%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP133-1.003 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 : Sat Jun 21 05:07:12 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP133-1.003 : TPTP v9.0.0. Released v1.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:48:03 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.18/0.40 % SZS status Unsatisfiable
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(product_type, type, (
% 0.18/0.40 product: ( $i * $i * $i ) > $o)).
% 0.18/0.40 tff(e_3_type, type, (
% 0.18/0.40 e_3: $i)).
% 0.18/0.40 tff(e_1_type, type, (
% 0.18/0.40 e_1: $i)).
% 0.18/0.40 tff(e_2_type, type, (
% 0.18/0.40 e_2: $i)).
% 0.18/0.40 tff(equalish_type, type, (
% 0.18/0.40 equalish: ( $i * $i ) > $o)).
% 0.18/0.40 tff(group_element_type, type, (
% 0.18/0.40 group_element: $i > $o)).
% 0.18/0.40 tff(1,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.18/0.40 tff(2,assumption,(product(e_3, e_3, e_1)), introduced(assumption)).
% 0.18/0.40 tff(3,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (^[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))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(5,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.40 tff(6,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(7,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[7])).
% 0.18/0.40 tff(9,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.18/0.40 tff(11,plain,
% 0.18/0.40 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.18/0.40 tff(12,plain,(
% 0.18/0.40 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[11])).
% 0.18/0.40 tff(13,plain,
% 0.18/0.40 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.18/0.40 tff(14,plain,
% 0.18/0.40 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(15,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.18/0.40 tff(16,plain,
% 0.18/0.40 (~equalish(e_1, e_2)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.40 tff(17,plain,
% 0.18/0.40 (((~![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_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_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(18,plain,
% 0.18/0.40 ((~![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_2)) | (~product(e_3, e_1, e_2)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(19,plain,
% 0.18/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.40 tff(20,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[19, 16, 13, 3, 1])).
% 0.18/0.40 tff(21,plain,((~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(22,plain,
% 0.18/0.40 (~product(e_3, e_2, e_2)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[21, 1])).
% 0.18/0.40 tff(23,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.18/0.40 tff(24,plain,
% 0.18/0.40 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(25,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.18/0.40 tff(26,plain,
% 0.18/0.40 (~equalish(e_2, e_3)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.18/0.40 tff(27,plain,
% 0.18/0.40 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(28,plain,
% 0.18/0.40 ((equalish(e_2, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_1))) <=> (equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(29,plain,
% 0.18/0.40 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_3, e_1))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[28])).
% 0.18/0.40 tff(30,plain,
% 0.18/0.40 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[29, 27])).
% 0.18/0.40 tff(31,plain,
% 0.18/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_3, e_1))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[32, 26, 13, 2, 23])).
% 0.18/0.40 tff(34,plain,((~product(e_3, e_2, e_1)) | (~product(e_3, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 (~product(e_3, e_2, e_1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[34, 2])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 (^[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))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.18/0.40 tff(38,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(39,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.18/0.40 tff(41,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.18/0.40 tff(44,plain,(
% 0.18/0.40 ![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)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[43])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 (group_element(e_3) <=> group_element(e_3)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(47,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 (group_element(e_3)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 (group_element(e_2) <=> group_element(e_2)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(50,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 (group_element(e_2)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 (((~![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_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | 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_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 ((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_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(54,plain,
% 0.18/0.41 (((~![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_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1)))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[53])).
% 0.18/0.41 tff(55,plain,
% 0.18/0.41 (((~![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_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1))),
% 0.18/0.41 inference(transitivity,[status(thm)],[54, 52])).
% 0.18/0.41 tff(56,plain,
% 0.18/0.41 ((~![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)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(57,plain,
% 0.18/0.41 ((~![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_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.41 tff(58,plain,
% 0.18/0.41 (product(e_3, e_2, e_2) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[57, 51, 48, 45])).
% 0.18/0.41 tff(59,plain,
% 0.18/0.41 (product(e_3, e_2, e_3)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[58, 35, 22])).
% 0.18/0.41 tff(60,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.18/0.41 tff(61,assumption,(product(e_3, e_3, e_3)), introduced(assumption)).
% 0.18/0.41 tff(62,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.18/0.41 tff(63,plain,
% 0.18/0.41 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(64,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.18/0.41 tff(65,plain,
% 0.18/0.41 (~equalish(e_3, e_1)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.18/0.41 tff(66,plain,
% 0.18/0.41 (((~![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_3, e_3, 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_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(67,plain,
% 0.18/0.41 ((equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3))) <=> (equalish(e_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(68,plain,
% 0.18/0.41 (((~![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_3, e_1, e_3)) | (~product(e_3, 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_3, e_3, e_3)) | (~product(e_3, e_1, e_3))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[67])).
% 0.18/0.41 tff(69,plain,
% 0.18/0.41 (((~![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_3, e_1, e_3)) | (~product(e_3, 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_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[68, 66])).
% 0.18/0.41 tff(70,plain,
% 0.18/0.41 ((~![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_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(71,plain,
% 0.18/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.41 tff(72,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[71, 65, 13, 61, 62])).
% 0.18/0.41 tff(73,plain,((~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(74,plain,
% 0.18/0.41 (~product(e_3, e_1, e_3)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[73, 61])).
% 0.18/0.41 tff(75,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.18/0.41 tff(76,plain,
% 0.18/0.41 (^[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))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(77,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[76])).
% 0.18/0.41 tff(78,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(79,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(80,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[79])).
% 0.18/0.41 tff(81,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.18/0.41 tff(82,plain,
% 0.18/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.41 tff(83,plain,
% 0.18/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.18/0.41 tff(84,plain,(
% 0.18/0.41 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[83])).
% 0.18/0.41 tff(85,plain,
% 0.18/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(87,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 (~equalish(e_1, e_3)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.41 tff(89,plain,
% 0.18/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(90,plain,
% 0.18/0.42 ((equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))) <=> (equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(91,plain,
% 0.18/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[90])).
% 0.18/0.42 tff(92,plain,
% 0.18/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.18/0.42 inference(transitivity,[status(thm)],[91, 89])).
% 0.18/0.42 tff(93,plain,
% 0.18/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(94,plain,
% 0.18/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.18/0.42 tff(95,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[94, 88, 85, 75, 61])).
% 0.18/0.42 tff(96,plain,((~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(97,plain,
% 0.18/0.42 (~product(e_1, e_3, e_3)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[96, 61])).
% 0.18/0.42 tff(98,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.18/0.42 tff(99,assumption,(product(e_3, e_3, e_2)), introduced(assumption)).
% 0.18/0.42 tff(100,plain,
% 0.18/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, 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_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(101,plain,
% 0.18/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(102,plain,
% 0.18/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.18/0.42 tff(103,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[102, 65, 85, 98, 99])).
% 0.18/0.42 tff(104,plain,((~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(105,plain,
% 0.18/0.42 (~product(e_3, e_3, e_2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[104, 98])).
% 0.18/0.42 tff(106,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.18/0.42 tff(107,plain,
% 0.18/0.42 (((~![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_1, e_3, 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_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(108,plain,
% 0.18/0.42 ((~![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_1, e_3, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(109,plain,
% 0.18/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_2))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.18/0.42 tff(110,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[109, 88, 13, 98, 106])).
% 0.18/0.42 tff(111,plain,((~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(112,plain,
% 0.18/0.42 (~product(e_1, e_1, e_2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[111, 98])).
% 0.18/0.42 tff(113,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.18/0.42 tff(114,plain,
% 0.18/0.42 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(115,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.18/0.42 tff(116,plain,
% 0.18/0.42 (~equalish(e_2, e_1)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.18/0.42 tff(117,plain,
% 0.18/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_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_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(118,plain,
% 0.18/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(119,plain,
% 0.18/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_2))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.18/0.42 tff(120,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[119, 116, 85, 98, 113])).
% 0.18/0.42 tff(121,plain,((~product(e_2, e_3, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(122,plain,
% 0.18/0.42 (~product(e_2, e_3, e_2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[121, 98])).
% 0.18/0.42 tff(123,assumption,(~product(e_3, e_3, e_2)), introduced(assumption)).
% 0.18/0.42 tff(124,assumption,(~product(e_3, e_3, e_1)), introduced(assumption)).
% 0.18/0.42 tff(125,plain,
% 0.18/0.42 (((~![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)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, X: $i] : (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)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(126,plain,
% 0.18/0.42 ((product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(127,plain,
% 0.18/0.42 (((~![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_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~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)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[126])).
% 0.18/0.42 tff(128,plain,
% 0.18/0.42 (((~![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_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~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)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))),
% 0.19/0.42 inference(transitivity,[status(thm)],[127, 125])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 ((~![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_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 ((~![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)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 (product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[130, 48, 45])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (product(e_3, e_3, e_3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[131, 124, 123])).
% 0.19/0.42 tff(133,assumption,(~product(e_1, e_1, e_2)), introduced(assumption)).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, 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_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ((equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))) <=> (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[135])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[136, 134])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[139, 26, 13, 61, 60])).
% 0.19/0.42 tff(141,plain,((~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (~product(e_3, e_2, e_3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[141, 132])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (~product(e_3, e_1, e_3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[73, 132])).
% 0.19/0.42 tff(144,assumption,(product(e_1, e_1, e_3)), introduced(assumption)).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[145])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(149,plain,
% 0.19/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[148])).
% 0.19/0.43 tff(150,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.19/0.43 tff(153,plain,(
% 0.19/0.43 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[152])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 (((~![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_1) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 (((~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3))) <=> (product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[156])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[157, 155])).
% 0.19/0.43 tff(159,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.43 tff(161,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[160, 154, 144, 124])).
% 0.19/0.43 tff(162,plain,((~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(163,plain,
% 0.19/0.43 (~product(e_1, e_1, e_3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[162, 124])).
% 0.19/0.43 tff(164,plain,
% 0.19/0.43 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(165,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.19/0.43 tff(166,plain,
% 0.19/0.43 (group_element(e_1)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.19/0.43 tff(167,plain,
% 0.19/0.43 (((~![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_1, e_3) | product(e_1, e_1, e_2) | product(e_1, 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_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(168,plain,
% 0.19/0.43 ((product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1))) <=> (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(169,plain,
% 0.19/0.43 (((~![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_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(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_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[168])).
% 0.19/0.43 tff(170,plain,
% 0.19/0.43 (((~![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_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(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_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[169, 167])).
% 0.19/0.43 tff(171,plain,
% 0.19/0.43 ((~![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_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(172,plain,
% 0.19/0.43 ((~![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_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.19/0.43 tff(173,plain,
% 0.19/0.43 (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[172, 166, 45])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 (product(e_1, e_1, e_1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[173, 163, 133])).
% 0.19/0.43 tff(175,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.19/0.43 tff(176,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.19/0.43 tff(177,plain,
% 0.19/0.43 (((~![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_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_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 ((equalish(e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))) <=> (equalish(e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 (((~![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_1, e_1)) | (~product(e_1, 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_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[178])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 (((~![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_1, e_1)) | (~product(e_1, 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_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[179, 177])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 ((~![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_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.19/0.43 tff(183,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[182, 88, 85, 176, 175])).
% 0.19/0.43 tff(184,plain,((~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(185,plain,
% 0.19/0.43 (~product(e_3, e_1, e_1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[184, 174])).
% 0.19/0.43 tff(186,plain,
% 0.19/0.43 (((~![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_1)) | (~group_element(e_3)) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3) | product(e_3, e_1, 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_1)) | (~group_element(e_3)) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 ((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))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 (((~![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)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[187])).
% 0.19/0.43 tff(189,plain,
% 0.19/0.43 (((~![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)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2))),
% 0.19/0.43 inference(transitivity,[status(thm)],[188, 186])).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 ((~![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)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 ((~![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_1)) | (~group_element(e_3)) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.19/0.44 tff(192,plain,
% 0.19/0.44 (product(e_3, e_1, e_1) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[191, 166, 48, 45])).
% 0.19/0.44 tff(193,plain,
% 0.19/0.44 (product(e_3, e_1, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[192, 185, 143])).
% 0.19/0.44 tff(194,plain,
% 0.19/0.44 (~product(e_3, e_2, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[21, 193])).
% 0.19/0.44 tff(195,plain,
% 0.19/0.44 (product(e_3, e_2, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[58, 194, 142])).
% 0.19/0.44 tff(196,assumption,(product(e_2, e_3, e_1)), introduced(assumption)).
% 0.19/0.44 tff(197,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~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_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(198,plain,
% 0.19/0.44 (((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_3, e_1))) <=> (product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(199,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~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_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[198])).
% 0.19/0.44 tff(200,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~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_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[199, 197])).
% 0.19/0.44 tff(201,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_3, e_1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(202,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.19/0.44 tff(203,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[202, 154, 133, 196, 23])).
% 0.19/0.44 tff(204,plain,((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(205,plain,
% 0.19/0.44 (~product(e_2, e_3, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[204, 195, 133])).
% 0.19/0.44 tff(206,assumption,(~product(e_2, e_3, e_2)), introduced(assumption)).
% 0.19/0.44 tff(207,plain,
% 0.19/0.44 (((~![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_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, 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)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(208,plain,
% 0.19/0.44 ((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_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(209,plain,
% 0.19/0.44 (((~![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_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_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[208])).
% 0.19/0.44 tff(210,plain,
% 0.19/0.44 (((~![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_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_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3))),
% 0.19/0.44 inference(transitivity,[status(thm)],[209, 207])).
% 0.19/0.44 tff(211,plain,
% 0.19/0.44 ((~![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_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)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(212,plain,
% 0.19/0.44 ((~![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_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.19/0.44 tff(213,plain,
% 0.19/0.44 (product(e_2, e_3, e_1) | product(e_2, e_3, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[212, 51, 48, 45, 206])).
% 0.19/0.44 tff(214,plain,
% 0.19/0.44 (product(e_2, e_3, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[213, 205])).
% 0.19/0.44 tff(215,plain,
% 0.19/0.44 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(216,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.19/0.44 tff(217,plain,
% 0.19/0.44 (~equalish(e_3, e_2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.19/0.44 tff(218,plain,
% 0.19/0.44 (((~![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_3, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(219,plain,
% 0.19/0.44 ((~![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_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(220,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.19/0.44 tff(221,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[220, 217, 85, 214, 132])).
% 0.19/0.44 tff(222,plain,(product(e_3, e_3, e_1) | product(e_2, e_3, e_2) | product(e_1, e_1, e_2) | product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(223,plain,
% 0.19/0.44 (product(e_3, e_3, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[222, 122, 112, 105])).
% 0.19/0.44 tff(224,plain,
% 0.19/0.44 (~product(e_3, e_2, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[34, 223])).
% 0.19/0.44 tff(225,plain,
% 0.19/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_3, e_3, 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_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(226,plain,
% 0.19/0.45 ((equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_3, e_1))) <=> (equalish(e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(227,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[226])).
% 0.19/0.45 tff(228,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[227, 225])).
% 0.19/0.45 tff(229,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(230,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.19/0.45 tff(231,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[230, 65, 13, 2, 175])).
% 0.19/0.45 tff(232,plain,((~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(233,plain,
% 0.19/0.45 (~product(e_3, e_1, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[232, 223])).
% 0.19/0.45 tff(234,assumption,(~product(e_2, e_3, e_1)), introduced(assumption)).
% 0.19/0.45 tff(235,plain,
% 0.19/0.45 (((~![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_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(236,plain,
% 0.19/0.45 (((~product(e_3, e_1, e_3)) | product(e_2, e_3, e_1) | (~product(e_1, e_3, e_2))) <=> (product(e_2, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(237,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_2, e_3, e_1) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_3))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[236])).
% 0.19/0.45 tff(238,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_2, e_3, e_1) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[237, 235])).
% 0.19/0.45 tff(239,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_2, e_3, e_1) | (~product(e_1, e_3, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(240,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.19/0.45 tff(241,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[240, 154, 98, 234, 62])).
% 0.19/0.45 tff(242,plain,(product(e_2, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(243,plain,
% 0.19/0.45 (~product(e_3, e_1, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[242, 234, 98])).
% 0.19/0.45 tff(244,plain,
% 0.19/0.45 (product(e_3, e_1, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[192, 243, 233])).
% 0.19/0.45 tff(245,plain,
% 0.19/0.45 (~product(e_3, e_2, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[21, 244])).
% 0.19/0.45 tff(246,plain,
% 0.19/0.45 (product(e_3, e_2, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[58, 245, 224])).
% 0.19/0.45 tff(247,plain,
% 0.19/0.45 (product(e_2, e_3, e_1) | product(e_2, e_3, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[212, 51, 48, 45, 122])).
% 0.19/0.45 tff(248,plain,
% 0.19/0.45 (product(e_2, e_3, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[247, 234])).
% 0.19/0.45 tff(249,plain,
% 0.19/0.45 (((~![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_3, e_3, e_2) | (~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_2, e_3, e_3)) | product(e_3, e_3, e_2) | (~product(e_3, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(250,plain,
% 0.19/0.45 (((~product(e_3, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_3, e_3))) <=> ((~product(e_2, e_3, e_3)) | product(e_3, e_3, e_2) | (~product(e_3, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(251,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_3, e_3, e_2) | (~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_2, e_3, e_3)) | product(e_3, e_3, e_2) | (~product(e_3, e_2, e_3))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[250])).
% 0.19/0.45 tff(252,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_3, e_3, e_2) | (~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_2, e_3, e_3)) | product(e_3, e_3, e_2) | (~product(e_3, e_2, e_3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[251, 249])).
% 0.19/0.45 tff(253,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_3, e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(254,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_3, e_3)) | product(e_3, e_3, e_2) | (~product(e_3, e_2, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.19/0.45 tff(255,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[254, 154, 248, 105, 246])).
% 0.19/0.45 tff(256,plain,(product(e_2, e_3, e_1) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(257,plain,
% 0.19/0.45 (product(e_2, e_3, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[256, 98])).
% 0.19/0.45 tff(258,plain,
% 0.19/0.45 (((~![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_3, e_1)) | (~product(e_3, 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_2, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(259,plain,
% 0.19/0.45 ((equalish(e_2, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_1))) <=> (equalish(e_2, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(260,plain,
% 0.19/0.45 (((~![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_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_2, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_3, e_1))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[259])).
% 0.19/0.45 tff(261,plain,
% 0.19/0.45 (((~![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_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_2, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[260, 258])).
% 0.19/0.45 tff(262,plain,
% 0.19/0.45 ((~![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_1)) | (~product(e_2, e_3, e_1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(263,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_3, e_1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.19/0.45 tff(264,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[263, 26, 85, 257, 223])).
% 0.19/0.45 tff(265,plain,(~product(e_1, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(266,plain,
% 0.19/0.45 (((~![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_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(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)))) | product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(267,plain,
% 0.19/0.45 ((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))) <=> (product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(268,plain,
% 0.19/0.45 (((~![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_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)))) | (product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[267])).
% 0.19/0.45 tff(269,plain,
% 0.19/0.45 (((~![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_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)))) | product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.19/0.45 inference(transitivity,[status(thm)],[268, 266])).
% 0.19/0.45 tff(270,plain,
% 0.19/0.45 ((~![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_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)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(271,plain,
% 0.19/0.45 ((~![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_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.19/0.45 tff(272,plain,
% 0.19/0.46 (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[271, 166, 48, 45])).
% 0.19/0.46 tff(273,plain,
% 0.19/0.46 (product(e_1, e_3, e_3) | product(e_1, e_3, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[272, 265])).
% 0.19/0.46 tff(274,plain,
% 0.19/0.46 (product(e_1, e_3, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[273, 97])).
% 0.19/0.46 tff(275,plain,
% 0.19/0.46 (~product(e_1, e_1, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[184, 175])).
% 0.19/0.46 tff(276,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.19/0.46 tff(277,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, 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_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(278,plain,
% 0.19/0.46 (((~product(e_3, e_1, e_1)) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1))) <=> (product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(279,plain,
% 0.19/0.46 (((~![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_1)) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[278])).
% 0.19/0.46 tff(280,plain,
% 0.19/0.46 (((~![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_1)) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[279, 277])).
% 0.19/0.46 tff(281,plain,
% 0.19/0.46 ((~![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_1)) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(282,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.19/0.46 tff(283,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[282, 154, 276, 275, 175])).
% 0.19/0.46 tff(284,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(285,plain,
% 0.19/0.46 (~product(e_3, e_1, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[284, 274])).
% 0.19/0.46 tff(286,plain,
% 0.19/0.46 (product(e_3, e_1, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[192, 285, 74])).
% 0.19/0.46 tff(287,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.19/0.46 tff(288,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(289,plain,
% 0.19/0.46 ((equalish(e_2, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_1))) <=> (equalish(e_2, e_3) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(290,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[289])).
% 0.19/0.46 tff(291,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[290, 288])).
% 0.19/0.46 tff(292,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(293,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.19/0.46 tff(294,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[293, 26, 13, 287, 276])).
% 0.19/0.46 tff(295,plain,((~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(296,plain,
% 0.19/0.46 (~product(e_1, e_2, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[295, 274])).
% 0.19/0.46 tff(297,plain,
% 0.19/0.46 (((~![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_1) | (~product(e_1, e_3, e_1)) | (~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_1, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(298,plain,
% 0.19/0.46 (((~product(e_3, e_1, e_2)) | product(e_1, e_2, e_1) | (~product(e_1, e_3, e_1))) <=> (product(e_1, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(299,plain,
% 0.19/0.46 (((~![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_1, e_2, e_1) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_2))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[298])).
% 0.19/0.46 tff(300,plain,
% 0.19/0.46 (((~![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_1, e_2, e_1) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[299, 297])).
% 0.19/0.46 tff(301,plain,
% 0.19/0.46 ((~![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_1, e_2, e_1) | (~product(e_1, e_3, e_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(302,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_2))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.19/0.46 tff(303,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[302, 154, 296, 274, 286])).
% 0.19/0.46 tff(304,plain,(~product(e_3, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(305,assumption,(product(e_2, e_3, e_3)), introduced(assumption)).
% 0.19/0.46 tff(306,plain,
% 0.19/0.46 (((~![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_3, e_3, 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_2, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(307,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(308,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.19/0.47 tff(309,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[308, 154, 305, 304, 60])).
% 0.19/0.47 tff(310,plain,((~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(311,plain,
% 0.19/0.47 (~product(e_2, e_3, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[310, 59])).
% 0.19/0.47 tff(312,assumption,(~product(e_2, e_3, e_3)), introduced(assumption)).
% 0.19/0.47 tff(313,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_1, 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_2, e_3, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(314,plain,
% 0.19/0.47 (((~product(e_1, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2))) <=> (product(e_2, e_3, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(315,plain,
% 0.19/0.47 (((~![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_2, e_3, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[314])).
% 0.19/0.47 tff(316,plain,
% 0.19/0.47 (((~![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_2, e_3, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[315, 313])).
% 0.19/0.47 tff(317,plain,
% 0.19/0.47 ((~![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)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(318,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.19/0.47 tff(319,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[318, 154, 312, 75, 1])).
% 0.19/0.47 tff(320,plain,(product(e_2, e_3, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(321,plain,
% 0.19/0.47 (~product(e_1, e_3, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[320, 311, 1])).
% 0.19/0.47 tff(322,plain,
% 0.19/0.47 (product(e_1, e_3, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[273, 321])).
% 0.19/0.47 tff(323,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, 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_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(324,plain,
% 0.19/0.47 ((equalish(e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_1))) <=> (equalish(e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(325,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_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_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_3, e_1))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[324])).
% 0.19/0.47 tff(326,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_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_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[325, 323])).
% 0.19/0.47 tff(327,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(328,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_3, e_1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.19/0.47 tff(329,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[328, 88, 85, 322, 2])).
% 0.19/0.47 tff(330,plain,((~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(331,plain,
% 0.19/0.47 (~product(e_3, e_3, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[330, 1])).
% 0.19/0.47 tff(332,plain,
% 0.19/0.47 (product(e_3, e_3, e_2) | product(e_3, e_3, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[131, 304])).
% 0.19/0.47 tff(333,plain,
% 0.19/0.47 (product(e_3, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[332, 331])).
% 0.19/0.47 tff(334,plain,
% 0.19/0.47 (((~![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_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_3, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(335,plain,
% 0.19/0.47 ((~![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_3, e_1, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(336,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.19/0.47 tff(337,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[336, 65, 13, 333, 1])).
% 0.19/0.47 tff(338,plain,(~product(e_3, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(339,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~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_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(340,plain,
% 0.19/0.47 ((equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2))) <=> (equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(341,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~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_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[340])).
% 0.19/0.47 tff(342,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~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_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[341, 339])).
% 0.19/0.47 tff(343,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(344,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.19/0.47 tff(345,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[344, 26, 13, 3, 99])).
% 0.19/0.47 tff(346,plain,((~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(347,plain,
% 0.19/0.47 (~product(e_3, e_2, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[346, 99])).
% 0.19/0.47 tff(348,plain,
% 0.19/0.47 (((~![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(349,plain,
% 0.19/0.47 ((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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(350,plain,
% 0.19/0.47 (((~![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))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[349])).
% 0.19/0.48 tff(351,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_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)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[350, 348])).
% 0.19/0.48 tff(352,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(353,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.19/0.48 tff(354,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[353, 16, 85, 276, 196])).
% 0.19/0.48 tff(355,plain,((~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(356,plain,
% 0.19/0.48 (~product(e_1, e_3, e_1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[355, 196])).
% 0.19/0.48 tff(357,plain,
% 0.19/0.48 (product(e_1, e_3, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[273, 356])).
% 0.19/0.48 tff(358,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(359,plain,
% 0.19/0.48 (((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3))) <=> (product(e_3, e_3, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(360,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_3))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[359])).
% 0.19/0.48 tff(361,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[360, 358])).
% 0.19/0.48 tff(362,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(363,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.19/0.48 tff(364,plain,
% 0.19/0.48 (~product(e_3, e_1, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[363, 154, 357, 304])).
% 0.19/0.48 tff(365,plain,
% 0.19/0.48 (product(e_3, e_1, e_1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[192, 364, 338])).
% 0.19/0.48 tff(366,assumption,(~product(e_3, e_2, e_2)), introduced(assumption)).
% 0.19/0.48 tff(367,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_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_2, e_3, e_1)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(368,plain,
% 0.19/0.48 (((~product(e_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_2, e_3, e_1)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(369,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(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_2, e_3, e_1)) | (~product(e_3, e_2, e_3))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[368])).
% 0.19/0.48 tff(370,plain,
% 0.19/0.48 (((~![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_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_2, e_3, e_1)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[369, 367])).
% 0.19/0.48 tff(371,plain,
% 0.19/0.48 ((~![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_1)) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(372,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_2, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.19/0.48 tff(373,plain,
% 0.19/0.48 (~product(e_3, e_2, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[372, 154, 196, 364])).
% 0.19/0.48 tff(374,plain,
% 0.19/0.48 (product(e_3, e_2, e_1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[58, 373, 366])).
% 0.19/0.48 tff(375,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_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_2, e_1) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(376,plain,
% 0.19/0.48 ((equalish(e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_2, e_1))) <=> (equalish(e_2, e_1) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(377,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[376])).
% 0.19/0.48 tff(378,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[377, 375])).
% 0.19/0.48 tff(379,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(380,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.19/0.48 tff(381,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[380, 116, 13, 374, 365])).
% 0.19/0.48 tff(382,plain,((~product(e_2, e_3, e_1)) | product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(383,plain,
% 0.19/0.48 (~product(e_2, e_3, e_1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[382, 347])).
% 0.19/0.48 tff(384,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_3, 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_2, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(385,plain,
% 0.19/0.48 ((equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_2, e_3, e_2))) <=> (equalish(e_2, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(386,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_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_2, e_3, e_2)) | (~product(e_3, e_3, e_2))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[385])).
% 0.19/0.48 tff(387,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_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_2, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[386, 384])).
% 0.19/0.48 tff(388,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(389,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_3, e_2))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.19/0.49 tff(390,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[389, 26, 85, 99, 113])).
% 0.19/0.49 tff(391,plain,((~product(e_2, e_3, e_2)) | (~product(e_3, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(392,plain,
% 0.19/0.49 (~product(e_2, e_3, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[391, 99])).
% 0.19/0.49 tff(393,plain,
% 0.19/0.49 (product(e_2, e_3, e_1) | product(e_2, e_3, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[212, 51, 48, 45, 392])).
% 0.19/0.49 tff(394,plain,
% 0.19/0.49 (product(e_2, e_3, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[393, 383])).
% 0.19/0.49 tff(395,plain,
% 0.19/0.49 (~product(e_3, e_2, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[310, 394])).
% 0.19/0.49 tff(396,plain,
% 0.19/0.49 (product(e_3, e_2, e_1)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[58, 395, 347])).
% 0.19/0.49 tff(397,plain,
% 0.19/0.49 (((~![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_3)) | product(e_3, e_1, e_2) | (~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_2, e_3, e_3)) | product(e_3, e_1, e_2) | (~product(e_3, e_2, e_1)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(398,plain,
% 0.19/0.49 (((~product(e_3, e_2, e_1)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_3))) <=> ((~product(e_2, e_3, e_3)) | product(e_3, e_1, e_2) | (~product(e_3, e_2, e_1)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(399,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_3, e_1, e_2) | (~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_2, e_3, e_3)) | product(e_3, e_1, e_2) | (~product(e_3, e_2, e_1))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[398])).
% 0.19/0.49 tff(400,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_3, e_1, e_2) | (~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_2, e_3, e_3)) | product(e_3, e_1, e_2) | (~product(e_3, e_2, e_1)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[399, 397])).
% 0.19/0.49 tff(401,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_3)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(402,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_3, e_3)) | product(e_3, e_1, e_2) | (~product(e_3, e_2, e_1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.19/0.49 tff(403,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[402, 154, 394, 396, 338])).
% 0.19/0.49 tff(404,plain,(~product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(405,plain,
% 0.19/0.49 (product(e_3, e_3, e_1)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[332, 404])).
% 0.19/0.49 tff(406,plain,
% 0.19/0.49 (~product(e_3, e_1, e_1)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[232, 405])).
% 0.19/0.49 tff(407,plain,
% 0.19/0.49 (product(e_3, e_1, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[192, 406, 338])).
% 0.19/0.49 tff(408,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[328, 88, 85, 276, 405])).
% 0.19/0.49 tff(409,plain,(~product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(410,plain,
% 0.19/0.49 (product(e_1, e_3, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[273, 409])).
% 0.19/0.49 tff(411,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[363, 154, 410, 304, 407])).
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------