TSTP Solution File: GRP128-4.003 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP128-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:26:10 EDT 2022
% Result : Unsatisfiable 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP128-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 15:02:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Unsatisfiable
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(product_type, type, (
% 0.21/0.42 product: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(e_2_type, type, (
% 0.21/0.42 e_2: $i)).
% 0.21/0.42 tff(e_3_type, type, (
% 0.21/0.42 e_3: $i)).
% 0.21/0.42 tff(e_1_type, type, (
% 0.21/0.42 e_1: $i)).
% 0.21/0.42 tff(equalish_type, type, (
% 0.21/0.42 equalish: ( $i * $i ) > $o)).
% 0.21/0.42 tff(group_element_type, type, (
% 0.21/0.42 group_element: $i > $o)).
% 0.21/0.42 tff(1,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.21/0.42 tff(2,assumption,(~product(e_3, e_3, e_3)), introduced(assumption)).
% 0.21/0.42 tff(3,assumption,(product(e_3, e_3, e_1)), introduced(assumption)).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1)) <=> ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (^[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(Z1, Y, Z2))) <=> (((~product(X, Z1, Z2)) | product(X, Y, Z1)) | (~product(Z1, Y, Z2))))), rewrite((((~product(X, Z1, Z2)) | product(X, Y, Z1)) | (~product(Z1, Y, Z2))) <=> ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))), (((product(X, Y, Z1) | (~product(X, Z1, Z2))) | (~product(Z1, Y, Z2))) <=> ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(X, Y, Z1) | (~product(X, Z1, Z2))) | (~product(Z1, Y, Z2))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[7])).
% 0.21/0.42 tff(9,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(X, Y, Z1) | (~product(X, Z1, Z2))) | (~product(Z1, Y, Z2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3_1')).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.21/0.42 tff(12,plain,(
% 0.21/0.42 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))),
% 0.21/0.42 inference(skolemize,[status(sab)],[11])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (((~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3)) <=> (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | ((~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[15])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | ((~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[16, 14])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | ((~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (product(e_3, e_3, e_3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[19, 13, 3])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, Y, W)) | (~product(X, Y, Z))) <=> ((~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)))), rewrite((((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.43 tff(26,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function2')).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.43 tff(29,plain,(
% 0.21/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[28])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(32,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (~equalish(e_3, e_1)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[36, 33, 30, 3, 20])).
% 0.21/0.43 tff(38,plain,(~product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (^[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)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 (![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))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 (![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))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (![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))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.43 tff(44,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')).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 (![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))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (![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))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.21/0.43 tff(47,plain,(
% 0.21/0.43 ![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))),
% 0.21/0.43 inference(skolemize,[status(sab)],[46])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (![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))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 (group_element(e_3) <=> group_element(e_3)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(50,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (group_element(e_3)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (((~![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)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2))) <=> ((~![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)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (((~group_element(e_3)) | (~group_element(e_3)) | 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)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (((~![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_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, 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))) | ((~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[53])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 (((~![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_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, 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))) | (~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2))),
% 0.21/0.43 inference(transitivity,[status(thm)],[54, 52])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 ((~![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_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 ((~![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)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (product(e_3, e_3, e_3) | product(e_3, e_3, e_2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[57, 51, 48, 38])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 (product(e_3, e_3, e_2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[58, 2])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (((~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_2)) | product(e_3, e_3, e_3)) <=> (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | ((~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_2)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | ((~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_2)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[62, 60])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | ((~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_2)) | product(e_3, e_3, e_3))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[65, 13, 59, 2])).
% 0.21/0.44 tff(67,plain,(product(e_3, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(68,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(69,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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.44 tff(70,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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.44 tff(73,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')).
% 0.21/0.44 tff(74,plain,
% 0.21/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.21/0.44 tff(76,plain,(
% 0.21/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[75])).
% 0.21/0.44 tff(77,plain,
% 0.21/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(79,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.21/0.44 tff(80,plain,
% 0.21/0.44 (~equalish(e_1, e_3)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.44 tff(81,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(82,plain,
% 0.21/0.44 ((equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))) <=> (equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(83,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[82])).
% 0.21/0.44 tff(84,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[83, 81])).
% 0.21/0.44 tff(85,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(86,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.44 tff(87,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[86, 80, 77, 67, 1])).
% 0.21/0.44 tff(88,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(89,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.21/0.44 tff(90,plain,
% 0.21/0.44 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1))) <=> ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(91,plain,
% 0.21/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.44 tff(92,plain,
% 0.21/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(93,plain,
% 0.21/0.44 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(94,plain,
% 0.21/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.44 tff(95,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.21/0.44 tff(96,plain,
% 0.21/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.21/0.44 tff(98,plain,(
% 0.21/0.44 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[97])).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 (((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1))) <=> ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[101])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1))),
% 0.21/0.44 inference(transitivity,[status(thm)],[102, 100])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | product(X, Z1, Z2) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[105, 99])).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 (product(e_1, e_1, e_1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[106, 89])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 (^[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(112,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)],[111])).
% 0.21/0.45 tff(113,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(114,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)],[113, 112])).
% 0.21/0.45 tff(115,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)],[114, 110])).
% 0.21/0.45 tff(116,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)],[115])).
% 0.21/0.45 tff(117,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)],[116, 109])).
% 0.21/0.45 tff(118,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_3, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 ((equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))) <=> (equalish(e_3, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(120,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_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[119])).
% 0.21/0.45 tff(121,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_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[120, 118])).
% 0.21/0.45 tff(122,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_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.21/0.45 tff(124,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[123, 33, 117, 89, 107])).
% 0.21/0.45 tff(125,plain,(~product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 (group_element(e_1) <=> group_element(e_1)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(127,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 (group_element(e_1)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 (((~![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_3) | product(e_1, e_3, e_2))) <=> ((~![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_3) | product(e_1, e_3, e_2))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(130,plain,
% 0.21/0.45 (((~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_3) | product(e_1, e_3, e_2))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(131,plain,
% 0.21/0.45 (((~![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_3) | product(e_1, e_3, e_2)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[130])).
% 0.21/0.45 tff(132,plain,
% 0.21/0.45 (((~![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_3) | product(e_1, e_3, e_2))),
% 0.21/0.45 inference(transitivity,[status(thm)],[131, 129])).
% 0.21/0.45 tff(133,plain,
% 0.21/0.45 ((~![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))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(134,plain,
% 0.21/0.45 ((~![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_3) | product(e_1, e_3, e_2)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.21/0.45 tff(135,plain,
% 0.21/0.45 (product(e_1, e_3, e_3) | product(e_1, e_3, e_2)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[134, 128, 51, 48, 125])).
% 0.21/0.45 tff(136,plain,
% 0.21/0.45 (product(e_1, e_3, e_2)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[135, 88])).
% 0.21/0.45 tff(137,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.21/0.45 tff(138,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.21/0.45 tff(139,plain,
% 0.21/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | ((~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_3, e_3, e_1))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(140,plain,
% 0.21/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | ((~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_3, e_3, e_1))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(141,plain,
% 0.21/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Z1, Y, Z2)) | (~product(X, Z1, Z2)) | product(X, Y, Z1))) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_3, e_3, e_1)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.21/0.45 tff(142,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[141, 13, 38, 138, 137])).
% 0.21/0.45 tff(143,plain,((~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(144,plain,
% 0.21/0.45 (~product(e_3, e_1, e_2)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[143, 136])).
% 0.21/0.45 tff(145,plain,
% 0.21/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(146,plain,
% 0.21/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[145])).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(148,plain,
% 0.21/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite((product(Z1, Y, Z2) | (~product(X, Z1, Z2))) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)))), (((product(Z1, Y, Z2) | (~product(X, Z1, Z2))) | (~product(X, Y, Z1))) <=> ((product(Z1, Y, Z2) | (~product(X, Z1, Z2))) | (~product(X, Y, Z1))))), rewrite(((product(Z1, Y, Z2) | (~product(X, Z1, Z2))) | (~product(X, Y, Z1))) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))), (((product(Z1, Y, Z2) | (~product(X, Z1, Z2))) | (~product(X, Y, Z1))) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(149,plain,
% 0.21/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(Z1, Y, Z2) | (~product(X, Z1, Z2))) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[148])).
% 0.21/0.45 tff(150,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(Z1, Y, Z2) | (~product(X, Z1, Z2))) | (~product(X, Y, Z1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3_2')).
% 0.21/0.45 tff(151,plain,
% 0.21/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.45 tff(152,plain,
% 0.21/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.21/0.45 tff(153,plain,(
% 0.21/0.45 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[152])).
% 0.21/0.45 tff(154,plain,
% 0.21/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.21/0.45 tff(155,plain,
% 0.21/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(156,plain,
% 0.21/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(157,plain,
% 0.21/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_3))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.21/0.45 tff(158,plain,
% 0.21/0.45 (~product(e_1, e_1, e_3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[157, 154, 144, 136])).
% 0.21/0.45 tff(159,plain,
% 0.21/0.45 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(160,plain,
% 0.21/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[159])).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(162,plain,
% 0.21/0.46 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y))), (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y)) | product(X, e_2, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y))), (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_3, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_3, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(163,plain,
% 0.21/0.46 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[162])).
% 0.21/0.46 tff(164,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','column_surjectivity')).
% 0.21/0.46 tff(165,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.21/0.46 tff(166,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.21/0.46 tff(167,plain,(
% 0.21/0.46 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.46 inference(skolemize,[status(sab)],[166])).
% 0.21/0.46 tff(168,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[167, 160])).
% 0.21/0.46 tff(169,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(170,plain,
% 0.21/0.46 (((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3)) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(171,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[170])).
% 0.21/0.46 tff(172,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3))),
% 0.21/0.46 inference(transitivity,[status(thm)],[171, 169])).
% 0.21/0.46 tff(173,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(174,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.21/0.46 tff(175,plain,
% 0.21/0.46 (product(e_1, e_2, e_3) | product(e_1, e_1, e_3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[174, 168, 128, 51, 88])).
% 0.21/0.46 tff(176,plain,
% 0.21/0.46 (product(e_1, e_2, e_3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[175, 158])).
% 0.21/0.46 tff(177,plain,
% 0.21/0.46 (^[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))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(178,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[177])).
% 0.21/0.46 tff(179,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(180,plain,
% 0.21/0.46 (^[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)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(181,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[180])).
% 0.21/0.46 tff(182,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')).
% 0.21/0.46 tff(183,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.21/0.46 tff(184,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.21/0.46 tff(185,plain,(
% 0.21/0.46 ![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)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[184])).
% 0.21/0.46 tff(186,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.21/0.46 tff(187,plain,
% 0.21/0.46 (((~![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))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(188,plain,
% 0.21/0.46 ((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))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(189,plain,
% 0.21/0.46 (((~![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)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[188])).
% 0.21/0.46 tff(190,plain,
% 0.21/0.46 (((~![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))),
% 0.21/0.46 inference(transitivity,[status(thm)],[189, 187])).
% 0.21/0.46 tff(191,plain,
% 0.21/0.46 ((~![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)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(192,plain,
% 0.21/0.47 ((~![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)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.21/0.47 tff(193,plain,
% 0.21/0.47 (product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | product(e_3, e_3, e_1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[192, 186, 128, 51])).
% 0.21/0.47 tff(194,plain,
% 0.21/0.47 (product(e_2, e_3, e_1) | product(e_3, e_3, e_1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[193, 125])).
% 0.21/0.47 tff(195,plain,
% 0.21/0.47 (product(e_2, e_3, e_1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[194, 38])).
% 0.21/0.47 tff(196,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(197,plain,
% 0.21/0.47 ((product(e_3, e_3, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_3, e_3))) <=> (product(e_3, e_3, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(198,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_3, e_1))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[197])).
% 0.21/0.47 tff(199,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[198, 196])).
% 0.21/0.47 tff(200,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_3, e_3)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(201,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_3, e_1))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.21/0.47 tff(202,plain,
% 0.21/0.47 (~product(e_2, e_3, e_3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[201, 154, 195, 38])).
% 0.21/0.47 tff(203,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(204,plain,
% 0.21/0.47 ((product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2))) <=> (product(e_2, e_3, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(205,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[204])).
% 0.21/0.47 tff(206,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[205, 203])).
% 0.21/0.47 tff(207,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(208,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.21/0.47 tff(209,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[208, 154, 202, 176, 136])).
% 0.21/0.47 % SZS output end Proof
%------------------------------------------------------------------------------