TSTP Solution File: GRP128-1.003 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP128-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 22:26:09 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP128-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 14:57:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(product_type, type, (
% 0.20/0.47 product: ( $i * $i * $i ) > $o)).
% 0.20/0.47 tff(e_1_type, type, (
% 0.20/0.47 e_1: $i)).
% 0.20/0.47 tff(e_2_type, type, (
% 0.20/0.47 e_2: $i)).
% 0.20/0.47 tff(e_3_type, type, (
% 0.20/0.47 e_3: $i)).
% 0.20/0.47 tff(equalish_type, type, (
% 0.20/0.47 equalish: ( $i * $i ) > $o)).
% 0.20/0.47 tff(group_element_type, type, (
% 0.20/0.47 group_element: $i > $o)).
% 0.20/0.47 tff(1,assumption,(~product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.47 tff(2,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.20/0.47 tff(3,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.20/0.47 tff(4,plain,
% 0.20/0.47 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.47 tff(6,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(7,plain,
% 0.20/0.47 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(8,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.47 tff(9,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.20/0.47 tff(10,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.47 tff(11,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.47 tff(12,plain,(
% 0.20/0.47 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[11])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.47 tff(14,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(15,plain,
% 0.20/0.47 ((product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1))) <=> (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(16,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[15])).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.47 tff(18,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(19,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[19, 13, 2, 3])).
% 0.20/0.47 tff(21,plain,((~product(e_1, e_2, e_1)) | product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 (product(e_1, e_1, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[21, 2])).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.47 tff(28,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.47 tff(31,plain,(
% 0.20/0.47 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[30])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(34,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (~equalish(e_2, e_1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, 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_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[38, 35, 32, 2, 22])).
% 0.20/0.48 tff(40,plain,(~product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (^[Y: $i, X: $i] : refl((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.48 tff(46,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.20/0.48 tff(49,plain,(
% 0.20/0.48 ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[48])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(52,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (group_element(e_2)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(55,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (group_element(e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 ((product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1))) <=> (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[58])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[59, 57])).
% 0.20/0.48 tff(61,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[62, 56, 53, 50])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[63, 40])).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 (product(e_1, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[64, 1])).
% 0.20/0.48 tff(66,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.48 tff(67,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[70, 13, 67, 66, 40])).
% 0.20/0.48 tff(72,plain,((~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 (~product(e_2, e_2, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[72, 65])).
% 0.20/0.48 tff(74,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 (^[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))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(76,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.48 tff(77,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(78,plain,
% 0.20/0.48 (^[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)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(79,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.48 tff(80,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.20/0.48 tff(81,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.48 tff(82,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.20/0.48 tff(83,plain,(
% 0.20/0.48 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[82])).
% 0.20/0.48 tff(84,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.20/0.48 tff(85,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[87, 35, 84, 74, 66])).
% 0.20/0.49 tff(89,plain,((~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 (~product(e_2, e_2, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[89, 65])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | 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] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(92,plain,
% 0.20/0.49 ((product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.49 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[96, 53, 50])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 (product(e_2, e_2, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[97, 90, 73])).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 ((product(e_1, e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2))) <=> (product(e_1, e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[100])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[101, 99])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[104, 13, 98, 1, 65])).
% 0.20/0.49 tff(106,plain,(product(e_1, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(107,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.49 tff(108,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, 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_1) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 ((equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3))) <=> (equalish(e_2, e_1) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, 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_1) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[110])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, 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_1) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[111, 109])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.50 tff(115,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[114, 35, 84, 108, 107])).
% 0.20/0.50 tff(116,plain,((~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(117,plain,
% 0.20/0.50 (~product(e_2, e_2, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[116, 106])).
% 0.20/0.50 tff(118,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.20/0.50 tff(119,plain,
% 0.20/0.50 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(120,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.50 tff(121,plain,
% 0.20/0.50 (~equalish(e_3, e_2)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.50 tff(122,plain,
% 0.20/0.50 (((~![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_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(123,plain,
% 0.20/0.50 ((~![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_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(124,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.50 tff(125,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[124, 121, 32, 107, 118])).
% 0.20/0.50 tff(126,plain,((~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(127,plain,
% 0.20/0.50 (~product(e_1, e_3, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[126, 107])).
% 0.20/0.50 tff(128,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.20/0.50 tff(129,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_1, e_2, 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(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(130,plain,
% 0.20/0.50 ((product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3))) <=> (product(e_1, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(131,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[130])).
% 0.20/0.50 tff(132,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[131, 129])).
% 0.20/0.50 tff(133,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(134,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.50 tff(135,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[134, 13, 128, 107, 127])).
% 0.20/0.50 tff(136,plain,((~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(137,plain,
% 0.20/0.50 (~product(e_3, e_2, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[136, 106])).
% 0.20/0.50 tff(138,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.50 tff(139,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(140,plain,
% 0.20/0.50 ((product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_1))) <=> (product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(141,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[140])).
% 0.20/0.50 tff(142,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[141, 139])).
% 0.20/0.50 tff(143,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(144,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.50 tff(145,plain,
% 0.20/0.50 (product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[144, 13])).
% 0.20/0.50 tff(146,plain,
% 0.20/0.50 (product(e_1, e_1, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[145, 138])).
% 0.20/0.50 tff(147,plain,
% 0.20/0.50 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(148,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.50 tff(149,plain,
% 0.20/0.50 (~equalish(e_3, e_1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.50 tff(150,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(151,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(152,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.50 tff(153,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[152, 149, 32, 146, 138])).
% 0.20/0.50 tff(154,plain,(~product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(155,assumption,(~product(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.51 tff(156,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.20/0.51 tff(157,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_3, e_2, 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(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(158,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(159,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.51 tff(160,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[159, 13, 156, 107, 155])).
% 0.20/0.51 tff(161,plain,(product(e_1, e_3, e_1) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(162,plain,
% 0.20/0.51 ((~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[161, 154])).
% 0.20/0.51 tff(163,plain,
% 0.20/0.51 (~product(e_3, e_2, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[162, 106])).
% 0.20/0.51 tff(164,plain,
% 0.20/0.51 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(165,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.20/0.51 tff(166,plain,
% 0.20/0.51 (group_element(e_3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.51 tff(167,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(168,plain,
% 0.20/0.51 ((product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(169,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[168])).
% 0.20/0.51 tff(170,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))),
% 0.20/0.51 inference(transitivity,[status(thm)],[169, 167])).
% 0.20/0.51 tff(171,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(172,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.51 tff(173,plain,
% 0.20/0.51 (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[172, 53, 166, 50])).
% 0.20/0.51 tff(174,plain,
% 0.20/0.51 (product(e_3, e_2, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[173, 163, 137])).
% 0.20/0.51 tff(175,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.20/0.51 tff(176,plain,
% 0.20/0.51 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(177,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.51 tff(178,plain,
% 0.20/0.51 (~equalish(e_2, e_3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.51 tff(179,plain,
% 0.20/0.51 (((~![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_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![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_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(180,plain,
% 0.20/0.51 ((~![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_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(181,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.20/0.51 tff(182,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[181, 178, 84, 175, 74])).
% 0.20/0.51 tff(183,plain,((~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(184,plain,
% 0.20/0.51 (~product(e_2, e_2, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[183, 174])).
% 0.20/0.51 tff(185,plain,
% 0.20/0.51 (product(e_2, e_2, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[97, 184, 117])).
% 0.20/0.51 tff(186,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(187,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(188,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.20/0.51 tff(189,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[188, 13, 174, 163, 185])).
% 0.20/0.51 % SZS output end Proof
%------------------------------------------------------------------------------