%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV176+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 05:31:39 AM UTC 2025
% Result : Theorem 0.12s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV176+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.12/0.12 % 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 09:31:09 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 % SZS output start Proof
% 0.12/0.41 tff(init_type, type, (
% 0.12/0.41 init: $i)).
% 0.12/0.41 tff(a_select2_type, type, (
% 0.12/0.41 a_select2: ( $i * $i ) > $i)).
% 0.12/0.41 tff(tptp_fun_J_13_type, type, (
% 0.12/0.41 tptp_fun_J_13: $i)).
% 0.12/0.41 tff(muold_init_type, type, (
% 0.12/0.41 muold_init: $i)).
% 0.12/0.41 tff(leq_type, type, (
% 0.12/0.41 leq: ( $i * $i ) > $o)).
% 0.12/0.41 tff(n4_type, type, (
% 0.12/0.41 n4: $i)).
% 0.12/0.41 tff(n0_type, type, (
% 0.12/0.41 n0: $i)).
% 0.12/0.41 tff(sigmaold_init_type, type, (
% 0.12/0.41 sigmaold_init: $i)).
% 0.12/0.41 tff(gt_type, type, (
% 0.12/0.41 gt: ( $i * $i ) > $o)).
% 0.12/0.41 tff(n1_type, type, (
% 0.12/0.41 n1: $i)).
% 0.12/0.41 tff(loopcounter_type, type, (
% 0.12/0.41 loopcounter: $i)).
% 0.12/0.41 tff(rhoold_init_type, type, (
% 0.12/0.41 rhoold_init: $i)).
% 0.12/0.41 tff(a_select3_type, type, (
% 0.12/0.41 a_select3: ( $i * $i * $i ) > $i)).
% 0.12/0.41 tff(center_init_type, type, (
% 0.12/0.41 center_init: $i)).
% 0.12/0.41 tff(sigma_init_type, type, (
% 0.12/0.41 sigma_init: $i)).
% 0.12/0.41 tff(pred_type, type, (
% 0.12/0.41 pred: $i > $i)).
% 0.12/0.41 tff(pv40_type, type, (
% 0.12/0.41 pv40: $i)).
% 0.12/0.41 tff(mu_init_type, type, (
% 0.12/0.41 mu_init: $i)).
% 0.12/0.41 tff(rho_init_type, type, (
% 0.12/0.41 rho_init: $i)).
% 0.12/0.41 tff(q_init_type, type, (
% 0.12/0.41 q_init: $i)).
% 0.12/0.41 tff(n135299_type, type, (
% 0.12/0.41 n135299: $i)).
% 0.12/0.41 tff(pv44_type, type, (
% 0.12/0.41 pv44: $i)).
% 0.12/0.41 tff(1,plain,
% 0.12/0.41 ((~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(muold_init, J) = init))) <=> (~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(muold_init, J) = init)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(2,plain,
% 0.12/0.41 ((~(((((((((((((leq(n0, pv40) & leq(n0, pv44)) & leq(pv40, n4)) & leq(pv44, n135299)) & gt(loopcounter, n1)) & ![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, n4)) => (a_select2(muold_init, J) = init)))) <=> (~((~(leq(n0, pv40) & leq(n0, pv44) & leq(pv40, n4) & leq(pv44, n135299) & gt(loopcounter, n1) & ![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, n4))) | (a_select2(muold_init, J) = init))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(3,axiom,(~(((((((((((((leq(n0, pv40) & leq(n0, pv44)) & leq(pv40, n4)) & leq(pv44, n135299)) & gt(loopcounter, n1)) & ![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, n4)) => (a_select2(muold_init, J) = init)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cl5_nebula_init_0056')).
% 0.12/0.42 tff(4,plain,
% 0.12/0.42 (~((~(leq(n0, pv40) & leq(n0, pv44) & leq(pv40, n4) & leq(pv44, n135299) & gt(loopcounter, n1) & ![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, n4))) | (a_select2(muold_init, J) = init)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.42 tff(5,plain,
% 0.12/0.42 (~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(muold_init, J) = init))),
% 0.12/0.42 inference(or_elim,[status(thm)],[4])).
% 0.12/0.42 tff(6,plain,
% 0.12/0.42 (~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(muold_init, J) = init))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.42 tff(7,plain,
% 0.12/0.42 (~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(muold_init, J) = init))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.42 tff(8,plain,
% 0.12/0.42 (~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(muold_init, J) = init))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.12/0.42 tff(9,plain,(
% 0.12/0.42 ~((~(leq(n0, J!13) & leq(J!13, n4))) | (a_select2(muold_init, J!13) = init))),
% 0.12/0.42 inference(skolemize,[status(sab)],[8])).
% 0.12/0.42 tff(10,plain,
% 0.12/0.42 (~(a_select2(muold_init, J!13) = init)),
% 0.12/0.42 inference(or_elim,[status(thm)],[9])).
% 0.12/0.42 tff(11,plain,
% 0.12/0.42 (leq(n0, J!13) & leq(J!13, n4)),
% 0.12/0.42 inference(or_elim,[status(thm)],[9])).
% 0.12/0.42 tff(12,plain,
% 0.12/0.42 (leq(J!13, n4)),
% 0.12/0.42 inference(and_elim,[status(thm)],[11])).
% 0.12/0.42 tff(13,plain,
% 0.12/0.42 (leq(n0, J!13)),
% 0.12/0.42 inference(and_elim,[status(thm)],[11])).
% 0.12/0.42 tff(14,plain,
% 0.12/0.42 (gt(loopcounter, n1) <=> gt(loopcounter, n1)),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(15,plain,
% 0.12/0.42 (leq(n0, pv40) & leq(n0, pv44) & leq(pv40, n4) & leq(pv44, n135299) & gt(loopcounter, n1) & ![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)))),
% 0.12/0.42 inference(or_elim,[status(thm)],[4])).
% 0.12/0.42 tff(16,plain,
% 0.12/0.42 (gt(loopcounter, n1)),
% 0.12/0.42 inference(and_elim,[status(thm)],[15])).
% 0.12/0.42 tff(17,plain,
% 0.12/0.42 (gt(loopcounter, n1)),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[16, 14])).
% 0.12/0.42 tff(18,plain,
% 0.12/0.42 (((~gt(loopcounter, n1)) | ![G: $i] : ((a_select2(muold_init, G) = init) | (~leq(n0, G)) | (~leq(G, n4)))) <=> ((~gt(loopcounter, n1)) | ![G: $i] : ((a_select2(muold_init, G) = init) | (~leq(n0, G)) | (~leq(G, n4))))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(19,plain,
% 0.12/0.42 (((~gt(loopcounter, n1)) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(muold_init, G) = init))) <=> ((~gt(loopcounter, n1)) | ![G: $i] : ((a_select2(muold_init, G) = init) | (~leq(n0, G)) | (~leq(G, n4))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (((~gt(loopcounter, n1)) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(muold_init, G) = init))) <=> ((~gt(loopcounter, n1)) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(muold_init, G) = init)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 ((~gt(loopcounter, n1)) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(muold_init, G) = init))),
% 0.20/0.42 inference(and_elim,[status(thm)],[15])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 ((~gt(loopcounter, n1)) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(muold_init, G) = init))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ((~gt(loopcounter, n1)) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(muold_init, G) = init))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 ((~gt(loopcounter, n1)) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(muold_init, G) = init))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.20/0.42 Proof display could not be completed: monotonicity rule is not handled
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------