%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV174+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:31:39 AM UTC 2025
% Result : Theorem 0.20s 0.43s
% 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 v9.0.0. Bugfixed v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:30:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(init_type, type, (
% 0.20/0.43 init: $i)).
% 0.20/0.43 tff(a_select3_type, type, (
% 0.20/0.43 a_select3: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_fun_D_14_type, type, (
% 0.20/0.43 tptp_fun_D_14: $i)).
% 0.20/0.43 tff(q_init_type, type, (
% 0.20/0.43 q_init: $i)).
% 0.20/0.43 tff(leq_type, type, (
% 0.20/0.43 leq: ( $i * $i ) > $o)).
% 0.20/0.43 tff(n4_type, type, (
% 0.20/0.43 n4: $i)).
% 0.20/0.43 tff(n0_type, type, (
% 0.20/0.43 n0: $i)).
% 0.20/0.43 tff(pred_type, type, (
% 0.20/0.43 pred: $i > $i)).
% 0.20/0.43 tff(pv10_type, type, (
% 0.20/0.43 pv10: $i)).
% 0.20/0.43 tff(gt_type, type, (
% 0.20/0.43 gt: ( $i * $i ) > $o)).
% 0.20/0.43 tff(tptp_fun_E_13_type, type, (
% 0.20/0.43 tptp_fun_E_13: $i)).
% 0.20/0.43 tff(n135299_type, type, (
% 0.20/0.43 n135299: $i)).
% 0.20/0.43 tff(center_init_type, type, (
% 0.20/0.43 center_init: $i)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 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')).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.43 tff(6,plain,(
% 0.20/0.43 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.43 inference(skolemize,[status(sab)],[5])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(D!14, pred(pv10)) <=> gt(pv10, D!14))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (leq(D!14, pred(pv10)) <=> gt(pv10, D!14)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 ((~((a_select3(q_init, D!14, E!13) = init) | (~gt(pv10, D!14)) | (~(leq(n0, D!14) & leq(n0, E!13) & leq(D!14, n135299) & leq(E!13, n4))))) <=> (~((a_select3(q_init, D!14, E!13) = init) | (~gt(pv10, D!14)) | (~(leq(n0, D!14) & leq(n0, E!13) & leq(D!14, n135299) & leq(E!13, n4)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 ((~![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)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 ((~((((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))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(13,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')).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (~((~(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)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 (~![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))))),
% 0.20/0.43 inference(or_elim,[status(thm)],[14])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (~![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (~![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (~![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.20/0.43 tff(19,plain,(
% 0.20/0.43 ~((a_select3(q_init, D!14, E!13) = init) | (~gt(pv10, D!14)) | (~(leq(n0, D!14) & leq(n0, E!13) & leq(D!14, n135299) & leq(E!13, n4))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[18])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (~((a_select3(q_init, D!14, E!13) = init) | (~gt(pv10, D!14)) | (~(leq(n0, D!14) & leq(n0, E!13) & leq(D!14, n135299) & leq(E!13, n4))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[19, 10])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (gt(pv10, D!14)),
% 0.20/0.43 inference(or_elim,[status(thm)],[20])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 ((~(leq(D!14, pred(pv10)) <=> gt(pv10, D!14))) | leq(D!14, pred(pv10)) | (~gt(pv10, D!14))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 ((~(leq(D!14, pred(pv10)) <=> gt(pv10, D!14))) | leq(D!14, pred(pv10))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (leq(D!14, pred(pv10))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[23, 9])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (leq(n0, D!14) & leq(n0, E!13) & leq(D!14, n135299) & leq(E!13, n4)),
% 0.20/0.43 inference(or_elim,[status(thm)],[20])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 (leq(n0, D!14)),
% 0.20/0.43 inference(and_elim,[status(thm)],[25])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (^[A: $i] : refl(((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4)))) <=> ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4)))) <=> ![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 (^[A: $i] : rewrite(((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4)))) <=> ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 (![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4)))) <=> ![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4)))) <=> ![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[30, 28])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, A) & leq(A, pred(pv10))) <=> (~((~leq(n0, A)) | (~leq(A, pred(pv10)))))), ((~(leq(n0, A) & leq(A, pred(pv10)))) <=> (~(~((~leq(n0, A)) | (~leq(A, pred(pv10)))))))), rewrite((~(~((~leq(n0, A)) | (~leq(A, pred(pv10)))))) <=> ((~leq(n0, A)) | (~leq(A, pred(pv10))))), ((~(leq(n0, A) & leq(A, pred(pv10)))) <=> ((~leq(n0, A)) | (~leq(A, pred(pv10)))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, B) & leq(B, n4)) <=> (~((~leq(n0, B)) | (~leq(B, n4))))), ((~(leq(n0, B) & leq(B, n4))) <=> (~(~((~leq(n0, B)) | (~leq(B, n4))))))), rewrite((~(~((~leq(n0, B)) | (~leq(B, n4))))) <=> ((~leq(n0, B)) | (~leq(B, n4)))), ((~(leq(n0, B) & leq(B, n4))) <=> ((~leq(n0, B)) | (~leq(B, n4))))), (((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init)) <=> (((~leq(n0, B)) | (~leq(B, n4))) | (a_select3(q_init, A, B) = init)))), rewrite((((~leq(n0, B)) | (~leq(B, n4))) | (a_select3(q_init, A, B) = init)) <=> ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4)))), (((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init)) <=> ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4)))))), (![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init)) <=> ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))), (((~(leq(n0, A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init))) <=> (((~leq(n0, A)) | (~leq(A, pred(pv10)))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4)))))), rewrite((((~leq(n0, A)) | (~leq(A, pred(pv10)))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4)))) <=> ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))), (((~(leq(n0, A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init))) <=> ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 (![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] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(35,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))),
% 0.20/0.44 inference(or_elim,[status(thm)],[14])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init)))),
% 0.20/0.44 inference(and_elim,[status(thm)],[35])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.20/0.44 tff(38,plain,(
% 0.20/0.44 ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n4))) | (a_select3(q_init, A, B) = init)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[37])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 (![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[39, 31])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (((~![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))) | ((~leq(n0, D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init)))) <=> ((~![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))) | (~leq(n0, D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (((~leq(n0, D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((a_select3(q_init, D!14, B) = init) | (~leq(n0, B)) | (~leq(B, n4)))) <=> ((~leq(n0, D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (((~![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))) | ((~leq(n0, D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((a_select3(q_init, D!14, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))) <=> ((~![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))) | ((~leq(n0, D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (((~![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))) | ((~leq(n0, D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((a_select3(q_init, D!14, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))) <=> ((~![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))) | (~leq(n0, D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[43, 41])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 ((~![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))) | ((~leq(n0, D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((a_select3(q_init, D!14, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 ((~![A: $i] : ((~leq(n0, A)) | (~leq(A, pred(pv10))) | ![B: $i] : ((a_select3(q_init, A, B) = init) | (~leq(n0, B)) | (~leq(B, n4))))) | (~leq(n0, D!14)) | (~leq(D!14, pred(pv10))) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 ((~leq(D!14, pred(pv10))) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[46, 40, 26])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[47, 24])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (leq(E!13, n4)),
% 0.20/0.44 inference(and_elim,[status(thm)],[25])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (leq(n0, E!13)),
% 0.20/0.44 inference(and_elim,[status(thm)],[25])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (~(a_select3(q_init, D!14, E!13) = init)),
% 0.20/0.44 inference(or_elim,[status(thm)],[20])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init))) | ((a_select3(q_init, D!14, E!13) = init) | (~leq(n0, E!13)) | (~leq(E!13, n4)))) <=> ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init))) | (a_select3(q_init, D!14, E!13) = init) | (~leq(n0, E!13)) | (~leq(E!13, n4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (((~leq(n0, E!13)) | (~leq(E!13, n4)) | (a_select3(q_init, D!14, E!13) = init)) <=> ((a_select3(q_init, D!14, E!13) = init) | (~leq(n0, E!13)) | (~leq(E!13, n4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init))) | ((~leq(n0, E!13)) | (~leq(E!13, n4)) | (a_select3(q_init, D!14, E!13) = init))) <=> ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init))) | ((a_select3(q_init, D!14, E!13) = init) | (~leq(n0, E!13)) | (~leq(E!13, n4))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init))) | ((~leq(n0, E!13)) | (~leq(E!13, n4)) | (a_select3(q_init, D!14, E!13) = init))) <=> ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init))) | (a_select3(q_init, D!14, E!13) = init) | (~leq(n0, E!13)) | (~leq(E!13, n4)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[54, 52])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init))) | ((~leq(n0, E!13)) | (~leq(E!13, n4)) | (a_select3(q_init, D!14, E!13) = init))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n4)) | (a_select3(q_init, D!14, B) = init))) | (a_select3(q_init, D!14, E!13) = init) | (~leq(n0, E!13)) | (~leq(E!13, n4))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[57, 51, 50, 49, 48])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------