%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV167+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:31:38 AM UTC 2025
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV167+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:30:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(init_type, type, (
% 0.21/0.43 init: $i)).
% 0.21/0.43 tff(a_select2_type, type, (
% 0.21/0.43 a_select2: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_J_13_type, type, (
% 0.21/0.43 tptp_fun_J_13: $i)).
% 0.21/0.43 tff(mu_init_type, type, (
% 0.21/0.43 mu_init: $i)).
% 0.21/0.43 tff(pv40_type, type, (
% 0.21/0.43 pv40: $i)).
% 0.21/0.43 tff(sigmaold_init_type, type, (
% 0.21/0.43 sigmaold_init: $i)).
% 0.21/0.43 tff(leq_type, type, (
% 0.21/0.43 leq: ( $i * $i ) > $o)).
% 0.21/0.43 tff(n4_type, type, (
% 0.21/0.43 n4: $i)).
% 0.21/0.43 tff(n0_type, type, (
% 0.21/0.43 n0: $i)).
% 0.21/0.43 tff(gt_type, type, (
% 0.21/0.43 gt: ( $i * $i ) > $o)).
% 0.21/0.43 tff(n1_type, type, (
% 0.21/0.43 n1: $i)).
% 0.21/0.43 tff(loopcounter_type, type, (
% 0.21/0.43 loopcounter: $i)).
% 0.21/0.43 tff(rhoold_init_type, type, (
% 0.21/0.43 rhoold_init: $i)).
% 0.21/0.43 tff(muold_init_type, type, (
% 0.21/0.43 muold_init: $i)).
% 0.21/0.43 tff(a_select3_type, type, (
% 0.21/0.43 a_select3: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(center_init_type, type, (
% 0.21/0.43 center_init: $i)).
% 0.21/0.43 tff(sigma_init_type, type, (
% 0.21/0.43 sigma_init: $i)).
% 0.21/0.43 tff(pred_type, type, (
% 0.21/0.43 pred: $i > $i)).
% 0.21/0.43 tff(rho_init_type, type, (
% 0.21/0.43 rho_init: $i)).
% 0.21/0.43 tff(q_init_type, type, (
% 0.21/0.43 q_init: $i)).
% 0.21/0.43 tff(n135299_type, type, (
% 0.21/0.43 n135299: $i)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 ((a_select2(mu_init, pv40) = init) <=> (a_select2(mu_init, pv40) = init)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 ((~(((((((((((((a_select2(mu_init, pv40) = init) & (a_select2(sigma_init, pv40) = init)) & leq(n0, pv40)) & leq(pv40, n4)) & ![A: $i] : ((leq(n0, A) & leq(A, n135299)) => ![B: $i] : ((leq(n0, B) & leq(B, n4)) => (a_select3(q_init, A, B) = init)))) & ![C: $i] : ((leq(n0, C) & leq(C, n4)) => (a_select2(rho_init, C) = init))) & ![D: $i] : ((leq(n0, D) & leq(D, pred(pv40))) => (a_select2(mu_init, D) = init))) & ![E: $i] : ((leq(n0, E) & leq(E, pred(pv40))) => (a_select2(sigma_init, E) = init))) & ![F: $i] : ((leq(n0, F) & leq(F, n4)) => (a_select3(center_init, F, n0) = init))) & (gt(loopcounter, n1) => ![G: $i] : ((leq(n0, G) & leq(G, n4)) => (a_select2(muold_init, G) = init)))) & (gt(loopcounter, n1) => ![H: $i] : ((leq(n0, H) & leq(H, n4)) => (a_select2(rhoold_init, H) = init)))) & (gt(loopcounter, n1) => ![I: $i] : ((leq(n0, I) & leq(I, n4)) => (a_select2(sigmaold_init, I) = init)))) => ![J: $i] : ((leq(n0, J) & leq(J, pv40)) => (a_select2(mu_init, J) = init)))) <=> (~((~((a_select2(mu_init, pv40) = init) & (a_select2(sigma_init, pv40) = init) & leq(n0, pv40) & leq(pv40, n4) & ![A: $i] : ((~(leq(n0, A) & leq(A, n135299))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init))) & ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select2(rho_init, C) = init)) & ![D: $i] : ((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init)) & ![E: $i] : ((~(leq(n0, E) & leq(E, pred(pv40)))) | (a_select2(sigma_init, E) = init)) & ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select3(center_init, F, n0) = init)) & ((~gt(loopcounter, n1)) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(muold_init, G) = init))) & ((~gt(loopcounter, n1)) | ![H: $i] : ((~(leq(n0, H) & leq(H, n4))) | (a_select2(rhoold_init, H) = init))) & ((~gt(loopcounter, n1)) | ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init))))) | ![J: $i] : ((~(leq(n0, J) & leq(J, pv40))) | (a_select2(mu_init, J) = init))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(3,axiom,(~(((((((((((((a_select2(mu_init, pv40) = init) & (a_select2(sigma_init, pv40) = init)) & leq(n0, pv40)) & leq(pv40, n4)) & ![A: $i] : ((leq(n0, A) & leq(A, n135299)) => ![B: $i] : ((leq(n0, B) & leq(B, n4)) => (a_select3(q_init, A, B) = init)))) & ![C: $i] : ((leq(n0, C) & leq(C, n4)) => (a_select2(rho_init, C) = init))) & ![D: $i] : ((leq(n0, D) & leq(D, pred(pv40))) => (a_select2(mu_init, D) = init))) & ![E: $i] : ((leq(n0, E) & leq(E, pred(pv40))) => (a_select2(sigma_init, E) = init))) & ![F: $i] : ((leq(n0, F) & leq(F, n4)) => (a_select3(center_init, F, n0) = init))) & (gt(loopcounter, n1) => ![G: $i] : ((leq(n0, G) & leq(G, n4)) => (a_select2(muold_init, G) = init)))) & (gt(loopcounter, n1) => ![H: $i] : ((leq(n0, H) & leq(H, n4)) => (a_select2(rhoold_init, H) = init)))) & (gt(loopcounter, n1) => ![I: $i] : ((leq(n0, I) & leq(I, n4)) => (a_select2(sigmaold_init, I) = init)))) => ![J: $i] : ((leq(n0, J) & leq(J, pv40)) => (a_select2(mu_init, J) = init)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cl5_nebula_init_0011')).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 (~((~((a_select2(mu_init, pv40) = init) & (a_select2(sigma_init, pv40) = init) & leq(n0, pv40) & leq(pv40, n4) & ![A: $i] : ((~(leq(n0, A) & leq(A, n135299))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init))) & ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select2(rho_init, C) = init)) & ![D: $i] : ((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init)) & ![E: $i] : ((~(leq(n0, E) & leq(E, pred(pv40)))) | (a_select2(sigma_init, E) = init)) & ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select3(center_init, F, n0) = init)) & ((~gt(loopcounter, n1)) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(muold_init, G) = init))) & ((~gt(loopcounter, n1)) | ![H: $i] : ((~(leq(n0, H) & leq(H, n4))) | (a_select2(rhoold_init, H) = init))) & ((~gt(loopcounter, n1)) | ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init))))) | ![J: $i] : ((~(leq(n0, J) & leq(J, pv40))) | (a_select2(mu_init, J) = init)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 ((a_select2(mu_init, pv40) = init) & (a_select2(sigma_init, pv40) = init) & leq(n0, pv40) & leq(pv40, n4) & ![A: $i] : ((~(leq(n0, A) & leq(A, n135299))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init))) & ![C: $i] : ((~(leq(n0, C) & leq(C, n4))) | (a_select2(rho_init, C) = init)) & ![D: $i] : ((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init)) & ![E: $i] : ((~(leq(n0, E) & leq(E, pred(pv40)))) | (a_select2(sigma_init, E) = init)) & ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select3(center_init, F, n0) = init)) & ((~gt(loopcounter, n1)) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(muold_init, G) = init))) & ((~gt(loopcounter, n1)) | ![H: $i] : ((~(leq(n0, H) & leq(H, n4))) | (a_select2(rhoold_init, H) = init))) & ((~gt(loopcounter, n1)) | ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init)))),
% 0.21/0.44 inference(or_elim,[status(thm)],[4])).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 (a_select2(mu_init, pv40) = init),
% 0.21/0.44 inference(and_elim,[status(thm)],[5])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (a_select2(mu_init, pv40) = init),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(11,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.44 tff(13,plain,(
% 0.21/0.44 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(skolemize,[status(sab)],[12])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(J!13, pred(pv40)) <=> gt(pv40, J!13))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(16,plain,
% 0.21/0.44 (leq(J!13, pred(pv40)) <=> gt(pv40, J!13)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.21/0.44 tff(17,plain,
% 0.21/0.44 ((~![J: $i] : ((~(leq(n0, J) & leq(J, pv40))) | (a_select2(mu_init, J) = init))) <=> (~![J: $i] : ((~(leq(n0, J) & leq(J, pv40))) | (a_select2(mu_init, J) = init)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 (~![J: $i] : ((~(leq(n0, J) & leq(J, pv40))) | (a_select2(mu_init, J) = init))),
% 0.21/0.44 inference(or_elim,[status(thm)],[4])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 (~![J: $i] : ((~(leq(n0, J) & leq(J, pv40))) | (a_select2(mu_init, J) = init))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.44 tff(20,plain,
% 0.21/0.44 (~![J: $i] : ((~(leq(n0, J) & leq(J, pv40))) | (a_select2(mu_init, J) = init))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 (~![J: $i] : ((~(leq(n0, J) & leq(J, pv40))) | (a_select2(mu_init, J) = init))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.21/0.44 tff(22,plain,(
% 0.21/0.44 ~((~(leq(n0, J!13) & leq(J!13, pv40))) | (a_select2(mu_init, J!13) = init))),
% 0.21/0.44 inference(skolemize,[status(sab)],[21])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 (~(a_select2(mu_init, J!13) = init)),
% 0.21/0.44 inference(or_elim,[status(thm)],[22])).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 (leq(n0, J!13) & leq(J!13, pv40)),
% 0.21/0.44 inference(or_elim,[status(thm)],[22])).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 (leq(n0, J!13)),
% 0.21/0.44 inference(and_elim,[status(thm)],[24])).
% 0.21/0.44 tff(26,plain,
% 0.21/0.44 (^[D: $i] : refl(((a_select2(mu_init, D) = init) | (~leq(n0, D)) | (~leq(D, pred(pv40)))) <=> ((a_select2(mu_init, D) = init) | (~leq(n0, D)) | (~leq(D, pred(pv40)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 (![D: $i] : ((a_select2(mu_init, D) = init) | (~leq(n0, D)) | (~leq(D, pred(pv40)))) <=> ![D: $i] : ((a_select2(mu_init, D) = init) | (~leq(n0, D)) | (~leq(D, pred(pv40))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 (^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, D) & leq(D, pred(pv40))) <=> (~((~leq(n0, D)) | (~leq(D, pred(pv40)))))), ((~(leq(n0, D) & leq(D, pred(pv40)))) <=> (~(~((~leq(n0, D)) | (~leq(D, pred(pv40)))))))), rewrite((~(~((~leq(n0, D)) | (~leq(D, pred(pv40)))))) <=> ((~leq(n0, D)) | (~leq(D, pred(pv40))))), ((~(leq(n0, D) & leq(D, pred(pv40)))) <=> ((~leq(n0, D)) | (~leq(D, pred(pv40)))))), (((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init)) <=> (((~leq(n0, D)) | (~leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init)))), rewrite((((~leq(n0, D)) | (~leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init)) <=> ((a_select2(mu_init, D) = init) | (~leq(n0, D)) | (~leq(D, pred(pv40))))), (((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init)) <=> ((a_select2(mu_init, D) = init) | (~leq(n0, D)) | (~leq(D, pred(pv40))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (![D: $i] : ((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init)) <=> ![D: $i] : ((a_select2(mu_init, D) = init) | (~leq(n0, D)) | (~leq(D, pred(pv40))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 (![D: $i] : ((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init)) <=> ![D: $i] : ((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 (![D: $i] : ((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init))),
% 0.21/0.44 inference(and_elim,[status(thm)],[5])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (![D: $i] : ((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.44 tff(33,plain,(
% 0.21/0.44 ![D: $i] : ((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init))),
% 0.21/0.44 inference(skolemize,[status(sab)],[32])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 (![D: $i] : ((a_select2(mu_init, D) = init) | (~leq(n0, D)) | (~leq(D, pred(pv40))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (![D: $i] : ((a_select2(mu_init, D) = init) | (~leq(n0, D)) | (~leq(D, pred(pv40))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (((~![D: $i] : ((a_select2(mu_init, D) = init) | (~leq(n0, D)) | (~leq(D, pred(pv40))))) | ((a_select2(mu_init, J!13) = init) | (~leq(n0, J!13)) | (~leq(J!13, pred(pv40))))) <=> ((~![D: $i] : ((a_select2(mu_init, D) = init) | (~leq(n0, D)) | (~leq(D, pred(pv40))))) | (a_select2(mu_init, J!13) = init) | (~leq(n0, J!13)) | (~leq(J!13, pred(pv40))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 ((~![D: $i] : ((a_select2(mu_init, D) = init) | (~leq(n0, D)) | (~leq(D, pred(pv40))))) | ((a_select2(mu_init, J!13) = init) | (~leq(n0, J!13)) | (~leq(J!13, pred(pv40))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 ((~![D: $i] : ((a_select2(mu_init, D) = init) | (~leq(n0, D)) | (~leq(D, pred(pv40))))) | (a_select2(mu_init, J!13) = init) | (~leq(n0, J!13)) | (~leq(J!13, pred(pv40)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (~leq(J!13, pred(pv40))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[38, 35, 25, 23])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 ((~(leq(J!13, pred(pv40)) <=> gt(pv40, J!13))) | leq(J!13, pred(pv40)) | (~gt(pv40, J!13))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 ((~(leq(J!13, pred(pv40)) <=> gt(pv40, J!13))) | (~gt(pv40, J!13))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (~gt(pv40, J!13)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[41, 16])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (leq(J!13, pv40)),
% 0.21/0.44 inference(and_elim,[status(thm)],[24])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : refl(((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & (~(X = Y))) <=> (~((~leq(X, Y)) | (X = Y)))), ((~(leq(X, Y) & (~(X = Y)))) <=> (~(~((~leq(X, Y)) | (X = Y)))))), rewrite((~(~((~leq(X, Y)) | (X = Y)))) <=> ((~leq(X, Y)) | (X = Y))), ((~(leq(X, Y) & (~(X = Y)))) <=> ((~leq(X, Y)) | (X = Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> (((~leq(X, Y)) | (X = Y)) | gt(Y, X)))), rewrite((((~leq(X, Y)) | (X = Y)) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.44 tff(51,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt2')).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.21/0.44 tff(54,plain,(
% 0.21/0.44 ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.44 inference(skolemize,[status(sab)],[53])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((J!13 = pv40) | gt(pv40, J!13) | (~leq(J!13, pv40)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (J!13 = pv40) | gt(pv40, J!13) | (~leq(J!13, pv40)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((J!13 = pv40) | gt(pv40, J!13) | (~leq(J!13, pv40)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (J!13 = pv40) | gt(pv40, J!13) | (~leq(J!13, pv40))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 ((J!13 = pv40) | gt(pv40, J!13)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[59, 56, 43])).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 (J!13 = pv40),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[60, 42])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 (a_select2(mu_init, J!13) = a_select2(mu_init, pv40)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.45 tff(63,plain,
% 0.21/0.45 (a_select2(mu_init, J!13) = init),
% 0.21/0.45 inference(transitivity,[status(thm)],[62, 7])).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[23, 63])).
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------