%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV041+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:31:23 AM UTC 2025
% Result : Theorem 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV041+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.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 09:23:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 tff(gt_type, type, (
% 0.19/0.50 gt: ( $i * $i ) > $o)).
% 0.19/0.50 tff(n0_type, type, (
% 0.19/0.50 n0: $i)).
% 0.19/0.50 tff(leq_type, type, (
% 0.19/0.50 leq: ( $i * $i ) > $o)).
% 0.19/0.50 tff(succ_type, type, (
% 0.19/0.50 succ: $i > $i)).
% 0.19/0.50 tff(tptp_minus_1_type, type, (
% 0.19/0.50 tptp_minus_1: $i)).
% 0.19/0.50 tff(minus_type, type, (
% 0.19/0.50 minus: ( $i * $i ) > $i)).
% 0.19/0.50 tff(n1_type, type, (
% 0.19/0.50 n1: $i)).
% 0.19/0.50 tff(pred_type, type, (
% 0.19/0.50 pred: $i > $i)).
% 0.19/0.50 tff(tptp_fun_B_14_type, type, (
% 0.19/0.50 tptp_fun_B_14: $i)).
% 0.19/0.50 tff(init_type, type, (
% 0.19/0.50 init: $i)).
% 0.19/0.50 tff(a_select3_type, type, (
% 0.19/0.50 a_select3: ( $i * $i * $i ) > $i)).
% 0.19/0.50 tff(tptp_fun_A_13_type, type, (
% 0.19/0.50 tptp_fun_A_13: $i)).
% 0.19/0.50 tff(tptp_const_array2_type, type, (
% 0.19/0.50 tptp_const_array2: ( $i * $i * $i ) > $i)).
% 0.19/0.50 tff(uninit_type, type, (
% 0.19/0.50 uninit: $i)).
% 0.19/0.50 tff(dim_type, type, (
% 0.19/0.50 dim: ( $i * $i ) > $i)).
% 0.19/0.50 tff(n2_type, type, (
% 0.19/0.50 n2: $i)).
% 0.19/0.50 tff(n3_type, type, (
% 0.19/0.50 n3: $i)).
% 0.19/0.50 tff(geq_type, type, (
% 0.19/0.50 geq: ( $i * $i ) > $o)).
% 0.19/0.50 tff(n410_type, type, (
% 0.19/0.50 n410: $i)).
% 0.19/0.50 tff(n330_type, type, (
% 0.19/0.50 n330: $i)).
% 0.19/0.50 tff(1,plain,
% 0.19/0.50 ((succ(tptp_minus_1) = n0) <=> (succ(tptp_minus_1) = n0)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(2,axiom,(succ(tptp_minus_1) = n0), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','succ_tptp_minus_1')).
% 0.19/0.50 tff(3,plain,
% 0.19/0.50 (succ(tptp_minus_1) = n0),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.19/0.50 tff(4,plain,
% 0.19/0.50 (n0 = succ(tptp_minus_1)),
% 0.19/0.50 inference(symmetry,[status(thm)],[3])).
% 0.19/0.50 tff(5,plain,
% 0.19/0.50 (leq(succ(n0), n0) <=> leq(succ(n0), succ(tptp_minus_1))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[4])).
% 0.19/0.50 tff(6,plain,
% 0.19/0.50 (leq(succ(n0), succ(tptp_minus_1)) <=> leq(succ(n0), n0)),
% 0.19/0.50 inference(symmetry,[status(thm)],[5])).
% 0.19/0.50 tff(7,plain,
% 0.19/0.50 (^[X: $i, Y: $i] : refl((leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> (leq(succ(X), succ(Y)) <=> leq(X, Y)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(8,plain,
% 0.19/0.50 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.50 tff(9,plain,
% 0.19/0.50 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(10,axiom,(![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_succ_succ')).
% 0.19/0.50 tff(11,plain,
% 0.19/0.50 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.50 tff(12,plain,(
% 0.19/0.50 ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 0.19/0.50 inference(skolemize,[status(sab)],[11])).
% 0.19/0.50 tff(13,plain,
% 0.19/0.50 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.50 tff(14,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))) | (leq(succ(n0), succ(tptp_minus_1)) <=> leq(n0, tptp_minus_1))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(15,plain,
% 0.19/0.50 (leq(succ(n0), succ(tptp_minus_1)) <=> leq(n0, tptp_minus_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.19/0.50 tff(16,plain,
% 0.19/0.50 (^[X: $i] : refl((minus(X, n1) = pred(X)) <=> (minus(X, n1) = pred(X)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(17,plain,
% 0.19/0.50 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.50 tff(18,plain,
% 0.19/0.50 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(19,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 0.19/0.50 tff(20,plain,
% 0.19/0.50 (![X: $i] : (minus(X, n1) = pred(X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.50 tff(21,plain,(
% 0.19/0.50 ![X: $i] : (minus(X, n1) = pred(X))),
% 0.19/0.50 inference(skolemize,[status(sab)],[20])).
% 0.19/0.50 tff(22,plain,
% 0.19/0.50 (![X: $i] : (minus(X, n1) = pred(X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.50 tff(23,plain,
% 0.19/0.50 ((~![X: $i] : (minus(X, n1) = pred(X))) | (minus(n0, n1) = pred(n0))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(24,plain,
% 0.19/0.50 (minus(n0, n1) = pred(n0)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.50 tff(25,plain,
% 0.19/0.50 (pred(n0) = minus(n0, n1)),
% 0.19/0.50 inference(symmetry,[status(thm)],[24])).
% 0.19/0.50 tff(26,plain,
% 0.19/0.50 (pred(succ(tptp_minus_1)) = pred(n0)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[3])).
% 0.19/0.50 tff(27,plain,
% 0.19/0.50 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(28,plain,
% 0.19/0.50 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(29,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 0.19/0.50 tff(30,plain,
% 0.19/0.50 (![X: $i] : (pred(succ(X)) = X)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.50 tff(31,plain,(
% 0.19/0.50 ![X: $i] : (pred(succ(X)) = X)),
% 0.19/0.50 inference(skolemize,[status(sab)],[30])).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 (![X: $i] : (pred(succ(X)) = X)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(tptp_minus_1)) = tptp_minus_1)),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(34,plain,
% 0.19/0.50 (pred(succ(tptp_minus_1)) = tptp_minus_1),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.50 tff(35,plain,
% 0.19/0.50 (tptp_minus_1 = pred(succ(tptp_minus_1))),
% 0.19/0.50 inference(symmetry,[status(thm)],[34])).
% 0.19/0.50 tff(36,plain,
% 0.19/0.50 (tptp_minus_1 = minus(n0, n1)),
% 0.19/0.50 inference(transitivity,[status(thm)],[35, 26, 25])).
% 0.19/0.50 tff(37,plain,
% 0.19/0.50 (leq(n0, tptp_minus_1) <=> leq(n0, minus(n0, n1))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.50 tff(38,plain,
% 0.19/0.50 (leq(n0, minus(n0, n1)) <=> leq(n0, tptp_minus_1)),
% 0.19/0.50 inference(symmetry,[status(thm)],[37])).
% 0.19/0.50 tff(39,plain,
% 0.19/0.50 (((leq(n0, A!13) & leq(A!13, n2)) & (~((~(leq(n0, B!14) & leq(B!14, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B!14, A!13) = init)))) <=> (leq(n0, A!13) & leq(A!13, n2) & (~((~(leq(n0, B!14) & leq(B!14, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B!14, A!13) = init))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(40,plain,
% 0.19/0.50 ((~![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init)))) <=> (~![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(41,plain,
% 0.19/0.50 ((~((geq(minus(n330, n1), n0) & geq(minus(n410, n1), n0)) => ![A: $i] : ((leq(n0, A) & leq(A, n2)) => ![B: $i] : ((leq(n0, B) & leq(B, minus(n0, n1))) => (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init))))) <=> (~((~(geq(minus(n330, n1), n0) & geq(minus(n410, n1), n0))) | ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(42,axiom,(~((geq(minus(n330, n1), n0) & geq(minus(n410, n1), n0)) => ![A: $i] : ((leq(n0, A) & leq(A, n2)) => ![B: $i] : ((leq(n0, B) & leq(B, minus(n0, n1))) => (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gauss_init_0077')).
% 0.19/0.50 tff(43,plain,
% 0.19/0.50 (~((~(geq(minus(n330, n1), n0) & geq(minus(n410, n1), n0))) | ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.50 tff(44,plain,
% 0.19/0.50 (~![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init)))),
% 0.19/0.50 inference(or_elim,[status(thm)],[43])).
% 0.19/0.50 tff(45,plain,
% 0.19/0.50 (~![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.50 tff(46,plain,
% 0.19/0.50 (~![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.19/0.50 tff(47,plain,
% 0.19/0.50 (~![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B, A) = init)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[46, 40])).
% 0.19/0.50 tff(48,plain,
% 0.19/0.50 (leq(n0, A!13) & leq(A!13, n2) & (~((~(leq(n0, B!14) & leq(B!14, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B!14, A!13) = init)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[47, 39])).
% 0.19/0.50 tff(49,plain,
% 0.19/0.50 (~((~(leq(n0, B!14) & leq(B!14, minus(n0, n1)))) | (a_select3(tptp_const_array2(dim(n0, n3), dim(n0, n2), uninit), B!14, A!13) = init))),
% 0.19/0.50 inference(and_elim,[status(thm)],[48])).
% 0.19/0.50 tff(50,plain,
% 0.19/0.50 (leq(n0, B!14) & leq(B!14, minus(n0, n1))),
% 0.19/0.50 inference(or_elim,[status(thm)],[49])).
% 0.19/0.50 tff(51,plain,
% 0.19/0.50 (leq(B!14, minus(n0, n1))),
% 0.19/0.50 inference(and_elim,[status(thm)],[50])).
% 0.19/0.50 tff(52,plain,
% 0.19/0.50 (leq(n0, B!14)),
% 0.19/0.50 inference(and_elim,[status(thm)],[50])).
% 0.19/0.50 tff(53,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(54,plain,
% 0.19/0.50 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(55,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.50 tff(56,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(57,plain,
% 0.19/0.50 (^[X: $i, Y: $i, Z: $i] : rewrite(((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(58,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.50 tff(59,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 0.19/0.50 tff(60,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.50 tff(61,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.50 tff(62,plain,(
% 0.19/0.50 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.50 inference(skolemize,[status(sab)],[61])).
% 0.19/0.50 tff(63,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.19/0.50 tff(64,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.19/0.50 tff(65,plain,
% 0.19/0.50 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(n0, B!14)) | leq(n0, minus(n0, n1)) | (~leq(B!14, minus(n0, n1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(n0, B!14)) | leq(n0, minus(n0, n1)) | (~leq(B!14, minus(n0, n1))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(66,plain,
% 0.19/0.50 ((leq(n0, minus(n0, n1)) | (~leq(B!14, minus(n0, n1))) | (~leq(n0, B!14))) <=> ((~leq(n0, B!14)) | leq(n0, minus(n0, n1)) | (~leq(B!14, minus(n0, n1))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(67,plain,
% 0.19/0.50 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n0, minus(n0, n1)) | (~leq(B!14, minus(n0, n1))) | (~leq(n0, B!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(n0, B!14)) | leq(n0, minus(n0, n1)) | (~leq(B!14, minus(n0, n1)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.50 tff(68,plain,
% 0.19/0.50 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n0, minus(n0, n1)) | (~leq(B!14, minus(n0, n1))) | (~leq(n0, B!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(n0, B!14)) | leq(n0, minus(n0, n1)) | (~leq(B!14, minus(n0, n1))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.50 tff(69,plain,
% 0.19/0.50 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n0, minus(n0, n1)) | (~leq(B!14, minus(n0, n1))) | (~leq(n0, B!14)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(70,plain,
% 0.19/0.50 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(n0, B!14)) | leq(n0, minus(n0, n1)) | (~leq(B!14, minus(n0, n1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.50 tff(71,plain,
% 0.19/0.50 (leq(n0, minus(n0, n1))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[70, 64, 52, 51])).
% 0.19/0.50 tff(72,plain,
% 0.19/0.50 (leq(n0, tptp_minus_1)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[71, 38])).
% 0.19/0.50 tff(73,plain,
% 0.19/0.50 ((~(leq(succ(n0), succ(tptp_minus_1)) <=> leq(n0, tptp_minus_1))) | leq(succ(n0), succ(tptp_minus_1)) | (~leq(n0, tptp_minus_1))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(74,plain,
% 0.19/0.50 (leq(succ(n0), succ(tptp_minus_1))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[73, 72, 15])).
% 0.19/0.50 tff(75,plain,
% 0.19/0.50 (leq(succ(n0), n0)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[74, 6])).
% 0.19/0.50 tff(76,plain,
% 0.19/0.50 (^[X: $i, Y: $i] : refl(((~leq(succ(X), Y)) | gt(Y, X)) <=> ((~leq(succ(X), Y)) | gt(Y, X)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(77,plain,
% 0.19/0.50 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.50 tff(78,plain,
% 0.19/0.50 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(79,plain,
% 0.19/0.50 (^[X: $i, Y: $i] : rewrite((leq(succ(X), Y) => gt(Y, X)) <=> ((~leq(succ(X), Y)) | gt(Y, X)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(80,plain,
% 0.19/0.50 (![X: $i, Y: $i] : (leq(succ(X), Y) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.50 tff(81,axiom,(![X: $i, Y: $i] : (leq(succ(X), Y) => gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_succ_gt')).
% 0.19/0.50 tff(82,plain,
% 0.19/0.50 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.50 tff(83,plain,
% 0.19/0.50 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.50 tff(84,plain,(
% 0.19/0.50 ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.19/0.50 inference(skolemize,[status(sab)],[83])).
% 0.19/0.50 tff(85,plain,
% 0.19/0.50 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.19/0.50 tff(86,plain,
% 0.19/0.50 (((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | ((~leq(succ(n0), n0)) | gt(n0, n0))) <=> ((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | (~leq(succ(n0), n0)) | gt(n0, n0))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(87,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | ((~leq(succ(n0), n0)) | gt(n0, n0))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(88,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | (~leq(succ(n0), n0)) | gt(n0, n0)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.51 tff(89,plain,
% 0.19/0.51 (gt(n0, n0)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[88, 85, 75])).
% 0.19/0.51 tff(90,plain,
% 0.19/0.51 (^[X: $i] : refl((~gt(X, X)) <=> (~gt(X, X)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(91,plain,
% 0.19/0.51 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.51 tff(92,plain,
% 0.19/0.51 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(93,axiom,(![X: $i] : (~gt(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','irreflexivity_gt')).
% 0.19/0.51 tff(94,plain,
% 0.19/0.51 (![X: $i] : (~gt(X, X))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.51 tff(95,plain,(
% 0.19/0.51 ![X: $i] : (~gt(X, X))),
% 0.19/0.51 inference(skolemize,[status(sab)],[94])).
% 0.19/0.51 tff(96,plain,
% 0.19/0.51 (![X: $i] : (~gt(X, X))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.19/0.51 tff(97,plain,
% 0.19/0.51 ((~![X: $i] : (~gt(X, X))) | (~gt(n0, n0))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(98,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[97, 96, 89])).
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------