TSTP Solution File: GRP129-4.004 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP129-4.004 : 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 22:26:13 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : GRP129-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 15:25:19 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(product_type, type, (
% 0.19/0.42 product: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(e_3_type, type, (
% 0.19/0.42 e_3: $i)).
% 0.19/0.42 tff(e_1_type, type, (
% 0.19/0.42 e_1: $i)).
% 0.19/0.42 tff(e_2_type, type, (
% 0.19/0.42 e_2: $i)).
% 0.19/0.42 tff(e_4_type, type, (
% 0.19/0.42 e_4: $i)).
% 0.19/0.42 tff(equalish_type, type, (
% 0.19/0.42 equalish: ( $i * $i ) > $o)).
% 0.19/0.42 tff(group_element_type, type, (
% 0.19/0.42 group_element: $i > $o)).
% 0.19/0.42 tff(1,assumption,(~product(e_3, e_3, e_3)), introduced(assumption)).
% 0.19/0.42 tff(2,assumption,(~product(e_3, e_3, e_1)), introduced(assumption)).
% 0.19/0.42 tff(3,assumption,(product(e_3, e_3, e_4)), introduced(assumption)).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1)) <=> ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite((product(Y, X, Z1) | (~product(Z1, Y, Z2))) <=> ((~product(Z1, Y, Z2)) | product(Y, X, Z1))), (((product(Y, X, Z1) | (~product(Z1, Y, Z2))) | (~product(X, Z1, Z2))) <=> (((~product(Z1, Y, Z2)) | product(Y, X, Z1)) | (~product(X, Z1, Z2))))), rewrite((((~product(Z1, Y, Z2)) | product(Y, X, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))), (((product(Y, X, Z1) | (~product(Z1, Y, Z2))) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(Y, X, Z1) | (~product(Z1, Y, Z2))) | (~product(X, Z1, Z2))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.42 tff(9,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(Y, X, Z1) | (~product(Z1, Y, Z2))) | (~product(X, Z1, Z2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3_1')).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.19/0.42 tff(12,plain,(
% 0.19/0.42 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.19/0.42 inference(skolemize,[status(sab)],[11])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (((~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3)) <=> ((~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3))),
% 0.19/0.43 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (product(e_3, e_3, e_3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[19, 13, 3])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.43 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')).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.43 tff(29,plain,(
% 0.19/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[28])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(32,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 (~equalish(e_3, e_4)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_3, e_4) | (~product(e_3, e_3, e_4)) | (~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_4) | (~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_3, e_4) | (~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_3, e_4) | (~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[36, 33, 30, 3, 20])).
% 0.19/0.43 tff(38,plain,(~product(e_3, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (^[Y: $i, X: $i] : trans(monotonicity(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)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_4)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (![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)) | product(X, Y, e_4)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.43 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)) | product(X, Y, e_4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.43 tff(47,plain,(
% 0.19/0.43 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.43 inference(skolemize,[status(sab)],[46])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (group_element(e_3) <=> group_element(e_3)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(50,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (group_element(e_3)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_3, e_3, e_4) | (~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_3, e_3, e_4) | (~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 (((~group_element(e_3)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1)) <=> (product(e_3, e_3, e_4) | (~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | 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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_3, e_3, e_4) | (~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | 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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_3, e_3, e_4) | (~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3))),
% 0.19/0.43 inference(transitivity,[status(thm)],[54, 52])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_3, e_3, e_4) | (~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (product(e_3, e_3, e_1) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[57, 51, 48, 38])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (product(e_3, e_3, e_2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[58, 1, 2])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (((~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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, 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(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, 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(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[62, 60])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_2)) | product(e_3, e_3, e_3))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[65, 13, 59, 1])).
% 0.19/0.43 tff(67,plain,(product(e_3, e_3, e_3) | product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (product(e_3, e_3, e_1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[67, 1])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (((~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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, 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(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[70])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, 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(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[71, 69])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[74, 13, 68, 1])).
% 0.19/0.44 tff(76,plain,(product(e_3, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(77,assumption,(product(e_3, e_2, e_4)), introduced(assumption)).
% 0.19/0.44 tff(78,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.19/0.44 tff(79,assumption,(~product(e_2, e_2, e_2)), introduced(assumption)).
% 0.19/0.44 tff(80,assumption,(~product(e_2, e_2, e_4)), introduced(assumption)).
% 0.19/0.44 tff(81,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_1)) | product(e_2, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_2, e_1)) | product(e_2, e_2, e_2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 (((~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_1)) | product(e_2, e_2, e_2)) <=> ((~product(e_2, e_2, e_1)) | product(e_2, e_2, e_2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_1)) | product(e_2, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_1)) | product(e_2, e_2, e_2)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_1)) | product(e_2, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_2, e_1)) | product(e_2, e_2, e_2))),
% 0.19/0.44 inference(transitivity,[status(thm)],[84, 82])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_1)) | product(e_2, e_2, e_2))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_2, e_1)) | product(e_2, e_2, e_2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[87, 13, 81, 79])).
% 0.19/0.44 tff(89,plain,((~product(e_2, e_2, e_1)) | product(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 (~product(e_2, e_2, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[89, 79])).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 (group_element(e_2) <=> group_element(e_2)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(92,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.19/0.44 tff(93,plain,
% 0.19/0.44 (group_element(e_2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_2, e_2, e_1) | (~group_element(e_2)) | product(e_2, e_2, e_4) | product(e_2, e_2, e_2) | product(e_2, e_2, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_2, e_2, e_1) | (~group_element(e_2)) | product(e_2, e_2, e_4) | product(e_2, e_2, e_2) | product(e_2, e_2, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 (((~group_element(e_2)) | (~group_element(e_2)) | product(e_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)) <=> (product(e_2, e_2, e_1) | (~group_element(e_2)) | product(e_2, e_2, e_4) | product(e_2, e_2, e_2) | product(e_2, e_2, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_2)) | product(e_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_2, e_2, e_1) | (~group_element(e_2)) | product(e_2, e_2, e_4) | product(e_2, e_2, e_2) | product(e_2, e_2, e_3)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_2)) | product(e_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_2, e_2, e_1) | (~group_element(e_2)) | product(e_2, e_2, e_4) | product(e_2, e_2, e_2) | product(e_2, e_2, e_3))),
% 0.19/0.44 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.44 tff(98,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_2)) | product(e_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_2, e_2, e_1) | (~group_element(e_2)) | product(e_2, e_2, e_4) | product(e_2, e_2, e_2) | product(e_2, e_2, e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 (product(e_2, e_2, e_1) | product(e_2, e_2, e_4) | product(e_2, e_2, e_2) | product(e_2, e_2, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[99, 93, 48])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 (product(e_2, e_2, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[100, 90, 80, 79])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 (((~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2)) <=> ((~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2))),
% 0.19/0.44 inference(transitivity,[status(thm)],[104, 102])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[107, 13, 79, 101])).
% 0.19/0.44 tff(109,plain,(product(e_2, e_2, e_2) | product(e_2, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(110,plain,
% 0.19/0.44 (product(e_2, e_2, e_4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[109, 79])).
% 0.19/0.44 tff(111,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_2, e_2, e_2) | (~product(e_2, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_2, e_2, e_2) | (~product(e_2, e_2, e_4)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(112,plain,
% 0.19/0.44 (((~product(e_2, e_2, e_4)) | (~product(e_2, e_2, e_4)) | product(e_2, e_2, e_2)) <=> (product(e_2, e_2, e_2) | (~product(e_2, e_2, e_4)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(113,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_4)) | (~product(e_2, e_2, e_4)) | product(e_2, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_2, e_2, e_2) | (~product(e_2, e_2, e_4))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[112])).
% 0.19/0.44 tff(114,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_4)) | (~product(e_2, e_2, e_4)) | product(e_2, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_2, e_2, e_2) | (~product(e_2, e_2, e_4)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[113, 111])).
% 0.19/0.44 tff(115,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_4)) | (~product(e_2, e_2, e_4)) | product(e_2, e_2, e_2))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(116,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_2, e_2, e_2) | (~product(e_2, e_2, e_4))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.44 tff(117,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[116, 13, 110, 79])).
% 0.19/0.44 tff(118,plain,(product(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(119,plain,
% 0.19/0.44 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(120,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.19/0.44 tff(121,plain,
% 0.19/0.44 (~equalish(e_3, e_2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.44 tff(122,plain,
% 0.19/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, 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_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(123,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(124,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.44 tff(125,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[124, 121, 30, 118, 78])).
% 0.19/0.44 tff(126,plain,(~product(e_2, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(127,assumption,(product(e_3, e_3, e_3)), introduced(assumption)).
% 0.19/0.44 tff(128,assumption,(~product(e_4, e_3, e_4)), introduced(assumption)).
% 0.19/0.44 tff(129,assumption,(~product(e_2, e_2, e_3)), introduced(assumption)).
% 0.19/0.44 tff(130,plain,
% 0.19/0.44 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(131,plain,
% 0.19/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.44 tff(132,plain,
% 0.19/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(133,plain,
% 0.19/0.44 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)))), (((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) | (~product(Y, X, Z1))) <=> ((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) | (~product(Y, X, Z1))))), rewrite(((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) | (~product(Y, X, Z1))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))), (((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) | (~product(Y, X, Z1))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[133])).
% 0.19/0.44 tff(135,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) | (~product(Y, X, Z1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3_2')).
% 0.19/0.44 tff(136,plain,
% 0.19/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.44 tff(137,plain,
% 0.19/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.19/0.44 tff(138,plain,(
% 0.19/0.44 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[137])).
% 0.19/0.44 tff(139,plain,
% 0.19/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.19/0.44 tff(140,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(141,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(142,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.45 tff(143,plain,
% 0.19/0.45 (~product(e_2, e_3, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[142, 139, 38, 77])).
% 0.19/0.45 tff(144,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(145,plain,
% 0.19/0.45 ((product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))) <=> ((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_2, e_3))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[145])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_2, e_3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[146, 144])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(149,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_2, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 (~product(e_3, e_2, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[149, 139, 127, 143])).
% 0.19/0.45 tff(151,assumption,(~product(e_3, e_3, e_2)), introduced(assumption)).
% 0.19/0.45 tff(152,assumption,(product(e_2, e_3, e_4)), introduced(assumption)).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(154,plain,
% 0.19/0.45 (((~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)) | product(e_3, e_3, e_2)) <=> (product(e_3, e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(155,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)) | product(e_3, e_3, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[154])).
% 0.19/0.45 tff(156,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)) | product(e_3, e_3, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[155, 153])).
% 0.19/0.45 tff(157,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)) | product(e_3, e_3, e_2))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(158,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.19/0.45 tff(159,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[158, 13, 152, 77, 151])).
% 0.19/0.45 tff(160,plain,((~product(e_2, e_3, e_4)) | (~product(e_3, e_2, e_4)) | product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(161,plain,
% 0.19/0.45 (~product(e_2, e_3, e_4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[160, 151, 77])).
% 0.19/0.45 tff(162,plain,
% 0.19/0.45 (group_element(e_4) <=> group_element(e_4)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(163,axiom,(group_element(e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_4')).
% 0.19/0.45 tff(164,plain,
% 0.19/0.45 (group_element(e_4)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.45 tff(165,plain,
% 0.19/0.45 (^[Y: $i, X: $i] : refl((product(e_4, 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_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(166,plain,
% 0.19/0.45 (![Y: $i, X: $i] : (product(e_4, X, Y) | 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_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[165])).
% 0.19/0.45 tff(167,plain,
% 0.19/0.45 (![Y: $i, X: $i] : (product(e_4, X, Y) | 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_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(168,plain,
% 0.19/0.45 (^[Y: $i, X: $i] : trans(monotonicity(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))))), (((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) | product(e_4, 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_4, X, Y)))), rewrite(((product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_4, X, Y)) <=> (product(e_4, 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_4, X, Y)) <=> (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(169,plain,
% 0.19/0.45 (![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)) | product(e_4, X, Y)) <=> ![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[168])).
% 0.19/0.45 tff(170,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)) | product(e_4, X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','row_surjectivity')).
% 0.19/0.45 tff(171,plain,
% 0.19/0.45 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.19/0.45 tff(172,plain,
% 0.19/0.45 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.19/0.45 tff(173,plain,(
% 0.19/0.45 ![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[172])).
% 0.19/0.45 tff(174,plain,
% 0.19/0.45 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[173, 166])).
% 0.19/0.45 tff(175,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : (product(e_4, 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_1, e_3, e_4) | product(e_3, e_3, e_4) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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_1, e_3, e_4) | product(e_3, e_3, e_4) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | (~group_element(e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(176,plain,
% 0.19/0.45 ((product(e_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3))) <=> (product(e_1, e_3, e_4) | product(e_3, e_3, e_4) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | (~group_element(e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(177,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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_1, e_3, e_4) | product(e_3, e_3, e_4) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | (~group_element(e_3))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[176])).
% 0.19/0.45 tff(178,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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_1, e_3, e_4) | product(e_3, e_3, e_4) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | (~group_element(e_3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[177, 175])).
% 0.19/0.45 tff(179,plain,
% 0.19/0.45 ((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(180,plain,
% 0.19/0.45 ((~![Y: $i, X: $i] : (product(e_4, 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_1, e_3, e_4) | product(e_3, e_3, e_4) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | (~group_element(e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.19/0.45 tff(181,plain,
% 0.19/0.45 (product(e_1, e_3, e_4) | product(e_3, e_3, e_4) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[180, 174, 51, 164])).
% 0.19/0.45 tff(182,plain,
% 0.19/0.45 (product(e_1, e_3, e_4) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[181, 38])).
% 0.19/0.45 tff(183,plain,
% 0.19/0.45 (product(e_1, e_3, e_4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[182, 161, 128])).
% 0.19/0.45 tff(184,plain,
% 0.19/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1))) <=> ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(185,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[184])).
% 0.19/0.45 tff(186,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(187,plain,
% 0.19/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)))), rewrite((((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)) <=> ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(188,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[187])).
% 0.19/0.45 tff(189,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.19/0.45 tff(190,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.19/0.45 tff(191,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.19/0.45 tff(192,plain,(
% 0.19/0.45 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[191])).
% 0.19/0.45 tff(193,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.19/0.45 tff(194,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_4)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(195,plain,
% 0.19/0.45 (((~product(e_1, e_3, e_4)) | product(e_3, e_3, e_4) | (~product(e_3, e_1, e_3))) <=> (product(e_3, e_3, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_4)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(196,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_4)) | product(e_3, e_3, e_4) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_4))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[195])).
% 0.19/0.45 tff(197,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_4)) | product(e_3, e_3, e_4) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_4)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[196, 194])).
% 0.19/0.45 tff(198,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_4)) | product(e_3, e_3, e_4) | (~product(e_3, e_1, e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(199,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_4))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.19/0.45 tff(200,plain,
% 0.19/0.45 (~product(e_3, e_1, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[199, 193, 183, 38])).
% 0.19/0.45 tff(201,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.19/0.45 tff(202,plain,
% 0.19/0.45 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(203,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[202])).
% 0.19/0.45 tff(204,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(205,plain,
% 0.19/0.45 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, W, Y)) | (~product(X, Z, Y))) <=> ((~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)))), rewrite((((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(206,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[205])).
% 0.19/0.46 tff(207,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')).
% 0.19/0.46 tff(208,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.46 tff(209,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.19/0.46 tff(210,plain,(
% 0.19/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[209])).
% 0.19/0.46 tff(211,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.19/0.46 tff(212,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(213,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(214,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.19/0.46 tff(215,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[214, 121, 211, 118, 201])).
% 0.19/0.46 tff(216,plain,(~product(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(217,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(218,plain,
% 0.19/0.46 (((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1)) <=> (product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(219,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[218])).
% 0.19/0.46 tff(220,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2))),
% 0.19/0.46 inference(transitivity,[status(thm)],[219, 217])).
% 0.19/0.46 tff(221,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(222,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.19/0.46 tff(223,plain,
% 0.19/0.46 (product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[222, 93, 51, 48, 216])).
% 0.19/0.46 tff(224,plain,
% 0.19/0.46 (product(e_2, e_3, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[223, 161, 143])).
% 0.19/0.46 tff(225,assumption,(~product(e_3, e_1, e_3)), introduced(assumption)).
% 0.19/0.46 tff(226,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.19/0.46 tff(227,assumption,(product(e_2, e_3, e_1)), introduced(assumption)).
% 0.19/0.46 tff(228,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(229,plain,
% 0.19/0.46 ((product(e_3, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_3, e_1))) <=> (product(e_3, e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(230,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_2, e_3))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[229])).
% 0.19/0.46 tff(231,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[230, 228])).
% 0.19/0.46 tff(232,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(233,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_2, e_3))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.19/0.46 tff(234,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[233, 139, 227, 226, 225])).
% 0.19/0.46 tff(235,plain,((~product(e_1, e_2, e_3)) | (~product(e_2, e_3, e_1)) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(236,plain,
% 0.19/0.46 (~product(e_1, e_2, e_3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[235, 224, 200])).
% 0.19/0.46 tff(237,assumption,(~product(e_3, e_2, e_3)), introduced(assumption)).
% 0.19/0.46 tff(238,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : (product(e_4, 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(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_3, e_2, e_3) | product(e_4, e_2, e_3) | product(e_1, e_2, e_3))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_3, e_2, e_3) | product(e_4, e_2, e_3) | product(e_1, e_2, e_3))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(239,plain,
% 0.19/0.46 ((product(e_4, e_2, e_3) | product(e_3, e_2, e_3) | product(e_2, e_2, e_3) | product(e_1, e_2, e_3) | (~group_element(e_3)) | (~group_element(e_2))) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_3, e_2, e_3) | product(e_4, e_2, e_3) | product(e_1, e_2, e_3))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(240,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : (product(e_4, 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_4, e_2, e_3) | product(e_3, e_2, e_3) | product(e_2, e_2, e_3) | product(e_1, e_2, e_3) | (~group_element(e_3)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_3, e_2, e_3) | product(e_4, e_2, e_3) | product(e_1, e_2, e_3)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[239])).
% 0.19/0.46 tff(241,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : (product(e_4, 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_4, e_2, e_3) | product(e_3, e_2, e_3) | product(e_2, e_2, e_3) | product(e_1, e_2, e_3) | (~group_element(e_3)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_3, e_2, e_3) | product(e_4, e_2, e_3) | product(e_1, e_2, e_3))),
% 0.19/0.46 inference(transitivity,[status(thm)],[240, 238])).
% 0.19/0.46 tff(242,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : (product(e_4, 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_4, e_2, e_3) | product(e_3, e_2, e_3) | product(e_2, e_2, e_3) | product(e_1, e_2, e_3) | (~group_element(e_3)) | (~group_element(e_2)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(243,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : (product(e_4, 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(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_3, e_2, e_3) | product(e_4, e_2, e_3) | product(e_1, e_2, e_3)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.19/0.46 tff(244,plain,
% 0.19/0.46 (product(e_4, e_2, e_3) | product(e_1, e_2, e_3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[243, 174, 93, 51, 129, 237])).
% 0.19/0.46 tff(245,plain,
% 0.19/0.46 (product(e_4, e_2, e_3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[244, 236])).
% 0.19/0.46 tff(246,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(247,plain,
% 0.19/0.46 (((~product(e_4, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_4, e_2))) <=> (product(e_2, e_2, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(248,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_2))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[247])).
% 0.19/0.46 tff(249,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_2)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[248, 246])).
% 0.19/0.46 tff(250,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_4, e_2)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(251,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_2))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.19/0.46 tff(252,plain,
% 0.19/0.46 (~product(e_2, e_4, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[251, 193, 129, 245])).
% 0.19/0.46 tff(253,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(254,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(255,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.19/0.46 tff(256,plain,
% 0.19/0.46 (~product(e_2, e_4, e_3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[255, 139, 128, 77])).
% 0.19/0.46 tff(257,plain,
% 0.19/0.46 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(258,plain,
% 0.19/0.46 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[257])).
% 0.19/0.46 tff(259,plain,
% 0.19/0.46 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(260,plain,
% 0.19/0.46 (^[Y: $i, X: $i] : trans(monotonicity(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)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) | product(X, e_4, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_4, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_4, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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)) | product(X, e_4, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(261,plain,
% 0.19/0.46 (![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)) | product(X, e_4, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[260])).
% 0.19/0.46 tff(262,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)) | product(X, e_4, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','column_surjectivity')).
% 0.19/0.46 tff(263,plain,
% 0.19/0.46 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.19/0.46 tff(264,plain,
% 0.19/0.46 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.19/0.46 tff(265,plain,(
% 0.19/0.46 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.46 inference(skolemize,[status(sab)],[264])).
% 0.19/0.46 tff(266,plain,
% 0.19/0.46 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.19/0.46 tff(267,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_1, e_3))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(268,plain,
% 0.19/0.47 (((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_1, e_3)) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_1, e_3))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(269,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_1, e_3)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[268])).
% 0.19/0.47 tff(270,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_1, e_3))),
% 0.19/0.47 inference(transitivity,[status(thm)],[269, 267])).
% 0.19/0.47 tff(271,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_1, e_3))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(272,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_1, e_3)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.19/0.47 tff(273,plain,
% 0.19/0.47 (product(e_2, e_1, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[272, 266, 93, 51, 129, 143, 256])).
% 0.19/0.47 tff(274,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(275,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(276,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.19/0.47 tff(277,plain,
% 0.19/0.47 (~product(e_1, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[276, 139, 237, 273])).
% 0.19/0.47 tff(278,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : (product(e_4, 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(e_3)) | (~group_element(e_2)) | product(e_3, e_3, e_2) | product(e_4, e_3, e_2) | product(e_1, e_3, e_2) | product(e_2, e_3, e_2))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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(e_3)) | (~group_element(e_2)) | product(e_3, e_3, e_2) | product(e_4, e_3, e_2) | product(e_1, e_3, e_2) | product(e_2, e_3, e_2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(279,plain,
% 0.19/0.47 ((product(e_4, e_3, e_2) | product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_3, e_2) | product(e_4, e_3, e_2) | product(e_1, e_3, e_2) | product(e_2, e_3, e_2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(280,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_2) | product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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(e_3)) | (~group_element(e_2)) | product(e_3, e_3, e_2) | product(e_4, e_3, e_2) | product(e_1, e_3, e_2) | product(e_2, e_3, e_2)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[279])).
% 0.19/0.47 tff(281,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_2) | product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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(e_3)) | (~group_element(e_2)) | product(e_3, e_3, e_2) | product(e_4, e_3, e_2) | product(e_1, e_3, e_2) | product(e_2, e_3, e_2))),
% 0.19/0.47 inference(transitivity,[status(thm)],[280, 278])).
% 0.19/0.47 tff(282,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_2) | product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(283,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : (product(e_4, 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(e_3)) | (~group_element(e_2)) | product(e_3, e_3, e_2) | product(e_4, e_3, e_2) | product(e_1, e_3, e_2) | product(e_2, e_3, e_2)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.19/0.47 tff(284,plain,
% 0.19/0.47 (product(e_3, e_3, e_2) | product(e_4, e_3, e_2) | product(e_1, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[283, 174, 93, 51, 216])).
% 0.19/0.47 tff(285,plain,
% 0.19/0.47 (product(e_4, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[284, 151, 277])).
% 0.19/0.47 tff(286,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_4)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_4)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(287,plain,
% 0.19/0.47 ((product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_2, e_4))) <=> ((~product(e_3, e_2, e_4)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(288,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_4)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[287])).
% 0.19/0.47 tff(289,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_4)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[288, 286])).
% 0.19/0.47 tff(290,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_2, e_4)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(291,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_4)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.19/0.47 tff(292,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[291, 139, 77, 285, 252])).
% 0.19/0.47 tff(293,plain,(product(e_3, e_3, e_2) | (~product(e_3, e_2, e_4)) | product(e_2, e_2, e_3) | product(e_3, e_2, e_3) | product(e_4, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(294,plain,
% 0.19/0.47 (product(e_3, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[293, 150, 129, 77, 128])).
% 0.19/0.47 tff(295,plain,
% 0.19/0.47 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(296,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.19/0.47 tff(297,plain,
% 0.19/0.47 (~equalish(e_2, e_3)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.19/0.47 tff(298,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(299,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(300,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.19/0.47 tff(301,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[300, 297, 30, 294, 127])).
% 0.19/0.47 tff(302,plain,((~product(e_3, e_3, e_3)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_4)) | product(e_4, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(303,plain,
% 0.19/0.47 (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_4)) | product(e_4, e_3, e_4)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[302, 76])).
% 0.19/0.47 tff(304,plain,
% 0.19/0.47 ((~product(e_3, e_2, e_4)) | product(e_4, e_3, e_4)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[303, 126])).
% 0.19/0.47 tff(305,plain,
% 0.19/0.47 (product(e_4, e_3, e_4)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[304, 77])).
% 0.19/0.47 tff(306,assumption,(product(e_4, e_3, e_3)), introduced(assumption)).
% 0.19/0.47 tff(307,assumption,(product(e_4, e_3, e_4)), introduced(assumption)).
% 0.19/0.47 tff(308,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, 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_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(309,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(310,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.19/0.48 tff(311,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[310, 33, 30, 307, 306])).
% 0.19/0.48 tff(312,plain,((~product(e_4, e_3, e_3)) | (~product(e_4, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(313,plain,
% 0.19/0.48 (~product(e_4, e_3, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[312, 305])).
% 0.19/0.48 tff(314,assumption,(~product(e_4, e_3, e_3)), introduced(assumption)).
% 0.19/0.48 tff(315,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.19/0.48 tff(316,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_4)) | product(e_4, e_3, e_3) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_4)) | product(e_4, e_3, e_3) | (~product(e_2, e_4, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(317,plain,
% 0.19/0.48 (((~product(e_2, e_4, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_2, e_4))) <=> ((~product(e_3, e_2, e_4)) | product(e_4, e_3, e_3) | (~product(e_2, e_4, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(318,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_4)) | product(e_4, e_3, e_3) | (~product(e_2, e_4, e_3))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[317])).
% 0.19/0.48 tff(319,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_4)) | product(e_4, e_3, e_3) | (~product(e_2, e_4, e_3)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[318, 316])).
% 0.19/0.48 tff(320,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_2, e_4)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(321,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_4)) | product(e_4, e_3, e_3) | (~product(e_2, e_4, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.19/0.48 tff(322,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[321, 193, 77, 315, 314])).
% 0.19/0.48 tff(323,plain,(product(e_4, e_3, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(324,plain,
% 0.19/0.48 (~product(e_2, e_4, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[323, 313, 77])).
% 0.19/0.48 tff(325,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_4, e_3, e_4)) | product(e_2, e_4, e_3) | (~product(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_4, e_3, e_4)) | product(e_2, e_4, e_3) | (~product(e_3, e_2, e_4)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(326,plain,
% 0.19/0.48 (((~product(e_4, e_3, e_4)) | (~product(e_3, e_2, e_4)) | product(e_2, e_4, e_3)) <=> ((~product(e_4, e_3, e_4)) | product(e_2, e_4, e_3) | (~product(e_3, e_2, e_4)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(327,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_4, e_3, e_4)) | (~product(e_3, e_2, e_4)) | product(e_2, e_4, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_4, e_3, e_4)) | product(e_2, e_4, e_3) | (~product(e_3, e_2, e_4))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[326])).
% 0.19/0.48 tff(328,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_4, e_3, e_4)) | (~product(e_3, e_2, e_4)) | product(e_2, e_4, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_4, e_3, e_4)) | product(e_2, e_4, e_3) | (~product(e_3, e_2, e_4)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[327, 325])).
% 0.19/0.48 tff(329,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_4, e_3, e_4)) | (~product(e_3, e_2, e_4)) | product(e_2, e_4, e_3))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(330,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_4, e_3, e_4)) | product(e_2, e_4, e_3) | (~product(e_3, e_2, e_4))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.19/0.48 tff(331,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[330, 13, 305, 77, 324])).
% 0.19/0.48 tff(332,plain,(~product(e_3, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(333,assumption,(product(e_2, e_3, e_3)), introduced(assumption)).
% 0.19/0.48 tff(334,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(335,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[334])).
% 0.19/0.48 tff(336,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(337,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(338,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[337])).
% 0.19/0.48 tff(339,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')).
% 0.19/0.48 tff(340,plain,
% 0.19/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.19/0.48 tff(341,plain,
% 0.19/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[340, 336])).
% 0.19/0.48 tff(342,plain,(
% 0.19/0.48 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[341])).
% 0.19/0.48 tff(343,plain,
% 0.19/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[342, 335])).
% 0.19/0.48 tff(344,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(345,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(346,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.19/0.48 tff(347,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[346, 297, 343, 76, 333])).
% 0.19/0.48 tff(348,plain,(~product(e_2, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(349,plain,
% 0.19/0.48 (~product(e_3, e_2, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[149, 139, 76, 348])).
% 0.19/0.48 tff(350,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(351,plain,
% 0.19/0.48 (((~product(e_2, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2))) <=> ((~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(352,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[351])).
% 0.19/0.48 tff(353,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2))),
% 0.19/0.48 inference(transitivity,[status(thm)],[352, 350])).
% 0.19/0.48 tff(354,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(355,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.19/0.48 tff(356,plain,
% 0.19/0.48 (~product(e_3, e_2, e_2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[355, 193, 118, 216])).
% 0.19/0.48 tff(357,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(358,plain,
% 0.19/0.48 (((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(359,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[358])).
% 0.19/0.48 tff(360,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))),
% 0.19/0.48 inference(transitivity,[status(thm)],[359, 357])).
% 0.19/0.48 tff(361,plain,
% 0.19/0.48 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(362,plain,
% 0.19/0.48 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.19/0.48 tff(363,plain,
% 0.19/0.48 (product(e_3, e_2, e_4) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[362, 93, 51, 48, 356])).
% 0.19/0.48 tff(364,plain,
% 0.19/0.48 (product(e_3, e_2, e_4) | product(e_3, e_2, e_1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[363, 349])).
% 0.19/0.48 tff(365,plain,
% 0.19/0.48 (product(e_3, e_2, e_1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[364, 332])).
% 0.19/0.48 tff(366,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.19/0.48 tff(367,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(368,plain,
% 0.19/0.48 (((~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(369,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[368])).
% 0.19/0.49 tff(370,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[369, 367])).
% 0.19/0.49 tff(371,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(372,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.19/0.49 tff(373,plain,
% 0.19/0.49 (~product(e_2, e_1, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[372, 193, 129, 226])).
% 0.19/0.49 tff(374,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(375,plain,
% 0.19/0.49 (((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2))) <=> (product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(376,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[375])).
% 0.19/0.49 tff(377,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[376, 374])).
% 0.19/0.49 tff(378,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(379,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_1, e_2))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.19/0.49 tff(380,plain,
% 0.19/0.49 (~product(e_3, e_1, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[379, 193, 348, 226])).
% 0.19/0.49 tff(381,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_3, e_2) | product(e_3, e_4, e_2) | product(e_3, e_1, e_2) | product(e_3, e_2, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_3, e_2) | product(e_3, e_4, e_2) | product(e_3, e_1, e_2) | product(e_3, e_2, e_2))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(382,plain,
% 0.19/0.49 (((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2)) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_3, e_2) | product(e_3, e_4, e_2) | product(e_3, e_1, e_2) | product(e_3, e_2, e_2))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(383,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_3, e_2) | product(e_3, e_4, e_2) | product(e_3, e_1, e_2) | product(e_3, e_2, e_2)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[382])).
% 0.19/0.49 tff(384,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_3, e_2) | product(e_3, e_4, e_2) | product(e_3, e_1, e_2) | product(e_3, e_2, e_2))),
% 0.19/0.49 inference(transitivity,[status(thm)],[383, 381])).
% 0.19/0.49 tff(385,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(386,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_3, e_2) | product(e_3, e_4, e_2) | product(e_3, e_1, e_2) | product(e_3, e_2, e_2)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.19/0.49 tff(387,plain,
% 0.19/0.49 (product(e_3, e_3, e_2) | product(e_3, e_4, e_2) | product(e_3, e_1, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[386, 266, 93, 51, 356])).
% 0.19/0.49 tff(388,plain,
% 0.19/0.49 (product(e_3, e_4, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[387, 380, 151])).
% 0.19/0.49 tff(389,assumption,(product(e_3, e_4, e_2)), introduced(assumption)).
% 0.19/0.49 tff(390,assumption,(product(e_4, e_3, e_2)), introduced(assumption)).
% 0.19/0.49 tff(391,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_2)) | product(e_3, e_3, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_2)) | product(e_3, e_3, e_4))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(392,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_2)) | product(e_3, e_3, e_4))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(393,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_2)) | product(e_3, e_3, e_4)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.19/0.49 tff(394,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[393, 13, 38, 390, 389])).
% 0.19/0.49 tff(395,plain,((~product(e_4, e_3, e_2)) | (~product(e_3, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(396,plain,
% 0.19/0.49 (~product(e_4, e_3, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[395, 388])).
% 0.19/0.49 tff(397,plain,
% 0.19/0.49 (product(e_1, e_3, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[284, 396, 151])).
% 0.19/0.49 tff(398,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_2, e_1, e_2) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_2, e_1, e_2) | (~product(e_3, e_2, e_1)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(399,plain,
% 0.19/0.49 ((product(e_2, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_1))) <=> ((~product(e_1, e_3, e_2)) | product(e_2, e_1, e_2) | (~product(e_3, e_2, e_1)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(400,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_2, e_1, e_2) | (~product(e_3, e_2, e_1))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[399])).
% 0.19/0.49 tff(401,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_2, e_1, e_2) | (~product(e_3, e_2, e_1)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[400, 398])).
% 0.19/0.49 tff(402,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_1)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(403,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_2, e_1, e_2) | (~product(e_3, e_2, e_1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.19/0.49 tff(404,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[403, 139, 397, 366, 373])).
% 0.19/0.49 tff(405,plain,((~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_1)) | product(e_3, e_3, e_2) | product(e_2, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(406,plain,
% 0.19/0.49 (~product(e_1, e_2, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[405, 129, 151, 366])).
% 0.19/0.49 tff(407,plain,
% 0.19/0.49 (product(e_2, e_2, e_3) | product(e_4, e_2, e_3) | product(e_1, e_2, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[243, 174, 93, 51, 349])).
% 0.19/0.49 tff(408,plain,
% 0.19/0.49 (product(e_4, e_2, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[407, 406, 129])).
% 0.19/0.49 tff(409,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_4, e_2)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(410,plain,
% 0.19/0.49 (((~product(e_4, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2))) <=> (product(e_2, e_3, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_4, e_2)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(411,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_4, e_2))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[410])).
% 0.19/0.49 tff(412,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_4, e_2)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[411, 409])).
% 0.19/0.49 tff(413,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(414,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_4, e_2))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.19/0.49 tff(415,plain,
% 0.19/0.49 (~product(e_3, e_4, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[414, 193, 348, 408])).
% 0.19/0.49 tff(416,plain,
% 0.19/0.49 (product(e_3, e_1, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[387, 415, 151])).
% 0.19/0.49 tff(417,assumption,(product(e_3, e_3, e_1)), introduced(assumption)).
% 0.19/0.49 tff(418,plain,
% 0.19/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, 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_2) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(419,plain,
% 0.19/0.49 ((equalish(e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_3, e_1))) <=> (equalish(e_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(420,plain,
% 0.19/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, 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_2) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_1))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[419])).
% 0.19/0.49 tff(421,plain,
% 0.19/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, 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_2) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[420, 418])).
% 0.19/0.49 tff(422,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(423,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.19/0.49 tff(424,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[423, 121, 211, 417, 366])).
% 0.19/0.49 tff(425,plain,((~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(426,plain,
% 0.19/0.49 (~product(e_3, e_3, e_1)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[425, 366])).
% 0.19/0.49 tff(427,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.19/0.49 tff(428,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.19/0.49 tff(429,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(430,plain,
% 0.19/0.50 (((~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_2)) | product(e_3, e_3, e_1)) <=> (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(431,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_2)) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[430])).
% 0.19/0.50 tff(432,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_2)) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[431, 429])).
% 0.19/0.50 tff(433,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_2)) | product(e_3, e_3, e_1))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(434,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.19/0.50 tff(435,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[434, 13, 2, 428, 427])).
% 0.19/0.50 tff(436,plain,((~product(e_1, e_3, e_2)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(437,plain,
% 0.19/0.50 (~product(e_1, e_3, e_2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[436, 416, 426])).
% 0.19/0.50 tff(438,plain,
% 0.19/0.50 (product(e_4, e_3, e_2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[284, 437, 151])).
% 0.19/0.50 tff(439,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_1, e_4, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_1, e_4, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(440,plain,
% 0.19/0.50 (((~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_1, e_4, e_3)) <=> (product(e_1, e_4, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(441,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_1, e_4, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_1, e_4, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_2))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[440])).
% 0.19/0.50 tff(442,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_1, e_4, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_1, e_4, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[441, 439])).
% 0.19/0.50 tff(443,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_1, e_4, e_3))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(444,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_1, e_4, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_2))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.19/0.50 tff(445,plain,
% 0.19/0.50 (product(e_1, e_4, e_3)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[444, 13, 438, 416])).
% 0.19/0.50 tff(446,assumption,(product(e_4, e_2, e_1)), introduced(assumption)).
% 0.19/0.50 tff(447,plain,
% 0.19/0.50 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(448,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.19/0.50 tff(449,plain,
% 0.19/0.50 (~equalish(e_4, e_3)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.19/0.50 tff(450,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(451,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(452,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.19/0.50 tff(453,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[452, 449, 343, 366, 446])).
% 0.19/0.50 tff(454,plain,((~product(e_4, e_2, e_1)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(455,plain,
% 0.19/0.50 (~product(e_4, e_2, e_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[454, 366])).
% 0.19/0.50 tff(456,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_2) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_3, e_2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(457,plain,
% 0.19/0.50 (((~product(e_4, e_3, e_2)) | product(e_3, e_2, e_2) | (~product(e_2, e_4, e_3))) <=> (product(e_3, e_2, e_2) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_3, e_2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(458,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_2)) | product(e_3, e_2, e_2) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_3, e_2))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[457])).
% 0.19/0.50 tff(459,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_2)) | product(e_3, e_2, e_2) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_2) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_3, e_2)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[458, 456])).
% 0.19/0.50 tff(460,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_2)) | product(e_3, e_2, e_2) | (~product(e_2, e_4, e_3)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(461,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_2) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_3, e_2))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.19/0.50 tff(462,plain,
% 0.19/0.50 (~product(e_2, e_4, e_3)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[461, 193, 356, 438])).
% 0.19/0.50 tff(463,plain,
% 0.19/0.50 (product(e_2, e_2, e_3) | product(e_2, e_4, e_3) | product(e_2, e_1, e_3)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[272, 266, 93, 51, 348])).
% 0.19/0.50 tff(464,plain,
% 0.19/0.50 (product(e_2, e_1, e_3)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[463, 462, 129])).
% 0.19/0.50 tff(465,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_4, e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_4, e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(466,plain,
% 0.19/0.50 (((~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_3)) | product(e_4, e_2, e_1)) <=> (product(e_4, e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(467,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_3)) | product(e_4, e_2, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_4, e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_3))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[466])).
% 0.19/0.50 tff(468,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_3)) | product(e_4, e_2, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_4, e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[467, 465])).
% 0.19/0.50 tff(469,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_3)) | product(e_4, e_2, e_1))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(470,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_4, e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_3))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.19/0.50 tff(471,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[470, 13, 464, 455, 445])).
% 0.19/0.50 tff(472,plain,(product(e_2, e_2, e_3) | product(e_3, e_3, e_2) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(473,plain,
% 0.19/0.50 (product(e_3, e_3, e_2) | (~product(e_3, e_2, e_1))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[472, 126])).
% 0.19/0.50 tff(474,plain,
% 0.19/0.50 (product(e_3, e_3, e_2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[473, 365])).
% 0.19/0.50 tff(475,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[300, 297, 30, 474, 76])).
% 0.19/0.50 % SZS output end Proof
%------------------------------------------------------------------------------