TSTP Solution File: GRP124-2.004 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP124-2.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 22:25:59 EDT 2022
% Result : Unsatisfiable 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP124-2.004 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 14:50:27 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(product_type, type, (
% 0.21/0.44 product: ( $i * $i * $i ) > $o)).
% 0.21/0.44 tff(e_3_type, type, (
% 0.21/0.44 e_3: $i)).
% 0.21/0.44 tff(e_1_type, type, (
% 0.21/0.44 e_1: $i)).
% 0.21/0.44 tff(e_4_type, type, (
% 0.21/0.44 e_4: $i)).
% 0.21/0.44 tff(e_2_type, type, (
% 0.21/0.44 e_2: $i)).
% 0.21/0.44 tff(equalish_type, type, (
% 0.21/0.44 equalish: ( $i * $i ) > $o)).
% 0.21/0.44 tff(next_type, type, (
% 0.21/0.44 next: ( $i * $i ) > $o)).
% 0.21/0.44 tff(greater_type, type, (
% 0.21/0.44 greater: ( $i * $i ) > $o)).
% 0.21/0.44 tff(group_element_type, type, (
% 0.21/0.44 group_element: $i > $o)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(4,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_idempotence')).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (![X: $i] : product(X, X, X)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.44 tff(6,plain,(
% 0.21/0.44 ![X: $i] : product(X, X, X)),
% 0.21/0.44 inference(skolemize,[status(sab)],[5])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (![X: $i] : product(X, X, X)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (product(e_2, e_2, e_2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.44 tff(10,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (product(e_1, e_1, e_1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[11, 7])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(16,plain,
% 0.21/0.45 (^[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)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(17,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.45 tff(18,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')).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.45 tff(20,plain,
% 0.21/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.45 tff(21,plain,(
% 0.21/0.45 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[20])).
% 0.21/0.45 tff(22,plain,
% 0.21/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.21/0.45 tff(23,plain,
% 0.21/0.45 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(24,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.21/0.45 tff(25,plain,
% 0.21/0.45 (~equalish(e_2, e_1)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.45 tff(26,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(27,plain,
% 0.21/0.45 ((equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(28,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.45 tff(29,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[28, 26])).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 ((~![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)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(31,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.45 tff(32,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[31, 25, 22, 12, 10])).
% 0.21/0.45 tff(33,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(34,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.21/0.45 tff(35,plain,
% 0.21/0.45 (^[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))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(38,plain,
% 0.21/0.45 (^[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)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(39,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.45 tff(40,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')).
% 0.21/0.45 tff(41,plain,
% 0.21/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.45 tff(42,plain,
% 0.21/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.21/0.45 tff(43,plain,(
% 0.21/0.45 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[42])).
% 0.21/0.45 tff(44,plain,
% 0.21/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.21/0.45 tff(45,plain,
% 0.21/0.45 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(46,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.21/0.45 tff(47,plain,
% 0.21/0.45 (~equalish(e_1, e_2)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.45 tff(48,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(49,plain,
% 0.21/0.45 ((~![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)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(50,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.45 tff(51,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[50, 47, 44, 34, 9])).
% 0.21/0.45 tff(52,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(53,plain,
% 0.21/0.45 (^[Y: $i, X: $i, X1: $i] : refl(((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(54,plain,
% 0.21/0.45 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.45 tff(55,plain,
% 0.21/0.45 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(56,plain,
% 0.21/0.45 (^[Y: $i, X: $i, X1: $i] : trans(monotonicity(rewrite(((~product(X, e_1, Y)) | (~next(X, X1))) <=> ((~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> (((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))))), rewrite((((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(57,plain,
% 0.21/0.45 (![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.45 tff(58,axiom,(![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','no_redundancy')).
% 0.21/0.45 tff(59,plain,
% 0.21/0.45 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.45 tff(60,plain,
% 0.21/0.45 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.45 tff(61,plain,(
% 0.21/0.45 ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[60])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.21/0.45 tff(63,plain,
% 0.21/0.45 (greater(e_4, e_3) <=> greater(e_4, e_3)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(64,axiom,(greater(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_3')).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 (greater(e_4, e_3)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.45 tff(66,plain,
% 0.21/0.45 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(67,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.21/0.45 tff(68,plain,
% 0.21/0.45 (next(e_2, e_3)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (~product(e_2, e_1, e_4)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[71, 68, 65, 62])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 (^[Y: $i, X: $i] : refl((product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[73])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)))), rewrite(((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(77,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.46 tff(78,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.21/0.46 tff(79,plain,
% 0.21/0.46 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.46 tff(80,plain,
% 0.21/0.46 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.46 tff(81,plain,(
% 0.21/0.46 ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[80])).
% 0.21/0.46 tff(82,plain,
% 0.21/0.46 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.21/0.46 tff(83,plain,
% 0.21/0.46 (group_element(e_2) <=> group_element(e_2)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(84,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.21/0.46 tff(85,plain,
% 0.21/0.46 (group_element(e_2)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.46 tff(86,plain,
% 0.21/0.46 (group_element(e_1) <=> group_element(e_1)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(87,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.21/0.46 tff(88,plain,
% 0.21/0.46 (group_element(e_1)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.46 tff(89,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(90,plain,
% 0.21/0.46 ((product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2))) <=> (product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(91,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.46 tff(92,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[91, 89])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(94,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[94, 88, 85, 82, 72])).
% 0.21/0.46 tff(96,plain,
% 0.21/0.46 (product(e_2, e_1, e_3) | product(e_2, e_1, e_1)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[95, 52])).
% 0.21/0.46 tff(97,plain,
% 0.21/0.46 (product(e_2, e_1, e_3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[96, 33])).
% 0.21/0.46 tff(98,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.21/0.46 tff(99,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.21/0.46 tff(100,plain,
% 0.21/0.46 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(101,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.21/0.46 tff(102,plain,
% 0.21/0.46 (~equalish(e_1, e_4)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~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_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 ((equalish(e_1, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_2, e_1, e_3))) <=> (equalish(e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(105,plain,
% 0.21/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[104])).
% 0.21/0.47 tff(106,plain,
% 0.21/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[105, 103])).
% 0.21/0.47 tff(107,plain,
% 0.21/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(108,plain,
% 0.21/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.47 tff(109,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[108, 102, 44, 99, 98])).
% 0.21/0.47 tff(110,plain,((~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 (~product(e_2, e_4, e_3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[110, 97])).
% 0.21/0.47 tff(112,assumption,(product(e_2, e_4, e_2)), introduced(assumption)).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(114,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.21/0.47 tff(115,plain,
% 0.21/0.47 (~equalish(e_4, e_2)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(117,plain,
% 0.21/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[118, 115, 44, 112, 9])).
% 0.21/0.47 tff(120,plain,(~product(e_2, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(121,assumption,(~product(e_4, e_4, e_4)), introduced(assumption)).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(123,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[122, 7, 121])).
% 0.21/0.47 tff(124,plain,(product(e_4, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(125,assumption,(product(e_2, e_4, e_4)), introduced(assumption)).
% 0.21/0.47 tff(126,plain,
% 0.21/0.47 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(127,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 (~equalish(e_2, e_4)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.47 tff(129,plain,
% 0.21/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[131, 128, 22, 125, 124])).
% 0.21/0.47 tff(133,plain,(~product(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (group_element(e_4) <=> group_element(e_4)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(135,axiom,(group_element(e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_4')).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (group_element(e_4)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_2, e_4, e_1) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_4, e_1) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(138,plain,
% 0.21/0.47 ((product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_4, e_1) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(139,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_2, e_4, e_1) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[138])).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_4, e_1) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2))),
% 0.21/0.47 inference(transitivity,[status(thm)],[139, 137])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(142,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_4, e_1) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (product(e_2, e_4, e_1) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[142, 85, 136, 82])).
% 0.21/0.47 tff(144,plain,
% 0.21/0.47 (product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[143, 133])).
% 0.21/0.47 tff(145,plain,
% 0.21/0.47 (product(e_2, e_4, e_1) | product(e_2, e_4, e_3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[144, 120])).
% 0.21/0.47 tff(146,plain,
% 0.21/0.47 (product(e_2, e_4, e_1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[145, 111])).
% 0.21/0.47 tff(147,plain,
% 0.21/0.47 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : refl(((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(148,plain,
% 0.21/0.47 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[147])).
% 0.21/0.47 tff(149,plain,
% 0.21/0.47 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(150,plain,
% 0.21/0.47 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) <=> ((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> (((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))))), rewrite((((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> (((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)))), rewrite((((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(151,plain,
% 0.21/0.47 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[150])).
% 0.21/0.47 tff(152,axiom,(![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg2_2')).
% 0.21/0.47 tff(153,plain,
% 0.21/0.47 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.47 tff(154,plain,
% 0.21/0.47 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.21/0.47 tff(155,plain,(
% 0.21/0.47 ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.47 inference(skolemize,[status(sab)],[154])).
% 0.21/0.47 tff(156,plain,
% 0.21/0.47 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.21/0.47 tff(157,plain,
% 0.21/0.47 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(158,plain,
% 0.21/0.47 (((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | equalish(e_1, e_2)) <=> (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(159,plain,
% 0.21/0.47 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[158])).
% 0.21/0.47 tff(160,plain,
% 0.21/0.47 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[159, 157])).
% 0.21/0.47 tff(161,plain,
% 0.21/0.47 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | equalish(e_1, e_2))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(162,plain,
% 0.21/0.48 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.48 tff(163,plain,
% 0.21/0.48 (~product(e_4, e_1, e_2)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[162, 47, 156, 146, 9])).
% 0.21/0.48 tff(164,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.21/0.48 tff(165,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.21/0.48 tff(166,plain,
% 0.21/0.48 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(167,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.21/0.48 tff(168,plain,
% 0.21/0.48 (~equalish(e_4, e_1)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.21/0.48 tff(169,plain,
% 0.21/0.48 (((~![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)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(170,plain,
% 0.21/0.48 ((~![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)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(171,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.21/0.48 tff(172,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[171, 168, 22, 165, 164])).
% 0.21/0.48 tff(173,plain,((~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(174,plain,
% 0.21/0.48 (~product(e_4, e_1, e_1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[173, 12])).
% 0.21/0.48 tff(175,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.21/0.48 tff(176,plain,
% 0.21/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_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)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(177,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(178,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.21/0.48 tff(179,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[178, 102, 44, 124, 175])).
% 0.21/0.48 tff(180,plain,(~product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(181,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(182,plain,
% 0.21/0.48 ((product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4))) <=> ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(183,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[182])).
% 0.21/0.48 tff(184,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1))),
% 0.21/0.48 inference(transitivity,[status(thm)],[183, 181])).
% 0.21/0.48 tff(185,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(186,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.21/0.48 tff(187,plain,
% 0.21/0.48 (product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[186, 88, 136, 82, 180])).
% 0.21/0.48 tff(188,plain,
% 0.21/0.48 (product(e_4, e_1, e_2) | product(e_4, e_1, e_3)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[187, 174])).
% 0.21/0.48 tff(189,plain,
% 0.21/0.48 (product(e_4, e_1, e_3)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[188, 163])).
% 0.21/0.48 tff(190,plain,
% 0.21/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(191,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(192,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.21/0.48 tff(193,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[192, 115, 22, 97, 189])).
% 0.21/0.48 % SZS output end Proof
%------------------------------------------------------------------------------