TSTP Solution File: GRP125-4.003 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP125-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 22:26:04 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP125-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 15:18:34 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(product_type, type, (
% 0.13/0.39 product: ( $i * $i * $i ) > $o)).
% 0.13/0.39 tff(e_3_type, type, (
% 0.13/0.39 e_3: $i)).
% 0.13/0.39 tff(e_1_type, type, (
% 0.13/0.39 e_1: $i)).
% 0.13/0.39 tff(equalish_type, type, (
% 0.13/0.39 equalish: ( $i * $i ) > $o)).
% 0.13/0.39 tff(e_2_type, type, (
% 0.13/0.39 e_2: $i)).
% 0.13/0.39 tff(group_element_type, type, (
% 0.13/0.39 group_element: $i > $o)).
% 0.13/0.39 tff(1,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.13/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_idempotence')).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![X: $i] : product(X, X, X)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.39 tff(7,plain,(
% 0.13/0.39 ![X: $i] : product(X, X, X)),
% 0.13/0.39 inference(skolemize,[status(sab)],[6])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![X: $i] : product(X, X, X)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (product(e_3, e_3, e_3)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X))) <=> ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(W, Y, X)) | (~product(Z, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)))), rewrite((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![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] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.39 tff(16,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.39 tff(19,plain,(
% 0.13/0.39 ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[18])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(22,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (~equalish(e_3, e_1)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (((~product(e_3, e_3, e_3)) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3))) <=> (equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_3, e_3, e_3)) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[25])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_3, e_3, e_3)) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[26, 24])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_3, e_3, e_3)) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[29, 23, 20, 10, 1])).
% 0.13/0.39 tff(31,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1))) <=> (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite((product(Y, X, Z2) | (~product(Z1, Z2, X))) <=> (product(Y, X, Z2) | (~product(Z1, Z2, X)))), (((product(Y, X, Z2) | (~product(Z1, Z2, X))) | (~product(X, Y, Z1))) <=> ((product(Y, X, Z2) | (~product(Z1, Z2, X))) | (~product(X, Y, Z1))))), rewrite(((product(Y, X, Z2) | (~product(Z1, Z2, X))) | (~product(X, Y, Z1))) <=> (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))), (((product(Y, X, Z2) | (~product(Z1, Z2, X))) | (~product(X, Y, Z1))) <=> (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(Y, X, Z2) | (~product(Z1, Z2, X))) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.13/0.39 tff(37,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(Y, X, Z2) | (~product(Z1, Z2, X))) | (~product(X, Y, Z1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3_2')).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.13/0.40 tff(40,plain,(
% 0.13/0.40 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[39])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 ((product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3))) <=> ((~product(e_3, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[44, 42])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (~product(e_3, e_1, e_3)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[47, 41, 10, 31])).
% 0.13/0.40 tff(49,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_1)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 ((product(e_3, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_1))) <=> (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_1)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_1))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[51])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_1)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[55, 41, 49, 48])).
% 0.19/0.40 tff(57,plain,(~product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (^[Y: $i, X: $i] : refl(((~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)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1)) | product(X, Y, e_2)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_3)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![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] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.40 tff(63,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/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.19/0.41 tff(66,plain,(
% 0.19/0.41 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.41 inference(skolemize,[status(sab)],[65])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (group_element(e_3) <=> group_element(e_3)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(69,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (group_element(e_3)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(72,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (group_element(e_1)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)) <=> (product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3))),
% 0.19/0.41 inference(transitivity,[status(thm)],[76, 74])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (product(e_1, e_3, e_1) | product(e_1, e_3, e_2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[79, 73, 70, 67, 31])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (product(e_1, e_3, e_2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[80, 57])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.41 tff(87,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.19/0.41 tff(90,plain,(
% 0.19/0.41 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[89])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (((~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1))) <=> (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[93])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[94, 92])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (~product(e_3, e_3, e_1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[97, 91, 10, 31])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (^[Y: $i, X: $i] : refl((product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) <=> (product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) <=> ((product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_2, X, Y)))), rewrite(((product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_2, X, Y)) <=> (product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) <=> (product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) <=> ((product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_3, X, Y)))), rewrite(((product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_3, X, Y)) <=> (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) <=> (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) <=> ![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.41 tff(104,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','row_surjectivity')).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.19/0.41 tff(107,plain,(
% 0.19/0.41 ![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[106])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_3, e_1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ((product(e_3, e_3, e_1) | product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> (product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_3, e_1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_1) | product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_3, e_1)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[110])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_1) | product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_3, e_1))),
% 0.19/0.42 inference(transitivity,[status(thm)],[111, 109])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_1) | product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_3, e_1)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | product(e_3, e_3, e_1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[114, 108, 73, 70])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 (product(e_2, e_3, e_1) | product(e_1, e_3, e_1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[115, 98])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (product(e_2, e_3, e_1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[116, 57])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[120, 41, 117, 81, 48])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------