TSTP Solution File: GRP133-1.003 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP133-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 22:26:17 EDT 2022
% Result : Unsatisfiable 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP133-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 15:22:21 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(product_type, type, (
% 0.21/0.43 product: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(e_1_type, type, (
% 0.21/0.43 e_1: $i)).
% 0.21/0.43 tff(e_2_type, type, (
% 0.21/0.43 e_2: $i)).
% 0.21/0.43 tff(e_3_type, type, (
% 0.21/0.43 e_3: $i)).
% 0.21/0.43 tff(equalish_type, type, (
% 0.21/0.43 equalish: ( $i * $i ) > $o)).
% 0.21/0.43 tff(group_element_type, type, (
% 0.21/0.43 group_element: $i > $o)).
% 0.21/0.43 tff(1,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.21/0.43 tff(2,assumption,(~product(e_2, e_2, e_3)), introduced(assumption)).
% 0.21/0.43 tff(3,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.21/0.43 tff(4,plain,
% 0.21/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[7])).
% 0.21/0.43 tff(9,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.21/0.43 tff(12,plain,(
% 0.21/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[11])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(15,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (~equalish(e_2, e_3)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (((~![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_2, e_2, e_1)) | (~product(e_3, 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_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 ((equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1))) <=> (equalish(e_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (((~![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_1)) | (~product(e_2, 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_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[18])).
% 0.21/0.44 tff(20,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, 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_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[19, 17])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[22, 16, 13, 1, 3])).
% 0.21/0.44 tff(24,plain,((~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 (~product(e_2, e_2, e_1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[24, 1])).
% 0.21/0.44 tff(26,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.44 tff(31,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.21/0.44 tff(34,plain,(
% 0.21/0.44 ![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)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[33])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (group_element(e_2) <=> group_element(e_2)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(37,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (group_element(e_2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (((~![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))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 ((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))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 (((~![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)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[40])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (((~![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))),
% 0.21/0.44 inference(transitivity,[status(thm)],[41, 39])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 ((~![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)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 ((~![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)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[44, 38, 35])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (product(e_2, e_2, e_2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[45, 25, 2])).
% 0.21/0.44 tff(47,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.21/0.44 tff(48,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, W, Y)) | (~product(X, Z, Y))) <=> ((~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)))), rewrite((((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.44 tff(54,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.21/0.44 tff(57,plain,(
% 0.21/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[56])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(60,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 (~equalish(e_3, e_2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (((~![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 ((~![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)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[64, 61, 58, 48, 47])).
% 0.21/0.44 tff(66,plain,((~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (~product(e_2, e_3, e_2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[66, 46])).
% 0.21/0.44 tff(68,assumption,(product(e_2, e_3, e_3)), introduced(assumption)).
% 0.21/0.44 tff(69,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(71,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 (~equalish(e_1, e_2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.44 tff(73,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_3, e_3))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[75, 72, 13, 68, 69])).
% 0.21/0.45 tff(77,plain,((~product(e_1, e_3, e_3)) | (~product(e_2, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 (~product(e_1, e_3, e_3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[77, 68])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[79])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[82])).
% 0.21/0.45 tff(84,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.21/0.45 tff(87,plain,(
% 0.21/0.45 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[86])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_3)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 (((~product(e_2, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1))) <=> (product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_3)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_3))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_3)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[91, 89])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_3))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[94, 88, 1, 68, 78])).
% 0.21/0.45 tff(96,plain,((~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 (~product(e_2, e_3, e_3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[96, 1])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 (group_element(e_3) <=> group_element(e_3)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(99,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (group_element(e_3)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.45 tff(101,plain,
% 0.21/0.45 (((~![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_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_2))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(102,plain,
% 0.21/0.45 ((product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2))) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_2))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(103,plain,
% 0.21/0.45 (((~![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_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~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_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_2)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[102])).
% 0.21/0.45 tff(104,plain,
% 0.21/0.45 (((~![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_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~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_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_2))),
% 0.21/0.45 inference(transitivity,[status(thm)],[103, 101])).
% 0.21/0.45 tff(105,plain,
% 0.21/0.45 ((~![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_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(106,plain,
% 0.21/0.45 ((~![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_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_2)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.45 tff(107,plain,
% 0.21/0.45 (product(e_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_2)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[106, 38, 100, 35])).
% 0.21/0.45 tff(108,plain,
% 0.21/0.45 (product(e_2, e_3, e_1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[107, 97, 67])).
% 0.21/0.45 tff(109,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.21/0.45 tff(110,assumption,(product(e_2, e_3, e_1)), introduced(assumption)).
% 0.21/0.45 tff(111,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(112,plain,
% 0.21/0.45 ((equalish(e_1, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_1))) <=> (equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(113,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[112])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[113, 111])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(116,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.21/0.45 tff(117,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[116, 72, 13, 110, 109])).
% 0.21/0.45 tff(118,plain,((~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 (~product(e_1, e_3, e_1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[118, 108])).
% 0.21/0.45 tff(120,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.21/0.46 tff(121,plain,
% 0.21/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(122,plain,
% 0.21/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(123,plain,
% 0.21/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.21/0.46 tff(124,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[123, 72, 58, 120, 1])).
% 0.21/0.46 tff(125,plain,((~product(e_3, e_1, e_1)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(126,plain,
% 0.21/0.46 (~product(e_3, e_1, e_1)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[125, 1])).
% 0.21/0.46 tff(127,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.21/0.46 tff(128,plain,
% 0.21/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(129,plain,
% 0.21/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(130,plain,
% 0.21/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.46 tff(131,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[130, 72, 58, 48, 127])).
% 0.21/0.46 tff(132,plain,((~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(133,plain,
% 0.21/0.46 (~product(e_2, e_1, e_2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[132, 46])).
% 0.21/0.46 tff(134,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.21/0.46 tff(135,plain,
% 0.21/0.46 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(136,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.21/0.46 tff(137,plain,
% 0.21/0.46 (~equalish(e_1, e_3)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.21/0.46 tff(138,plain,
% 0.21/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_1, e_1)) | (~product(e_2, 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_1, e_3) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(139,plain,
% 0.21/0.46 ((equalish(e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_1, e_3) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(140,plain,
% 0.21/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[139])).
% 0.21/0.46 tff(141,plain,
% 0.21/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[140, 138])).
% 0.21/0.46 tff(142,plain,
% 0.21/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(143,plain,
% 0.21/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_3, e_1))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.21/0.46 tff(144,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[143, 137, 58, 110, 134])).
% 0.21/0.46 tff(145,plain,((~product(e_2, e_1, e_1)) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(146,plain,
% 0.21/0.46 (~product(e_2, e_1, e_1)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[145, 108])).
% 0.21/0.46 tff(147,plain,
% 0.21/0.46 (group_element(e_1) <=> group_element(e_1)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(148,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.21/0.46 tff(149,plain,
% 0.21/0.46 (group_element(e_1)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.21/0.46 tff(150,plain,
% 0.21/0.46 (((~![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)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, 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_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(151,plain,
% 0.21/0.46 ((product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(152,plain,
% 0.21/0.46 (((~![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_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~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)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[151])).
% 0.21/0.46 tff(153,plain,
% 0.21/0.46 (((~![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_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~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)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))),
% 0.21/0.46 inference(transitivity,[status(thm)],[152, 150])).
% 0.21/0.46 tff(154,plain,
% 0.21/0.46 ((~![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_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(155,plain,
% 0.21/0.46 ((~![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)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.21/0.46 tff(156,plain,
% 0.21/0.46 (product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[155, 149, 38, 35])).
% 0.21/0.46 tff(157,plain,
% 0.21/0.46 (product(e_2, e_1, e_3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[156, 146, 133])).
% 0.21/0.46 tff(158,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.21/0.46 tff(159,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.21/0.46 tff(160,plain,
% 0.21/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(162,plain,
% 0.21/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.46 tff(163,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[162, 61, 13, 159, 158])).
% 0.21/0.46 tff(164,plain,((~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(165,plain,
% 0.21/0.46 (~product(e_3, e_1, e_3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[164, 157])).
% 0.21/0.46 tff(166,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, 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_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(167,plain,
% 0.21/0.46 ((product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> (product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(168,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[167])).
% 0.21/0.46 tff(169,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[168, 166])).
% 0.21/0.46 tff(170,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(171,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.21/0.47 tff(172,plain,
% 0.21/0.47 (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[171, 149, 100, 35])).
% 0.21/0.47 tff(173,plain,
% 0.21/0.47 (product(e_3, e_1, e_2)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[172, 165, 126])).
% 0.21/0.47 tff(174,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.21/0.47 tff(175,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.21/0.47 tff(176,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(177,plain,
% 0.21/0.47 (((~product(e_1, e_3, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_1, e_2))) <=> ((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(178,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[177])).
% 0.21/0.47 tff(179,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[178, 176])).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_1, e_2)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(181,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.21/0.47 tff(182,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[181, 88, 175, 2, 174])).
% 0.21/0.47 tff(183,plain,((~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(184,plain,
% 0.21/0.47 (~product(e_1, e_3, e_2)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[183, 173, 2])).
% 0.21/0.47 tff(185,plain,
% 0.21/0.47 (((~![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_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : (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_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(186,plain,
% 0.21/0.47 ((product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1))) <=> ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(187,plain,
% 0.21/0.47 (((~![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_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~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)))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[186])).
% 0.21/0.47 tff(188,plain,
% 0.21/0.47 (((~![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_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~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)))) | (~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.21/0.47 inference(transitivity,[status(thm)],[187, 185])).
% 0.21/0.47 tff(189,plain,
% 0.21/0.47 ((~![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_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(190,plain,
% 0.21/0.47 ((~![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_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.21/0.47 tff(191,plain,
% 0.21/0.47 (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[190, 149, 100, 35])).
% 0.21/0.47 tff(192,plain,
% 0.21/0.47 (product(e_1, e_3, e_3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[191, 184, 119])).
% 0.21/0.47 tff(193,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_3)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(194,plain,
% 0.21/0.47 (((~product(e_1, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2))) <=> ((~product(e_3, e_1, e_2)) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_3)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(195,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_3))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[194])).
% 0.21/0.47 tff(196,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_3)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[195, 193])).
% 0.21/0.47 tff(197,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(198,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_3))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.21/0.47 tff(199,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[198, 88, 173, 97, 192])).
% 0.21/0.47 tff(200,plain,((~product(e_3, e_2, e_1)) | product(e_2, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(201,plain,
% 0.21/0.47 (product(e_2, e_2, e_3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[200, 1])).
% 0.21/0.47 tff(202,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(203,plain,
% 0.21/0.47 (((~product(e_2, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3))) <=> (product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(204,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[203])).
% 0.21/0.47 tff(205,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[204, 202])).
% 0.21/0.47 tff(206,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(207,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.21/0.47 tff(208,plain,
% 0.21/0.47 (product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[207, 88])).
% 0.21/0.47 tff(209,plain,
% 0.21/0.47 (product(e_3, e_3, e_2)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[208, 201])).
% 0.21/0.47 tff(210,assumption,(product(e_3, e_3, e_2)), introduced(assumption)).
% 0.21/0.47 tff(211,plain,
% 0.21/0.47 (((~![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_2)) | (~product(e_2, e_3, 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_3, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(212,plain,
% 0.21/0.47 ((~![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_2)) | (~product(e_2, e_3, e_2)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(213,plain,
% 0.21/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_2, e_3, e_2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.21/0.47 tff(214,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[213, 16, 13, 47, 210])).
% 0.21/0.47 tff(215,plain,((~product(e_2, e_3, e_2)) | (~product(e_3, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(216,plain,
% 0.21/0.47 (~product(e_2, e_3, e_2)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[215, 209])).
% 0.21/0.47 tff(217,plain,
% 0.21/0.47 (product(e_2, e_3, e_1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[107, 216, 97])).
% 0.21/0.47 tff(218,plain,
% 0.21/0.47 (~product(e_2, e_1, e_1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[145, 217])).
% 0.21/0.47 tff(219,plain,
% 0.21/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(220,plain,
% 0.21/0.48 ((equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(221,plain,
% 0.21/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_2))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[220])).
% 0.21/0.48 tff(222,plain,
% 0.21/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[221, 219])).
% 0.21/0.48 tff(223,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(224,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_2))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.21/0.48 tff(225,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[224, 137, 58, 175, 210])).
% 0.21/0.48 tff(226,plain,((~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(227,plain,
% 0.21/0.48 (~product(e_3, e_1, e_2)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[226, 209])).
% 0.21/0.48 tff(228,plain,
% 0.21/0.48 (product(e_3, e_1, e_3)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[172, 227, 126])).
% 0.21/0.48 tff(229,plain,
% 0.21/0.48 (~product(e_2, e_1, e_3)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[164, 228])).
% 0.21/0.48 tff(230,plain,
% 0.21/0.48 (product(e_2, e_1, e_2)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[156, 229, 218])).
% 0.21/0.48 tff(231,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(232,plain,
% 0.21/0.48 (((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_2) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(233,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_2) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[232])).
% 0.21/0.48 tff(234,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_2) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[233, 231])).
% 0.21/0.48 tff(235,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_2) | (~product(e_2, e_1, e_2)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(236,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.21/0.48 tff(237,plain,
% 0.21/0.48 (product(e_2, e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[236, 88])).
% 0.21/0.48 tff(238,plain,
% 0.21/0.48 (~product(e_1, e_2, e_3)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[237, 230, 216])).
% 0.21/0.48 tff(239,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(240,plain,
% 0.21/0.48 (((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2))) <=> (product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(241,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_2))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[240])).
% 0.21/0.48 tff(242,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[241, 239])).
% 0.21/0.48 tff(243,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(244,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_2))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.21/0.48 tff(245,plain,
% 0.21/0.48 (~product(e_1, e_2, e_2)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[244, 88, 25, 230])).
% 0.21/0.48 tff(246,plain,
% 0.21/0.48 (((~![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)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(247,plain,
% 0.21/0.48 ((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)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(248,plain,
% 0.21/0.48 (((~![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))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[247])).
% 0.21/0.48 tff(249,plain,
% 0.21/0.48 (((~![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)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[248, 246])).
% 0.21/0.48 tff(250,plain,
% 0.21/0.48 ((~![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)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(251,plain,
% 0.21/0.48 ((~![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))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.21/0.48 tff(252,plain,
% 0.21/0.48 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[251, 149, 38, 35])).
% 0.21/0.48 tff(253,plain,
% 0.21/0.48 (product(e_1, e_2, e_1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[252, 245, 238])).
% 0.21/0.48 tff(254,plain,
% 0.21/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, 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_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(255,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(256,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.21/0.48 tff(257,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[256, 137, 13, 1, 253])).
% 0.21/0.48 tff(258,plain,(~product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(259,assumption,(~product(e_3, e_2, e_1)), introduced(assumption)).
% 0.21/0.48 tff(260,assumption,(~product(e_2, e_2, e_1)), introduced(assumption)).
% 0.21/0.48 tff(261,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.21/0.48 tff(262,plain,
% 0.21/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(263,plain,
% 0.21/0.48 ((equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2))) <=> (equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(264,plain,
% 0.21/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[263])).
% 0.21/0.48 tff(265,plain,
% 0.21/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[264, 262])).
% 0.21/0.48 tff(266,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(267,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.21/0.48 tff(268,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[267, 61, 58, 261, 210])).
% 0.21/0.48 tff(269,plain,((~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(270,plain,
% 0.21/0.48 (~product(e_3, e_3, e_2)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[269, 261])).
% 0.21/0.48 tff(271,plain,
% 0.21/0.48 (~product(e_2, e_2, e_3)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[208, 270])).
% 0.21/0.48 tff(272,plain,
% 0.21/0.48 (product(e_2, e_2, e_2)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[45, 271, 260])).
% 0.21/0.48 tff(273,plain,
% 0.21/0.48 (((~![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_2, e_2, e_2)) | (~product(e_3, 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_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(274,plain,
% 0.21/0.48 ((equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))) <=> (equalish(e_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(275,plain,
% 0.21/0.48 (((~![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_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_2, e_2, e_2)) | (~product(e_3, e_2, e_2))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[274])).
% 0.21/0.48 tff(276,plain,
% 0.21/0.48 (((~![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_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_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[275, 273])).
% 0.21/0.48 tff(277,plain,
% 0.21/0.48 ((~![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_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(278,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.21/0.48 tff(279,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[278, 16, 13, 261, 272])).
% 0.21/0.48 tff(280,plain,((~product(e_3, e_2, e_2)) | product(e_2, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(281,plain,
% 0.21/0.48 (~product(e_3, e_2, e_2)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[280, 260])).
% 0.21/0.48 tff(282,plain,
% 0.21/0.48 (((~![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)))) | ((~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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(283,plain,
% 0.21/0.49 ((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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(284,plain,
% 0.21/0.49 (((~![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_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)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[283])).
% 0.21/0.49 tff(285,plain,
% 0.21/0.49 (((~![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_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))),
% 0.21/0.49 inference(transitivity,[status(thm)],[284, 282])).
% 0.21/0.49 tff(286,plain,
% 0.21/0.49 ((~![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_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)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(287,plain,
% 0.21/0.49 ((~![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_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)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.21/0.49 tff(288,plain,
% 0.21/0.49 (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[287, 38, 100, 35])).
% 0.21/0.49 tff(289,plain,
% 0.21/0.49 (product(e_3, e_2, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[288, 281, 259])).
% 0.21/0.49 tff(290,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.21/0.49 tff(291,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.21/0.49 tff(292,plain,
% 0.21/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, 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_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(293,plain,
% 0.21/0.49 ((equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_2, e_3))) <=> (equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(294,plain,
% 0.21/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, 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_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[293])).
% 0.21/0.49 tff(295,plain,
% 0.21/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, 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_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[294, 292])).
% 0.21/0.49 tff(296,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(297,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.21/0.49 tff(298,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[297, 16, 13, 291, 290])).
% 0.21/0.49 tff(299,plain,((~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(300,plain,
% 0.21/0.49 (~product(e_2, e_2, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[299, 289])).
% 0.21/0.49 tff(301,plain,
% 0.21/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(302,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(303,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_3))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.21/0.49 tff(304,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[303, 72, 58, 159, 291])).
% 0.21/0.49 tff(305,plain,((~product(e_3, e_1, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(306,plain,
% 0.21/0.49 (~product(e_3, e_1, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[305, 289])).
% 0.21/0.49 tff(307,plain,
% 0.21/0.49 (~product(e_3, e_1, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[305, 291])).
% 0.21/0.49 tff(308,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(309,plain,
% 0.21/0.49 (((~product(e_2, e_3, e_1)) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3))) <=> (product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(310,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[309])).
% 0.21/0.49 tff(311,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[310, 308])).
% 0.21/0.49 tff(312,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(313,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.21/0.49 tff(314,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[313, 88, 307, 291, 110])).
% 0.21/0.49 tff(315,plain,((~product(e_2, e_3, e_1)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(316,plain,
% 0.21/0.49 (~product(e_2, e_3, e_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[315, 289])).
% 0.21/0.49 tff(317,plain,
% 0.21/0.49 (product(e_2, e_2, e_2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[45, 300, 260])).
% 0.21/0.49 tff(318,plain,
% 0.21/0.49 (~product(e_2, e_3, e_2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[66, 317])).
% 0.21/0.49 tff(319,plain,
% 0.21/0.49 (product(e_2, e_3, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[107, 318, 316])).
% 0.21/0.49 tff(320,plain,
% 0.21/0.49 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(321,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.21/0.49 tff(322,plain,
% 0.21/0.49 (~equalish(e_3, e_1)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.21/0.49 tff(323,plain,
% 0.21/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(324,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(325,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_3))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.21/0.49 tff(326,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[325, 322, 58, 68, 158])).
% 0.21/0.49 tff(327,plain,((~product(e_2, e_3, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(328,plain,
% 0.21/0.49 (~product(e_2, e_1, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[327, 319])).
% 0.21/0.49 tff(329,plain,
% 0.21/0.49 (~product(e_2, e_1, e_2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[132, 317])).
% 0.21/0.49 tff(330,plain,
% 0.21/0.49 (product(e_2, e_1, e_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[156, 329, 328])).
% 0.21/0.49 tff(331,plain,
% 0.21/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(332,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(333,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.21/0.49 tff(334,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[333, 61, 13, 120, 134])).
% 0.21/0.49 tff(335,plain,((~product(e_3, e_1, e_1)) | (~product(e_2, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(336,plain,
% 0.21/0.49 (~product(e_3, e_1, e_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[335, 330])).
% 0.21/0.49 tff(337,plain,
% 0.21/0.49 (product(e_3, e_1, e_2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[172, 336, 306])).
% 0.21/0.49 tff(338,plain,
% 0.21/0.49 (~product(e_1, e_3, e_2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[183, 337, 300])).
% 0.21/0.49 tff(339,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(340,plain,
% 0.21/0.49 (((~product(e_1, e_3, e_1)) | product(e_2, e_1, e_3) | (~product(e_3, e_1, e_2))) <=> ((~product(e_3, e_1, e_2)) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(341,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_2, e_1, e_3) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_1))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[340])).
% 0.21/0.49 tff(342,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_2, e_1, e_3) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_1)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[341, 339])).
% 0.21/0.49 tff(343,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_2, e_1, e_3) | (~product(e_3, e_1, e_2)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(344,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.21/0.49 tff(345,plain,
% 0.21/0.49 ((~product(e_3, e_1, e_2)) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[344, 88])).
% 0.21/0.49 tff(346,plain,
% 0.21/0.49 (~product(e_1, e_3, e_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[345, 337, 328])).
% 0.21/0.49 tff(347,plain,
% 0.21/0.49 (product(e_1, e_3, e_3) | product(e_1, e_3, e_2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[190, 149, 100, 35, 346])).
% 0.21/0.49 tff(348,plain,
% 0.21/0.49 (product(e_1, e_3, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[347, 338])).
% 0.21/0.49 tff(349,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[75, 72, 13, 319, 348])).
% 0.21/0.49 tff(350,plain,(product(e_2, e_2, e_1) | product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(351,plain,
% 0.21/0.49 (product(e_2, e_2, e_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[350, 258])).
% 0.21/0.49 tff(352,plain,
% 0.21/0.49 (((~![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_2, e_2, e_1)) | (~product(e_2, 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_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(353,plain,
% 0.21/0.49 ((~![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_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(354,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.21/0.49 tff(355,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[354, 61, 58, 3, 110])).
% 0.21/0.49 tff(356,plain,((~product(e_2, e_3, e_1)) | (~product(e_2, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(357,plain,
% 0.21/0.49 (~product(e_2, e_3, e_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[356, 351])).
% 0.21/0.49 tff(358,plain,
% 0.21/0.49 (product(e_2, e_2, e_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[350, 259])).
% 0.21/0.49 tff(359,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_1)) | product(e_1, e_1, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_1, e_1, e_2))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(360,plain,
% 0.21/0.49 (((~product(e_2, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_2, e_1))) <=> ((~product(e_2, e_2, e_1)) | product(e_1, e_1, e_2))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(361,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_1)) | product(e_1, e_1, e_2)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[360])).
% 0.21/0.49 tff(362,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_1, e_1, e_2))),
% 0.21/0.49 inference(transitivity,[status(thm)],[361, 359])).
% 0.21/0.49 tff(363,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_2, e_1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(364,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_1, e_1, e_2)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.21/0.49 tff(365,plain,
% 0.21/0.49 ((~product(e_2, e_2, e_1)) | product(e_1, e_1, e_2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[364, 88])).
% 0.21/0.49 tff(366,plain,
% 0.21/0.49 (product(e_1, e_1, e_2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[365, 358])).
% 0.21/0.49 tff(367,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.21/0.49 tff(368,plain,
% 0.21/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_1, 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_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(369,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(370,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.21/0.49 tff(371,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[370, 72, 13, 3, 367])).
% 0.21/0.49 tff(372,plain,((~product(e_1, e_2, e_1)) | (~product(e_2, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(373,plain,
% 0.21/0.49 (~product(e_1, e_2, e_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[372, 358])).
% 0.21/0.49 tff(374,assumption,(~product(e_3, e_2, e_2)), introduced(assumption)).
% 0.21/0.49 tff(375,plain,
% 0.21/0.49 (product(e_3, e_2, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[288, 259, 374])).
% 0.21/0.50 tff(376,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.21/0.50 tff(377,plain,
% 0.21/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, 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_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(378,plain,
% 0.21/0.50 ((equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3))) <=> (equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(379,plain,
% 0.21/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_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_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[378])).
% 0.21/0.50 tff(380,plain,
% 0.21/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_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_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[379, 377])).
% 0.21/0.50 tff(381,plain,
% 0.21/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(382,plain,
% 0.21/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.21/0.50 tff(383,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[382, 137, 13, 291, 376])).
% 0.21/0.50 tff(384,plain,((~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(385,plain,
% 0.21/0.50 (~product(e_1, e_2, e_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[384, 375])).
% 0.21/0.50 tff(386,plain,
% 0.21/0.50 (product(e_1, e_2, e_2)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[252, 385, 373])).
% 0.21/0.50 tff(387,plain,
% 0.21/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(388,plain,
% 0.21/0.50 ((equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2))) <=> (equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(389,plain,
% 0.21/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[388])).
% 0.21/0.50 tff(390,plain,
% 0.21/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[389, 387])).
% 0.21/0.50 tff(391,plain,
% 0.21/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(392,plain,
% 0.21/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.21/0.50 tff(393,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[392, 72, 58, 386, 366])).
% 0.21/0.50 tff(394,plain,(product(e_3, e_2, e_1) | product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(395,plain,
% 0.21/0.50 (product(e_3, e_2, e_2)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[394, 258])).
% 0.21/0.50 tff(396,plain,
% 0.21/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(397,plain,
% 0.21/0.50 (((~product(e_2, e_3, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2))) <=> (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(398,plain,
% 0.21/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[397])).
% 0.21/0.50 tff(399,plain,
% 0.21/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[398, 396])).
% 0.21/0.50 tff(400,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(401,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.21/0.50 tff(402,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[401, 88, 261, 271, 47])).
% 0.21/0.50 tff(403,plain,((~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(404,plain,
% 0.21/0.50 (~product(e_2, e_3, e_2)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[403, 395])).
% 0.21/0.50 tff(405,plain,
% 0.21/0.50 (product(e_2, e_3, e_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[107, 404, 357])).
% 0.21/0.50 tff(406,plain,
% 0.21/0.50 (~product(e_2, e_1, e_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[327, 405])).
% 0.21/0.50 tff(407,plain,
% 0.21/0.50 (~product(e_1, e_2, e_1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[372, 351])).
% 0.21/0.50 tff(408,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.21/0.50 tff(409,plain,
% 0.21/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_1, 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_1, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(410,plain,
% 0.21/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(411,plain,
% 0.21/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.21/0.50 tff(412,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[411, 137, 13, 261, 408])).
% 0.21/0.50 tff(413,plain,((~product(e_1, e_2, e_2)) | (~product(e_3, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(414,plain,
% 0.21/0.50 (~product(e_1, e_2, e_2)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[413, 395])).
% 0.21/0.50 tff(415,plain,
% 0.21/0.50 (product(e_1, e_2, e_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[252, 414, 407])).
% 0.21/0.50 tff(416,plain,
% 0.21/0.50 (~product(e_2, e_1, e_2)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[237, 415, 404])).
% 0.21/0.50 tff(417,plain,
% 0.21/0.50 (product(e_2, e_1, e_1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[156, 416, 406])).
% 0.21/0.50 tff(418,plain,
% 0.21/0.50 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(419,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.21/0.50 tff(420,plain,
% 0.21/0.50 (~equalish(e_2, e_1)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[419, 418])).
% 0.21/0.50 tff(421,plain,
% 0.21/0.50 (((~![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_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(422,plain,
% 0.21/0.50 ((equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1))) <=> (equalish(e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(423,plain,
% 0.21/0.50 (((~![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_2, e_1, e_1)) | (~product(e_2, 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_2, e_2, e_1)) | (~product(e_2, e_1, e_1))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[422])).
% 0.21/0.50 tff(424,plain,
% 0.21/0.50 (((~![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_2, e_1, e_1)) | (~product(e_2, 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_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[423, 421])).
% 0.21/0.50 tff(425,plain,
% 0.21/0.50 ((~![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_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(426,plain,
% 0.21/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.21/0.50 tff(427,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[426, 420, 58, 351, 417])).
% 0.21/0.50 % SZS output end Proof
%------------------------------------------------------------------------------