TSTP Solution File: SWV174+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV174+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 15:10:14 EDT 2022
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV174+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 02:01:27 EDT 2022
% 0.13/0.34 % 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.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(init_type, type, (
% 0.20/0.44 init: $i)).
% 0.20/0.44 tff(a_select3_type, type, (
% 0.20/0.44 a_select3: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(tptp_fun_D_14_type, type, (
% 0.20/0.44 tptp_fun_D_14: $i)).
% 0.20/0.44 tff(q_init_type, type, (
% 0.20/0.44 q_init: $i)).
% 0.20/0.44 tff(leq_type, type, (
% 0.20/0.44 leq: ( $i * $i ) > $o)).
% 0.20/0.44 tff(succ_type, type, (
% 0.20/0.44 succ: $i > $i)).
% 0.20/0.44 tff(tptp_minus_1_type, type, (
% 0.20/0.44 tptp_minus_1: $i)).
% 0.20/0.44 tff(pred_type, type, (
% 0.20/0.44 pred: $i > $i)).
% 0.20/0.44 tff(pv10_type, type, (
% 0.20/0.44 pv10: $i)).
% 0.20/0.44 tff(gt_type, type, (
% 0.20/0.44 gt: ( $i * $i ) > $o)).
% 0.20/0.44 tff(tptp_fun_E_13_type, type, (
% 0.20/0.44 tptp_fun_E_13: $i)).
% 0.20/0.44 tff(n135299_type, type, (
% 0.20/0.44 n135299: $i)).
% 0.20/0.44 tff(n4_type, type, (
% 0.20/0.44 n4: $i)).
% 0.20/0.44 tff(n0_type, type, (
% 0.20/0.44 n0: $i)).
% 0.20/0.44 tff(center_init_type, type, (
% 0.20/0.44 center_init: $i)).
% 0.20/0.44 tff(1,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(2,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 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')).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.44 tff(6,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.44 inference(skolemize,[status(sab)],[5])).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(D!14, pred(pv10)) <=> gt(pv10, D!14))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 (leq(D!14, pred(pv10)) <=> gt(pv10, D!14)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 ((~((a_select3(q_init, D!14, E!13) = init) | (~gt(pv10, D!14)) | (~(leq(succ(tptp_minus_1), D!14) & leq(succ(tptp_minus_1), E!13) & leq(D!14, n135299) & leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> (~((a_select3(q_init, D!14, E!13) = init) | (~gt(pv10, D!14)) | (~(leq(succ(tptp_minus_1), D!14) & leq(succ(tptp_minus_1), E!13) & leq(D!14, n135299) & leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(11,plain,
% 0.20/0.44 ((~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(succ(tptp_minus_1), D) & leq(succ(tptp_minus_1), E) & leq(D, n135299) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> (~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(succ(tptp_minus_1), D) & leq(succ(tptp_minus_1), E) & leq(D, n135299) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 ((~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(n0, D) & leq(n0, E) & leq(D, n135299) & leq(E, n4))))) <=> (~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(succ(tptp_minus_1), D) & leq(succ(tptp_minus_1), E) & leq(D, n135299) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 ((~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(n0, D) & leq(n0, E) & leq(D, n135299) & leq(E, n4))))) <=> (~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(n0, D) & leq(n0, E) & leq(D, n135299) & leq(E, n4)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 ((~((((leq(n0, pv10) & leq(pv10, n135299)) & ![A: $i] : ((leq(n0, A) & leq(A, pred(pv10))) => ![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))) => ![D: $i, E: $i] : ((((leq(n0, D) & leq(n0, E)) & leq(D, n135299)) & leq(E, n4)) => (gt(pv10, D) => (a_select3(q_init, D, E) = init))))) <=> (~((~(leq(n0, pv10) & leq(pv10, n135299) & ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | ![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)))) | ![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(n0, D) & leq(n0, E) & leq(D, n135299) & leq(E, n4))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(15,axiom,(~((((leq(n0, pv10) & leq(pv10, n135299)) & ![A: $i] : ((leq(n0, A) & leq(A, pred(pv10))) => ![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))) => ![D: $i, E: $i] : ((((leq(n0, D) & leq(n0, E)) & leq(D, n135299)) & leq(E, n4)) => (gt(pv10, D) => (a_select3(q_init, D, E) = init))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cl5_nebula_init_0046')).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 (~((~(leq(n0, pv10) & leq(pv10, n135299) & ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | ![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)))) | ![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(n0, D) & leq(n0, E) & leq(D, n135299) & leq(E, n4)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 (~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(n0, D) & leq(n0, E) & leq(D, n135299) & leq(E, n4))))),
% 0.20/0.45 inference(or_elim,[status(thm)],[16])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 (~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(n0, D) & leq(n0, E) & leq(D, n135299) & leq(E, n4))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 (~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(n0, D) & leq(n0, E) & leq(D, n135299) & leq(E, n4))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 (~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(n0, D) & leq(n0, E) & leq(D, n135299) & leq(E, n4))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 (~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(succ(tptp_minus_1), D) & leq(succ(tptp_minus_1), E) & leq(D, n135299) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 (~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(succ(tptp_minus_1), D) & leq(succ(tptp_minus_1), E) & leq(D, n135299) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.20/0.45 tff(23,plain,
% 0.20/0.45 (~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(succ(tptp_minus_1), D) & leq(succ(tptp_minus_1), E) & leq(D, n135299) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[22, 11])).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (~![D: $i, E: $i] : ((a_select3(q_init, D, E) = init) | (~gt(pv10, D)) | (~(leq(succ(tptp_minus_1), D) & leq(succ(tptp_minus_1), E) & leq(D, n135299) & leq(E, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[23, 11])).
% 0.20/0.45 tff(25,plain,(
% 0.20/0.45 ~((a_select3(q_init, D!14, E!13) = init) | (~gt(pv10, D!14)) | (~(leq(succ(tptp_minus_1), D!14) & leq(succ(tptp_minus_1), E!13) & leq(D!14, n135299) & leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[24])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (~((a_select3(q_init, D!14, E!13) = init) | (~gt(pv10, D!14)) | (~(leq(succ(tptp_minus_1), D!14) & leq(succ(tptp_minus_1), E!13) & leq(D!14, n135299) & leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[25, 10])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (gt(pv10, D!14)),
% 0.20/0.45 inference(or_elim,[status(thm)],[26])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 ((~(leq(D!14, pred(pv10)) <=> gt(pv10, D!14))) | leq(D!14, pred(pv10)) | (~gt(pv10, D!14))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 ((~(leq(D!14, pred(pv10)) <=> gt(pv10, D!14))) | leq(D!14, pred(pv10))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (leq(D!14, pred(pv10))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[29, 9])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (leq(succ(tptp_minus_1), D!14) & leq(succ(tptp_minus_1), E!13) & leq(D!14, n135299) & leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.45 inference(or_elim,[status(thm)],[26])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 (leq(succ(tptp_minus_1), D!14)),
% 0.20/0.45 inference(and_elim,[status(thm)],[31])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 (^[A: $i] : refl(((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 (![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (^[A: $i] : rewrite(((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 (![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 (![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[36, 34])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), A) & leq(A, pred(pv10))) <=> (~((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))))), ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) <=> (~(~((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))))))), rewrite((~(~((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))))), ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) <=> (~((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))), ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> (~(~((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))), ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))), (((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, A, B) = init)) <=> (((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, A, B) = init)))), rewrite((((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, A, B) = init)) <=> ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))), (((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, A, B) = init)) <=> ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))))), (![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, A, B) = init)) <=> ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))), (((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, A, B) = init))) <=> (((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))))), rewrite((((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10)))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))), (((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, A, B) = init))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, A, B) = init))) <=> ![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (^[A: $i] : rewrite(((~(leq(n0, A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init))) <=> ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, A, B) = init))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init))) <=> ![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, A, B) = init)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init))) <=> ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 (leq(n0, pv10) & leq(pv10, n135299) & ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | ![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))),
% 0.20/0.46 inference(or_elim,[status(thm)],[16])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init)))),
% 0.20/0.46 inference(and_elim,[status(thm)],[43])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[44, 42])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 (![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, A, B) = init)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.46 tff(47,plain,(
% 0.20/0.46 ![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(q_init, A, B) = init)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[46])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 (![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[47, 39])).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 (![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[48, 37])).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 (((~![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) | ((~leq(D!14, pred(pv10))) | (~leq(succ(tptp_minus_1), D!14)) | ![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init)))) <=> ((~![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) | (~leq(D!14, pred(pv10))) | (~leq(succ(tptp_minus_1), D!14)) | ![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 (((~leq(succ(tptp_minus_1), D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init))) <=> ((~leq(D!14, pred(pv10))) | (~leq(succ(tptp_minus_1), D!14)) | ![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 (^[B: $i] : rewrite(((a_select3(q_init, D!14, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 (![B: $i] : ((a_select3(q_init, D!14, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> ![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 (((~leq(succ(tptp_minus_1), D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((a_select3(q_init, D!14, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~leq(succ(tptp_minus_1), D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 (((~leq(succ(tptp_minus_1), D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((a_select3(q_init, D!14, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~leq(D!14, pred(pv10))) | (~leq(succ(tptp_minus_1), D!14)) | ![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[54, 51])).
% 0.20/0.46 tff(56,plain,
% 0.20/0.46 (((~![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) | ((~leq(succ(tptp_minus_1), D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((a_select3(q_init, D!14, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> ((~![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) | ((~leq(D!14, pred(pv10))) | (~leq(succ(tptp_minus_1), D!14)) | ![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[55])).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 (((~![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) | ((~leq(succ(tptp_minus_1), D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((a_select3(q_init, D!14, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> ((~![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) | (~leq(D!14, pred(pv10))) | (~leq(succ(tptp_minus_1), D!14)) | ![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[56, 50])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 ((~![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) | ((~leq(succ(tptp_minus_1), D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((a_select3(q_init, D!14, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 ((~![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1)))))))))) | (~leq(D!14, pred(pv10))) | (~leq(succ(tptp_minus_1), D!14)) | ![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 ((~leq(D!14, pred(pv10))) | ![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[59, 49, 32])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 (![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[60, 30])).
% 0.20/0.46 tff(62,plain,
% 0.20/0.46 (leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.46 inference(and_elim,[status(thm)],[31])).
% 0.20/0.46 tff(63,plain,
% 0.20/0.46 (leq(succ(tptp_minus_1), E!13)),
% 0.20/0.46 inference(and_elim,[status(thm)],[31])).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 (~(a_select3(q_init, D!14, E!13) = init)),
% 0.20/0.46 inference(or_elim,[status(thm)],[26])).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 (((~![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init))) | ((~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, E!13) = init))) <=> ((~![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init))) | (~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, E!13) = init))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(66,plain,
% 0.20/0.46 ((~![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init))) | ((~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, E!13) = init))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(67,plain,
% 0.20/0.46 ((~![B: $i] : ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, B) = init))) | (~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(q_init, D!14, E!13) = init)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.46 tff(68,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[67, 64, 63, 62, 61])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------