TSTP Solution File: SWV182+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV182+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 15:10:16 EDT 2022
% Result : Theorem 0.12s 0.31s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SWV182+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.00/0.08 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.07/0.26 % Computer : n027.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Sun Sep 4 01:55:36 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.07/0.26 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.07/0.26 Usage: tptp [options] [-file:]file
% 0.07/0.26 -h, -? prints this message.
% 0.07/0.26 -smt2 print SMT-LIB2 benchmark.
% 0.07/0.26 -m, -model generate model.
% 0.07/0.26 -p, -proof generate proof.
% 0.07/0.26 -c, -core generate unsat core of named formulas.
% 0.07/0.26 -st, -statistics display statistics.
% 0.07/0.26 -t:timeout set timeout (in second).
% 0.07/0.26 -smt2status display status in smt2 format instead of SZS.
% 0.07/0.26 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.07/0.26 -<param>:<value> configuration parameter and value.
% 0.07/0.26 -o:<output-file> file to place output in.
% 0.12/0.31 % SZS status Theorem
% 0.12/0.31 % SZS output start Proof
% 0.12/0.31 tff(init_type, type, (
% 0.12/0.31 init: $i)).
% 0.12/0.31 tff(a_select2_type, type, (
% 0.12/0.31 a_select2: ( $i * $i ) > $i)).
% 0.12/0.31 tff(tptp_fun_G_13_type, type, (
% 0.12/0.31 tptp_fun_G_13: $i)).
% 0.12/0.31 tff(rho_init_type, type, (
% 0.12/0.31 rho_init: $i)).
% 0.12/0.31 tff(leq_type, type, (
% 0.12/0.31 leq: ( $i * $i ) > $o)).
% 0.12/0.31 tff(succ_type, type, (
% 0.12/0.31 succ: $i > $i)).
% 0.12/0.31 tff(tptp_minus_1_type, type, (
% 0.12/0.31 tptp_minus_1: $i)).
% 0.12/0.31 tff(n4_type, type, (
% 0.12/0.31 n4: $i)).
% 0.12/0.31 tff(n0_type, type, (
% 0.12/0.31 n0: $i)).
% 0.12/0.31 tff(sigma_init_type, type, (
% 0.12/0.31 sigma_init: $i)).
% 0.12/0.31 tff(gt_type, type, (
% 0.12/0.31 gt: ( $i * $i ) > $o)).
% 0.12/0.31 tff(loopcounter_type, type, (
% 0.12/0.31 loopcounter: $i)).
% 0.12/0.31 tff(mu_init_type, type, (
% 0.12/0.31 mu_init: $i)).
% 0.12/0.31 tff(a_select3_type, type, (
% 0.12/0.31 a_select3: ( $i * $i * $i ) > $i)).
% 0.12/0.31 tff(center_init_type, type, (
% 0.12/0.31 center_init: $i)).
% 0.12/0.31 tff(q_init_type, type, (
% 0.12/0.31 q_init: $i)).
% 0.12/0.31 tff(n135299_type, type, (
% 0.12/0.31 n135299: $i)).
% 0.12/0.31 tff(n1_type, type, (
% 0.12/0.31 n1: $i)).
% 0.12/0.31 tff(pv76_type, type, (
% 0.12/0.31 pv76: $i)).
% 0.12/0.31 tff(tptp_float_0_001_type, type, (
% 0.12/0.31 tptp_float_0_001: $i)).
% 0.12/0.31 tff(1,plain,
% 0.12/0.31 ((~![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, G) = init))) <=> (~![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, G) = init)))),
% 0.12/0.31 inference(rewrite,[status(thm)],[])).
% 0.12/0.31 tff(2,plain,
% 0.12/0.31 ((~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init))) <=> (~![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, G) = init)))),
% 0.12/0.31 inference(rewrite,[status(thm)],[])).
% 0.12/0.31 tff(3,plain,
% 0.12/0.31 ((~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init))) <=> (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init)))),
% 0.12/0.31 inference(rewrite,[status(thm)],[])).
% 0.12/0.31 tff(4,plain,
% 0.12/0.31 ((~(((((((leq(tptp_float_0_001, pv76) & leq(n1, loopcounter)) & ![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, n0) => ![D: $i] : ((leq(n0, D) & leq(D, n4)) => (a_select2(mu_init, D) = init)))) & (gt(loopcounter, n0) => ![E: $i] : ((leq(n0, E) & leq(E, n4)) => (a_select2(rho_init, E) = init)))) & (gt(loopcounter, n0) => ![F: $i] : ((leq(n0, F) & leq(F, n4)) => (a_select2(sigma_init, F) = init)))) => ![G: $i] : ((leq(n0, G) & leq(G, n4)) => (a_select2(rho_init, G) = init)))) <=> (~((~(leq(tptp_float_0_001, pv76) & leq(n1, loopcounter) & ![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, n0)) | ![D: $i] : ((~(leq(n0, D) & leq(D, n4))) | (a_select2(mu_init, D) = init))) & ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))) & ((~gt(loopcounter, n0)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigma_init, F) = init))))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init))))),
% 0.12/0.31 inference(rewrite,[status(thm)],[])).
% 0.12/0.31 tff(5,axiom,(~(((((((leq(tptp_float_0_001, pv76) & leq(n1, loopcounter)) & ![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, n0) => ![D: $i] : ((leq(n0, D) & leq(D, n4)) => (a_select2(mu_init, D) = init)))) & (gt(loopcounter, n0) => ![E: $i] : ((leq(n0, E) & leq(E, n4)) => (a_select2(rho_init, E) = init)))) & (gt(loopcounter, n0) => ![F: $i] : ((leq(n0, F) & leq(F, n4)) => (a_select2(sigma_init, F) = init)))) => ![G: $i] : ((leq(n0, G) & leq(G, n4)) => (a_select2(rho_init, G) = init)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cl5_nebula_init_0086')).
% 0.12/0.31 tff(6,plain,
% 0.12/0.31 (~((~(leq(tptp_float_0_001, pv76) & leq(n1, loopcounter) & ![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, n0)) | ![D: $i] : ((~(leq(n0, D) & leq(D, n4))) | (a_select2(mu_init, D) = init))) & ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))) & ((~gt(loopcounter, n0)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigma_init, F) = init))))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init)))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.31 tff(7,plain,
% 0.12/0.31 (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init))),
% 0.12/0.31 inference(or_elim,[status(thm)],[6])).
% 0.12/0.31 tff(8,plain,
% 0.12/0.31 (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.31 tff(9,plain,
% 0.12/0.31 (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.12/0.31 tff(10,plain,
% 0.12/0.31 (~![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(rho_init, G) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.12/0.31 tff(11,plain,
% 0.12/0.31 (~![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, G) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.12/0.31 tff(12,plain,
% 0.12/0.31 (~![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, G) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.12/0.31 tff(13,plain,
% 0.12/0.31 (~![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, G) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.12/0.31 tff(14,plain,
% 0.12/0.31 (~![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, G) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[13, 1])).
% 0.12/0.31 tff(15,plain,(
% 0.12/0.31 ~((~(leq(succ(tptp_minus_1), G!13) & leq(G!13, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, G!13) = init))),
% 0.12/0.31 inference(skolemize,[status(sab)],[14])).
% 0.12/0.31 tff(16,plain,
% 0.12/0.31 (~(a_select2(rho_init, G!13) = init)),
% 0.12/0.31 inference(or_elim,[status(thm)],[15])).
% 0.12/0.31 tff(17,plain,
% 0.12/0.31 (leq(succ(tptp_minus_1), G!13) & leq(G!13, succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.12/0.31 inference(or_elim,[status(thm)],[15])).
% 0.12/0.31 tff(18,plain,
% 0.12/0.31 (leq(G!13, succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.12/0.31 inference(and_elim,[status(thm)],[17])).
% 0.12/0.31 tff(19,plain,
% 0.12/0.31 (leq(succ(tptp_minus_1), G!13)),
% 0.12/0.31 inference(and_elim,[status(thm)],[17])).
% 0.12/0.31 tff(20,plain,
% 0.12/0.31 (leq(n1, loopcounter) <=> leq(succ(succ(tptp_minus_1)), loopcounter)),
% 0.12/0.31 inference(rewrite,[status(thm)],[])).
% 0.12/0.31 tff(21,plain,
% 0.12/0.31 (leq(n1, loopcounter) <=> leq(n1, loopcounter)),
% 0.12/0.31 inference(rewrite,[status(thm)],[])).
% 0.12/0.31 tff(22,plain,
% 0.12/0.31 (leq(tptp_float_0_001, pv76) & leq(n1, loopcounter) & ![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, n0)) | ![D: $i] : ((~(leq(n0, D) & leq(D, n4))) | (a_select2(mu_init, D) = init))) & ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))) & ((~gt(loopcounter, n0)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(sigma_init, F) = init)))),
% 0.12/0.31 inference(or_elim,[status(thm)],[6])).
% 0.12/0.31 tff(23,plain,
% 0.12/0.31 (leq(n1, loopcounter)),
% 0.12/0.31 inference(and_elim,[status(thm)],[22])).
% 0.12/0.31 tff(24,plain,
% 0.12/0.31 (leq(n1, loopcounter)),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.12/0.31 tff(25,plain,
% 0.12/0.31 (leq(succ(succ(tptp_minus_1)), loopcounter)),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.31 tff(26,plain,
% 0.12/0.31 (^[X: $i, Y: $i] : refl(((~leq(succ(X), Y)) | gt(Y, X)) <=> ((~leq(succ(X), Y)) | gt(Y, X)))),
% 0.12/0.31 inference(bind,[status(th)],[])).
% 0.12/0.31 tff(27,plain,
% 0.12/0.31 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.12/0.31 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.31 tff(28,plain,
% 0.12/0.31 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.12/0.31 inference(rewrite,[status(thm)],[])).
% 0.12/0.31 tff(29,plain,
% 0.12/0.31 (^[X: $i, Y: $i] : rewrite((leq(succ(X), Y) => gt(Y, X)) <=> ((~leq(succ(X), Y)) | gt(Y, X)))),
% 0.12/0.31 inference(bind,[status(th)],[])).
% 0.12/0.31 tff(30,plain,
% 0.12/0.31 (![X: $i, Y: $i] : (leq(succ(X), Y) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.12/0.31 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.31 tff(31,axiom,(![X: $i, Y: $i] : (leq(succ(X), Y) => gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_succ_gt')).
% 0.12/0.31 tff(32,plain,
% 0.12/0.31 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.31 tff(33,plain,
% 0.12/0.31 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.12/0.31 tff(34,plain,(
% 0.12/0.31 ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.12/0.31 inference(skolemize,[status(sab)],[33])).
% 0.12/0.31 tff(35,plain,
% 0.12/0.31 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.12/0.31 tff(36,plain,
% 0.12/0.31 (((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | ((~leq(succ(succ(tptp_minus_1)), loopcounter)) | gt(loopcounter, succ(tptp_minus_1)))) <=> ((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | (~leq(succ(succ(tptp_minus_1)), loopcounter)) | gt(loopcounter, succ(tptp_minus_1)))),
% 0.12/0.31 inference(rewrite,[status(thm)],[])).
% 0.12/0.31 tff(37,plain,
% 0.12/0.31 ((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | ((~leq(succ(succ(tptp_minus_1)), loopcounter)) | gt(loopcounter, succ(tptp_minus_1)))),
% 0.12/0.31 inference(quant_inst,[status(thm)],[])).
% 0.12/0.31 tff(38,plain,
% 0.12/0.31 ((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | (~leq(succ(succ(tptp_minus_1)), loopcounter)) | gt(loopcounter, succ(tptp_minus_1))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.31 tff(39,plain,
% 0.12/0.31 (gt(loopcounter, succ(tptp_minus_1))),
% 0.12/0.31 inference(unit_resolution,[status(thm)],[38, 35, 25])).
% 0.12/0.31 tff(40,plain,
% 0.12/0.31 (((~gt(loopcounter, succ(tptp_minus_1))) | ![E: $i] : ((a_select2(rho_init, E) = init) | (~leq(succ(tptp_minus_1), E)) | (~leq(E, succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~gt(loopcounter, succ(tptp_minus_1))) | ![E: $i] : ((a_select2(rho_init, E) = init) | (~leq(succ(tptp_minus_1), E)) | (~leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.12/0.31 inference(rewrite,[status(thm)],[])).
% 0.12/0.31 tff(41,plain,
% 0.12/0.31 (((~gt(loopcounter, succ(tptp_minus_1))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, E) = init))) <=> ((~gt(loopcounter, succ(tptp_minus_1))) | ![E: $i] : ((a_select2(rho_init, E) = init) | (~leq(succ(tptp_minus_1), E)) | (~leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.12/0.31 inference(rewrite,[status(thm)],[])).
% 0.12/0.31 tff(42,plain,
% 0.12/0.31 (((~gt(loopcounter, succ(tptp_minus_1))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, E) = init))) <=> ((~gt(loopcounter, succ(tptp_minus_1))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, E) = init)))),
% 0.12/0.31 inference(rewrite,[status(thm)],[])).
% 0.12/0.31 tff(43,plain,
% 0.12/0.31 (((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))) <=> ((~gt(loopcounter, succ(tptp_minus_1))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, E) = init)))),
% 0.12/0.31 inference(rewrite,[status(thm)],[])).
% 0.12/0.31 tff(44,plain,
% 0.12/0.31 (((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))) <=> ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init)))),
% 0.12/0.31 inference(rewrite,[status(thm)],[])).
% 0.12/0.31 tff(45,plain,
% 0.12/0.31 ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))),
% 0.12/0.31 inference(and_elim,[status(thm)],[22])).
% 0.12/0.31 tff(46,plain,
% 0.12/0.31 ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.31 tff(47,plain,
% 0.12/0.31 ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[46, 44])).
% 0.12/0.31 tff(48,plain,
% 0.12/0.31 ((~gt(loopcounter, n0)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(rho_init, E) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[47, 44])).
% 0.12/0.31 tff(49,plain,
% 0.12/0.31 ((~gt(loopcounter, succ(tptp_minus_1))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, E) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[48, 43])).
% 0.12/0.31 tff(50,plain,
% 0.12/0.31 ((~gt(loopcounter, succ(tptp_minus_1))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, E) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.12/0.31 tff(51,plain,
% 0.12/0.31 ((~gt(loopcounter, succ(tptp_minus_1))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, E) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[50, 42])).
% 0.12/0.31 tff(52,plain,
% 0.12/0.31 ((~gt(loopcounter, succ(tptp_minus_1))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(rho_init, E) = init))),
% 0.12/0.31 inference(modus_ponens,[status(thm)],[51, 42])).
% 0.12/0.31 Proof display could not be completed: monotonicity rule is not handled
%------------------------------------------------------------------------------