%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV187+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 05:31:40 AM UTC 2025
% Result : Theorem 0.19s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV187+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:32:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(init_type, type, (
% 0.19/0.40 init: $i)).
% 0.19/0.40 tff(a_select2_type, type, (
% 0.19/0.40 a_select2: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_G_13_type, type, (
% 0.19/0.40 tptp_fun_G_13: $i)).
% 0.19/0.40 tff(sigmaold_init_type, type, (
% 0.19/0.40 sigmaold_init: $i)).
% 0.19/0.40 tff(leq_type, type, (
% 0.19/0.40 leq: ( $i * $i ) > $o)).
% 0.19/0.40 tff(n4_type, type, (
% 0.19/0.40 n4: $i)).
% 0.19/0.40 tff(n0_type, type, (
% 0.19/0.40 n0: $i)).
% 0.19/0.40 tff(gt_type, type, (
% 0.19/0.40 gt: ( $i * $i ) > $o)).
% 0.19/0.40 tff(n1_type, type, (
% 0.19/0.40 n1: $i)).
% 0.19/0.40 tff(loopcounter_type, type, (
% 0.19/0.40 loopcounter: $i)).
% 0.19/0.40 tff(rhoold_init_type, type, (
% 0.19/0.40 rhoold_init: $i)).
% 0.19/0.40 tff(muold_init_type, type, (
% 0.19/0.40 muold_init: $i)).
% 0.19/0.40 tff(a_select3_type, type, (
% 0.19/0.40 a_select3: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(center_init_type, type, (
% 0.19/0.40 center_init: $i)).
% 0.19/0.40 tff(q_init_type, type, (
% 0.19/0.40 q_init: $i)).
% 0.19/0.40 tff(n135299_type, type, (
% 0.19/0.40 n135299: $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 ((~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(sigmaold_init, G) = init))) <=> (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(sigmaold_init, G) = init)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((~((((((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_select3(center_init, C, n0) = init))) & (gt(loopcounter, n1) => ![D: $i] : ((leq(n0, D) & leq(D, n4)) => (a_select2(muold_init, D) = init)))) & (gt(loopcounter, n1) => ![E: $i] : ((leq(n0, E) & leq(E, n4)) => (a_select2(rhoold_init, E) = init)))) & (gt(loopcounter, n1) => ![F: $i] : ((leq(n0, F) & leq(F, n4)) => (a_select2(sigmaold_init, F) = init)))) => ![G: $i] : ((leq(n0, G) & leq(G, n4)) => (a_select2(sigmaold_init, G) = init)))) <=> (~((~(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_select3(center_init, C, n0) = init)) & ((~gt(loopcounter, n1)) | ![D: $i] : ((~(leq(n0, D) & leq(D, n4))) | (a_select2(muold_init, D) = init))) & ((~gt(loopcounter, n1)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rhoold_init, E) = init))) & ((~gt(loopcounter, n1)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigmaold_init, F) = init))))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(sigmaold_init, G) = init))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(3,axiom,(~((((((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_select3(center_init, C, n0) = init))) & (gt(loopcounter, n1) => ![D: $i] : ((leq(n0, D) & leq(D, n4)) => (a_select2(muold_init, D) = init)))) & (gt(loopcounter, n1) => ![E: $i] : ((leq(n0, E) & leq(E, n4)) => (a_select2(rhoold_init, E) = init)))) & (gt(loopcounter, n1) => ![F: $i] : ((leq(n0, F) & leq(F, n4)) => (a_select2(sigmaold_init, F) = init)))) => ![G: $i] : ((leq(n0, G) & leq(G, n4)) => (a_select2(sigmaold_init, G) = init)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cl5_nebula_init_0111')).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (~((~(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_select3(center_init, C, n0) = init)) & ((~gt(loopcounter, n1)) | ![D: $i] : ((~(leq(n0, D) & leq(D, n4))) | (a_select2(muold_init, D) = init))) & ((~gt(loopcounter, n1)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rhoold_init, E) = init))) & ((~gt(loopcounter, n1)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigmaold_init, F) = init))))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(sigmaold_init, G) = init)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(sigmaold_init, G) = init))),
% 0.19/0.40 inference(or_elim,[status(thm)],[4])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(sigmaold_init, G) = init))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(sigmaold_init, G) = init))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(sigmaold_init, G) = init))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.19/0.41 tff(9,plain,(
% 0.19/0.41 ~((~(leq(n0, G!13) & leq(G!13, n4))) | (a_select2(sigmaold_init, G!13) = init))),
% 0.19/0.41 inference(skolemize,[status(sab)],[8])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (~(a_select2(sigmaold_init, G!13) = init)),
% 0.19/0.41 inference(or_elim,[status(thm)],[9])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (leq(n0, G!13) & leq(G!13, n4)),
% 0.19/0.41 inference(or_elim,[status(thm)],[9])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (leq(G!13, n4)),
% 0.19/0.41 inference(and_elim,[status(thm)],[11])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (leq(n0, G!13)),
% 0.19/0.41 inference(and_elim,[status(thm)],[11])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (gt(loopcounter, n1) <=> gt(loopcounter, n1)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (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_select3(center_init, C, n0) = init)) & ((~gt(loopcounter, n1)) | ![D: $i] : ((~(leq(n0, D) & leq(D, n4))) | (a_select2(muold_init, D) = init))) & ((~gt(loopcounter, n1)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rhoold_init, E) = init))) & ((~gt(loopcounter, n1)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigmaold_init, F) = init)))),
% 0.19/0.41 inference(or_elim,[status(thm)],[4])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (gt(loopcounter, n1)),
% 0.19/0.41 inference(and_elim,[status(thm)],[15])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (gt(loopcounter, n1)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[16, 14])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (((~gt(loopcounter, n1)) | ![F: $i] : ((a_select2(sigmaold_init, F) = init) | (~leq(n0, F)) | (~leq(F, n4)))) <=> ((~gt(loopcounter, n1)) | ![F: $i] : ((a_select2(sigmaold_init, F) = init) | (~leq(n0, F)) | (~leq(F, n4))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (((~gt(loopcounter, n1)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigmaold_init, F) = init))) <=> ((~gt(loopcounter, n1)) | ![F: $i] : ((a_select2(sigmaold_init, F) = init) | (~leq(n0, F)) | (~leq(F, n4))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (((~gt(loopcounter, n1)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigmaold_init, F) = init))) <=> ((~gt(loopcounter, n1)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigmaold_init, F) = init)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 ((~gt(loopcounter, n1)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigmaold_init, F) = init))),
% 0.19/0.41 inference(and_elim,[status(thm)],[15])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 ((~gt(loopcounter, n1)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigmaold_init, F) = init))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 ((~gt(loopcounter, n1)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigmaold_init, F) = init))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 ((~gt(loopcounter, n1)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigmaold_init, F) = init))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.19/0.41 Proof display could not be completed: monotonicity rule is not handled
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------