TSTP Solution File: SWV167+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV167+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Thu Sep 29 15:10:13 EDT 2022
% Result : Theorem 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV167+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 01:23:49 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46 % SZS output start Proof
% 0.21/0.46 tff(a_select2_type, type, (
% 0.21/0.46 a_select2: ( $i * $i ) > $i)).
% 0.21/0.46 tff(pv40_type, type, (
% 0.21/0.46 pv40: $i)).
% 0.21/0.46 tff(mu_init_type, type, (
% 0.21/0.46 mu_init: $i)).
% 0.21/0.46 tff(tptp_fun_J_13_type, type, (
% 0.21/0.46 tptp_fun_J_13: $i)).
% 0.21/0.46 tff(gt_type, type, (
% 0.21/0.46 gt: ( $i * $i ) > $o)).
% 0.21/0.46 tff(leq_type, type, (
% 0.21/0.46 leq: ( $i * $i ) > $o)).
% 0.21/0.46 tff(pred_type, type, (
% 0.21/0.46 pred: $i > $i)).
% 0.21/0.46 tff(succ_type, type, (
% 0.21/0.46 succ: $i > $i)).
% 0.21/0.46 tff(tptp_minus_1_type, type, (
% 0.21/0.46 tptp_minus_1: $i)).
% 0.21/0.46 tff(init_type, type, (
% 0.21/0.46 init: $i)).
% 0.21/0.46 tff(n0_type, type, (
% 0.21/0.46 n0: $i)).
% 0.21/0.46 tff(sigmaold_init_type, type, (
% 0.21/0.46 sigmaold_init: $i)).
% 0.21/0.46 tff(n4_type, type, (
% 0.21/0.46 n4: $i)).
% 0.21/0.46 tff(n1_type, type, (
% 0.21/0.46 n1: $i)).
% 0.21/0.46 tff(loopcounter_type, type, (
% 0.21/0.46 loopcounter: $i)).
% 0.21/0.46 tff(rhoold_init_type, type, (
% 0.21/0.46 rhoold_init: $i)).
% 0.21/0.46 tff(muold_init_type, type, (
% 0.21/0.46 muold_init: $i)).
% 0.21/0.46 tff(a_select3_type, type, (
% 0.21/0.46 a_select3: ( $i * $i * $i ) > $i)).
% 0.21/0.46 tff(center_init_type, type, (
% 0.21/0.46 center_init: $i)).
% 0.21/0.46 tff(sigma_init_type, type, (
% 0.21/0.46 sigma_init: $i)).
% 0.21/0.46 tff(rho_init_type, type, (
% 0.21/0.46 rho_init: $i)).
% 0.21/0.46 tff(q_init_type, type, (
% 0.21/0.46 q_init: $i)).
% 0.21/0.46 tff(n135299_type, type, (
% 0.21/0.46 n135299: $i)).
% 0.21/0.46 tff(1,plain,
% 0.21/0.46 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(2,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.46 tff(3,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(4,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 0.21/0.46 tff(5,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.46 tff(6,plain,(
% 0.21/0.46 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.46 inference(skolemize,[status(sab)],[5])).
% 0.21/0.46 tff(7,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.46 tff(8,plain,
% 0.21/0.46 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(J!13, pred(pv40)) <=> gt(pv40, J!13))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(9,plain,
% 0.21/0.46 (leq(J!13, pred(pv40)) <=> gt(pv40, J!13)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.46 tff(10,plain,
% 0.21/0.46 ((~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, pv40))) | (a_select2(mu_init, J) = a_select2(mu_init, pv40)))) <=> (~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, pv40))) | (a_select2(mu_init, J) = a_select2(mu_init, pv40))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(11,plain,
% 0.21/0.46 ((~![J: $i] : ((~(leq(n0, J) & leq(J, pv40))) | (a_select2(mu_init, J) = init))) <=> (~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, pv40))) | (a_select2(mu_init, J) = a_select2(mu_init, pv40))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(12,plain,
% 0.21/0.46 ((~![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(13,plain,
% 0.21/0.46 ((~(((((((((((((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))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(14,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/sandbox2/benchmark/theBenchmark.p','cl5_nebula_init_0011')).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 (~((~((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)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (~![J: $i] : ((~(leq(n0, J) & leq(J, pv40))) | (a_select2(mu_init, J) = init))),
% 0.21/0.47 inference(or_elim,[status(thm)],[15])).
% 0.21/0.47 tff(17,plain,
% 0.21/0.47 (~![J: $i] : ((~(leq(n0, J) & leq(J, pv40))) | (a_select2(mu_init, J) = init))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 (~![J: $i] : ((~(leq(n0, J) & leq(J, pv40))) | (a_select2(mu_init, J) = init))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.21/0.47 tff(19,plain,
% 0.21/0.47 (~![J: $i] : ((~(leq(n0, J) & leq(J, pv40))) | (a_select2(mu_init, J) = init))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.21/0.47 tff(20,plain,
% 0.21/0.47 (~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, pv40))) | (a_select2(mu_init, J) = a_select2(mu_init, pv40)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.21/0.47 tff(21,plain,
% 0.21/0.47 (~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, pv40))) | (a_select2(mu_init, J) = a_select2(mu_init, pv40)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.21/0.47 tff(22,plain,
% 0.21/0.47 (~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, pv40))) | (a_select2(mu_init, J) = a_select2(mu_init, pv40)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[21, 10])).
% 0.21/0.47 tff(23,plain,
% 0.21/0.47 (~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, pv40))) | (a_select2(mu_init, J) = a_select2(mu_init, pv40)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[22, 10])).
% 0.21/0.47 tff(24,plain,(
% 0.21/0.47 ~((~(leq(succ(tptp_minus_1), J!13) & leq(J!13, pv40))) | (a_select2(mu_init, J!13) = a_select2(mu_init, pv40)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[23])).
% 0.21/0.47 tff(25,plain,
% 0.21/0.47 (~(a_select2(mu_init, J!13) = a_select2(mu_init, pv40))),
% 0.21/0.47 inference(or_elim,[status(thm)],[24])).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 (leq(succ(tptp_minus_1), J!13) & leq(J!13, pv40)),
% 0.21/0.47 inference(or_elim,[status(thm)],[24])).
% 0.21/0.47 tff(27,plain,
% 0.21/0.47 (leq(succ(tptp_minus_1), J!13)),
% 0.21/0.47 inference(and_elim,[status(thm)],[26])).
% 0.21/0.47 tff(28,plain,
% 0.21/0.47 (^[D: $i] : refl(((a_select2(mu_init, D) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40)))) <=> ((a_select2(mu_init, D) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(29,plain,
% 0.21/0.47 (![D: $i] : ((a_select2(mu_init, D) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40)))) <=> ![D: $i] : ((a_select2(mu_init, D) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 (^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), D) & leq(D, pred(pv40))) <=> (~((~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40)))))), ((~(leq(succ(tptp_minus_1), D) & leq(D, pred(pv40)))) <=> (~(~((~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40)))))))), rewrite((~(~((~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40)))))) <=> ((~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40))))), ((~(leq(succ(tptp_minus_1), D) & leq(D, pred(pv40)))) <=> ((~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40)))))), (((~(leq(succ(tptp_minus_1), D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = a_select2(mu_init, pv40))) <=> (((~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40)))) | (a_select2(mu_init, D) = a_select2(mu_init, pv40))))), rewrite((((~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40)))) | (a_select2(mu_init, D) = a_select2(mu_init, pv40))) <=> ((a_select2(mu_init, D) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40))))), (((~(leq(succ(tptp_minus_1), D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = a_select2(mu_init, pv40))) <=> ((a_select2(mu_init, D) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(31,plain,
% 0.21/0.47 (![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = a_select2(mu_init, pv40))) <=> ![D: $i] : ((a_select2(mu_init, D) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.47 tff(32,plain,
% 0.21/0.47 (^[D: $i] : rewrite(((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init)) <=> ((~(leq(succ(tptp_minus_1), D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = a_select2(mu_init, pv40))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(33,plain,
% 0.21/0.47 (![D: $i] : ((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init)) <=> ![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = a_select2(mu_init, pv40)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.47 tff(34,plain,
% 0.21/0.47 (![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))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(35,plain,
% 0.21/0.47 ((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)))),
% 0.21/0.47 inference(or_elim,[status(thm)],[15])).
% 0.21/0.47 tff(36,plain,
% 0.21/0.47 (![D: $i] : ((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init))),
% 0.21/0.47 inference(and_elim,[status(thm)],[35])).
% 0.21/0.47 tff(37,plain,
% 0.21/0.47 (![D: $i] : ((~(leq(n0, D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = init))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.21/0.47 tff(38,plain,
% 0.21/0.47 (![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = a_select2(mu_init, pv40)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.47 tff(39,plain,(
% 0.21/0.47 ![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, pred(pv40)))) | (a_select2(mu_init, D) = a_select2(mu_init, pv40)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[38])).
% 0.21/0.47 tff(40,plain,
% 0.21/0.47 (![D: $i] : ((a_select2(mu_init, D) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[39, 31])).
% 0.21/0.47 tff(41,plain,
% 0.21/0.47 (![D: $i] : ((a_select2(mu_init, D) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[40, 29])).
% 0.21/0.47 tff(42,plain,
% 0.21/0.47 (((~![D: $i] : ((a_select2(mu_init, D) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40))))) | ((a_select2(mu_init, J!13) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(J!13, pred(pv40))))) <=> ((~![D: $i] : ((a_select2(mu_init, D) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40))))) | (a_select2(mu_init, J!13) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(J!13, pred(pv40))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(43,plain,
% 0.21/0.47 ((~![D: $i] : ((a_select2(mu_init, D) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40))))) | ((a_select2(mu_init, J!13) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(J!13, pred(pv40))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(44,plain,
% 0.21/0.47 ((~![D: $i] : ((a_select2(mu_init, D) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, pred(pv40))))) | (a_select2(mu_init, J!13) = a_select2(mu_init, pv40)) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(J!13, pred(pv40)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.47 tff(45,plain,
% 0.21/0.47 (~leq(J!13, pred(pv40))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[44, 41, 27, 25])).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 ((~(leq(J!13, pred(pv40)) <=> gt(pv40, J!13))) | leq(J!13, pred(pv40)) | (~gt(pv40, J!13))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 ((~(leq(J!13, pred(pv40)) <=> gt(pv40, J!13))) | (~gt(pv40, J!13))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 (~gt(pv40, J!13)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[47, 9])).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 (leq(J!13, pv40)),
% 0.21/0.47 inference(and_elim,[status(thm)],[26])).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 (^[X: $i, Y: $i] : refl(((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(51,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.47 tff(52,plain,
% 0.21/0.47 (^[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)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(53,plain,
% 0.21/0.48 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.48 tff(54,plain,
% 0.21/0.48 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(55,plain,
% 0.21/0.48 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(56,plain,
% 0.21/0.48 (![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[55])).
% 0.21/0.48 tff(57,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt2')).
% 0.21/0.48 tff(58,plain,
% 0.21/0.48 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.48 tff(59,plain,
% 0.21/0.48 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.21/0.48 tff(60,plain,(
% 0.21/0.48 ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.21/0.48 inference(skolemize,[status(sab)],[59])).
% 0.21/0.48 tff(61,plain,
% 0.21/0.48 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.21/0.48 tff(62,plain,
% 0.21/0.48 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.21/0.48 tff(63,plain,
% 0.21/0.48 (((~![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)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(64,plain,
% 0.21/0.48 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((J!13 = pv40) | gt(pv40, J!13) | (~leq(J!13, pv40)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(65,plain,
% 0.21/0.48 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (J!13 = pv40) | gt(pv40, J!13) | (~leq(J!13, pv40))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.48 tff(66,plain,
% 0.21/0.48 ((J!13 = pv40) | gt(pv40, J!13)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[65, 62, 49])).
% 0.21/0.48 tff(67,plain,
% 0.21/0.48 (J!13 = pv40),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[66, 48])).
% 0.21/0.48 tff(68,plain,
% 0.21/0.48 (a_select2(mu_init, J!13) = a_select2(mu_init, pv40)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[67])).
% 0.21/0.48 tff(69,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[25, 68])).
% 0.21/0.48 % SZS output end Proof
%------------------------------------------------------------------------------