TSTP Solution File: SWV178+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV178+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 15:10:15 EDT 2022
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV178+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n005.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Sep 4 01:39:48 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.35 Usage: tptp [options] [-file:]file
% 0.15/0.35 -h, -? prints this message.
% 0.15/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.35 -m, -model generate model.
% 0.15/0.35 -p, -proof generate proof.
% 0.15/0.35 -c, -core generate unsat core of named formulas.
% 0.15/0.35 -st, -statistics display statistics.
% 0.15/0.35 -t:timeout set timeout (in second).
% 0.15/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.35 -<param>:<value> configuration parameter and value.
% 0.15/0.35 -o:<output-file> file to place output in.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 tff(init_type, type, (
% 0.21/0.45 init: $i)).
% 0.21/0.45 tff(a_select2_type, type, (
% 0.21/0.45 a_select2: ( $i * $i ) > $i)).
% 0.21/0.45 tff(tptp_fun_J_13_type, type, (
% 0.21/0.45 tptp_fun_J_13: $i)).
% 0.21/0.45 tff(sigmaold_init_type, type, (
% 0.21/0.45 sigmaold_init: $i)).
% 0.21/0.45 tff(leq_type, type, (
% 0.21/0.45 leq: ( $i * $i ) > $o)).
% 0.21/0.45 tff(succ_type, type, (
% 0.21/0.45 succ: $i > $i)).
% 0.21/0.45 tff(tptp_minus_1_type, type, (
% 0.21/0.45 tptp_minus_1: $i)).
% 0.21/0.45 tff(n4_type, type, (
% 0.21/0.45 n4: $i)).
% 0.21/0.45 tff(n0_type, type, (
% 0.21/0.45 n0: $i)).
% 0.21/0.45 tff(gt_type, type, (
% 0.21/0.45 gt: ( $i * $i ) > $o)).
% 0.21/0.45 tff(n1_type, type, (
% 0.21/0.45 n1: $i)).
% 0.21/0.45 tff(loopcounter_type, type, (
% 0.21/0.45 loopcounter: $i)).
% 0.21/0.45 tff(rhoold_init_type, type, (
% 0.21/0.45 rhoold_init: $i)).
% 0.21/0.45 tff(muold_init_type, type, (
% 0.21/0.45 muold_init: $i)).
% 0.21/0.45 tff(a_select3_type, type, (
% 0.21/0.45 a_select3: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(center_init_type, type, (
% 0.21/0.45 center_init: $i)).
% 0.21/0.45 tff(sigma_init_type, type, (
% 0.21/0.45 sigma_init: $i)).
% 0.21/0.45 tff(pred_type, type, (
% 0.21/0.45 pred: $i > $i)).
% 0.21/0.45 tff(pv40_type, type, (
% 0.21/0.45 pv40: $i)).
% 0.21/0.45 tff(mu_init_type, type, (
% 0.21/0.45 mu_init: $i)).
% 0.21/0.45 tff(rho_init_type, type, (
% 0.21/0.45 rho_init: $i)).
% 0.21/0.45 tff(q_init_type, type, (
% 0.21/0.45 q_init: $i)).
% 0.21/0.45 tff(n135299_type, type, (
% 0.21/0.45 n135299: $i)).
% 0.21/0.45 tff(1,plain,
% 0.21/0.45 ((~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, J) = init))) <=> (~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, J) = init)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(2,plain,
% 0.21/0.45 ((~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(sigmaold_init, J) = init))) <=> (~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, J) = init)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(3,plain,
% 0.21/0.45 ((~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(sigmaold_init, J) = init))) <=> (~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(sigmaold_init, J) = init)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(4,plain,
% 0.21/0.45 ((~(((((((((((leq(n0, pv40) & leq(pv40, n4)) & 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(sigmaold_init, J) = init)))) <=> (~((~(leq(n0, pv40) & leq(pv40, n4) & 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(sigmaold_init, J) = init))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(5,axiom,(~(((((((((((leq(n0, pv40) & leq(pv40, n4)) & 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(sigmaold_init, J) = init)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cl5_nebula_init_0066')).
% 0.21/0.45 tff(6,plain,
% 0.21/0.45 (~((~(leq(n0, pv40) & leq(pv40, n4) & 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(sigmaold_init, J) = init)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.45 tff(7,plain,
% 0.21/0.45 (~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(sigmaold_init, J) = init))),
% 0.21/0.45 inference(or_elim,[status(thm)],[6])).
% 0.21/0.45 tff(8,plain,
% 0.21/0.45 (~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(sigmaold_init, J) = init))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.45 tff(9,plain,
% 0.21/0.45 (~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(sigmaold_init, J) = init))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.21/0.45 tff(10,plain,
% 0.21/0.45 (~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(sigmaold_init, J) = init))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.21/0.45 tff(11,plain,
% 0.21/0.45 (~![J: $i] : ((~(leq(n0, J) & leq(J, n4))) | (a_select2(sigmaold_init, J) = init))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.21/0.45 tff(12,plain,
% 0.21/0.45 (~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, J) = init))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.21/0.45 tff(13,plain,
% 0.21/0.45 (~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, J) = init))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.21/0.45 tff(14,plain,
% 0.21/0.45 (~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, J) = init))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[13, 1])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (~![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, J) = init))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[14, 1])).
% 0.21/0.45 tff(16,plain,(
% 0.21/0.45 ~((~(leq(succ(tptp_minus_1), J!13) & leq(J!13, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, J!13) = init))),
% 0.21/0.45 inference(skolemize,[status(sab)],[15])).
% 0.21/0.45 tff(17,plain,
% 0.21/0.45 (~(a_select2(sigmaold_init, J!13) = init)),
% 0.21/0.45 inference(or_elim,[status(thm)],[16])).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 (leq(succ(tptp_minus_1), J!13) & leq(J!13, succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.21/0.45 inference(or_elim,[status(thm)],[16])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 (leq(J!13, succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.21/0.45 inference(and_elim,[status(thm)],[18])).
% 0.21/0.45 tff(20,plain,
% 0.21/0.45 (leq(succ(tptp_minus_1), J!13)),
% 0.21/0.45 inference(and_elim,[status(thm)],[18])).
% 0.21/0.45 tff(21,plain,
% 0.21/0.45 (^[I: $i] : refl(((a_select2(sigmaold_init, I) = init) | (~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> ((a_select2(sigmaold_init, I) = init) | (~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(22,plain,
% 0.21/0.45 (![I: $i] : ((a_select2(sigmaold_init, I) = init) | (~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> ![I: $i] : ((a_select2(sigmaold_init, I) = init) | (~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.45 tff(23,plain,
% 0.21/0.45 (^[I: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), I) & leq(I, succ(succ(succ(succ(succ(tptp_minus_1))))))) <=> (~((~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))))), ((~(leq(succ(tptp_minus_1), I) & leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> (~(~((~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> ((~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1))))))))), ((~(leq(succ(tptp_minus_1), I) & leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))))), (((~(leq(succ(tptp_minus_1), I) & leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, I) = init)) <=> (((~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, I) = init)))), rewrite((((~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, I) = init)) <=> ((a_select2(sigmaold_init, I) = init) | (~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1))))))))), (((~(leq(succ(tptp_minus_1), I) & leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, I) = init)) <=> ((a_select2(sigmaold_init, I) = init) | (~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(24,plain,
% 0.21/0.45 (![I: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, I) = init)) <=> ![I: $i] : ((a_select2(sigmaold_init, I) = init) | (~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.45 tff(25,plain,
% 0.21/0.45 (^[I: $i] : rewrite(((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init)) <=> ((~(leq(succ(tptp_minus_1), I) & leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, I) = init)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(26,plain,
% 0.21/0.45 (![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init)) <=> ![I: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, I) = init))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.45 tff(27,plain,
% 0.21/0.45 (![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init)) <=> ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(28,plain,
% 0.21/0.45 (($false | ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init))) <=> ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(29,plain,
% 0.21/0.45 ((~$true) <=> $false),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 (leq(n0, pv40) & leq(pv40, n4) & 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)))),
% 0.21/0.46 inference(or_elim,[status(thm)],[6])).
% 0.21/0.46 tff(31,plain,
% 0.21/0.46 (gt(loopcounter, n1)),
% 0.21/0.46 inference(and_elim,[status(thm)],[30])).
% 0.21/0.46 tff(32,plain,
% 0.21/0.46 (gt(loopcounter, n1) <=> $true),
% 0.21/0.46 inference(iff_true,[status(thm)],[31])).
% 0.21/0.46 tff(33,plain,
% 0.21/0.46 ((~gt(loopcounter, n1)) <=> (~$true)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[32])).
% 0.21/0.46 tff(34,plain,
% 0.21/0.46 ((~gt(loopcounter, n1)) <=> $false),
% 0.21/0.46 inference(transitivity,[status(thm)],[33, 29])).
% 0.21/0.46 tff(35,plain,
% 0.21/0.46 (((~gt(loopcounter, n1)) | ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init))) <=> ($false | ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[34])).
% 0.21/0.46 tff(36,plain,
% 0.21/0.46 (((~gt(loopcounter, n1)) | ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init))) <=> ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init))),
% 0.21/0.46 inference(transitivity,[status(thm)],[35, 28])).
% 0.21/0.46 tff(37,plain,
% 0.21/0.46 (((~gt(loopcounter, n1)) | ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init))) <=> ((~gt(loopcounter, n1)) | ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(38,plain,
% 0.21/0.46 ((~gt(loopcounter, n1)) | ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init))),
% 0.21/0.46 inference(and_elim,[status(thm)],[30])).
% 0.21/0.46 tff(39,plain,
% 0.21/0.46 ((~gt(loopcounter, n1)) | ![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.46 tff(40,plain,
% 0.21/0.46 (![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.21/0.46 tff(41,plain,
% 0.21/0.46 (![I: $i] : ((~(leq(n0, I) & leq(I, n4))) | (a_select2(sigmaold_init, I) = init))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[40, 27])).
% 0.21/0.46 tff(42,plain,
% 0.21/0.46 (![I: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, I) = init))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[41, 26])).
% 0.21/0.46 tff(43,plain,(
% 0.21/0.46 ![I: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(I, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(sigmaold_init, I) = init))),
% 0.21/0.46 inference(skolemize,[status(sab)],[42])).
% 0.21/0.46 tff(44,plain,
% 0.21/0.46 (![I: $i] : ((a_select2(sigmaold_init, I) = init) | (~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[43, 24])).
% 0.21/0.46 tff(45,plain,
% 0.21/0.46 (![I: $i] : ((a_select2(sigmaold_init, I) = init) | (~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[44, 22])).
% 0.21/0.46 tff(46,plain,
% 0.21/0.46 (((~![I: $i] : ((a_select2(sigmaold_init, I) = init) | (~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1))))))))) | ((a_select2(sigmaold_init, J!13) = init) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(J!13, succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~![I: $i] : ((a_select2(sigmaold_init, I) = init) | (~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(sigmaold_init, J!13) = init) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(J!13, succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(47,plain,
% 0.21/0.46 ((~![I: $i] : ((a_select2(sigmaold_init, I) = init) | (~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1))))))))) | ((a_select2(sigmaold_init, J!13) = init) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(J!13, succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(48,plain,
% 0.21/0.46 ((~![I: $i] : ((a_select2(sigmaold_init, I) = init) | (~leq(succ(tptp_minus_1), I)) | (~leq(I, succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(sigmaold_init, J!13) = init) | (~leq(succ(tptp_minus_1), J!13)) | (~leq(J!13, succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.46 tff(49,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[48, 45, 20, 19, 17])).
% 0.21/0.46 % SZS output end Proof
%------------------------------------------------------------------------------