TSTP Solution File: GRP130-2.003 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP130-2.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 22:26:14 EDT 2022
% Result : Unsatisfiable 0.16s 0.37s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GRP130-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n006.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Wed Aug 31 15:04:09 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.16/0.37 % SZS status Unsatisfiable
% 0.16/0.37 % SZS output start Proof
% 0.16/0.37 tff(product_type, type, (
% 0.16/0.37 product: ( $i * $i * $i ) > $o)).
% 0.16/0.37 tff(e_2_type, type, (
% 0.16/0.37 e_2: $i)).
% 0.16/0.37 tff(e_3_type, type, (
% 0.16/0.37 e_3: $i)).
% 0.16/0.37 tff(e_1_type, type, (
% 0.16/0.37 e_1: $i)).
% 0.16/0.37 tff(equalish_type, type, (
% 0.16/0.37 equalish: ( $i * $i ) > $o)).
% 0.16/0.37 tff(group_element_type, type, (
% 0.16/0.37 group_element: $i > $o)).
% 0.16/0.37 tff(next_type, type, (
% 0.16/0.37 next: ( $i * $i ) > $o)).
% 0.16/0.37 tff(greater_type, type, (
% 0.16/0.37 greater: ( $i * $i ) > $o)).
% 0.16/0.37 tff(1,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.16/0.37 tff(2,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.16/0.37 tff(3,assumption,(product(e_3, e_3, e_3)), introduced(assumption)).
% 0.16/0.37 tff(4,plain,
% 0.16/0.37 (^[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))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(5,plain,
% 0.16/0.37 (![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)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.16/0.37 tff(6,plain,
% 0.16/0.37 (![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)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(7,plain,
% 0.16/0.37 (^[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)))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(8,plain,
% 0.16/0.37 (![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)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[7])).
% 0.16/0.37 tff(9,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.16/0.37 tff(10,plain,
% 0.16/0.37 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.16/0.37 tff(11,plain,
% 0.16/0.37 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.16/0.37 tff(12,plain,(
% 0.16/0.37 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.16/0.37 inference(skolemize,[status(sab)],[11])).
% 0.16/0.37 tff(13,plain,
% 0.16/0.37 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.16/0.37 tff(14,plain,
% 0.16/0.37 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(15,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.16/0.37 tff(16,plain,
% 0.16/0.37 (~equalish(e_3, e_1)),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.16/0.37 tff(17,plain,
% 0.16/0.37 (((~![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_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(18,plain,
% 0.16/0.37 ((~![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_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(19,plain,
% 0.16/0.37 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.16/0.37 tff(20,plain,
% 0.16/0.37 ($false),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[19, 16, 13, 2, 3])).
% 0.16/0.37 tff(21,plain,((~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.37 tff(22,plain,
% 0.16/0.37 (~product(e_3, e_3, e_3)),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[21, 2])).
% 0.16/0.37 tff(23,plain,
% 0.16/0.37 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(24,plain,
% 0.16/0.37 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.16/0.37 tff(25,plain,
% 0.16/0.37 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(26,plain,
% 0.16/0.37 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(X, Y, Z1)))), ((((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> (((~product(X, Z1, Z2)) | (~product(X, Y, Z1))) | product(Z2, Y, X)))), rewrite((((~product(X, Z1, Z2)) | (~product(X, Y, Z1))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))), ((((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(27,plain,
% 0.16/0.37 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.16/0.37 tff(28,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.16/0.37 tff(29,plain,
% 0.16/0.37 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.16/0.37 tff(30,plain,
% 0.16/0.37 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.16/0.37 tff(31,plain,(
% 0.16/0.37 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.16/0.37 inference(skolemize,[status(sab)],[30])).
% 0.16/0.37 tff(32,plain,
% 0.16/0.37 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.16/0.37 tff(33,plain,
% 0.16/0.37 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(34,plain,
% 0.16/0.37 ((product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1))) <=> ((~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(35,plain,
% 0.16/0.37 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1))))),
% 0.16/0.37 inference(monotonicity,[status(thm)],[34])).
% 0.16/0.37 tff(36,plain,
% 0.16/0.37 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.16/0.37 inference(transitivity,[status(thm)],[35, 33])).
% 0.16/0.37 tff(37,plain,
% 0.16/0.37 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(38,plain,
% 0.16/0.37 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.16/0.37 tff(39,plain,
% 0.16/0.37 (~product(e_3, e_3, e_1)),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[38, 32, 2, 22])).
% 0.16/0.37 tff(40,plain,
% 0.16/0.37 (^[Y: $i, X: $i] : refl((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(41,plain,
% 0.16/0.37 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[40])).
% 0.16/0.37 tff(42,plain,
% 0.16/0.37 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(43,plain,
% 0.16/0.37 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(44,plain,
% 0.16/0.37 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[43])).
% 0.16/0.37 tff(45,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.16/0.38 tff(46,plain,
% 0.16/0.38 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.16/0.38 tff(47,plain,
% 0.16/0.38 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.16/0.38 tff(48,plain,(
% 0.16/0.38 ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.16/0.38 inference(skolemize,[status(sab)],[47])).
% 0.16/0.38 tff(49,plain,
% 0.16/0.38 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.16/0.38 tff(50,plain,
% 0.16/0.38 (group_element(e_3) <=> group_element(e_3)),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(51,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.16/0.38 tff(52,plain,
% 0.16/0.38 (group_element(e_3)),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.16/0.38 tff(53,plain,
% 0.16/0.38 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(54,plain,
% 0.16/0.38 ((product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(55,plain,
% 0.16/0.38 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3)))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[54])).
% 0.16/0.38 tff(56,plain,
% 0.16/0.38 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3))),
% 0.16/0.38 inference(transitivity,[status(thm)],[55, 53])).
% 0.16/0.38 tff(57,plain,
% 0.16/0.38 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3)))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(58,plain,
% 0.16/0.38 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3)),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.16/0.38 tff(59,plain,
% 0.16/0.38 (product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[58, 52, 49])).
% 0.16/0.38 tff(60,plain,
% 0.16/0.38 (product(e_3, e_3, e_2)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[59, 39, 22])).
% 0.16/0.38 tff(61,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.16/0.38 tff(62,plain,
% 0.16/0.38 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(63,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.16/0.38 tff(64,plain,
% 0.16/0.38 (~equalish(e_2, e_1)),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.16/0.38 tff(65,plain,
% 0.16/0.38 (((~![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_3, e_1, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(66,plain,
% 0.16/0.38 ((~![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_3, e_1, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(67,plain,
% 0.16/0.38 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_2, e_3))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.16/0.38 tff(68,plain,
% 0.16/0.38 ($false),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[67, 64, 13, 2, 61])).
% 0.16/0.38 tff(69,plain,((~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.38 tff(70,plain,
% 0.16/0.38 (~product(e_3, e_2, e_3)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[69, 2])).
% 0.16/0.38 tff(71,assumption,(~product(e_3, e_2, e_3)), introduced(assumption)).
% 0.16/0.38 tff(72,assumption,(~product(e_3, e_2, e_2)), introduced(assumption)).
% 0.16/0.38 tff(73,plain,
% 0.16/0.38 (group_element(e_2) <=> group_element(e_2)),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(74,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.16/0.38 tff(75,plain,
% 0.16/0.38 (group_element(e_2)),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.16/0.38 tff(76,plain,
% 0.16/0.38 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(77,plain,
% 0.16/0.38 ((product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(78,plain,
% 0.16/0.38 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2)))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[77])).
% 0.16/0.38 tff(79,plain,
% 0.16/0.38 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2))),
% 0.16/0.38 inference(transitivity,[status(thm)],[78, 76])).
% 0.16/0.38 tff(80,plain,
% 0.16/0.38 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(81,plain,
% 0.16/0.38 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2)),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.16/0.38 tff(82,plain,
% 0.16/0.38 (product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[81, 75, 52, 49])).
% 0.16/0.38 tff(83,plain,
% 0.16/0.38 (product(e_3, e_2, e_1)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[82, 71, 72])).
% 0.16/0.38 tff(84,plain,
% 0.16/0.38 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_2, e_1)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(85,plain,
% 0.16/0.38 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_2, e_1)))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(86,plain,
% 0.16/0.38 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_2, e_1))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.16/0.38 tff(87,plain,
% 0.16/0.38 (product(e_3, e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_2, e_1))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[86, 32])).
% 0.16/0.38 tff(88,plain,
% 0.16/0.38 ($false),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[87, 83, 71, 2])).
% 0.16/0.38 tff(89,plain,(product(e_3, e_2, e_3) | (~product(e_3, e_1, e_3)) | product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.38 tff(90,plain,
% 0.16/0.38 (product(e_3, e_2, e_2)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[89, 70, 2])).
% 0.16/0.38 tff(91,plain,
% 0.16/0.38 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(92,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.16/0.38 tff(93,plain,
% 0.16/0.38 (~equalish(e_3, e_2)),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.16/0.38 tff(94,plain,
% 0.16/0.38 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(95,plain,
% 0.16/0.38 ((equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2))) <=> (equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(96,plain,
% 0.16/0.38 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2))))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[95])).
% 0.16/0.38 tff(97,plain,
% 0.16/0.38 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.16/0.38 inference(transitivity,[status(thm)],[96, 94])).
% 0.16/0.39 tff(98,plain,
% 0.16/0.39 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(99,plain,
% 0.16/0.39 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.16/0.39 tff(100,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[99, 93, 13, 90, 60])).
% 0.16/0.39 tff(101,plain,(~product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.39 tff(102,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.16/0.39 tff(103,plain,
% 0.16/0.39 (^[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))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(104,plain,
% 0.16/0.39 (![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)))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[103])).
% 0.16/0.39 tff(105,plain,
% 0.16/0.39 (![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)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(106,plain,
% 0.16/0.39 (^[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)))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(107,plain,
% 0.16/0.39 (![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)))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[106])).
% 0.16/0.39 tff(108,axiom,(![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_redundancy')).
% 0.16/0.39 tff(109,plain,
% 0.16/0.39 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.16/0.39 tff(110,plain,
% 0.16/0.39 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.16/0.39 tff(111,plain,(
% 0.16/0.39 ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.16/0.39 inference(skolemize,[status(sab)],[110])).
% 0.16/0.39 tff(112,plain,
% 0.16/0.39 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.16/0.39 tff(113,plain,
% 0.16/0.39 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(114,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.16/0.39 tff(115,plain,
% 0.16/0.39 (greater(e_3, e_2)),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.16/0.39 tff(116,plain,
% 0.16/0.39 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(117,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.16/0.39 tff(118,plain,
% 0.16/0.39 (next(e_1, e_2)),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.16/0.39 tff(119,plain,
% 0.16/0.39 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(120,plain,
% 0.16/0.39 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(121,plain,
% 0.16/0.39 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.16/0.39 tff(122,plain,
% 0.16/0.39 (~product(e_1, e_1, e_3)),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[121, 118, 115, 112])).
% 0.16/0.39 tff(123,plain,
% 0.16/0.39 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(124,plain,
% 0.16/0.39 ((product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_1, e_1))) <=> (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(125,plain,
% 0.16/0.39 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1))))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[124])).
% 0.16/0.39 tff(126,plain,
% 0.16/0.39 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)))),
% 0.16/0.39 inference(transitivity,[status(thm)],[125, 123])).
% 0.16/0.39 tff(127,plain,
% 0.16/0.39 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(128,plain,
% 0.16/0.39 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.16/0.39 tff(129,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[128, 32, 122, 102])).
% 0.16/0.39 tff(130,plain,(~product(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.39 tff(131,plain,
% 0.16/0.39 (group_element(e_1) <=> group_element(e_1)),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(132,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.16/0.39 tff(133,plain,
% 0.16/0.39 (group_element(e_1)),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.16/0.39 tff(134,plain,
% 0.16/0.39 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(135,plain,
% 0.16/0.39 ((product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(136,plain,
% 0.16/0.39 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[135])).
% 0.16/0.39 tff(137,plain,
% 0.16/0.39 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.16/0.39 inference(transitivity,[status(thm)],[136, 134])).
% 0.16/0.39 tff(138,plain,
% 0.16/0.39 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(139,plain,
% 0.16/0.39 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.16/0.39 tff(140,plain,
% 0.16/0.39 (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[139, 133, 52, 49])).
% 0.16/0.39 tff(141,plain,
% 0.16/0.39 (product(e_3, e_1, e_3) | product(e_3, e_1, e_2)),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[140, 130])).
% 0.16/0.39 tff(142,plain,
% 0.16/0.39 (product(e_3, e_1, e_2)),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[141, 101])).
% 0.16/0.39 tff(143,plain,
% 0.16/0.39 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(144,plain,
% 0.16/0.39 ((product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_2))) <=> (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(145,plain,
% 0.16/0.39 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1))))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[144])).
% 0.16/0.39 tff(146,plain,
% 0.16/0.39 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1)))),
% 0.16/0.39 inference(transitivity,[status(thm)],[145, 143])).
% 0.16/0.39 tff(147,plain,
% 0.16/0.39 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(148,plain,
% 0.16/0.39 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.16/0.40 tff(149,plain,
% 0.16/0.40 ($false),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[148, 32, 122, 142, 1])).
% 0.16/0.40 tff(150,plain,(~product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.40 tff(151,plain,
% 0.16/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_3)))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(152,plain,
% 0.16/0.40 ((product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_2))) <=> (product(e_3, e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_3)))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(153,plain,
% 0.16/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_3))))),
% 0.16/0.40 inference(monotonicity,[status(thm)],[152])).
% 0.16/0.40 tff(154,plain,
% 0.16/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_3)))),
% 0.16/0.40 inference(transitivity,[status(thm)],[153, 151])).
% 0.16/0.40 tff(155,plain,
% 0.16/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(156,plain,
% 0.16/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_3))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.16/0.40 tff(157,plain,
% 0.16/0.40 ($false),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[156, 32, 101, 142, 61])).
% 0.16/0.40 tff(158,plain,(~product(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.40 tff(159,plain,
% 0.16/0.40 (product(e_3, e_2, e_2)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[82, 158, 150])).
% 0.16/0.40 tff(160,plain,
% 0.16/0.40 (((~![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_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(161,plain,
% 0.16/0.40 ((~![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_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(162,plain,
% 0.16/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.16/0.40 tff(163,plain,
% 0.16/0.40 ($false),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[162, 64, 13, 142, 159])).
% 0.16/0.40 % SZS output end Proof
%------------------------------------------------------------------------------