%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV103+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:31:30 AM UTC 2025
% Result : Theorem 47.63s 47.79s
% Output : Proof 47.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV103+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:28:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 47.63/47.79 % SZS status Theorem
% 47.63/47.79 % SZS output start Proof
% 47.63/47.79 tff(gt_type, type, (
% 47.63/47.79 gt: ( $i * $i ) > $o)).
% 47.63/47.79 tff(n0_type, type, (
% 47.63/47.79 n0: $i)).
% 47.63/47.79 tff(n1_type, type, (
% 47.63/47.79 n1: $i)).
% 47.63/47.79 tff(n3_type, type, (
% 47.63/47.79 n3: $i)).
% 47.63/47.79 tff(succ_type, type, (
% 47.63/47.79 succ: $i > $i)).
% 47.63/47.79 tff(a_select2_type, type, (
% 47.63/47.79 a_select2: ( $i * $i ) > $i)).
% 47.63/47.79 tff(tptp_update2_type, type, (
% 47.63/47.79 tptp_update2: ( $i * $i * $i ) > $i)).
% 47.63/47.79 tff(use_type, type, (
% 47.63/47.79 use: $i)).
% 47.63/47.79 tff(n2_type, type, (
% 47.63/47.79 n2: $i)).
% 47.63/47.79 tff(sigma_defuse_type, type, (
% 47.63/47.79 sigma_defuse: $i)).
% 47.63/47.79 tff(n5_type, type, (
% 47.63/47.79 n5: $i)).
% 47.63/47.79 tff(n4_type, type, (
% 47.63/47.79 n4: $i)).
% 47.63/47.79 tff(xinit_defuse_type, type, (
% 47.63/47.79 xinit_defuse: $i)).
% 47.63/47.79 tff(a_select3_type, type, (
% 47.63/47.79 a_select3: ( $i * $i * $i ) > $i)).
% 47.63/47.79 tff(u_defuse_type, type, (
% 47.63/47.79 u_defuse: $i)).
% 47.63/47.79 tff(1,assumption,(n2 = n0), introduced(assumption)).
% 47.63/47.79 tff(2,plain,
% 47.63/47.79 (n0 = n2),
% 47.63/47.79 inference(symmetry,[status(thm)],[1])).
% 47.63/47.79 tff(3,plain,
% 47.63/47.79 ((succ(n0) = n1) <=> (succ(n0) = n1)),
% 47.63/47.79 inference(rewrite,[status(thm)],[])).
% 47.63/47.79 tff(4,axiom,(succ(n0) = n1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','successor_1')).
% 47.63/47.79 tff(5,plain,
% 47.63/47.79 (succ(n0) = n1),
% 47.63/47.79 inference(modus_ponens,[status(thm)],[4, 3])).
% 47.63/47.79 tff(6,plain,
% 47.63/47.79 (n1 = succ(n0)),
% 47.63/47.79 inference(symmetry,[status(thm)],[5])).
% 47.63/47.79 tff(7,plain,
% 47.63/47.79 (gt(n1, n0) <=> gt(succ(n0), n2)),
% 47.63/47.79 inference(monotonicity,[status(thm)],[6, 2])).
% 47.63/47.79 tff(8,plain,
% 47.63/47.79 (gt(succ(n0), n2) <=> gt(n1, n0)),
% 47.63/47.79 inference(symmetry,[status(thm)],[7])).
% 47.63/47.79 tff(9,plain,
% 47.63/47.79 ((~gt(succ(n0), n2)) <=> (~gt(n1, n0))),
% 47.63/47.79 inference(monotonicity,[status(thm)],[8])).
% 47.63/47.79 tff(10,plain,
% 47.63/47.79 (gt(n1, n2) <=> gt(succ(n0), n2)),
% 47.63/47.79 inference(monotonicity,[status(thm)],[6])).
% 47.63/47.79 tff(11,plain,
% 47.63/47.79 ((~gt(n1, n2)) <=> (~gt(succ(n0), n2))),
% 47.63/47.79 inference(monotonicity,[status(thm)],[10])).
% 47.63/47.79 tff(12,plain,
% 47.63/47.79 (^[X: $i] : refl((~gt(X, X)) <=> (~gt(X, X)))),
% 47.63/47.79 inference(bind,[status(th)],[])).
% 47.63/47.79 tff(13,plain,
% 47.63/47.79 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 47.63/47.79 inference(quant_intro,[status(thm)],[12])).
% 47.63/47.79 tff(14,plain,
% 47.63/47.79 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 47.63/47.79 inference(rewrite,[status(thm)],[])).
% 47.63/47.79 tff(15,axiom,(![X: $i] : (~gt(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','irreflexivity_gt')).
% 47.63/47.79 tff(16,plain,
% 47.63/47.79 (![X: $i] : (~gt(X, X))),
% 47.63/47.79 inference(modus_ponens,[status(thm)],[15, 14])).
% 47.63/47.79 tff(17,plain,(
% 47.63/47.79 ![X: $i] : (~gt(X, X))),
% 47.63/47.79 inference(skolemize,[status(sab)],[16])).
% 47.63/47.79 tff(18,plain,
% 47.63/47.79 (![X: $i] : (~gt(X, X))),
% 47.63/47.79 inference(modus_ponens,[status(thm)],[17, 13])).
% 47.63/47.79 tff(19,plain,
% 47.63/47.79 ((~![X: $i] : (~gt(X, X))) | (~gt(n1, n1))),
% 47.63/47.79 inference(quant_inst,[status(thm)],[])).
% 47.63/47.79 tff(20,plain,
% 47.63/47.79 (~gt(n1, n1)),
% 47.63/47.79 inference(unit_resolution,[status(thm)],[19, 18])).
% 47.63/47.79 tff(21,plain,
% 47.63/47.79 (gt(n2, n1) <=> gt(n2, n1)),
% 47.63/47.79 inference(rewrite,[status(thm)],[])).
% 47.63/47.79 tff(22,axiom,(gt(n2, n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_2_1')).
% 47.63/47.79 tff(23,plain,
% 47.63/47.79 (gt(n2, n1)),
% 47.63/47.79 inference(modus_ponens,[status(thm)],[22, 21])).
% 47.63/47.79 tff(24,plain,
% 47.63/47.79 (![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))),
% 47.63/47.79 inference(rewrite,[status(thm)],[])).
% 47.63/47.79 tff(25,plain,
% 47.63/47.79 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((gt(X, Y) & gt(Y, Z)) <=> (~((~gt(X, Y)) | (~gt(Y, Z))))), ((~(gt(X, Y) & gt(Y, Z))) <=> (~(~((~gt(X, Y)) | (~gt(Y, Z))))))), rewrite((~(~((~gt(X, Y)) | (~gt(Y, Z))))) <=> ((~gt(X, Y)) | (~gt(Y, Z)))), ((~(gt(X, Y) & gt(Y, Z))) <=> ((~gt(X, Y)) | (~gt(Y, Z))))), (((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z)) <=> (((~gt(X, Y)) | (~gt(Y, Z))) | gt(X, Z)))), rewrite((((~gt(X, Y)) | (~gt(Y, Z))) | gt(X, Z)) <=> (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))), (((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z)) <=> (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))))),
% 47.63/47.79 inference(bind,[status(th)],[])).
% 47.63/47.79 tff(26,plain,
% 47.63/47.79 (![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))),
% 47.63/47.79 inference(quant_intro,[status(thm)],[25])).
% 47.63/47.79 tff(27,plain,
% 47.63/47.79 (![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z))),
% 47.63/47.79 inference(rewrite,[status(thm)],[])).
% 47.63/47.79 tff(28,plain,
% 47.63/47.79 (^[X: $i, Y: $i, Z: $i] : rewrite(((gt(X, Y) & gt(Y, Z)) => gt(X, Z)) <=> ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z)))),
% 47.63/47.79 inference(bind,[status(th)],[])).
% 47.63/47.79 tff(29,plain,
% 47.63/47.79 (![X: $i, Y: $i, Z: $i] : ((gt(X, Y) & gt(Y, Z)) => gt(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z))),
% 47.63/47.79 inference(quant_intro,[status(thm)],[28])).
% 47.63/47.79 tff(30,axiom,(![X: $i, Y: $i, Z: $i] : ((gt(X, Y) & gt(Y, Z)) => gt(X, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','transitivity_gt')).
% 47.63/47.79 tff(31,plain,
% 47.63/47.79 (![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z))),
% 47.63/47.79 inference(modus_ponens,[status(thm)],[30, 29])).
% 47.63/47.79 tff(32,plain,
% 47.63/47.79 (![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z))),
% 47.63/47.79 inference(modus_ponens,[status(thm)],[31, 27])).
% 47.63/47.79 tff(33,plain,(
% 47.63/47.79 ![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z))),
% 47.63/47.79 inference(skolemize,[status(sab)],[32])).
% 47.63/47.79 tff(34,plain,
% 47.63/47.79 (![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))),
% 47.63/47.79 inference(modus_ponens,[status(thm)],[33, 26])).
% 47.63/47.79 tff(35,plain,
% 47.63/47.79 (![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))),
% 47.63/47.79 inference(modus_ponens,[status(thm)],[34, 24])).
% 47.63/47.79 tff(36,plain,
% 47.63/47.79 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | ((~gt(n2, n1)) | gt(n1, n1) | (~gt(n1, n2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n2, n1)) | gt(n1, n1) | (~gt(n1, n2)))),
% 47.63/47.79 inference(rewrite,[status(thm)],[])).
% 47.63/47.79 tff(37,plain,
% 47.63/47.79 ((gt(n1, n1) | (~gt(n1, n2)) | (~gt(n2, n1))) <=> ((~gt(n2, n1)) | gt(n1, n1) | (~gt(n1, n2)))),
% 47.63/47.79 inference(rewrite,[status(thm)],[])).
% 47.63/47.79 tff(38,plain,
% 47.63/47.79 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n1, n1) | (~gt(n1, n2)) | (~gt(n2, n1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | ((~gt(n2, n1)) | gt(n1, n1) | (~gt(n1, n2))))),
% 47.63/47.79 inference(monotonicity,[status(thm)],[37])).
% 47.63/47.79 tff(39,plain,
% 47.63/47.79 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n1, n1) | (~gt(n1, n2)) | (~gt(n2, n1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n2, n1)) | gt(n1, n1) | (~gt(n1, n2)))),
% 47.63/47.79 inference(transitivity,[status(thm)],[38, 36])).
% 47.63/47.79 tff(40,plain,
% 47.63/47.79 ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n1, n1) | (~gt(n1, n2)) | (~gt(n2, n1)))),
% 47.63/47.79 inference(quant_inst,[status(thm)],[])).
% 47.63/47.79 tff(41,plain,
% 47.63/47.79 ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n2, n1)) | gt(n1, n1) | (~gt(n1, n2))),
% 47.63/47.79 inference(modus_ponens,[status(thm)],[40, 39])).
% 47.63/47.79 tff(42,plain,
% 47.63/47.79 (~gt(n1, n2)),
% 47.63/47.79 inference(unit_resolution,[status(thm)],[41, 35, 23, 20])).
% 47.63/47.79 tff(43,plain,
% 47.63/47.79 (~gt(succ(n0), n2)),
% 47.63/47.79 inference(modus_ponens,[status(thm)],[42, 11])).
% 47.63/47.79 tff(44,plain,
% 47.63/47.79 (~gt(n1, n0)),
% 47.63/47.79 inference(modus_ponens,[status(thm)],[43, 9])).
% 47.63/47.79 tff(45,plain,
% 47.63/47.79 (gt(n1, n0) <=> gt(n1, n0)),
% 47.63/47.79 inference(rewrite,[status(thm)],[])).
% 47.63/47.79 tff(46,axiom,(gt(n1, n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_1_0')).
% 47.63/47.79 tff(47,plain,
% 47.63/47.79 (gt(n1, n0)),
% 47.63/47.79 inference(modus_ponens,[status(thm)],[46, 45])).
% 47.63/47.79 tff(48,plain,
% 47.63/47.79 ($false),
% 47.63/47.79 inference(unit_resolution,[status(thm)],[47, 44])).
% 47.63/47.79 tff(49,plain,(~(n2 = n0)), inference(lemma,lemma(discharge,[]))).
% 47.63/47.79 tff(50,plain,
% 47.63/47.79 (![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL) <=> ![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 47.63/47.79 inference(rewrite,[status(thm)],[])).
% 47.63/47.79 tff(51,plain,
% 47.63/47.79 (![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL) <=> ![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 47.63/47.79 inference(rewrite,[status(thm)],[])).
% 47.63/47.79 tff(52,axiom,(![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','sel2_update_1')).
% 47.63/47.79 tff(53,plain,
% 47.63/47.79 (![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[52, 51])).
% 47.63/47.80 tff(54,plain,(
% 47.63/47.80 ![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 47.63/47.80 inference(skolemize,[status(sab)],[53])).
% 47.63/47.80 tff(55,plain,
% 47.63/47.80 (![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[54, 50])).
% 47.63/47.80 tff(56,plain,
% 47.63/47.80 ((~![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)) | (a_select2(tptp_update2(sigma_defuse, n0, use), n0) = use)),
% 47.63/47.80 inference(quant_inst,[status(thm)],[])).
% 47.63/47.80 tff(57,plain,
% 47.63/47.80 (a_select2(tptp_update2(sigma_defuse, n0, use), n0) = use),
% 47.63/47.80 inference(unit_resolution,[status(thm)],[56, 55])).
% 47.63/47.80 tff(58,assumption,(n1 = n0), introduced(assumption)).
% 47.63/47.80 tff(59,plain,
% 47.63/47.80 (n0 = n1),
% 47.63/47.80 inference(symmetry,[status(thm)],[58])).
% 47.63/47.80 tff(60,plain,
% 47.63/47.80 (gt(n1, n0) <=> gt(succ(n0), n1)),
% 47.63/47.80 inference(monotonicity,[status(thm)],[6, 59])).
% 47.63/47.80 tff(61,plain,
% 47.63/47.80 (gt(succ(n0), n1) <=> gt(n1, n0)),
% 47.63/47.80 inference(symmetry,[status(thm)],[60])).
% 47.63/47.80 tff(62,plain,
% 47.63/47.80 ((~gt(succ(n0), n1)) <=> (~gt(n1, n0))),
% 47.63/47.80 inference(monotonicity,[status(thm)],[61])).
% 47.63/47.80 tff(63,plain,
% 47.63/47.80 (gt(n1, n1) <=> gt(succ(n0), n1)),
% 47.63/47.80 inference(monotonicity,[status(thm)],[6])).
% 47.63/47.80 tff(64,plain,
% 47.63/47.80 ((~gt(n1, n1)) <=> (~gt(succ(n0), n1))),
% 47.63/47.80 inference(monotonicity,[status(thm)],[63])).
% 47.63/47.80 tff(65,plain,
% 47.63/47.80 (~gt(succ(n0), n1)),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[20, 64])).
% 47.63/47.80 tff(66,plain,
% 47.63/47.80 (~gt(n1, n0)),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[65, 62])).
% 47.63/47.80 tff(67,plain,
% 47.63/47.80 ($false),
% 47.63/47.80 inference(unit_resolution,[status(thm)],[47, 66])).
% 47.63/47.80 tff(68,plain,(~(n1 = n0)), inference(lemma,lemma(discharge,[]))).
% 47.63/47.80 tff(69,plain,
% 47.63/47.80 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(70,plain,
% 47.63/47.80 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(71,plain,
% 47.63/47.80 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 47.63/47.80 inference(elim_unused_vars,[status(thm)],[])).
% 47.63/47.80 tff(72,plain,
% 47.63/47.80 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((~((~(I = U)) & (a_select2(X, U) = VAL))) | (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 47.63/47.80 inference(destructive_equality_resolution,[status(thm)],[])).
% 47.63/47.80 tff(73,plain,
% 47.63/47.80 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((~((~(I = U)) & (a_select2(X, U) = VAL))) | (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 47.63/47.80 inference(transitivity,[status(thm)],[72, 71])).
% 47.63/47.80 tff(74,plain,
% 47.63/47.80 (^[I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : rewrite((((~(I = U)) & (a_select2(X, U) = VAL)) => (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ((~((~(I = U)) & (a_select2(X, U) = VAL))) | (a_select2(tptp_update2(X, I, VAL2), U) = VAL)))),
% 47.63/47.80 inference(bind,[status(th)],[])).
% 47.63/47.80 tff(75,plain,
% 47.63/47.80 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : (((~(I = U)) & (a_select2(X, U) = VAL)) => (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((~((~(I = U)) & (a_select2(X, U) = VAL))) | (a_select2(tptp_update2(X, I, VAL2), U) = VAL))),
% 47.63/47.80 inference(quant_intro,[status(thm)],[74])).
% 47.63/47.80 tff(76,plain,
% 47.63/47.80 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : (((~(I = U)) & (a_select2(X, U) = VAL)) => (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 47.63/47.80 inference(transitivity,[status(thm)],[75, 73])).
% 47.63/47.80 tff(77,axiom,(![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : (((~(I = U)) & (a_select2(X, U) = VAL)) => (a_select2(tptp_update2(X, I, VAL2), U) = VAL))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','sel2_update_2')).
% 47.63/47.80 tff(78,plain,
% 47.63/47.80 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[77, 76])).
% 47.63/47.80 tff(79,plain,
% 47.63/47.80 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[78, 70])).
% 47.63/47.80 tff(80,plain,(
% 47.63/47.80 ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 47.63/47.80 inference(skolemize,[status(sab)],[79])).
% 47.63/47.80 tff(81,plain,
% 47.63/47.80 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[80, 69])).
% 47.63/47.80 tff(82,plain,
% 47.63/47.80 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n1 = n0) | (a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(sigma_defuse, n0, use), n0)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n1 = n0) | (a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(sigma_defuse, n0, use), n0)))),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(83,plain,
% 47.63/47.80 (((a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(sigma_defuse, n0, use), n0)) | (n1 = n0)) <=> ((n1 = n0) | (a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(sigma_defuse, n0, use), n0)))),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(84,plain,
% 47.63/47.80 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(sigma_defuse, n0, use), n0)) | (n1 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n1 = n0) | (a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(sigma_defuse, n0, use), n0))))),
% 47.63/47.80 inference(monotonicity,[status(thm)],[83])).
% 47.63/47.80 tff(85,plain,
% 47.63/47.80 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(sigma_defuse, n0, use), n0)) | (n1 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n1 = n0) | (a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(sigma_defuse, n0, use), n0)))),
% 47.63/47.80 inference(transitivity,[status(thm)],[84, 82])).
% 47.63/47.80 tff(86,plain,
% 47.63/47.80 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(sigma_defuse, n0, use), n0)) | (n1 = n0))),
% 47.63/47.80 inference(quant_inst,[status(thm)],[])).
% 47.63/47.80 tff(87,plain,
% 47.63/47.80 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n1 = n0) | (a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(sigma_defuse, n0, use), n0))),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[86, 85])).
% 47.63/47.80 tff(88,plain,
% 47.63/47.80 (a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(sigma_defuse, n0, use), n0)),
% 47.63/47.80 inference(unit_resolution,[status(thm)],[87, 81, 68])).
% 47.63/47.80 tff(89,assumption,(~(n2 = n0)), introduced(assumption)).
% 47.63/47.80 tff(90,plain,
% 47.63/47.80 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n2 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n2 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0)))),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(91,plain,
% 47.63/47.80 (((a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0)) | (n2 = n0)) <=> ((n2 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0)))),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(92,plain,
% 47.63/47.80 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0)) | (n2 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n2 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0))))),
% 47.63/47.80 inference(monotonicity,[status(thm)],[91])).
% 47.63/47.80 tff(93,plain,
% 47.63/47.80 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0)) | (n2 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n2 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0)))),
% 47.63/47.80 inference(transitivity,[status(thm)],[92, 90])).
% 47.63/47.80 tff(94,plain,
% 47.63/47.80 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0)) | (n2 = n0))),
% 47.63/47.80 inference(quant_inst,[status(thm)],[])).
% 47.63/47.80 tff(95,plain,
% 47.63/47.80 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n2 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0))),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[94, 93])).
% 47.63/47.80 tff(96,plain,
% 47.63/47.80 (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n0)),
% 47.63/47.80 inference(unit_resolution,[status(thm)],[95, 81, 89])).
% 47.63/47.80 tff(97,assumption,(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0)), introduced(assumption)).
% 47.63/47.80 tff(98,assumption,(n4 = n0), introduced(assumption)).
% 47.63/47.80 tff(99,plain,
% 47.63/47.80 (n0 = n4),
% 47.63/47.80 inference(symmetry,[status(thm)],[98])).
% 47.63/47.80 tff(100,plain,
% 47.63/47.80 ((succ(succ(succ(n0))) = n3) <=> (succ(succ(succ(n0))) = n3)),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(101,axiom,(succ(succ(succ(n0))) = n3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','successor_3')).
% 47.63/47.80 tff(102,plain,
% 47.63/47.80 (succ(succ(succ(n0))) = n3),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[101, 100])).
% 47.63/47.80 tff(103,plain,
% 47.63/47.80 (n3 = succ(succ(succ(n0)))),
% 47.63/47.80 inference(symmetry,[status(thm)],[102])).
% 47.63/47.80 tff(104,plain,
% 47.63/47.80 (succ(n3) = succ(succ(succ(succ(n0))))),
% 47.63/47.80 inference(monotonicity,[status(thm)],[103])).
% 47.63/47.80 tff(105,plain,
% 47.63/47.80 (succ(succ(succ(succ(n0)))) = succ(n3)),
% 47.63/47.80 inference(symmetry,[status(thm)],[104])).
% 47.63/47.80 tff(106,plain,
% 47.63/47.80 ((succ(succ(succ(succ(n0)))) = n4) <=> (succ(succ(succ(succ(n0)))) = n4)),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(107,axiom,(succ(succ(succ(succ(n0)))) = n4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','successor_4')).
% 47.63/47.80 tff(108,plain,
% 47.63/47.80 (succ(succ(succ(succ(n0)))) = n4),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[107, 106])).
% 47.63/47.80 tff(109,plain,
% 47.63/47.80 (n4 = succ(succ(succ(succ(n0))))),
% 47.63/47.80 inference(symmetry,[status(thm)],[108])).
% 47.63/47.80 tff(110,plain,
% 47.63/47.80 (n4 = succ(n3)),
% 47.63/47.80 inference(transitivity,[status(thm)],[109, 105])).
% 47.63/47.80 tff(111,plain,
% 47.63/47.80 (gt(n4, n0) <=> gt(succ(n3), n4)),
% 47.63/47.80 inference(monotonicity,[status(thm)],[110, 99])).
% 47.63/47.80 tff(112,plain,
% 47.63/47.80 (gt(succ(n3), n4) <=> gt(n4, n0)),
% 47.63/47.80 inference(symmetry,[status(thm)],[111])).
% 47.63/47.80 tff(113,plain,
% 47.63/47.80 ((~gt(succ(n3), n4)) <=> (~gt(n4, n0))),
% 47.63/47.80 inference(monotonicity,[status(thm)],[112])).
% 47.63/47.80 tff(114,plain,
% 47.63/47.80 (gt(n4, n4) <=> gt(succ(n3), n4)),
% 47.63/47.80 inference(monotonicity,[status(thm)],[110])).
% 47.63/47.80 tff(115,plain,
% 47.63/47.80 ((~gt(n4, n4)) <=> (~gt(succ(n3), n4))),
% 47.63/47.80 inference(monotonicity,[status(thm)],[114])).
% 47.63/47.80 tff(116,plain,
% 47.63/47.80 ((~![X: $i] : (~gt(X, X))) | (~gt(n4, n4))),
% 47.63/47.80 inference(quant_inst,[status(thm)],[])).
% 47.63/47.80 tff(117,plain,
% 47.63/47.80 (~gt(n4, n4)),
% 47.63/47.80 inference(unit_resolution,[status(thm)],[116, 18])).
% 47.63/47.80 tff(118,plain,
% 47.63/47.80 (~gt(succ(n3), n4)),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[117, 115])).
% 47.63/47.80 tff(119,plain,
% 47.63/47.80 (~gt(n4, n0)),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[118, 113])).
% 47.63/47.80 tff(120,plain,
% 47.63/47.80 (gt(n4, n0) <=> gt(n4, n0)),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(121,axiom,(gt(n4, n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_4_0')).
% 47.63/47.80 tff(122,plain,
% 47.63/47.80 (gt(n4, n0)),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[121, 120])).
% 47.63/47.80 tff(123,plain,
% 47.63/47.80 ($false),
% 47.63/47.80 inference(unit_resolution,[status(thm)],[122, 119])).
% 47.63/47.80 tff(124,plain,(~(n4 = n0)), inference(lemma,lemma(discharge,[]))).
% 47.63/47.80 tff(125,plain,
% 47.63/47.80 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n4 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n4 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0)))),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(126,plain,
% 47.63/47.80 (((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0)) | (n4 = n0)) <=> ((n4 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0)))),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(127,plain,
% 47.63/47.80 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0)) | (n4 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n4 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0))))),
% 47.63/47.80 inference(monotonicity,[status(thm)],[126])).
% 47.63/47.80 tff(128,plain,
% 47.63/47.80 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0)) | (n4 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n4 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0)))),
% 47.63/47.80 inference(transitivity,[status(thm)],[127, 125])).
% 47.63/47.80 tff(129,plain,
% 47.63/47.80 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0)) | (n4 = n0))),
% 47.63/47.80 inference(quant_inst,[status(thm)],[])).
% 47.63/47.80 tff(130,plain,
% 47.63/47.80 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n4 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0))),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[129, 128])).
% 47.63/47.80 tff(131,plain,
% 47.63/47.80 ((n4 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0))),
% 47.63/47.80 inference(unit_resolution,[status(thm)],[130, 81])).
% 47.63/47.80 tff(132,plain,
% 47.63/47.80 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0)),
% 47.63/47.80 inference(unit_resolution,[status(thm)],[131, 124])).
% 47.63/47.80 tff(133,assumption,(n5 = n0), introduced(assumption)).
% 47.63/47.80 tff(134,plain,
% 47.63/47.80 (n0 = n5),
% 47.63/47.80 inference(symmetry,[status(thm)],[133])).
% 47.63/47.80 tff(135,plain,
% 47.63/47.80 (gt(n4, n0) <=> gt(succ(n3), n5)),
% 47.63/47.80 inference(monotonicity,[status(thm)],[110, 134])).
% 47.63/47.80 tff(136,plain,
% 47.63/47.80 (gt(succ(n3), n5) <=> gt(n4, n0)),
% 47.63/47.80 inference(symmetry,[status(thm)],[135])).
% 47.63/47.80 tff(137,plain,
% 47.63/47.80 ((~gt(succ(n3), n5)) <=> (~gt(n4, n0))),
% 47.63/47.80 inference(monotonicity,[status(thm)],[136])).
% 47.63/47.80 tff(138,plain,
% 47.63/47.80 (gt(n4, n5) <=> gt(succ(n3), n5)),
% 47.63/47.80 inference(monotonicity,[status(thm)],[110])).
% 47.63/47.80 tff(139,plain,
% 47.63/47.80 ((~gt(n4, n5)) <=> (~gt(succ(n3), n5))),
% 47.63/47.80 inference(monotonicity,[status(thm)],[138])).
% 47.63/47.80 tff(140,plain,
% 47.63/47.80 (gt(n5, n4) <=> gt(n5, n4)),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(141,axiom,(gt(n5, n4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_5_4')).
% 47.63/47.80 tff(142,plain,
% 47.63/47.80 (gt(n5, n4)),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[141, 140])).
% 47.63/47.80 tff(143,plain,
% 47.63/47.80 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | ((~gt(n5, n4)) | (~gt(n4, n5)) | gt(n4, n4))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n5, n4)) | (~gt(n4, n5)) | gt(n4, n4))),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(144,plain,
% 47.63/47.80 ((gt(n4, n4) | (~gt(n4, n5)) | (~gt(n5, n4))) <=> ((~gt(n5, n4)) | (~gt(n4, n5)) | gt(n4, n4))),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(145,plain,
% 47.63/47.80 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n4, n4) | (~gt(n4, n5)) | (~gt(n5, n4)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | ((~gt(n5, n4)) | (~gt(n4, n5)) | gt(n4, n4)))),
% 47.63/47.80 inference(monotonicity,[status(thm)],[144])).
% 47.63/47.80 tff(146,plain,
% 47.63/47.80 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n4, n4) | (~gt(n4, n5)) | (~gt(n5, n4)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n5, n4)) | (~gt(n4, n5)) | gt(n4, n4))),
% 47.63/47.80 inference(transitivity,[status(thm)],[145, 143])).
% 47.63/47.80 tff(147,plain,
% 47.63/47.80 ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n4, n4) | (~gt(n4, n5)) | (~gt(n5, n4)))),
% 47.63/47.80 inference(quant_inst,[status(thm)],[])).
% 47.63/47.80 tff(148,plain,
% 47.63/47.80 ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n5, n4)) | (~gt(n4, n5)) | gt(n4, n4)),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[147, 146])).
% 47.63/47.80 tff(149,plain,
% 47.63/47.80 ((~gt(n4, n5)) | gt(n4, n4)),
% 47.63/47.80 inference(unit_resolution,[status(thm)],[148, 35, 142])).
% 47.63/47.80 tff(150,plain,
% 47.63/47.80 (~gt(n4, n5)),
% 47.63/47.80 inference(unit_resolution,[status(thm)],[149, 117])).
% 47.63/47.80 tff(151,plain,
% 47.63/47.80 (~gt(succ(n3), n5)),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[150, 139])).
% 47.63/47.80 tff(152,plain,
% 47.63/47.80 (~gt(n4, n0)),
% 47.63/47.80 inference(modus_ponens,[status(thm)],[151, 137])).
% 47.63/47.80 tff(153,plain,
% 47.63/47.80 ($false),
% 47.63/47.80 inference(unit_resolution,[status(thm)],[122, 152])).
% 47.63/47.80 tff(154,plain,(~(n5 = n0)), inference(lemma,lemma(discharge,[]))).
% 47.63/47.80 tff(155,plain,
% 47.63/47.80 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n5 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0)))),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(156,plain,
% 47.63/47.80 (((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0)) | (n5 = n0)) <=> ((n5 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0)))),
% 47.63/47.80 inference(rewrite,[status(thm)],[])).
% 47.63/47.80 tff(157,plain,
% 47.63/47.80 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0)) | (n5 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n5 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0))))),
% 47.63/47.81 inference(monotonicity,[status(thm)],[156])).
% 47.63/47.81 tff(158,plain,
% 47.63/47.81 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0)) | (n5 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0)))),
% 47.63/47.81 inference(transitivity,[status(thm)],[157, 155])).
% 47.63/47.81 tff(159,plain,
% 47.63/47.81 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0)) | (n5 = n0))),
% 47.63/47.81 inference(quant_inst,[status(thm)],[])).
% 47.63/47.81 tff(160,plain,
% 47.63/47.81 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0))),
% 47.63/47.81 inference(modus_ponens,[status(thm)],[159, 158])).
% 47.63/47.81 tff(161,plain,
% 47.63/47.81 ((n5 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0))),
% 47.63/47.81 inference(unit_resolution,[status(thm)],[160, 81])).
% 47.63/47.81 tff(162,plain,
% 47.63/47.81 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n0)),
% 47.63/47.81 inference(unit_resolution,[status(thm)],[161, 154])).
% 47.63/47.81 tff(163,plain,
% 47.63/47.81 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use),
% 47.63/47.81 inference(transitivity,[status(thm)],[162, 132, 97, 96, 88, 57])).
% 47.63/47.81 tff(164,assumption,(n2 = n1), introduced(assumption)).
% 47.63/47.81 tff(165,plain,
% 47.63/47.81 (n1 = n2),
% 47.63/47.81 inference(symmetry,[status(thm)],[164])).
% 47.63/47.81 tff(166,plain,
% 47.63/47.81 (succ(n1) = succ(succ(n0))),
% 47.63/47.81 inference(monotonicity,[status(thm)],[6])).
% 47.63/47.81 tff(167,plain,
% 47.63/47.81 (succ(succ(n0)) = succ(n1)),
% 47.63/47.81 inference(symmetry,[status(thm)],[166])).
% 47.63/47.81 tff(168,plain,
% 47.63/47.81 ((succ(succ(n0)) = n2) <=> (succ(succ(n0)) = n2)),
% 47.63/47.81 inference(rewrite,[status(thm)],[])).
% 47.63/47.81 tff(169,axiom,(succ(succ(n0)) = n2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','successor_2')).
% 47.63/47.81 tff(170,plain,
% 47.63/47.81 (succ(succ(n0)) = n2),
% 47.63/47.81 inference(modus_ponens,[status(thm)],[169, 168])).
% 47.63/47.81 tff(171,plain,
% 47.63/47.81 (n2 = succ(succ(n0))),
% 47.63/47.81 inference(symmetry,[status(thm)],[170])).
% 47.63/47.81 tff(172,plain,
% 47.63/47.81 (n2 = succ(n1)),
% 47.63/47.81 inference(transitivity,[status(thm)],[171, 167])).
% 47.63/47.81 tff(173,plain,
% 47.63/47.81 (gt(n2, n1) <=> gt(succ(n1), n2)),
% 47.63/47.81 inference(monotonicity,[status(thm)],[172, 165])).
% 47.63/47.81 tff(174,plain,
% 47.63/47.81 (gt(succ(n1), n2) <=> gt(n2, n1)),
% 47.63/47.81 inference(symmetry,[status(thm)],[173])).
% 47.63/47.81 tff(175,plain,
% 47.63/47.81 ((~gt(succ(n1), n2)) <=> (~gt(n2, n1))),
% 47.63/47.81 inference(monotonicity,[status(thm)],[174])).
% 47.63/47.81 tff(176,plain,
% 47.63/47.81 (gt(n2, n2) <=> gt(succ(n1), n2)),
% 47.63/47.81 inference(monotonicity,[status(thm)],[172])).
% 47.63/47.81 tff(177,plain,
% 47.63/47.81 ((~gt(n2, n2)) <=> (~gt(succ(n1), n2))),
% 47.63/47.81 inference(monotonicity,[status(thm)],[176])).
% 47.63/47.81 tff(178,plain,
% 47.63/47.81 ((~![X: $i] : (~gt(X, X))) | (~gt(n2, n2))),
% 47.63/47.81 inference(quant_inst,[status(thm)],[])).
% 47.63/47.81 tff(179,plain,
% 47.63/47.81 (~gt(n2, n2)),
% 47.63/47.81 inference(unit_resolution,[status(thm)],[178, 18])).
% 47.63/47.81 tff(180,plain,
% 47.63/47.81 (~gt(succ(n1), n2)),
% 47.63/47.81 inference(modus_ponens,[status(thm)],[179, 177])).
% 47.63/47.81 tff(181,plain,
% 47.63/47.81 (~gt(n2, n1)),
% 47.63/47.81 inference(modus_ponens,[status(thm)],[180, 175])).
% 47.63/47.81 tff(182,plain,
% 47.63/47.81 ($false),
% 47.63/47.81 inference(unit_resolution,[status(thm)],[23, 181])).
% 47.63/47.81 tff(183,plain,(~(n2 = n1)), inference(lemma,lemma(discharge,[]))).
% 47.63/47.81 tff(184,assumption,(~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1))), introduced(assumption)).
% 47.63/47.81 tff(185,assumption,(n3 = n1), introduced(assumption)).
% 47.63/47.81 tff(186,plain,
% 47.63/47.81 (n1 = n3),
% 47.63/47.81 inference(symmetry,[status(thm)],[185])).
% 47.63/47.81 tff(187,plain,
% 47.63/47.81 (gt(n2, n1) <=> gt(succ(n1), n3)),
% 47.63/47.81 inference(monotonicity,[status(thm)],[172, 186])).
% 47.63/47.81 tff(188,plain,
% 47.63/47.81 (gt(succ(n1), n3) <=> gt(n2, n1)),
% 47.63/47.81 inference(symmetry,[status(thm)],[187])).
% 47.63/47.81 tff(189,plain,
% 47.63/47.81 ((~gt(succ(n1), n3)) <=> (~gt(n2, n1))),
% 47.63/47.81 inference(monotonicity,[status(thm)],[188])).
% 47.63/47.81 tff(190,plain,
% 47.63/47.81 (gt(n2, n3) <=> gt(succ(n1), n3)),
% 47.63/47.81 inference(monotonicity,[status(thm)],[172])).
% 47.63/47.81 tff(191,plain,
% 47.63/47.81 ((~gt(n2, n3)) <=> (~gt(succ(n1), n3))),
% 47.63/47.81 inference(monotonicity,[status(thm)],[190])).
% 47.63/47.81 tff(192,plain,
% 47.63/47.81 (gt(n3, n2) <=> gt(n3, n2)),
% 47.63/47.81 inference(rewrite,[status(thm)],[])).
% 47.63/47.81 tff(193,axiom,(gt(n3, n2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_3_2')).
% 47.63/47.81 tff(194,plain,
% 47.63/47.81 (gt(n3, n2)),
% 47.63/47.81 inference(modus_ponens,[status(thm)],[193, 192])).
% 47.63/47.81 tff(195,plain,
% 47.63/47.81 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | ((~gt(n3, n2)) | gt(n2, n2) | (~gt(n2, n3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n3, n2)) | gt(n2, n2) | (~gt(n2, n3)))),
% 47.63/47.81 inference(rewrite,[status(thm)],[])).
% 47.63/47.81 tff(196,plain,
% 47.63/47.81 ((gt(n2, n2) | (~gt(n2, n3)) | (~gt(n3, n2))) <=> ((~gt(n3, n2)) | gt(n2, n2) | (~gt(n2, n3)))),
% 47.63/47.81 inference(rewrite,[status(thm)],[])).
% 47.63/47.81 tff(197,plain,
% 47.63/47.81 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n2, n2) | (~gt(n2, n3)) | (~gt(n3, n2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | ((~gt(n3, n2)) | gt(n2, n2) | (~gt(n2, n3))))),
% 47.63/47.81 inference(monotonicity,[status(thm)],[196])).
% 47.63/47.81 tff(198,plain,
% 47.63/47.81 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n2, n2) | (~gt(n2, n3)) | (~gt(n3, n2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n3, n2)) | gt(n2, n2) | (~gt(n2, n3)))),
% 47.63/47.81 inference(transitivity,[status(thm)],[197, 195])).
% 47.63/47.81 tff(199,plain,
% 47.63/47.81 ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n2, n2) | (~gt(n2, n3)) | (~gt(n3, n2)))),
% 47.63/47.81 inference(quant_inst,[status(thm)],[])).
% 47.63/47.81 tff(200,plain,
% 47.63/47.81 ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n3, n2)) | gt(n2, n2) | (~gt(n2, n3))),
% 47.63/47.81 inference(modus_ponens,[status(thm)],[199, 198])).
% 47.63/47.81 tff(201,plain,
% 47.63/47.81 (~gt(n2, n3)),
% 47.63/47.81 inference(unit_resolution,[status(thm)],[200, 35, 194, 179])).
% 47.63/47.81 tff(202,plain,
% 47.63/47.81 (~gt(succ(n1), n3)),
% 47.63/47.81 inference(modus_ponens,[status(thm)],[201, 191])).
% 47.63/47.81 tff(203,plain,
% 47.63/47.81 (~gt(n2, n1)),
% 47.63/47.81 inference(modus_ponens,[status(thm)],[202, 189])).
% 47.63/47.81 tff(204,plain,
% 47.63/47.81 ($false),
% 47.63/47.81 inference(unit_resolution,[status(thm)],[23, 203])).
% 47.63/47.81 tff(205,plain,(~(n3 = n1)), inference(lemma,lemma(discharge,[]))).
% 47.63/47.81 tff(206,plain,
% 47.63/47.81 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n3 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n3 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1)))),
% 47.63/47.81 inference(rewrite,[status(thm)],[])).
% 47.63/47.81 tff(207,plain,
% 47.63/47.81 (((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1)) | (n3 = n1)) <=> ((n3 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1)))),
% 47.63/47.81 inference(rewrite,[status(thm)],[])).
% 47.63/47.81 tff(208,plain,
% 47.63/47.81 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1)) | (n3 = n1))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n3 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1))))),
% 47.63/47.81 inference(monotonicity,[status(thm)],[207])).
% 47.63/47.81 tff(209,plain,
% 47.63/47.81 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1)) | (n3 = n1))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n3 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1)))),
% 47.63/47.81 inference(transitivity,[status(thm)],[208, 206])).
% 47.63/47.81 tff(210,plain,
% 47.63/47.81 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1)) | (n3 = n1))),
% 47.63/47.81 inference(quant_inst,[status(thm)],[])).
% 47.63/47.81 tff(211,plain,
% 47.63/47.81 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n3 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1))),
% 47.63/47.81 inference(modus_ponens,[status(thm)],[210, 209])).
% 47.63/47.81 tff(212,plain,
% 47.63/47.81 ($false),
% 47.63/47.81 inference(unit_resolution,[status(thm)],[211, 81, 205, 184])).
% 47.63/47.81 tff(213,plain,(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1)), inference(lemma,lemma(discharge,[]))).
% 47.66/47.81 tff(214,plain,
% 47.66/47.81 ((~![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)) | (a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n1) = use)),
% 47.66/47.81 inference(quant_inst,[status(thm)],[])).
% 47.66/47.81 tff(215,plain,
% 47.66/47.81 (a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n1) = use),
% 47.66/47.81 inference(unit_resolution,[status(thm)],[214, 55])).
% 47.66/47.81 tff(216,assumption,(~(n2 = n1)), introduced(assumption)).
% 47.66/47.81 tff(217,plain,
% 47.66/47.81 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n2 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n1)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n2 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n1)))),
% 47.66/47.81 inference(rewrite,[status(thm)],[])).
% 47.66/47.81 tff(218,plain,
% 47.66/47.81 (((a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n1)) | (n2 = n1)) <=> ((n2 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n1)))),
% 47.66/47.81 inference(rewrite,[status(thm)],[])).
% 47.66/47.81 tff(219,plain,
% 47.66/47.81 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n1)) | (n2 = n1))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n2 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n1))))),
% 47.66/47.81 inference(monotonicity,[status(thm)],[218])).
% 47.66/47.81 tff(220,plain,
% 47.66/47.81 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n1)) | (n2 = n1))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n2 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n1)))),
% 47.66/47.81 inference(transitivity,[status(thm)],[219, 217])).
% 47.66/47.81 tff(221,plain,
% 47.66/47.81 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n1)) | (n2 = n1))),
% 47.66/47.81 inference(quant_inst,[status(thm)],[])).
% 47.66/47.81 tff(222,plain,
% 47.66/47.81 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n2 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n1))),
% 47.66/47.81 inference(modus_ponens,[status(thm)],[221, 220])).
% 47.66/47.81 tff(223,plain,
% 47.66/47.81 (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n1)),
% 47.66/47.81 inference(unit_resolution,[status(thm)],[222, 81, 216])).
% 47.66/47.81 tff(224,assumption,(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1)), introduced(assumption)).
% 47.66/47.81 tff(225,assumption,(n4 = n1), introduced(assumption)).
% 47.66/47.81 tff(226,plain,
% 47.66/47.81 (n1 = n4),
% 47.66/47.81 inference(symmetry,[status(thm)],[225])).
% 47.66/47.81 tff(227,plain,
% 47.66/47.81 (gt(n4, n1) <=> gt(succ(n3), n4)),
% 47.66/47.81 inference(monotonicity,[status(thm)],[110, 226])).
% 47.66/47.81 tff(228,plain,
% 47.66/47.81 (gt(succ(n3), n4) <=> gt(n4, n1)),
% 47.66/47.81 inference(symmetry,[status(thm)],[227])).
% 47.66/47.81 tff(229,plain,
% 47.66/47.81 ((~gt(succ(n3), n4)) <=> (~gt(n4, n1))),
% 47.66/47.81 inference(monotonicity,[status(thm)],[228])).
% 47.66/47.81 tff(230,plain,
% 47.66/47.81 (~gt(n4, n1)),
% 47.66/47.81 inference(modus_ponens,[status(thm)],[118, 229])).
% 47.66/47.81 tff(231,plain,
% 47.66/47.81 (gt(n4, n1) <=> gt(n4, n1)),
% 47.66/47.81 inference(rewrite,[status(thm)],[])).
% 47.66/47.81 tff(232,axiom,(gt(n4, n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_4_1')).
% 47.66/47.81 tff(233,plain,
% 47.66/47.81 (gt(n4, n1)),
% 47.66/47.81 inference(modus_ponens,[status(thm)],[232, 231])).
% 47.66/47.81 tff(234,plain,
% 47.66/47.81 ($false),
% 47.66/47.81 inference(unit_resolution,[status(thm)],[233, 230])).
% 47.66/47.81 tff(235,plain,(~(n4 = n1)), inference(lemma,lemma(discharge,[]))).
% 47.66/47.81 tff(236,plain,
% 47.66/47.81 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n4 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n4 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1)))),
% 47.66/47.81 inference(rewrite,[status(thm)],[])).
% 47.66/47.81 tff(237,plain,
% 47.66/47.81 (((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1)) | (n4 = n1)) <=> ((n4 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1)))),
% 47.66/47.81 inference(rewrite,[status(thm)],[])).
% 47.66/47.81 tff(238,plain,
% 47.66/47.81 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1)) | (n4 = n1))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n4 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1))))),
% 47.66/47.81 inference(monotonicity,[status(thm)],[237])).
% 47.66/47.81 tff(239,plain,
% 47.66/47.81 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1)) | (n4 = n1))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n4 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1)))),
% 47.66/47.82 inference(transitivity,[status(thm)],[238, 236])).
% 47.66/47.82 tff(240,plain,
% 47.66/47.82 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1)) | (n4 = n1))),
% 47.66/47.82 inference(quant_inst,[status(thm)],[])).
% 47.66/47.82 tff(241,plain,
% 47.66/47.82 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n4 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1))),
% 47.66/47.82 inference(modus_ponens,[status(thm)],[240, 239])).
% 47.66/47.82 tff(242,plain,
% 47.66/47.82 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1)),
% 47.66/47.82 inference(unit_resolution,[status(thm)],[241, 81, 235])).
% 47.66/47.82 tff(243,assumption,(n5 = n1), introduced(assumption)).
% 47.66/47.82 tff(244,plain,
% 47.66/47.82 (n1 = n5),
% 47.66/47.82 inference(symmetry,[status(thm)],[243])).
% 47.66/47.82 tff(245,plain,
% 47.66/47.82 (gt(n4, n1) <=> gt(succ(n3), n5)),
% 47.66/47.82 inference(monotonicity,[status(thm)],[110, 244])).
% 47.66/47.82 tff(246,plain,
% 47.66/47.82 (gt(succ(n3), n5) <=> gt(n4, n1)),
% 47.66/47.82 inference(symmetry,[status(thm)],[245])).
% 47.66/47.82 tff(247,plain,
% 47.66/47.82 ((~gt(succ(n3), n5)) <=> (~gt(n4, n1))),
% 47.66/47.82 inference(monotonicity,[status(thm)],[246])).
% 47.66/47.82 tff(248,plain,
% 47.66/47.82 (~gt(n4, n1)),
% 47.66/47.82 inference(modus_ponens,[status(thm)],[151, 247])).
% 47.66/47.82 tff(249,plain,
% 47.66/47.82 ($false),
% 47.66/47.82 inference(unit_resolution,[status(thm)],[233, 248])).
% 47.66/47.82 tff(250,plain,(~(n5 = n1)), inference(lemma,lemma(discharge,[]))).
% 47.66/47.82 tff(251,plain,
% 47.66/47.82 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n5 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1)))),
% 47.66/47.82 inference(rewrite,[status(thm)],[])).
% 47.66/47.82 tff(252,plain,
% 47.66/47.82 (((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1)) | (n5 = n1)) <=> ((n5 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1)))),
% 47.66/47.82 inference(rewrite,[status(thm)],[])).
% 47.66/47.82 tff(253,plain,
% 47.66/47.82 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1)) | (n5 = n1))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n5 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1))))),
% 47.66/47.82 inference(monotonicity,[status(thm)],[252])).
% 47.66/47.82 tff(254,plain,
% 47.66/47.82 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1)) | (n5 = n1))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1)))),
% 47.66/47.82 inference(transitivity,[status(thm)],[253, 251])).
% 47.66/47.82 tff(255,plain,
% 47.66/47.82 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1)) | (n5 = n1))),
% 47.66/47.82 inference(quant_inst,[status(thm)],[])).
% 47.66/47.82 tff(256,plain,
% 47.66/47.82 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1))),
% 47.66/47.82 inference(modus_ponens,[status(thm)],[255, 254])).
% 47.66/47.82 tff(257,plain,
% 47.66/47.82 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n1)),
% 47.66/47.82 inference(unit_resolution,[status(thm)],[256, 81, 250])).
% 47.66/47.82 tff(258,plain,
% 47.66/47.82 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use),
% 47.66/47.82 inference(transitivity,[status(thm)],[257, 242, 224, 223, 215])).
% 47.66/47.82 tff(259,assumption,(~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use)), introduced(assumption)).
% 47.66/47.82 tff(260,plain,
% 47.66/47.82 ($false),
% 47.66/47.82 inference(unit_resolution,[status(thm)],[259, 258])).
% 47.66/47.82 tff(261,plain,((~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n1) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n1))) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use) | (n2 = n1)), inference(lemma,lemma(discharge,[]))).
% 47.66/47.82 tff(262,plain,
% 47.66/47.82 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use),
% 47.66/47.82 inference(unit_resolution,[status(thm)],[261, 213, 183])).
% 47.66/47.82 tff(263,plain,
% 47.66/47.82 ((~![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n4) = use)),
% 47.66/47.82 inference(quant_inst,[status(thm)],[])).
% 47.66/47.82 tff(264,plain,
% 47.66/47.82 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n4) = use),
% 47.66/47.82 inference(unit_resolution,[status(thm)],[263, 55])).
% 47.66/47.82 tff(265,assumption,(n5 = n4), introduced(assumption)).
% 47.66/47.82 tff(266,plain,
% 47.66/47.82 (n5 = succ(n3)),
% 47.66/47.82 inference(transitivity,[status(thm)],[265, 109, 105])).
% 47.66/47.82 tff(267,plain,
% 47.66/47.82 (gt(n5, n4) <=> gt(succ(n3), n4)),
% 47.66/47.82 inference(monotonicity,[status(thm)],[266])).
% 47.66/47.82 tff(268,plain,
% 47.66/47.82 (gt(succ(n3), n4) <=> gt(n5, n4)),
% 47.66/47.82 inference(symmetry,[status(thm)],[267])).
% 47.66/47.82 tff(269,plain,
% 47.66/47.82 ((~gt(succ(n3), n4)) <=> (~gt(n5, n4))),
% 47.66/47.82 inference(monotonicity,[status(thm)],[268])).
% 47.66/47.82 tff(270,plain,
% 47.66/47.82 (~gt(n5, n4)),
% 47.66/47.82 inference(modus_ponens,[status(thm)],[118, 269])).
% 47.66/47.82 tff(271,plain,
% 47.66/47.82 ($false),
% 47.66/47.82 inference(unit_resolution,[status(thm)],[142, 270])).
% 47.66/47.82 tff(272,plain,(~(n5 = n4)), inference(lemma,lemma(discharge,[]))).
% 47.66/47.82 tff(273,plain,
% 47.66/47.82 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n5 = n4) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n4)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n4) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n4)))),
% 47.66/47.82 inference(rewrite,[status(thm)],[])).
% 47.66/47.82 tff(274,plain,
% 47.66/47.82 (((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n4)) | (n5 = n4)) <=> ((n5 = n4) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n4)))),
% 47.66/47.82 inference(rewrite,[status(thm)],[])).
% 47.66/47.82 tff(275,plain,
% 47.66/47.82 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n4)) | (n5 = n4))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n5 = n4) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n4))))),
% 47.66/47.82 inference(monotonicity,[status(thm)],[274])).
% 47.66/47.82 tff(276,plain,
% 47.66/47.82 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n4)) | (n5 = n4))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n4) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n4)))),
% 47.66/47.82 inference(transitivity,[status(thm)],[275, 273])).
% 47.66/47.82 tff(277,plain,
% 47.66/47.82 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n4)) | (n5 = n4))),
% 47.66/47.82 inference(quant_inst,[status(thm)],[])).
% 47.66/47.82 tff(278,plain,
% 47.66/47.82 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n4) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n4))),
% 47.66/47.82 inference(modus_ponens,[status(thm)],[277, 276])).
% 47.66/47.82 tff(279,plain,
% 47.66/47.82 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n4)),
% 47.66/47.82 inference(unit_resolution,[status(thm)],[278, 81, 272])).
% 47.66/47.82 tff(280,plain,
% 47.66/47.82 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use),
% 47.66/47.82 inference(transitivity,[status(thm)],[279, 264])).
% 47.66/47.82 tff(281,assumption,(~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use)), introduced(assumption)).
% 47.66/47.82 tff(282,plain,
% 47.66/47.82 ($false),
% 47.66/47.82 inference(unit_resolution,[status(thm)],[281, 280])).
% 47.66/47.82 tff(283,plain,(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use), inference(lemma,lemma(discharge,[]))).
% 47.66/47.82 tff(284,assumption,(n4 = n2), introduced(assumption)).
% 47.66/47.82 tff(285,plain,
% 47.66/47.82 (n4 = succ(n1)),
% 47.66/47.82 inference(transitivity,[status(thm)],[284, 171, 167])).
% 47.66/47.82 tff(286,plain,
% 47.66/47.82 (gt(n4, n2) <=> gt(succ(n1), n2)),
% 47.66/47.82 inference(monotonicity,[status(thm)],[285])).
% 47.66/47.82 tff(287,plain,
% 47.66/47.82 (gt(succ(n1), n2) <=> gt(n4, n2)),
% 47.66/47.82 inference(symmetry,[status(thm)],[286])).
% 47.66/47.82 tff(288,plain,
% 47.66/47.82 ((~gt(succ(n1), n2)) <=> (~gt(n4, n2))),
% 47.66/47.82 inference(monotonicity,[status(thm)],[287])).
% 47.66/47.82 tff(289,plain,
% 47.66/47.82 (~gt(n4, n2)),
% 47.66/47.82 inference(modus_ponens,[status(thm)],[180, 288])).
% 47.66/47.82 tff(290,plain,
% 47.66/47.82 (gt(n4, n2) <=> gt(n4, n2)),
% 47.66/47.82 inference(rewrite,[status(thm)],[])).
% 47.66/47.82 tff(291,axiom,(gt(n4, n2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_4_2')).
% 47.66/47.82 tff(292,plain,
% 47.66/47.82 (gt(n4, n2)),
% 47.66/47.82 inference(modus_ponens,[status(thm)],[291, 290])).
% 47.66/47.83 tff(293,plain,
% 47.66/47.83 ($false),
% 47.66/47.83 inference(unit_resolution,[status(thm)],[292, 289])).
% 47.66/47.83 tff(294,plain,(~(n4 = n2)), inference(lemma,lemma(discharge,[]))).
% 47.66/47.83 tff(295,assumption,(~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2))), introduced(assumption)).
% 47.66/47.83 tff(296,assumption,(n5 = n2), introduced(assumption)).
% 47.66/47.83 tff(297,plain,
% 47.66/47.83 (n5 = succ(n1)),
% 47.66/47.83 inference(transitivity,[status(thm)],[296, 171, 167])).
% 47.66/47.83 tff(298,plain,
% 47.66/47.83 (gt(n5, n4) <=> gt(succ(n1), n4)),
% 47.66/47.83 inference(monotonicity,[status(thm)],[297])).
% 47.66/47.83 tff(299,plain,
% 47.66/47.83 (gt(succ(n1), n4) <=> gt(n5, n4)),
% 47.66/47.83 inference(symmetry,[status(thm)],[298])).
% 47.66/47.83 tff(300,plain,
% 47.66/47.83 ((~gt(succ(n1), n4)) <=> (~gt(n5, n4))),
% 47.66/47.83 inference(monotonicity,[status(thm)],[299])).
% 47.66/47.83 tff(301,plain,
% 47.66/47.83 (gt(n2, n4) <=> gt(succ(n1), n4)),
% 47.66/47.83 inference(monotonicity,[status(thm)],[172])).
% 47.66/47.83 tff(302,plain,
% 47.66/47.83 ((~gt(n2, n4)) <=> (~gt(succ(n1), n4))),
% 47.66/47.83 inference(monotonicity,[status(thm)],[301])).
% 47.66/47.83 tff(303,plain,
% 47.66/47.83 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | ((~gt(n4, n2)) | gt(n2, n2) | (~gt(n2, n4)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n4, n2)) | gt(n2, n2) | (~gt(n2, n4)))),
% 47.66/47.83 inference(rewrite,[status(thm)],[])).
% 47.66/47.83 tff(304,plain,
% 47.66/47.83 ((gt(n2, n2) | (~gt(n2, n4)) | (~gt(n4, n2))) <=> ((~gt(n4, n2)) | gt(n2, n2) | (~gt(n2, n4)))),
% 47.66/47.83 inference(rewrite,[status(thm)],[])).
% 47.66/47.83 tff(305,plain,
% 47.66/47.83 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n2, n2) | (~gt(n2, n4)) | (~gt(n4, n2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | ((~gt(n4, n2)) | gt(n2, n2) | (~gt(n2, n4))))),
% 47.66/47.83 inference(monotonicity,[status(thm)],[304])).
% 47.66/47.83 tff(306,plain,
% 47.66/47.83 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n2, n2) | (~gt(n2, n4)) | (~gt(n4, n2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n4, n2)) | gt(n2, n2) | (~gt(n2, n4)))),
% 47.66/47.83 inference(transitivity,[status(thm)],[305, 303])).
% 47.66/47.83 tff(307,plain,
% 47.66/47.83 ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n2, n2) | (~gt(n2, n4)) | (~gt(n4, n2)))),
% 47.66/47.83 inference(quant_inst,[status(thm)],[])).
% 47.66/47.83 tff(308,plain,
% 47.66/47.83 ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n4, n2)) | gt(n2, n2) | (~gt(n2, n4))),
% 47.66/47.83 inference(modus_ponens,[status(thm)],[307, 306])).
% 47.66/47.83 tff(309,plain,
% 47.66/47.83 (~gt(n2, n4)),
% 47.66/47.83 inference(unit_resolution,[status(thm)],[308, 35, 292, 179])).
% 47.66/47.83 tff(310,plain,
% 47.66/47.83 (~gt(succ(n1), n4)),
% 47.66/47.83 inference(modus_ponens,[status(thm)],[309, 302])).
% 47.66/47.83 tff(311,plain,
% 47.66/47.83 (~gt(n5, n4)),
% 47.66/47.83 inference(modus_ponens,[status(thm)],[310, 300])).
% 47.66/47.83 tff(312,plain,
% 47.66/47.83 ($false),
% 47.66/47.83 inference(unit_resolution,[status(thm)],[142, 311])).
% 47.66/47.83 tff(313,plain,(~(n5 = n2)), inference(lemma,lemma(discharge,[]))).
% 47.66/47.83 tff(314,plain,
% 47.66/47.83 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n5 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2)))),
% 47.66/47.83 inference(rewrite,[status(thm)],[])).
% 47.66/47.83 tff(315,plain,
% 47.66/47.83 (((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2)) | (n5 = n2)) <=> ((n5 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2)))),
% 47.66/47.83 inference(rewrite,[status(thm)],[])).
% 47.66/47.83 tff(316,plain,
% 47.66/47.83 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2)) | (n5 = n2))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n5 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2))))),
% 47.66/47.83 inference(monotonicity,[status(thm)],[315])).
% 47.66/47.83 tff(317,plain,
% 47.66/47.83 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2)) | (n5 = n2))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2)))),
% 47.66/47.83 inference(transitivity,[status(thm)],[316, 314])).
% 47.66/47.83 tff(318,plain,
% 47.66/47.83 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2)) | (n5 = n2))),
% 47.66/47.83 inference(quant_inst,[status(thm)],[])).
% 47.66/47.83 tff(319,plain,
% 47.66/47.83 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2))),
% 47.66/47.83 inference(modus_ponens,[status(thm)],[318, 317])).
% 47.66/47.83 tff(320,plain,
% 47.66/47.83 ($false),
% 47.66/47.83 inference(unit_resolution,[status(thm)],[319, 81, 313, 295])).
% 47.66/47.83 tff(321,plain,(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2)), inference(lemma,lemma(discharge,[]))).
% 47.66/47.83 tff(322,assumption,(n3 = n2), introduced(assumption)).
% 47.66/47.83 tff(323,plain,
% 47.66/47.83 (n2 = n3),
% 47.66/47.83 inference(symmetry,[status(thm)],[322])).
% 47.66/47.83 tff(324,plain,
% 47.66/47.83 (succ(n2) = succ(succ(succ(n0)))),
% 47.66/47.83 inference(monotonicity,[status(thm)],[171])).
% 47.66/47.83 tff(325,plain,
% 47.66/47.83 (succ(succ(succ(n0))) = succ(n2)),
% 47.66/47.83 inference(symmetry,[status(thm)],[324])).
% 47.66/47.83 tff(326,plain,
% 47.66/47.83 (n3 = succ(n2)),
% 47.66/47.83 inference(transitivity,[status(thm)],[103, 325])).
% 47.66/47.83 tff(327,plain,
% 47.66/47.83 (gt(n3, n2) <=> gt(succ(n2), n3)),
% 47.66/47.83 inference(monotonicity,[status(thm)],[326, 323])).
% 47.66/47.83 tff(328,plain,
% 47.66/47.83 (gt(succ(n2), n3) <=> gt(n3, n2)),
% 47.66/47.83 inference(symmetry,[status(thm)],[327])).
% 47.66/47.83 tff(329,plain,
% 47.66/47.83 ((~gt(succ(n2), n3)) <=> (~gt(n3, n2))),
% 47.66/47.83 inference(monotonicity,[status(thm)],[328])).
% 47.66/47.83 tff(330,plain,
% 47.66/47.83 (gt(n3, n3) <=> gt(succ(n2), n3)),
% 47.66/47.83 inference(monotonicity,[status(thm)],[326])).
% 47.66/47.83 tff(331,plain,
% 47.66/47.83 ((~gt(n3, n3)) <=> (~gt(succ(n2), n3))),
% 47.66/47.83 inference(monotonicity,[status(thm)],[330])).
% 47.66/47.83 tff(332,plain,
% 47.66/47.83 ((~![X: $i] : (~gt(X, X))) | (~gt(n3, n3))),
% 47.66/47.83 inference(quant_inst,[status(thm)],[])).
% 47.66/47.83 tff(333,plain,
% 47.66/47.83 (~gt(n3, n3)),
% 47.66/47.83 inference(unit_resolution,[status(thm)],[332, 18])).
% 47.66/47.83 tff(334,plain,
% 47.66/47.83 (~gt(succ(n2), n3)),
% 47.66/47.83 inference(modus_ponens,[status(thm)],[333, 331])).
% 47.66/47.83 tff(335,plain,
% 47.66/47.83 (~gt(n3, n2)),
% 47.66/47.83 inference(modus_ponens,[status(thm)],[334, 329])).
% 47.66/47.83 tff(336,plain,
% 47.66/47.83 ($false),
% 47.66/47.83 inference(unit_resolution,[status(thm)],[194, 335])).
% 47.66/47.83 tff(337,plain,(~(n3 = n2)), inference(lemma,lemma(discharge,[]))).
% 47.66/47.83 tff(338,plain,
% 47.66/47.83 ((~![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)) | (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n2) = use)),
% 47.66/47.83 inference(quant_inst,[status(thm)],[])).
% 47.66/47.83 tff(339,plain,
% 47.66/47.83 (a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n2) = use),
% 47.66/47.83 inference(unit_resolution,[status(thm)],[338, 55])).
% 47.66/47.83 tff(340,assumption,(~(n3 = n2)), introduced(assumption)).
% 47.66/47.83 tff(341,plain,
% 47.66/47.83 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n3 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n2)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n3 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n2)))),
% 47.66/47.83 inference(rewrite,[status(thm)],[])).
% 47.66/47.83 tff(342,plain,
% 47.66/47.83 (((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n2)) | (n3 = n2)) <=> ((n3 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n2)))),
% 47.66/47.83 inference(rewrite,[status(thm)],[])).
% 47.66/47.83 tff(343,plain,
% 47.66/47.83 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n2)) | (n3 = n2))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n3 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n2))))),
% 47.66/47.83 inference(monotonicity,[status(thm)],[342])).
% 47.66/47.83 tff(344,plain,
% 47.66/47.83 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n2)) | (n3 = n2))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n3 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n2)))),
% 47.66/47.83 inference(transitivity,[status(thm)],[343, 341])).
% 47.66/47.83 tff(345,plain,
% 47.66/47.83 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n2)) | (n3 = n2))),
% 47.66/47.83 inference(quant_inst,[status(thm)],[])).
% 47.66/47.83 tff(346,plain,
% 47.66/47.83 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n3 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n2))),
% 47.66/47.83 inference(modus_ponens,[status(thm)],[345, 344])).
% 47.66/47.83 tff(347,plain,
% 47.66/47.83 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n2)),
% 47.66/47.83 inference(unit_resolution,[status(thm)],[346, 81, 340])).
% 47.66/47.83 tff(348,assumption,(~(n4 = n2)), introduced(assumption)).
% 47.66/47.83 tff(349,plain,
% 47.66/47.83 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n4 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n4 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2)))),
% 47.66/47.83 inference(rewrite,[status(thm)],[])).
% 47.66/47.83 tff(350,plain,
% 47.66/47.83 (((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2)) | (n4 = n2)) <=> ((n4 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2)))),
% 47.66/47.83 inference(rewrite,[status(thm)],[])).
% 47.66/47.83 tff(351,plain,
% 47.66/47.83 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2)) | (n4 = n2))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n4 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2))))),
% 47.66/47.83 inference(monotonicity,[status(thm)],[350])).
% 47.66/47.83 tff(352,plain,
% 47.66/47.83 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2)) | (n4 = n2))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n4 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2)))),
% 47.66/47.83 inference(transitivity,[status(thm)],[351, 349])).
% 47.66/47.83 tff(353,plain,
% 47.66/47.83 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2)) | (n4 = n2))),
% 47.66/47.83 inference(quant_inst,[status(thm)],[])).
% 47.66/47.83 tff(354,plain,
% 47.66/47.83 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n4 = n2) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2))),
% 47.66/47.83 inference(modus_ponens,[status(thm)],[353, 352])).
% 47.66/47.83 tff(355,plain,
% 47.66/47.83 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n2)),
% 47.66/47.83 inference(unit_resolution,[status(thm)],[354, 81, 348])).
% 47.66/47.83 tff(356,assumption,(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2)), introduced(assumption)).
% 47.66/47.83 tff(357,plain,
% 47.66/47.83 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use),
% 47.66/47.83 inference(transitivity,[status(thm)],[356, 355, 347, 339])).
% 47.66/47.83 tff(358,assumption,(~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use)), introduced(assumption)).
% 47.66/47.83 tff(359,plain,
% 47.66/47.83 ($false),
% 47.66/47.83 inference(unit_resolution,[status(thm)],[358, 357])).
% 47.66/47.83 tff(360,plain,((~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2))) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use) | (n3 = n2) | (n4 = n2)), inference(lemma,lemma(discharge,[]))).
% 47.66/47.83 tff(361,plain,
% 47.66/47.83 ((~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n2))) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use) | (n4 = n2)),
% 47.66/47.84 inference(unit_resolution,[status(thm)],[360, 337])).
% 47.66/47.84 tff(362,plain,
% 47.66/47.84 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use),
% 47.66/47.84 inference(unit_resolution,[status(thm)],[361, 321, 294])).
% 47.66/47.84 tff(363,assumption,(n4 = n3), introduced(assumption)).
% 47.66/47.84 tff(364,plain,
% 47.66/47.84 (n4 = succ(n2)),
% 47.66/47.84 inference(transitivity,[status(thm)],[363, 103, 325])).
% 47.66/47.84 tff(365,plain,
% 47.66/47.84 (gt(n4, n3) <=> gt(succ(n2), n3)),
% 47.66/47.84 inference(monotonicity,[status(thm)],[364])).
% 47.66/47.84 tff(366,plain,
% 47.66/47.84 (gt(succ(n2), n3) <=> gt(n4, n3)),
% 47.66/47.84 inference(symmetry,[status(thm)],[365])).
% 47.66/47.84 tff(367,plain,
% 47.66/47.84 ((~gt(succ(n2), n3)) <=> (~gt(n4, n3))),
% 47.66/47.84 inference(monotonicity,[status(thm)],[366])).
% 47.66/47.84 tff(368,plain,
% 47.66/47.84 (~gt(n4, n3)),
% 47.66/47.84 inference(modus_ponens,[status(thm)],[334, 367])).
% 47.66/47.84 tff(369,plain,
% 47.66/47.84 (gt(n4, n3) <=> gt(n4, n3)),
% 47.66/47.84 inference(rewrite,[status(thm)],[])).
% 47.66/47.84 tff(370,axiom,(gt(n4, n3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_4_3')).
% 47.66/47.84 tff(371,plain,
% 47.66/47.84 (gt(n4, n3)),
% 47.66/47.84 inference(modus_ponens,[status(thm)],[370, 369])).
% 47.66/47.84 tff(372,plain,
% 47.66/47.84 ($false),
% 47.66/47.84 inference(unit_resolution,[status(thm)],[371, 368])).
% 47.66/47.84 tff(373,plain,(~(n4 = n3)), inference(lemma,lemma(discharge,[]))).
% 47.66/47.84 tff(374,assumption,(~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3))), introduced(assumption)).
% 47.66/47.84 tff(375,assumption,(n5 = n3), introduced(assumption)).
% 47.66/47.84 tff(376,plain,
% 47.66/47.84 (succ(n3) = n4),
% 47.66/47.84 inference(transitivity,[status(thm)],[104, 108])).
% 47.66/47.84 tff(377,plain,
% 47.66/47.84 (gt(succ(n3), n5) <=> gt(n4, n3)),
% 47.66/47.84 inference(monotonicity,[status(thm)],[376, 375])).
% 47.66/47.84 tff(378,plain,
% 47.66/47.84 (gt(n4, n3) <=> gt(succ(n3), n5)),
% 47.66/47.84 inference(symmetry,[status(thm)],[377])).
% 47.66/47.84 tff(379,plain,
% 47.66/47.84 (gt(succ(n3), n5)),
% 47.66/47.84 inference(modus_ponens,[status(thm)],[371, 378])).
% 47.66/47.84 tff(380,plain,
% 47.66/47.84 ($false),
% 47.66/47.84 inference(unit_resolution,[status(thm)],[151, 379])).
% 47.66/47.84 tff(381,plain,(~(n5 = n3)), inference(lemma,lemma(discharge,[]))).
% 47.66/47.84 tff(382,plain,
% 47.66/47.84 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n5 = n3) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n3) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3)))),
% 47.66/47.84 inference(rewrite,[status(thm)],[])).
% 47.66/47.84 tff(383,plain,
% 47.66/47.84 (((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3)) | (n5 = n3)) <=> ((n5 = n3) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3)))),
% 47.66/47.84 inference(rewrite,[status(thm)],[])).
% 47.66/47.84 tff(384,plain,
% 47.66/47.84 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3)) | (n5 = n3))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n5 = n3) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3))))),
% 47.66/47.84 inference(monotonicity,[status(thm)],[383])).
% 47.66/47.84 tff(385,plain,
% 47.66/47.84 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3)) | (n5 = n3))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n3) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3)))),
% 47.66/47.84 inference(transitivity,[status(thm)],[384, 382])).
% 47.66/47.84 tff(386,plain,
% 47.66/47.84 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3)) | (n5 = n3))),
% 47.66/47.84 inference(quant_inst,[status(thm)],[])).
% 47.66/47.84 tff(387,plain,
% 47.66/47.84 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n5 = n3) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3))),
% 47.66/47.84 inference(modus_ponens,[status(thm)],[386, 385])).
% 47.66/47.84 tff(388,plain,
% 47.66/47.84 ($false),
% 47.66/47.84 inference(unit_resolution,[status(thm)],[387, 81, 381, 374])).
% 47.66/47.84 tff(389,plain,(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3)), inference(lemma,lemma(discharge,[]))).
% 47.66/47.84 tff(390,plain,
% 47.66/47.84 ((~![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n3) = use)),
% 47.66/47.84 inference(quant_inst,[status(thm)],[])).
% 47.66/47.84 tff(391,plain,
% 47.66/47.84 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n3) = use),
% 47.66/47.84 inference(unit_resolution,[status(thm)],[390, 55])).
% 47.66/47.84 tff(392,assumption,(~(n4 = n3)), introduced(assumption)).
% 47.66/47.84 tff(393,plain,
% 47.66/47.84 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n4 = n3) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n3)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n4 = n3) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n3)))),
% 47.66/47.84 inference(rewrite,[status(thm)],[])).
% 47.66/47.84 tff(394,plain,
% 47.66/47.84 (((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n3)) | (n4 = n3)) <=> ((n4 = n3) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n3)))),
% 47.66/47.84 inference(rewrite,[status(thm)],[])).
% 47.66/47.84 tff(395,plain,
% 47.66/47.84 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n3)) | (n4 = n3))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n4 = n3) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n3))))),
% 47.66/47.84 inference(monotonicity,[status(thm)],[394])).
% 47.66/47.84 tff(396,plain,
% 47.66/47.84 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n3)) | (n4 = n3))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n4 = n3) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n3)))),
% 47.66/47.84 inference(transitivity,[status(thm)],[395, 393])).
% 47.66/47.84 tff(397,plain,
% 47.66/47.84 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n3)) | (n4 = n3))),
% 47.66/47.84 inference(quant_inst,[status(thm)],[])).
% 47.66/47.84 tff(398,plain,
% 47.66/47.84 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n4 = n3) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n3))),
% 47.66/47.84 inference(modus_ponens,[status(thm)],[397, 396])).
% 47.66/47.84 tff(399,plain,
% 47.66/47.84 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n3)),
% 47.69/47.84 inference(unit_resolution,[status(thm)],[398, 81, 392])).
% 47.69/47.84 tff(400,assumption,(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3)), introduced(assumption)).
% 47.69/47.84 tff(401,plain,
% 47.69/47.84 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use),
% 47.69/47.84 inference(transitivity,[status(thm)],[400, 399, 391])).
% 47.69/47.84 tff(402,assumption,(~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use)), introduced(assumption)).
% 47.69/47.84 tff(403,plain,
% 47.69/47.84 ($false),
% 47.69/47.84 inference(unit_resolution,[status(thm)],[402, 401])).
% 47.69/47.84 tff(404,plain,((~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n3))) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use) | (n4 = n3)), inference(lemma,lemma(discharge,[]))).
% 47.69/47.84 tff(405,plain,
% 47.69/47.84 (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use),
% 47.69/47.84 inference(unit_resolution,[status(thm)],[404, 389, 373])).
% 47.69/47.84 tff(406,assumption,(~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use)), introduced(assumption)).
% 47.69/47.84 tff(407,plain,
% 47.69/47.84 ((~![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use)),
% 47.69/47.84 inference(quant_inst,[status(thm)],[])).
% 47.69/47.84 tff(408,plain,
% 47.69/47.84 ($false),
% 47.69/47.84 inference(unit_resolution,[status(thm)],[407, 55, 406])).
% 47.69/47.84 tff(409,plain,(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use), inference(lemma,lemma(discharge,[]))).
% 47.69/47.84 tff(410,plain,
% 47.69/47.84 ((a_select2(xinit_defuse, n5) = use) <=> (a_select2(xinit_defuse, n5) = use)),
% 47.69/47.84 inference(rewrite,[status(thm)],[])).
% 47.69/47.84 tff(411,plain,
% 47.69/47.84 ((~(((((((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) => ((((((((((((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use)))) <=> (~((~((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use))) | ((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use))))),
% 47.69/47.84 inference(rewrite,[status(thm)],[])).
% 47.69/47.84 tff(412,axiom,(~(((((((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) => ((((((((((((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_inuse_0015')).
% 47.69/47.84 tff(413,plain,
% 47.69/47.84 (~((~((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use))) | ((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use)))),
% 47.69/47.85 inference(modus_ponens,[status(thm)],[412, 411])).
% 47.69/47.85 tff(414,plain,
% 47.69/47.85 ((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use)),
% 47.69/47.85 inference(or_elim,[status(thm)],[413])).
% 47.69/47.85 tff(415,plain,
% 47.69/47.85 (a_select2(xinit_defuse, n5) = use),
% 47.69/47.85 inference(and_elim,[status(thm)],[414])).
% 47.69/47.85 tff(416,plain,
% 47.69/47.85 (a_select2(xinit_defuse, n5) = use),
% 47.69/47.85 inference(modus_ponens,[status(thm)],[415, 410])).
% 47.69/47.85 tff(417,plain,
% 47.69/47.85 ((a_select2(xinit_defuse, n4) = use) <=> (a_select2(xinit_defuse, n4) = use)),
% 47.69/47.85 inference(rewrite,[status(thm)],[])).
% 47.69/47.85 tff(418,plain,
% 47.69/47.85 (a_select2(xinit_defuse, n4) = use),
% 47.69/47.85 inference(and_elim,[status(thm)],[414])).
% 47.69/47.85 tff(419,plain,
% 47.69/47.85 (a_select2(xinit_defuse, n4) = use),
% 47.69/47.85 inference(modus_ponens,[status(thm)],[418, 417])).
% 47.69/47.85 tff(420,plain,
% 47.69/47.85 ((a_select2(xinit_defuse, n3) = use) <=> (a_select2(xinit_defuse, n3) = use)),
% 47.69/47.85 inference(rewrite,[status(thm)],[])).
% 47.69/47.85 tff(421,plain,
% 47.69/47.85 (a_select2(xinit_defuse, n3) = use),
% 47.69/47.85 inference(and_elim,[status(thm)],[414])).
% 47.69/47.85 tff(422,plain,
% 47.69/47.85 (a_select2(xinit_defuse, n3) = use),
% 47.69/47.85 inference(modus_ponens,[status(thm)],[421, 420])).
% 47.69/47.85 tff(423,plain,
% 47.69/47.85 ((a_select3(u_defuse, n2, n0) = use) <=> (a_select3(u_defuse, n2, n0) = use)),
% 47.69/47.85 inference(rewrite,[status(thm)],[])).
% 47.69/47.85 tff(424,plain,
% 47.69/47.85 (a_select3(u_defuse, n2, n0) = use),
% 47.69/47.85 inference(and_elim,[status(thm)],[414])).
% 47.69/47.85 tff(425,plain,
% 47.69/47.85 (a_select3(u_defuse, n2, n0) = use),
% 47.69/47.85 inference(modus_ponens,[status(thm)],[424, 423])).
% 47.69/47.85 tff(426,plain,
% 47.69/47.85 ((a_select3(u_defuse, n1, n0) = use) <=> (a_select3(u_defuse, n1, n0) = use)),
% 47.69/47.85 inference(rewrite,[status(thm)],[])).
% 47.69/47.85 tff(427,plain,
% 47.69/47.85 (a_select3(u_defuse, n1, n0) = use),
% 47.69/47.85 inference(and_elim,[status(thm)],[414])).
% 47.69/47.85 tff(428,plain,
% 47.69/47.85 (a_select3(u_defuse, n1, n0) = use),
% 47.69/47.85 inference(modus_ponens,[status(thm)],[427, 426])).
% 47.69/47.85 tff(429,plain,
% 47.69/47.85 ((a_select3(u_defuse, n0, n0) = use) <=> (a_select3(u_defuse, n0, n0) = use)),
% 47.69/47.85 inference(rewrite,[status(thm)],[])).
% 47.69/47.85 tff(430,plain,
% 47.69/47.85 (a_select3(u_defuse, n0, n0) = use),
% 47.69/47.85 inference(and_elim,[status(thm)],[414])).
% 47.69/47.85 tff(431,plain,
% 47.69/47.85 (a_select3(u_defuse, n0, n0) = use),
% 47.69/47.85 inference(modus_ponens,[status(thm)],[430, 429])).
% 47.69/47.85 tff(432,plain,
% 47.69/47.85 ((~(~((~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use))))) <=> ((~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use)))),
% 47.69/47.85 inference(rewrite,[status(thm)],[])).
% 47.69/47.85 tff(433,plain,
% 47.69/47.85 (((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use)) <=> (~((~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use))))),
% 47.69/47.85 inference(rewrite,[status(thm)],[])).
% 47.69/47.85 tff(434,plain,
% 47.69/47.85 ((~((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use))) <=> (~(~((~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use)))))),
% 47.69/47.85 inference(monotonicity,[status(thm)],[433])).
% 47.69/47.85 tff(435,plain,
% 47.69/47.85 ((~((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use))) <=> ((~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use)))),
% 47.69/47.86 inference(transitivity,[status(thm)],[434, 432])).
% 47.69/47.86 tff(436,plain,
% 47.69/47.86 ((~((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use))) <=> (~((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use)))),
% 47.69/47.86 inference(rewrite,[status(thm)],[])).
% 47.69/47.86 tff(437,plain,
% 47.69/47.86 (~((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use))),
% 47.69/47.86 inference(or_elim,[status(thm)],[413])).
% 47.69/47.86 tff(438,plain,
% 47.69/47.86 (~((a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use))),
% 47.69/47.86 inference(modus_ponens,[status(thm)],[437, 436])).
% 47.69/47.86 tff(439,plain,
% 47.69/47.86 ((~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use))),
% 47.69/47.86 inference(modus_ponens,[status(thm)],[438, 435])).
% 47.69/47.86 tff(440,plain,
% 47.69/47.86 ((~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n5) = use))),
% 47.69/47.86 inference(unit_resolution,[status(thm)],[439, 431, 428, 425, 422, 419, 416])).
% 47.69/47.86 tff(441,plain,
% 47.69/47.86 ((~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n3) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use))),
% 47.69/47.86 inference(unit_resolution,[status(thm)],[440, 409])).
% 47.69/47.86 tff(442,plain,
% 47.69/47.86 ((~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n2) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use))),
% 47.69/47.86 inference(unit_resolution,[status(thm)],[441, 405])).
% 47.69/47.86 tff(443,plain,
% 47.69/47.86 ((~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n4) = use))),
% 47.69/47.86 inference(unit_resolution,[status(thm)],[442, 362])).
% 47.69/47.86 tff(444,plain,
% 47.69/47.86 (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n4, use), n5, use), n0) = use)),
% 47.69/47.86 inference(unit_resolution,[status(thm)],[443, 283, 262])).
% 47.69/47.86 tff(445,plain,
% 47.69/47.86 ($false),
% 47.69/47.86 inference(unit_resolution,[status(thm)],[444, 163])).
% 47.69/47.86 tff(446,plain,((~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0))) | (n2 = n0)), inference(lemma,lemma(discharge,[]))).
% 47.69/47.86 tff(447,plain,
% 47.69/47.86 (~(a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0))),
% 47.69/47.86 inference(unit_resolution,[status(thm)],[446, 49])).
% 47.69/47.86 tff(448,plain,
% 47.69/47.86 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n3 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n3 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0)))),
% 47.69/47.86 inference(rewrite,[status(thm)],[])).
% 47.69/47.86 tff(449,plain,
% 47.69/47.86 (((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0)) | (n3 = n0)) <=> ((n3 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0)))),
% 47.69/47.86 inference(rewrite,[status(thm)],[])).
% 47.69/47.86 tff(450,plain,
% 47.69/47.86 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0)) | (n3 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n3 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0))))),
% 47.69/47.86 inference(monotonicity,[status(thm)],[449])).
% 47.69/47.86 tff(451,plain,
% 47.69/47.86 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0)) | (n3 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n3 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0)))),
% 47.69/47.86 inference(transitivity,[status(thm)],[450, 448])).
% 47.69/47.86 tff(452,plain,
% 47.69/47.86 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0)) | (n3 = n0))),
% 47.69/47.92 inference(quant_inst,[status(thm)],[])).
% 47.69/47.92 tff(453,plain,
% 47.69/47.92 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n3 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0))),
% 47.69/47.92 inference(modus_ponens,[status(thm)],[452, 451])).
% 47.69/47.92 tff(454,plain,
% 47.69/47.92 ((n3 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n3, use), n0) = a_select2(tptp_update2(tptp_update2(tptp_update2(sigma_defuse, n0, use), n1, use), n2, use), n0))),
% 47.69/47.92 inference(unit_resolution,[status(thm)],[453, 81])).
% 47.69/47.92 tff(455,plain,
% 47.69/47.92 (n3 = n0),
% 47.69/47.92 inference(unit_resolution,[status(thm)],[454, 447])).
% 47.69/47.92 tff(456,plain,
% 47.69/47.92 (n0 = n3),
% 47.69/47.92 inference(symmetry,[status(thm)],[455])).
% 47.69/47.92 tff(457,plain,
% 47.69/47.92 (gt(n1, n0) <=> gt(succ(n0), n3)),
% 47.69/47.92 inference(monotonicity,[status(thm)],[6, 456])).
% 47.69/47.92 tff(458,plain,
% 47.69/47.92 (gt(succ(n0), n3) <=> gt(n1, n0)),
% 47.69/47.92 inference(symmetry,[status(thm)],[457])).
% 47.69/47.92 tff(459,plain,
% 47.69/47.92 ((~gt(succ(n0), n3)) <=> (~gt(n1, n0))),
% 47.69/47.92 inference(monotonicity,[status(thm)],[458])).
% 47.69/47.92 tff(460,plain,
% 47.69/47.92 (gt(n1, n3) <=> gt(succ(n0), n3)),
% 47.69/47.92 inference(monotonicity,[status(thm)],[6])).
% 47.69/47.92 tff(461,plain,
% 47.69/47.92 ((~gt(n1, n3)) <=> (~gt(succ(n0), n3))),
% 47.69/47.92 inference(monotonicity,[status(thm)],[460])).
% 47.69/47.92 tff(462,plain,
% 47.69/47.92 (gt(n3, n1) <=> gt(n3, n1)),
% 47.69/47.92 inference(rewrite,[status(thm)],[])).
% 47.69/47.92 tff(463,axiom,(gt(n3, n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_3_1')).
% 47.69/47.92 tff(464,plain,
% 47.69/47.92 (gt(n3, n1)),
% 47.69/47.92 inference(modus_ponens,[status(thm)],[463, 462])).
% 47.69/47.92 tff(465,plain,
% 47.69/47.92 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | ((~gt(n3, n1)) | gt(n1, n1) | (~gt(n1, n3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n3, n1)) | gt(n1, n1) | (~gt(n1, n3)))),
% 47.69/47.92 inference(rewrite,[status(thm)],[])).
% 47.69/47.92 tff(466,plain,
% 47.69/47.92 ((gt(n1, n1) | (~gt(n1, n3)) | (~gt(n3, n1))) <=> ((~gt(n3, n1)) | gt(n1, n1) | (~gt(n1, n3)))),
% 47.69/47.92 inference(rewrite,[status(thm)],[])).
% 47.69/47.92 tff(467,plain,
% 47.69/47.92 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n1, n1) | (~gt(n1, n3)) | (~gt(n3, n1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | ((~gt(n3, n1)) | gt(n1, n1) | (~gt(n1, n3))))),
% 47.69/47.92 inference(monotonicity,[status(thm)],[466])).
% 47.69/47.92 tff(468,plain,
% 47.69/47.92 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n1, n1) | (~gt(n1, n3)) | (~gt(n3, n1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n3, n1)) | gt(n1, n1) | (~gt(n1, n3)))),
% 47.69/47.92 inference(transitivity,[status(thm)],[467, 465])).
% 47.69/47.92 tff(469,plain,
% 47.69/47.92 ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n1, n1) | (~gt(n1, n3)) | (~gt(n3, n1)))),
% 47.69/47.92 inference(quant_inst,[status(thm)],[])).
% 47.69/47.92 tff(470,plain,
% 47.69/47.92 ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n3, n1)) | gt(n1, n1) | (~gt(n1, n3))),
% 47.69/47.92 inference(modus_ponens,[status(thm)],[469, 468])).
% 47.69/47.92 tff(471,plain,
% 47.69/47.92 (~gt(n1, n3)),
% 47.69/47.92 inference(unit_resolution,[status(thm)],[470, 35, 464, 20])).
% 47.69/47.92 tff(472,plain,
% 47.69/47.92 (~gt(succ(n0), n3)),
% 47.69/47.92 inference(modus_ponens,[status(thm)],[471, 461])).
% 47.69/47.92 tff(473,plain,
% 47.69/47.92 (~gt(n1, n0)),
% 47.69/47.92 inference(modus_ponens,[status(thm)],[472, 459])).
% 47.69/47.92 tff(474,plain,
% 47.69/47.92 ($false),
% 47.69/47.92 inference(unit_resolution,[status(thm)],[47, 473])).
% 47.69/47.92 % SZS output end Proof
% 47.77/47.93 % E exiting
%------------------------------------------------------------------------------