~![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_5, e_4)) | (~product(e_2, e_5, e_4)))),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(673,plain,
% 0.80/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_5, e_4)) | (~product(e_1, e_5, e_4))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.80/0.82 tff(674,plain,
% 0.80/0.82 ($false),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[673, 27, 24, 667, 666])).
% 0.80/0.82 tff(675,plain,((~product(e_2, e_5, e_4)) | (~product(e_1, e_5, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.82 tff(676,plain,
% 0.80/0.82 (~product(e_2, e_5, e_4)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[675, 560])).
% 0.80/0.82 tff(677,assumption,(product(e_2, e_5, e_2)), introduced(assumption)).
% 0.80/0.82 tff(678,plain,
% 0.80/0.82 ((~equalish(e_5, e_2)) <=> (~equalish(e_5, e_2))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(679,axiom,(~equalish(e_5, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_is_not_e_2')).
% 0.80/0.82 tff(680,plain,
% 0.80/0.82 (~equalish(e_5, e_2)),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[679, 678])).
% 0.80/0.82 tff(681,plain,
% 0.80/0.82 (((~![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)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(682,plain,
% 0.80/0.82 ((~![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)))),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(683,plain,
% 0.80/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[682, 681])).
% 0.80/0.82 tff(684,plain,
% 0.80/0.82 ($false),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[683, 680, 72, 677, 61])).
% 0.80/0.82 tff(685,plain,(~product(e_2, e_5, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.82 tff(686,plain,
% 0.80/0.82 ((~![X: $i] : product(X, X, X)) | product(e_5, e_5, e_5)),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(687,plain,
% 0.80/0.82 (product(e_5, e_5, e_5)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[686, 9])).
% 0.80/0.82 tff(688,assumption,(product(e_2, e_5, e_5)), introduced(assumption)).
% 0.80/0.82 tff(689,plain,
% 0.80/0.82 (((~![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)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(690,plain,
% 0.80/0.82 ((~![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)))),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(691,plain,
% 0.80/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_2, e_5, e_5))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.80/0.82 tff(692,plain,
% 0.80/0.82 ($false),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[691, 295, 24, 688, 687])).
% 0.80/0.82 tff(693,plain,(~product(e_2, e_5, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.82 tff(694,plain,
% 0.80/0.82 (group_element(e_5) <=> group_element(e_5)),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(695,axiom,(group_element(e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_5')).
% 0.80/0.82 tff(696,plain,
% 0.80/0.82 (group_element(e_5)),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.80/0.82 tff(697,plain,
% 0.80/0.82 (((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(698,plain,
% 0.80/0.82 (((~group_element(e_2)) | 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_5)) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(699,plain,
% 0.80/0.82 (((~![Y: $i, X: $i] : ((~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(e_2)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1)))),
% 0.80/0.82 inference(monotonicity,[status(thm)],[698])).
% 0.80/0.82 tff(700,plain,
% 0.80/0.82 (((~![Y: $i, X: $i] : ((~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(e_2)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1))),
% 0.80/0.82 inference(transitivity,[status(thm)],[699, 697])).
% 0.80/0.82 tff(701,plain,
% 0.80/0.82 ((~![Y: $i, X: $i] : ((~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(e_2)) | 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)))),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(702,plain,
% 0.80/0.82 ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1)),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[701, 700])).
% 0.80/0.82 tff(703,plain,
% 0.80/0.82 (product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[702, 215, 696, 212])).
% 0.80/0.82 tff(704,plain,
% 0.80/0.82 (product(e_2, e_5, e_4) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[703, 631])).
% 0.80/0.82 tff(705,plain,
% 0.80/0.82 (product(e_2, e_5, e_4) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[704, 693])).
% 0.80/0.82 tff(706,plain,
% 0.80/0.82 (product(e_2, e_5, e_4) | product(e_2, e_5, e_1)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[705, 685])).
% 0.80/0.82 tff(707,plain,
% 0.80/0.82 (product(e_2, e_5, e_1)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[706, 676])).
% 0.80/0.82 tff(708,assumption,(product(e_2, e_5, e_1)), introduced(assumption)).
% 0.80/0.82 tff(709,assumption,(product(e_5, e_2, e_3)), introduced(assumption)).
% 0.80/0.82 tff(710,plain,
% 0.80/0.82 (((~![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)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(711,plain,
% 0.80/0.82 (((~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)))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(712,plain,
% 0.80/0.82 (((~![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))))),
% 0.80/0.82 inference(monotonicity,[status(thm)],[711])).
% 0.80/0.82 tff(713,plain,
% 0.80/0.83 (((~![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)))),
% 0.80/0.83 inference(transitivity,[status(thm)],[712, 710])).
% 0.80/0.83 tff(714,plain,
% 0.80/0.83 ((~![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)))),
% 0.80/0.83 inference(quant_inst,[status(thm)],[])).
% 0.80/0.83 tff(715,plain,
% 0.80/0.83 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_5, e_1))),
% 0.80/0.83 inference(modus_ponens,[status(thm)],[714, 713])).
% 0.80/0.83 tff(716,plain,
% 0.80/0.83 ($false),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[715, 44, 518, 709, 708])).
% 0.80/0.83 tff(717,plain,((~product(e_2, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.80/0.83 tff(718,plain,
% 0.80/0.83 ((~product(e_2, e_5, e_1)) | (~product(e_5, e_2, e_3))),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[717, 663])).
% 0.80/0.83 tff(719,plain,
% 0.80/0.83 (~product(e_5, e_2, e_3)),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[718, 708])).
% 0.80/0.83 tff(720,assumption,(product(e_5, e_2, e_1)), introduced(assumption)).
% 0.80/0.83 tff(721,assumption,(~product(e_1, e_1, e_2)), introduced(assumption)).
% 0.80/0.83 tff(722,plain,
% 0.80/0.83 (((~![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_2) | (~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_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_1)))),
% 0.80/0.83 inference(rewrite,[status(thm)],[])).
% 0.80/0.83 tff(723,plain,
% 0.80/0.83 (((~product(e_5, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_5, e_1))) <=> (product(e_1, e_1, e_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_1)))),
% 0.80/0.83 inference(rewrite,[status(thm)],[])).
% 0.80/0.83 tff(724,plain,
% 0.80/0.83 (((~![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_1, e_1, 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_1, e_1, e_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_1))))),
% 0.80/0.83 inference(monotonicity,[status(thm)],[723])).
% 0.80/0.83 tff(725,plain,
% 0.80/0.83 (((~![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_1, e_1, 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_1, e_1, e_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_1)))),
% 0.80/0.83 inference(transitivity,[status(thm)],[724, 722])).
% 0.80/0.83 tff(726,plain,
% 0.80/0.83 ((~![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_1, e_1, e_2) | (~product(e_2, e_5, e_1)))),
% 0.80/0.83 inference(quant_inst,[status(thm)],[])).
% 0.80/0.83 tff(727,plain,
% 0.80/0.83 ((~![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_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_1))),
% 0.80/0.83 inference(modus_ponens,[status(thm)],[726, 725])).
% 0.80/0.83 tff(728,plain,
% 0.80/0.83 (~product(e_2, e_5, e_1)),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[727, 44, 721, 720])).
% 0.80/0.83 tff(729,assumption,(~product(e_2, e_5, e_5)), introduced(assumption)).
% 0.80/0.83 tff(730,assumption,(~product(e_2, e_5, e_3)), introduced(assumption)).
% 0.80/0.83 tff(731,plain,
% 0.80/0.83 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_5, e_2, e_1)) | (~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_4, e_1, e_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_4)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(732,plain,
% 0.86/0.83 (((~product(e_5, e_2, e_1)) | product(e_4, e_1, e_2) | (~product(e_2, e_5, e_4))) <=> (product(e_4, e_1, e_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_4)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(733,plain,
% 0.86/0.83 (((~![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_4, e_1, e_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_4))))),
% 0.86/0.83 inference(monotonicity,[status(thm)],[732])).
% 0.86/0.83 tff(734,plain,
% 0.86/0.83 (((~![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_4, e_1, e_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_4)))),
% 0.86/0.83 inference(transitivity,[status(thm)],[733, 731])).
% 0.86/0.83 tff(735,plain,
% 0.86/0.83 ((~![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)))),
% 0.86/0.83 inference(quant_inst,[status(thm)],[])).
% 0.86/0.83 tff(736,plain,
% 0.86/0.83 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_4))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[735, 734])).
% 0.86/0.83 tff(737,plain,
% 0.86/0.83 (~product(e_2, e_5, e_4)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[736, 44, 312, 720])).
% 0.86/0.83 tff(738,plain,
% 0.86/0.83 (((~![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_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, 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_1, e_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_2)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(739,plain,
% 0.86/0.83 (((~product(e_5, e_2, e_1)) | product(e_2, e_1, e_2) | (~product(e_2, e_5, e_2))) <=> (product(e_2, e_1, e_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_2)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(740,plain,
% 0.86/0.83 (((~![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_2, e_1, e_2) | (~product(e_2, 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_1, e_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_2))))),
% 0.86/0.83 inference(monotonicity,[status(thm)],[739])).
% 0.86/0.83 tff(741,plain,
% 0.86/0.83 (((~![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_2, e_1, e_2) | (~product(e_2, 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_1, e_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_2)))),
% 0.86/0.83 inference(transitivity,[status(thm)],[740, 738])).
% 0.86/0.83 tff(742,plain,
% 0.86/0.83 ((~![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_2, e_1, e_2) | (~product(e_2, e_5, e_2)))),
% 0.86/0.83 inference(quant_inst,[status(thm)],[])).
% 0.86/0.83 tff(743,plain,
% 0.86/0.83 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_5, e_2, e_1)) | (~product(e_2, e_5, e_2))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[742, 741])).
% 0.86/0.83 tff(744,plain,
% 0.86/0.83 (~product(e_2, e_5, e_2)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[743, 44, 83, 720])).
% 0.86/0.83 tff(745,plain,
% 0.86/0.83 ($false),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[703, 744, 737, 730, 729, 728])).
% 0.86/0.83 tff(746,plain,((~product(e_5, e_2, e_1)) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_1, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.86/0.83 tff(747,plain,
% 0.86/0.83 ((~product(e_5, e_2, e_1)) | product(e_2, e_5, e_5) | product(e_1, e_1, e_2)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[746, 631])).
% 0.86/0.83 tff(748,plain,
% 0.86/0.83 ((~product(e_5, e_2, e_1)) | product(e_1, e_1, e_2)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[747, 693])).
% 0.86/0.83 tff(749,plain,
% 0.86/0.83 (~product(e_5, e_2, e_1)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[748, 52])).
% 0.86/0.83 tff(750,assumption,(product(e_5, e_2, e_2)), introduced(assumption)).
% 0.86/0.83 tff(751,plain,
% 0.86/0.83 (((~![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)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(752,plain,
% 0.86/0.83 ((~![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)))),
% 0.86/0.83 inference(quant_inst,[status(thm)],[])).
% 0.86/0.83 tff(753,plain,
% 0.86/0.83 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_5, e_2, e_2))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[752, 751])).
% 0.86/0.83 tff(754,plain,
% 0.86/0.83 ($false),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[753, 680, 24, 750, 61])).
% 0.86/0.83 tff(755,plain,(~product(e_5, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.86/0.83 tff(756,assumption,(product(e_5, e_2, e_5)), introduced(assumption)).
% 0.86/0.83 tff(757,plain,
% 0.86/0.83 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_5, e_2, 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_2, e_5) | (~product(e_5, e_2, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(758,plain,
% 0.86/0.83 ((equalish(e_2, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_2, e_5))) <=> (equalish(e_2, e_5) | (~product(e_5, e_2, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(759,plain,
% 0.86/0.83 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_5, e_2, e_5)) | (~product(e_5, e_5, e_5))))),
% 0.86/0.83 inference(monotonicity,[status(thm)],[758])).
% 0.86/0.83 tff(760,plain,
% 0.86/0.83 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_5, e_2, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.86/0.83 inference(transitivity,[status(thm)],[759, 757])).
% 0.86/0.83 tff(761,plain,
% 0.86/0.83 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_2, e_5)))),
% 0.86/0.83 inference(quant_inst,[status(thm)],[])).
% 0.86/0.83 tff(762,plain,
% 0.86/0.83 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_5, e_2, e_5)) | (~product(e_5, e_5, e_5))),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[761, 760])).
% 0.86/0.83 tff(763,plain,
% 0.86/0.83 ($false),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[762, 295, 72, 756, 687])).
% 0.86/0.83 tff(764,plain,(~product(e_5, e_2, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.86/0.83 tff(765,plain,
% 0.86/0.83 (((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_5, e_2, e_1) | (~group_element(e_5)) | product(e_5, e_2, e_2) | product(e_5, e_2, e_4) | product(e_5, e_2, e_5) | product(e_5, e_2, e_3))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_5, e_2, e_1) | (~group_element(e_5)) | product(e_5, e_2, e_2) | product(e_5, e_2, e_4) | product(e_5, e_2, e_5) | product(e_5, e_2, e_3))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(766,plain,
% 0.86/0.83 (((~group_element(e_5)) | 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_2)) | product(e_5, e_2, e_1) | (~group_element(e_5)) | product(e_5, e_2, e_2) | product(e_5, e_2, e_4) | product(e_5, e_2, e_5) | product(e_5, e_2, e_3))),
% 0.86/0.83 inference(rewrite,[status(thm)],[])).
% 0.86/0.83 tff(767,plain,
% 0.86/0.83 (((~![Y: $i, X: $i] : ((~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(e_5)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_5, e_2, e_1) | (~group_element(e_5)) | product(e_5, e_2, e_2) | product(e_5, e_2, e_4) | product(e_5, e_2, e_5) | product(e_5, e_2, e_3)))),
% 0.86/0.83 inference(monotonicity,[status(thm)],[766])).
% 0.86/0.83 tff(768,plain,
% 0.86/0.83 (((~![Y: $i, X: $i] : ((~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(e_5)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_5, e_2, e_1) | (~group_element(e_5)) | product(e_5, e_2, e_2) | product(e_5, e_2, e_4) | product(e_5, e_2, e_5) | product(e_5, e_2, e_3))),
% 0.86/0.83 inference(transitivity,[status(thm)],[767, 765])).
% 0.86/0.83 tff(769,plain,
% 0.86/0.83 ((~![Y: $i, X: $i] : ((~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(e_5)) | 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)))),
% 0.86/0.83 inference(quant_inst,[status(thm)],[])).
% 0.86/0.83 tff(770,plain,
% 0.86/0.83 ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_5, e_2, e_1) | (~group_element(e_5)) | product(e_5, e_2, e_2) | product(e_5, e_2, e_4) | product(e_5, e_2, e_5) | product(e_5, e_2, e_3)),
% 0.86/0.83 inference(modus_ponens,[status(thm)],[769, 768])).
% 0.86/0.83 tff(771,plain,
% 0.86/0.83 (product(e_5, e_2, e_1) | product(e_5, e_2, e_2) | product(e_5, e_2, e_4) | product(e_5, e_2, e_5) | product(e_5, e_2, e_3)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[770, 215, 696, 212])).
% 0.86/0.83 tff(772,plain,
% 0.86/0.83 (product(e_5, e_2, e_1) | product(e_5, e_2, e_4) | product(e_5, e_2, e_3)),
% 0.86/0.83 inference(unit_resolution,[status(thm)],[771, 764, 755])).
% 0.86/0.83 tff(773,plain,
% 0.86/0.83 (product(e_5, e_2, e_4) | product(e_5, e_2, e_3)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[772, 749])).
% 0.86/0.84 tff(774,plain,
% 0.86/0.84 (product(e_5, e_2, e_4)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[773, 719])).
% 0.86/0.84 tff(775,assumption,(product(e_1, e_2, e_4)), introduced(assumption)).
% 0.86/0.84 tff(776,assumption,(product(e_5, e_2, e_4)), introduced(assumption)).
% 0.86/0.84 tff(777,plain,
% 0.86/0.84 ((~equalish(e_1, e_5)) <=> (~equalish(e_1, e_5))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(778,axiom,(~equalish(e_1, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_5')).
% 0.86/0.84 tff(779,plain,
% 0.86/0.84 (~equalish(e_1, e_5)),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[778, 777])).
% 0.86/0.84 tff(780,plain,
% 0.86/0.84 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_5, e_2, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_5) | (~product(e_5, e_2, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(781,plain,
% 0.86/0.84 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_5, e_2, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(782,plain,
% 0.86/0.84 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_5) | (~product(e_5, e_2, e_4)) | (~product(e_1, e_2, e_4))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[781, 780])).
% 0.86/0.84 tff(783,plain,
% 0.86/0.84 ($false),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[782, 779, 24, 776, 775])).
% 0.86/0.84 tff(784,plain,((~product(e_1, e_2, e_4)) | (~product(e_5, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.86/0.84 tff(785,plain,
% 0.86/0.84 (~product(e_1, e_2, e_4)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[784, 774])).
% 0.86/0.84 tff(786,assumption,(product(e_3, e_3, e_2)), introduced(assumption)).
% 0.86/0.84 tff(787,plain,
% 0.86/0.84 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(788,plain,
% 0.86/0.84 (product(e_3, e_3, e_3)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[787, 9])).
% 0.86/0.84 tff(789,plain,
% 0.86/0.84 (^[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))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(790,plain,
% 0.86/0.84 (![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)))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[789])).
% 0.86/0.84 tff(791,plain,
% 0.86/0.84 (![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)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(792,plain,
% 0.86/0.84 (^[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)))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(793,plain,
% 0.86/0.84 (![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)))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[792])).
% 0.86/0.84 tff(794,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function2')).
% 0.86/0.84 tff(795,plain,
% 0.86/0.84 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.86/0.84 tff(796,plain,
% 0.86/0.84 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[795, 791])).
% 0.86/0.84 tff(797,plain,(
% 0.86/0.84 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.86/0.84 inference(skolemize,[status(sab)],[796])).
% 0.86/0.84 tff(798,plain,
% 0.86/0.84 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[797, 790])).
% 0.86/0.84 tff(799,plain,
% 0.86/0.84 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(800,plain,
% 0.86/0.84 ((equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2))) <=> (equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(801,plain,
% 0.86/0.84 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, 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_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3))))),
% 0.86/0.84 inference(monotonicity,[status(thm)],[800])).
% 0.86/0.84 tff(802,plain,
% 0.86/0.84 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, 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_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3)))),
% 0.86/0.84 inference(transitivity,[status(thm)],[801, 799])).
% 0.86/0.84 tff(803,plain,
% 0.86/0.84 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(804,plain,
% 0.86/0.84 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[803, 802])).
% 0.86/0.84 tff(805,plain,
% 0.86/0.84 ($false),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[804, 447, 798, 788, 786])).
% 0.86/0.84 tff(806,plain,(~product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.86/0.84 tff(807,plain,
% 0.86/0.84 (((~![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_2) | (~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_3, e_3, e_2) | (~product(e_1, e_2, e_3)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(808,plain,
% 0.86/0.84 (((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(809,plain,
% 0.86/0.84 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_1, 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_3, e_3, e_2) | (~product(e_1, e_2, e_3))))),
% 0.86/0.84 inference(monotonicity,[status(thm)],[808])).
% 0.86/0.84 tff(810,plain,
% 0.86/0.84 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_1, 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_3, e_3, e_2) | (~product(e_1, e_2, e_3)))),
% 0.86/0.84 inference(transitivity,[status(thm)],[809, 807])).
% 0.86/0.84 tff(811,plain,
% 0.86/0.84 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_1, e_3)))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(812,plain,
% 0.86/0.84 ((~![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_2) | (~product(e_1, e_2, e_3))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[811, 810])).
% 0.86/0.84 tff(813,plain,
% 0.86/0.84 (product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3))),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[812, 44, 534])).
% 0.86/0.84 tff(814,plain,
% 0.86/0.84 (~product(e_1, e_2, e_3)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[813, 806])).
% 0.86/0.84 tff(815,plain,
% 0.86/0.84 (((~![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_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_2, e_1, e_3)) | (~product(e_1, e_2, e_1)) | product(e_1, e_3, e_1))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(816,plain,
% 0.86/0.84 (((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1))) <=> ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)) | product(e_1, e_3, e_1))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(817,plain,
% 0.86/0.84 (((~![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_2, e_1, e_3)) | (~product(e_1, e_2, e_1)) | product(e_1, e_3, e_1)))),
% 0.86/0.84 inference(monotonicity,[status(thm)],[816])).
% 0.86/0.84 tff(818,plain,
% 0.86/0.84 (((~![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_2, e_1, e_3)) | (~product(e_1, e_2, e_1)) | product(e_1, e_3, e_1))),
% 0.86/0.84 inference(transitivity,[status(thm)],[817, 815])).
% 0.86/0.84 tff(819,plain,
% 0.86/0.84 ((~![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)))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(820,plain,
% 0.86/0.84 ((~![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_1)) | product(e_1, e_3, e_1)),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[819, 818])).
% 0.86/0.84 tff(821,plain,
% 0.86/0.84 (~product(e_1, e_2, e_1)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[820, 44, 534, 612])).
% 0.86/0.84 tff(822,plain,
% 0.86/0.84 (((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2) | product(e_1, e_2, e_4) | product(e_1, e_2, e_5) | product(e_1, e_2, e_3))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2) | product(e_1, e_2, e_4) | product(e_1, e_2, e_5) | product(e_1, e_2, e_3))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(823,plain,
% 0.86/0.84 (((~group_element(e_1)) | 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_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2) | product(e_1, e_2, e_4) | product(e_1, e_2, e_5) | product(e_1, e_2, e_3))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(824,plain,
% 0.86/0.84 (((~![Y: $i, X: $i] : ((~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(e_1)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2) | product(e_1, e_2, e_4) | product(e_1, e_2, e_5) | product(e_1, e_2, e_3)))),
% 0.86/0.84 inference(monotonicity,[status(thm)],[823])).
% 0.86/0.84 tff(825,plain,
% 0.86/0.84 (((~![Y: $i, X: $i] : ((~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(e_1)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2) | product(e_1, e_2, e_4) | product(e_1, e_2, e_5) | product(e_1, e_2, e_3))),
% 0.86/0.84 inference(transitivity,[status(thm)],[824, 822])).
% 0.86/0.84 tff(826,plain,
% 0.86/0.84 ((~![Y: $i, X: $i] : ((~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(e_1)) | 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)))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(827,plain,
% 0.86/0.84 ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2) | product(e_1, e_2, e_4) | product(e_1, e_2, e_5) | product(e_1, e_2, e_3)),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[826, 825])).
% 0.86/0.84 tff(828,plain,
% 0.86/0.84 (product(e_1, e_2, e_2) | product(e_1, e_2, e_4) | product(e_1, e_2, e_5) | product(e_1, e_2, e_3)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[827, 218, 215, 212, 821])).
% 0.86/0.84 tff(829,plain,
% 0.86/0.84 (product(e_1, e_2, e_2) | product(e_1, e_2, e_4) | product(e_1, e_2, e_5)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[828, 814])).
% 0.86/0.84 tff(830,plain,
% 0.86/0.84 (product(e_1, e_2, e_4) | product(e_1, e_2, e_5)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[829, 582])).
% 0.86/0.84 tff(831,plain,
% 0.86/0.84 (product(e_1, e_2, e_5)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[830, 785])).
% 0.86/0.84 tff(832,assumption,(~product(e_1, e_3, e_4)), introduced(assumption)).
% 0.86/0.84 tff(833,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.86/0.84 tff(834,assumption,(product(e_2, e_4, e_1)), introduced(assumption)).
% 0.86/0.84 tff(835,plain,
% 0.86/0.84 ((~equalish(e_4, e_5)) <=> (~equalish(e_4, e_5))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(836,axiom,(~equalish(e_4, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_5')).
% 0.86/0.84 tff(837,plain,
% 0.86/0.84 (~equalish(e_4, e_5)),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.86/0.84 tff(838,plain,
% 0.86/0.84 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, 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_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(839,plain,
% 0.86/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(840,plain,
% 0.86/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, e_4, e_1))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[839, 838])).
% 0.86/0.85 tff(841,plain,
% 0.86/0.85 ($false),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[840, 837, 72, 834, 708])).
% 0.86/0.85 tff(842,plain,((~product(e_2, e_4, e_1)) | (~product(e_2, e_5, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.86/0.85 tff(843,plain,
% 0.86/0.85 (~product(e_2, e_4, e_1)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[842, 708])).
% 0.86/0.85 tff(844,assumption,(product(e_4, e_2, e_3)), introduced(assumption)).
% 0.86/0.85 tff(845,plain,
% 0.86/0.85 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_4, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(846,plain,
% 0.86/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(847,plain,
% 0.86/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_4, e_2, e_3))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[846, 845])).
% 0.86/0.85 tff(848,plain,
% 0.86/0.85 ($false),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[847, 837, 24, 709, 844])).
% 0.86/0.85 tff(849,plain,((~product(e_4, e_2, e_3)) | (~product(e_5, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.86/0.85 tff(850,plain,
% 0.86/0.85 (~product(e_5, e_2, e_3)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[849, 844])).
% 0.86/0.85 tff(851,plain,
% 0.86/0.85 (product(e_5, e_2, e_4)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[772, 850, 749])).
% 0.86/0.85 tff(852,assumption,(product(e_3, e_2, e_4)), introduced(assumption)).
% 0.86/0.85 tff(853,plain,
% 0.86/0.85 (((~![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_2, e_4)) | (~product(e_3, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_5) | (~product(e_5, e_2, e_4)) | (~product(e_3, e_2, e_4)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(854,plain,
% 0.86/0.85 ((~![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_2, e_4)) | (~product(e_3, e_2, e_4)))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(855,plain,
% 0.86/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_5) | (~product(e_5, e_2, e_4)) | (~product(e_3, e_2, e_4))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.86/0.85 tff(856,plain,
% 0.86/0.85 ($false),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[855, 315, 24, 776, 852])).
% 0.86/0.85 tff(857,plain,((~product(e_3, e_2, e_4)) | (~product(e_5, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.86/0.85 tff(858,plain,
% 0.86/0.85 (~product(e_3, e_2, e_4)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[857, 851])).
% 0.86/0.85 tff(859,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.86/0.85 tff(860,plain,
% 0.86/0.85 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(861,plain,
% 0.86/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(862,plain,
% 0.86/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_2, e_3))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[861, 860])).
% 0.86/0.85 tff(863,plain,
% 0.86/0.85 ($false),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[862, 496, 24, 859, 844])).
% 0.86/0.85 tff(864,plain,((~product(e_3, e_2, e_3)) | (~product(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.86/0.85 tff(865,plain,
% 0.86/0.85 (~product(e_3, e_2, e_3)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[864, 844])).
% 0.86/0.85 tff(866,plain,
% 0.86/0.85 (~product(e_1, e_2, e_4)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[784, 851])).
% 0.86/0.85 tff(867,plain,
% 0.86/0.85 (product(e_1, e_2, e_5)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[830, 866])).
% 0.86/0.85 tff(868,assumption,(product(e_3, e_2, e_5)), introduced(assumption)).
% 0.86/0.85 tff(869,assumption,(product(e_1, e_2, e_5)), introduced(assumption)).
% 0.86/0.85 tff(870,plain,
% 0.86/0.85 (((~![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_2, e_5)) | (~product(e_1, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_2, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(871,plain,
% 0.86/0.85 ((equalish(e_3, e_1) | (~product(e_1, e_2, e_5)) | (~product(e_3, e_2, e_5))) <=> (equalish(e_3, e_1) | (~product(e_3, e_2, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(872,plain,
% 0.86/0.85 (((~![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_2, e_5)) | (~product(e_3, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_2, e_5)) | (~product(e_1, e_2, e_5))))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[871])).
% 0.86/0.85 tff(873,plain,
% 0.86/0.85 (((~![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_2, e_5)) | (~product(e_3, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_2, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.86/0.85 inference(transitivity,[status(thm)],[872, 870])).
% 0.86/0.85 tff(874,plain,
% 0.86/0.85 ((~![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_2, e_5)) | (~product(e_3, e_2, e_5)))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(875,plain,
% 0.86/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_2, e_5)) | (~product(e_1, e_2, e_5))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[874, 873])).
% 0.86/0.85 tff(876,plain,
% 0.86/0.85 ($false),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[875, 95, 24, 869, 868])).
% 0.86/0.85 tff(877,plain,((~product(e_3, e_2, e_5)) | (~product(e_1, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.86/0.85 tff(878,plain,
% 0.86/0.85 (~product(e_3, e_2, e_5)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[877, 867])).
% 0.86/0.85 tff(879,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.86/0.85 tff(880,plain,
% 0.86/0.85 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(881,plain,
% 0.86/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(882,plain,
% 0.86/0.85 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[881, 880])).
% 0.86/0.85 tff(883,plain,
% 0.86/0.85 ($false),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[882, 384, 24, 61, 879])).
% 0.86/0.85 tff(884,plain,(~product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.86/0.85 tff(885,plain,
% 0.86/0.85 (((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_2) | product(e_3, e_2, e_3) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_4))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_2) | product(e_3, e_2, e_3) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_4))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(886,plain,
% 0.86/0.85 (((~group_element(e_3)) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_2) | product(e_3, e_2, e_3) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_4))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(887,plain,
% 0.86/0.85 (((~![Y: $i, X: $i] : ((~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(e_3)) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_2) | product(e_3, e_2, e_3) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_4)))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[886])).
% 0.86/0.85 tff(888,plain,
% 0.86/0.85 (((~![Y: $i, X: $i] : ((~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(e_3)) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_2) | product(e_3, e_2, e_3) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_4))),
% 0.86/0.85 inference(transitivity,[status(thm)],[887, 885])).
% 0.86/0.85 tff(889,plain,
% 0.86/0.85 ((~![Y: $i, X: $i] : ((~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(e_3)) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(890,plain,
% 0.86/0.85 ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_2) | product(e_3, e_2, e_3) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_4)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[889, 888])).
% 0.86/0.85 tff(891,plain,
% 0.86/0.85 (product(e_3, e_2, e_2) | product(e_3, e_2, e_3) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_4)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[890, 215, 439, 212])).
% 0.86/0.85 tff(892,plain,
% 0.86/0.85 (product(e_3, e_2, e_3) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_4)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[891, 884])).
% 0.86/0.85 tff(893,plain,
% 0.86/0.85 (product(e_3, e_2, e_1)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[892, 878, 865, 858])).
% 0.86/0.85 tff(894,plain,
% 0.86/0.85 (((~![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_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, 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_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_2)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(895,plain,
% 0.86/0.85 (((~product(e_3, e_2, e_1)) | product(e_2, e_1, e_2) | (~product(e_2, e_3, e_2))) <=> (product(e_2, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_2)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(896,plain,
% 0.86/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_2, e_1, e_2) | (~product(e_2, 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_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_2))))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[895])).
% 0.86/0.85 tff(897,plain,
% 0.86/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_2, e_1, e_2) | (~product(e_2, 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_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_2)))),
% 0.86/0.85 inference(transitivity,[status(thm)],[896, 894])).
% 0.86/0.85 tff(898,plain,
% 0.86/0.85 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_2, e_1, e_2) | (~product(e_2, e_3, e_2)))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(899,plain,
% 0.86/0.85 ((~![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_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_2))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[898, 897])).
% 0.86/0.85 tff(900,plain,
% 0.86/0.85 (~product(e_2, e_3, e_2)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[899, 44, 83, 893])).
% 0.86/0.85 tff(901,plain,
% 0.86/0.85 (((~![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_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, 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_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(902,plain,
% 0.86/0.85 (((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_4, e_3))) <=> (product(e_3, e_3, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(903,plain,
% 0.86/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, 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_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_3))))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[902])).
% 0.86/0.85 tff(904,plain,
% 0.86/0.85 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, 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_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.86/0.86 inference(transitivity,[status(thm)],[903, 901])).
% 0.86/0.86 tff(905,plain,
% 0.86/0.86 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_4, e_3)))),
% 0.86/0.86 inference(quant_inst,[status(thm)],[])).
% 0.86/0.86 tff(906,plain,
% 0.86/0.86 ((~![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_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_3))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[905, 904])).
% 0.86/0.86 tff(907,plain,
% 0.86/0.86 (~product(e_2, e_4, e_3)),
% 0.86/0.86 inference(unit_resolution,[status(thm)],[906, 44, 844, 806])).
% 0.86/0.86 tff(908,assumption,(~product(e_2, e_4, e_1)), introduced(assumption)).
% 0.86/0.86 tff(909,plain,
% 0.86/0.86 (((~![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_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(910,plain,
% 0.86/0.86 (((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_3, e_1))) <=> (product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(911,plain,
% 0.86/0.86 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, 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_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.86/0.86 inference(monotonicity,[status(thm)],[910])).
% 0.86/0.86 tff(912,plain,
% 0.86/0.86 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, 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_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.86/0.86 inference(transitivity,[status(thm)],[911, 909])).
% 0.86/0.86 tff(913,plain,
% 0.86/0.86 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_3, e_1)))),
% 0.86/0.86 inference(quant_inst,[status(thm)],[])).
% 0.86/0.86 tff(914,plain,
% 0.86/0.86 ((~![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_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[913, 912])).
% 0.86/0.86 tff(915,plain,
% 0.86/0.86 (~product(e_2, e_3, e_1)),
% 0.86/0.86 inference(unit_resolution,[status(thm)],[914, 44, 52, 893])).
% 0.86/0.86 tff(916,plain,
% 0.86/0.86 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_3, 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_4, e_1, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_2, e_1)))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(917,plain,
% 0.86/0.86 (((~product(e_3, e_2, e_1)) | product(e_4, e_1, e_2) | (~product(e_2, e_3, e_4))) <=> (product(e_4, e_1, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_2, e_1)))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(918,plain,
% 0.86/0.86 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_4, e_1, e_2) | (~product(e_2, 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_4, e_1, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_2, e_1))))),
% 0.86/0.86 inference(monotonicity,[status(thm)],[917])).
% 0.86/0.86 tff(919,plain,
% 0.86/0.86 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_4, e_1, e_2) | (~product(e_2, 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_4, e_1, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_2, e_1)))),
% 0.86/0.86 inference(transitivity,[status(thm)],[918, 916])).
% 0.86/0.86 tff(920,plain,
% 0.86/0.86 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_4, e_1, e_2) | (~product(e_2, e_3, e_4)))),
% 0.86/0.86 inference(quant_inst,[status(thm)],[])).
% 0.86/0.86 tff(921,plain,
% 0.86/0.86 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_2, e_1))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[920, 919])).
% 0.86/0.86 tff(922,plain,
% 0.86/0.86 (~product(e_2, e_3, e_4)),
% 0.86/0.86 inference(unit_resolution,[status(thm)],[921, 44, 312, 893])).
% 0.86/0.86 tff(923,assumption,(product(e_2, e_3, e_3)), introduced(assumption)).
% 0.86/0.86 tff(924,plain,
% 0.86/0.86 (((~![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_3, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(925,plain,
% 0.86/0.86 ((equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3))) <=> (equalish(e_2, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(926,plain,
% 0.86/0.86 (((~![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_3, e_3)) | (~product(e_2, 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_2, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.86/0.86 inference(monotonicity,[status(thm)],[925])).
% 0.86/0.86 tff(927,plain,
% 0.86/0.86 (((~![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_3, e_3)) | (~product(e_2, 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_2, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.86/0.86 inference(transitivity,[status(thm)],[926, 924])).
% 0.86/0.86 tff(928,plain,
% 0.86/0.86 ((~![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_3, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.86/0.86 inference(quant_inst,[status(thm)],[])).
% 0.86/0.86 tff(929,plain,
% 0.86/0.86 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[928, 927])).
% 0.86/0.86 tff(930,plain,
% 0.86/0.86 ($false),
% 0.86/0.86 inference(unit_resolution,[status(thm)],[929, 447, 24, 788, 923])).
% 0.86/0.86 tff(931,plain,(~product(e_2, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.86/0.86 tff(932,plain,
% 0.86/0.86 (((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_2) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_5))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_2) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_5))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(933,plain,
% 0.86/0.86 (((~group_element(e_2)) | product(e_2, e_3, e_5) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_2) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_5))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(934,plain,
% 0.86/0.86 (((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_3, e_5) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_2) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_5)))),
% 0.86/0.86 inference(monotonicity,[status(thm)],[933])).
% 0.86/0.86 tff(935,plain,
% 0.86/0.86 (((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_3, e_5) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_2) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_5))),
% 0.86/0.86 inference(transitivity,[status(thm)],[934, 932])).
% 0.86/0.86 tff(936,plain,
% 0.86/0.86 ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_3, e_5) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)))),
% 0.86/0.86 inference(quant_inst,[status(thm)],[])).
% 0.86/0.86 tff(937,plain,
% 0.86/0.86 ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_2) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_5)),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[936, 935])).
% 0.86/0.86 tff(938,plain,
% 0.86/0.86 (product(e_2, e_3, e_4) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_5)),
% 0.86/0.86 inference(unit_resolution,[status(thm)],[937, 215, 439, 212, 931])).
% 0.86/0.86 tff(939,plain,
% 0.86/0.86 (product(e_2, e_3, e_5)),
% 0.86/0.86 inference(unit_resolution,[status(thm)],[938, 922, 900, 915])).
% 0.86/0.86 tff(940,assumption,(product(e_2, e_3, e_5)), introduced(assumption)).
% 0.86/0.86 tff(941,assumption,(product(e_2, e_4, e_5)), introduced(assumption)).
% 0.86/0.86 tff(942,plain,
% 0.86/0.86 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_2, e_4, e_5)) | (~product(e_2, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_2, e_4, e_5)) | (~product(e_2, e_3, e_5)))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(943,plain,
% 0.86/0.86 ((equalish(e_4, e_3) | (~product(e_2, e_3, e_5)) | (~product(e_2, e_4, e_5))) <=> (equalish(e_4, e_3) | (~product(e_2, e_4, e_5)) | (~product(e_2, e_3, e_5)))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(944,plain,
% 0.86/0.86 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_2, e_3, e_5)) | (~product(e_2, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_2, e_4, e_5)) | (~product(e_2, e_3, e_5))))),
% 0.90/0.86 inference(monotonicity,[status(thm)],[943])).
% 0.90/0.86 tff(945,plain,
% 0.90/0.86 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_2, e_3, e_5)) | (~product(e_2, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_2, e_4, e_5)) | (~product(e_2, e_3, e_5)))),
% 0.90/0.86 inference(transitivity,[status(thm)],[944, 942])).
% 0.90/0.86 tff(946,plain,
% 0.90/0.86 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_2, e_3, e_5)) | (~product(e_2, e_4, e_5)))),
% 0.90/0.86 inference(quant_inst,[status(thm)],[])).
% 0.90/0.86 tff(947,plain,
% 0.90/0.86 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_2, e_4, e_5)) | (~product(e_2, e_3, e_5))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[946, 945])).
% 0.90/0.86 tff(948,plain,
% 0.90/0.86 ($false),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[947, 411, 72, 941, 940])).
% 0.90/0.86 tff(949,plain,((~product(e_2, e_4, e_5)) | (~product(e_2, e_3, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.90/0.86 tff(950,plain,
% 0.90/0.86 (~product(e_2, e_4, e_5)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[949, 939])).
% 0.90/0.86 tff(951,plain,
% 0.90/0.86 (product(e_2, e_4, e_2)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[553, 950, 908, 907])).
% 0.90/0.86 tff(952,plain,
% 0.90/0.86 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, 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_3, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(953,plain,
% 0.90/0.86 (((~product(e_4, e_2, e_3)) | product(e_2, e_3, e_2) | (~product(e_2, e_4, e_2))) <=> (product(e_2, e_3, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(954,plain,
% 0.90/0.86 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_3, e_2) | (~product(e_2, e_4, 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_3, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_2, e_3))))),
% 0.90/0.86 inference(monotonicity,[status(thm)],[953])).
% 0.90/0.86 tff(955,plain,
% 0.90/0.86 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_3, e_2) | (~product(e_2, e_4, 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_3, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.90/0.86 inference(transitivity,[status(thm)],[954, 952])).
% 0.90/0.86 tff(956,plain,
% 0.90/0.86 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_3, e_2) | (~product(e_2, e_4, e_2)))),
% 0.90/0.86 inference(quant_inst,[status(thm)],[])).
% 0.90/0.86 tff(957,plain,
% 0.90/0.86 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_2, e_3))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[956, 955])).
% 0.90/0.86 tff(958,plain,
% 0.90/0.86 ($false),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[957, 44, 951, 844, 900])).
% 0.90/0.86 tff(959,plain,((~product(e_4, e_2, e_3)) | product(e_2, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.86 tff(960,plain,
% 0.90/0.86 (~product(e_4, e_2, e_3)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[959, 843])).
% 0.90/0.87 tff(961,plain,
% 0.90/0.87 (((~![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_2, e_3) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_2, e_3) | (~product(e_1, e_3, e_2)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(962,plain,
% 0.90/0.87 (((~product(e_1, e_3, e_2)) | product(e_4, e_2, e_3) | (~product(e_3, e_1, e_4))) <=> ((~product(e_3, e_1, e_4)) | product(e_4, e_2, e_3) | (~product(e_1, e_3, e_2)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(963,plain,
% 0.90/0.87 (((~![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_2)) | product(e_4, e_2, e_3) | (~product(e_3, e_1, e_4)))) <=> ((~![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_2, e_3) | (~product(e_1, e_3, e_2))))),
% 0.90/0.87 inference(monotonicity,[status(thm)],[962])).
% 0.90/0.87 tff(964,plain,
% 0.90/0.87 (((~![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_2)) | product(e_4, e_2, e_3) | (~product(e_3, e_1, e_4)))) <=> ((~![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_2, e_3) | (~product(e_1, e_3, e_2)))),
% 0.90/0.87 inference(transitivity,[status(thm)],[963, 961])).
% 0.90/0.87 tff(965,plain,
% 0.90/0.87 ((~![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_2)) | product(e_4, e_2, e_3) | (~product(e_3, e_1, e_4)))),
% 0.90/0.87 inference(quant_inst,[status(thm)],[])).
% 0.90/0.87 tff(966,plain,
% 0.90/0.87 ((~![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_2, e_3) | (~product(e_1, e_3, e_2))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[965, 964])).
% 0.90/0.87 tff(967,plain,
% 0.90/0.87 ((~product(e_3, e_1, e_4)) | product(e_4, e_2, e_3) | (~product(e_1, e_3, e_2))),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[966, 44])).
% 0.90/0.87 tff(968,plain,
% 0.90/0.87 (~product(e_1, e_3, e_2)),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[967, 960, 833])).
% 0.90/0.87 tff(969,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.90/0.87 tff(970,plain,
% 0.90/0.87 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(971,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.90/0.87 tff(972,plain,
% 0.90/0.87 (~equalish(e_1, e_3)),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[971, 970])).
% 0.90/0.87 tff(973,plain,
% 0.90/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(974,plain,
% 0.90/0.87 ((equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))) <=> (equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(975,plain,
% 0.90/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.90/0.87 inference(monotonicity,[status(thm)],[974])).
% 0.90/0.87 tff(976,plain,
% 0.90/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.90/0.87 inference(transitivity,[status(thm)],[975, 973])).
% 0.90/0.87 tff(977,plain,
% 0.90/0.87 ((~![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)))),
% 0.90/0.87 inference(quant_inst,[status(thm)],[])).
% 0.90/0.87 tff(978,plain,
% 0.90/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[977, 976])).
% 0.90/0.87 tff(979,plain,
% 0.90/0.87 ($false),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[978, 972, 24, 969, 788])).
% 0.90/0.87 tff(980,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.87 tff(981,plain,
% 0.90/0.87 (product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_2)),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[619, 980])).
% 0.90/0.87 tff(982,plain,
% 0.90/0.87 (product(e_1, e_3, e_5)),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[981, 968, 832])).
% 0.90/0.87 tff(983,plain,
% 0.90/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(984,plain,
% 0.90/0.87 ((equalish(e_3, e_2) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_3, e_5))) <=> (equalish(e_3, e_2) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(985,plain,
% 0.90/0.87 (((~![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_3, e_5)) | (~product(e_1, e_2, e_5))))),
% 0.90/0.87 inference(monotonicity,[status(thm)],[984])).
% 0.90/0.87 tff(986,plain,
% 0.90/0.87 (((~![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_3, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.90/0.87 inference(transitivity,[status(thm)],[985, 983])).
% 0.90/0.87 tff(987,plain,
% 0.90/0.87 ((~![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)))),
% 0.90/0.87 inference(quant_inst,[status(thm)],[])).
% 0.90/0.87 tff(988,plain,
% 0.90/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_2, e_5))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[987, 986])).
% 0.90/0.87 tff(989,plain,
% 0.90/0.87 ($false),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[988, 384, 72, 982, 831])).
% 0.90/0.87 tff(990,plain,((~product(e_2, e_5, e_1)) | product(e_1, e_3, e_4) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.90/0.87 tff(991,plain,
% 0.90/0.87 (product(e_1, e_3, e_4)),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[990, 707, 665])).
% 0.90/0.87 tff(992,plain,
% 0.90/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(993,plain,
% 0.90/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.90/0.87 inference(quant_inst,[status(thm)],[])).
% 0.90/0.87 tff(994,plain,
% 0.90/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_3, e_4))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[993, 992])).
% 0.90/0.87 tff(995,plain,
% 0.90/0.87 ($false),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[994, 315, 72, 991, 560])).
% 0.90/0.87 tff(996,plain,(~product(e_4, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.87 tff(997,assumption,(product(e_4, e_2, e_5)), introduced(assumption)).
% 0.90/0.87 tff(998,plain,
% 0.90/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_2, e_5)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(999,plain,
% 0.90/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_2, e_5)))),
% 0.90/0.87 inference(quant_inst,[status(thm)],[])).
% 0.90/0.87 tff(1000,plain,
% 0.90/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_2, e_5))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[999, 998])).
% 0.90/0.87 tff(1001,plain,
% 0.90/0.87 ($false),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[1000, 27, 72, 349, 997])).
% 0.90/0.87 tff(1002,plain,(~product(e_4, e_2, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.87 tff(1003,assumption,(product(e_4, e_2, e_2)), introduced(assumption)).
% 0.90/0.87 tff(1004,plain,
% 0.90/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(1005,plain,
% 0.90/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.90/0.87 inference(quant_inst,[status(thm)],[])).
% 0.90/0.87 tff(1006,plain,
% 0.90/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 0.90/0.87 tff(1007,plain,
% 0.90/0.87 ($false),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[1006, 397, 24, 61, 1003])).
% 0.90/0.87 tff(1008,plain,(~product(e_4, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.87 tff(1009,assumption,(product(e_4, e_2, e_4)), introduced(assumption)).
% 0.90/0.87 tff(1010,plain,
% 0.90/0.87 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(1011,plain,
% 0.90/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.90/0.87 inference(quant_inst,[status(thm)],[])).
% 0.90/0.87 tff(1012,plain,
% 0.90/0.87 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4))),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 0.90/0.87 tff(1013,plain,
% 0.90/0.87 ($false),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[1012, 354, 72, 332, 1009])).
% 0.90/0.87 tff(1014,plain,(~product(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.87 tff(1015,plain,
% 0.90/0.87 (((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(1016,plain,
% 0.90/0.87 (((~group_element(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(1017,plain,
% 0.90/0.87 (((~![Y: $i, X: $i] : ((~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(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1)))),
% 0.90/0.87 inference(monotonicity,[status(thm)],[1016])).
% 0.90/0.87 tff(1018,plain,
% 0.90/0.87 (((~![Y: $i, X: $i] : ((~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(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1))),
% 0.90/0.87 inference(transitivity,[status(thm)],[1017, 1015])).
% 0.90/0.87 tff(1019,plain,
% 0.90/0.87 ((~![Y: $i, X: $i] : ((~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(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)))),
% 0.90/0.87 inference(quant_inst,[status(thm)],[])).
% 0.90/0.87 tff(1020,plain,
% 0.90/0.87 ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1)),
% 0.90/0.87 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 0.90/0.87 tff(1021,plain,
% 0.90/0.87 (product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1)),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[1020, 215, 286, 212])).
% 0.90/0.87 tff(1022,plain,
% 0.90/0.87 (product(e_4, e_2, e_5) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1)),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[1021, 1014])).
% 0.90/0.87 tff(1023,plain,
% 0.90/0.87 (product(e_4, e_2, e_3) | product(e_4, e_2, e_1)),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[1022, 1008, 1002])).
% 0.90/0.87 tff(1024,plain,
% 0.90/0.87 (product(e_4, e_2, e_3)),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[1023, 996])).
% 0.90/0.87 tff(1025,plain,
% 0.90/0.87 (product(e_2, e_4, e_1)),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[959, 1024])).
% 0.90/0.87 tff(1026,plain,
% 0.90/0.87 (~product(e_2, e_5, e_1)),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[842, 1025])).
% 0.90/0.87 tff(1027,plain,
% 0.90/0.87 (~product(e_5, e_2, e_3)),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[849, 1024])).
% 0.90/0.87 tff(1028,plain,
% 0.90/0.87 (product(e_5, e_2, e_4)),
% 0.90/0.87 inference(unit_resolution,[status(thm)],[773, 1027])).
% 0.90/0.87 tff(1029,assumption,(product(e_4, e_4, e_2)), introduced(assumption)).
% 0.90/0.87 tff(1030,plain,
% 0.90/0.87 (((~![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_4, e_2, e_4) | (~product(e_4, e_4, e_2)))) <=> ((~![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_4, e_2, e_4) | (~product(e_4, e_4, e_2)))),
% 0.90/0.87 inference(rewrite,[status(thm)],[])).
% 0.90/0.87 tff(1031,plain,
% 0.90/0.87 (((~product(e_4, e_4, e_2)) | product(e_4, e_2, e_4) | (~product(e_4, e_4, e_4))) <=> ((~product(e_4, e_4, e_4)) | product(e_4, e_2, e_4) | (~product(e_4, e_4, e_2)))),
% 0.90/0.88 inference(rewrite,[status(thm)],[])).
% 0.90/0.88 tff(1032,plain,
% 0.90/0.88 (((~![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_2)) | product(e_4, e_2, e_4) | (~product(e_4, e_4, e_4)))) <=> ((~![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_4, e_2, e_4) | (~product(e_4, e_4, e_2))))),
% 0.90/0.88 inference(monotonicity,[status(thm)],[1031])).
% 0.90/0.88 tff(1033,plain,
% 0.90/0.88 (((~![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_2)) | product(e_4, e_2, e_4) | (~product(e_4, e_4, e_4)))) <=> ((~![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_4, e_2, e_4) | (~product(e_4, e_4, e_2)))),
% 0.90/0.88 inference(transitivity,[status(thm)],[1032, 1030])).
% 0.90/0.88 tff(1034,plain,
% 0.90/0.88 ((~![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_2)) | product(e_4, e_2, e_4) | (~product(e_4, e_4, e_4)))),
% 0.90/0.88 inference(quant_inst,[status(thm)],[])).
% 0.90/0.88 tff(1035,plain,
% 0.90/0.88 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_4)) | product(e_4, e_2, e_4) | (~product(e_4, e_4, e_2))),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 0.90/0.88 tff(1036,plain,
% 0.90/0.88 ($false),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[1035, 44, 332, 1014, 1029])).
% 0.90/0.88 tff(1037,plain,(~product(e_4, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.88 tff(1038,assumption,(~product(e_4, e_4, e_2)), introduced(assumption)).
% 0.90/0.88 tff(1039,plain,
% 0.90/0.88 (((~![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_4)) | (~product(e_2, e_5, e_4)) | product(e_4, e_4, 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_4)) | (~product(e_2, e_5, e_4)) | product(e_4, e_4, e_2))),
% 0.90/0.88 inference(rewrite,[status(thm)],[])).
% 0.90/0.88 tff(1040,plain,
% 0.90/0.88 (((~product(e_5, e_2, e_4)) | product(e_4, e_4, e_2) | (~product(e_2, e_5, e_4))) <=> ((~product(e_5, e_2, e_4)) | (~product(e_2, e_5, e_4)) | product(e_4, e_4, e_2))),
% 0.90/0.88 inference(rewrite,[status(thm)],[])).
% 0.90/0.88 tff(1041,plain,
% 0.90/0.88 (((~![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_4)) | product(e_4, e_4, 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_4)) | (~product(e_2, e_5, e_4)) | product(e_4, e_4, e_2)))),
% 0.90/0.88 inference(monotonicity,[status(thm)],[1040])).
% 0.90/0.88 tff(1042,plain,
% 0.90/0.88 (((~![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_4)) | product(e_4, e_4, 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_4)) | (~product(e_2, e_5, e_4)) | product(e_4, e_4, e_2))),
% 0.90/0.88 inference(transitivity,[status(thm)],[1041, 1039])).
% 0.90/0.88 tff(1043,plain,
% 0.90/0.88 ((~![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_4)) | product(e_4, e_4, e_2) | (~product(e_2, e_5, e_4)))),
% 0.90/0.88 inference(quant_inst,[status(thm)],[])).
% 0.90/0.88 tff(1044,plain,
% 0.90/0.88 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_5, e_2, e_4)) | (~product(e_2, e_5, e_4)) | product(e_4, e_4, e_2)),
% 0.90/0.88 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 0.90/0.88 tff(1045,plain,
% 0.90/0.88 ($false),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[1044, 44, 776, 667, 1038])).
% 0.90/0.88 tff(1046,plain,(product(e_4, e_4, e_2) | (~product(e_5, e_2, e_4)) | (~product(e_2, e_5, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.90/0.88 tff(1047,plain,
% 0.90/0.88 ((~product(e_5, e_2, e_4)) | (~product(e_2, e_5, e_4))),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[1046, 1037])).
% 0.90/0.88 tff(1048,plain,
% 0.90/0.88 (~product(e_2, e_5, e_4)),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[1047, 1028])).
% 0.90/0.88 tff(1049,plain,
% 0.90/0.88 ($false),
% 0.90/0.88 inference(unit_resolution,[status(thm)],[706, 1048, 1026])).
% 0.90/0.88 % SZS output end Proof
%------------------------------------------------------------------------------