%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV188+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:31:40 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
% 0.11/0.12 % Problem : SWV188+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:35:05 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(gt_type, type, (
% 0.20/0.43 gt: ( $i * $i ) > $o)).
% 0.20/0.43 tff(n4_type, type, (
% 0.20/0.43 n4: $i)).
% 0.20/0.43 tff(n5_type, type, (
% 0.20/0.43 n5: $i)).
% 0.20/0.43 tff(succ_type, type, (
% 0.20/0.43 succ: $i > $i)).
% 0.20/0.43 tff(n3_type, type, (
% 0.20/0.43 n3: $i)).
% 0.20/0.43 tff(n0_type, type, (
% 0.20/0.43 n0: $i)).
% 0.20/0.43 tff(tptp_minus_1_type, type, (
% 0.20/0.43 tptp_minus_1: $i)).
% 0.20/0.43 tff(plus_type, type, (
% 0.20/0.43 plus: ( $i * $i ) > $i)).
% 0.20/0.43 tff(leq_type, type, (
% 0.20/0.43 leq: ( $i * $i ) > $o)).
% 0.20/0.43 tff(tptp_fun_H_13_type, type, (
% 0.20/0.43 tptp_fun_H_13: $i)).
% 0.20/0.43 tff(init_type, type, (
% 0.20/0.43 init: $i)).
% 0.20/0.43 tff(a_select2_type, type, (
% 0.20/0.43 a_select2: ( $i * $i ) > $i)).
% 0.20/0.43 tff(mu_init_type, type, (
% 0.20/0.43 mu_init: $i)).
% 0.20/0.43 tff(sigmaold_init_type, type, (
% 0.20/0.43 sigmaold_init: $i)).
% 0.20/0.43 tff(n1_type, type, (
% 0.20/0.43 n1: $i)).
% 0.20/0.43 tff(loopcounter_type, type, (
% 0.20/0.43 loopcounter: $i)).
% 0.20/0.43 tff(rhoold_init_type, type, (
% 0.20/0.43 rhoold_init: $i)).
% 0.20/0.43 tff(muold_init_type, type, (
% 0.20/0.43 muold_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(center_init_type, type, (
% 0.20/0.43 center_init: $i)).
% 0.20/0.43 tff(rho_init_type, type, (
% 0.20/0.43 rho_init: $i)).
% 0.20/0.43 tff(q_init_type, type, (
% 0.20/0.43 q_init: $i)).
% 0.20/0.43 tff(n135299_type, type, (
% 0.20/0.43 n135299: $i)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 ((succ(succ(succ(n0))) = n3) <=> (succ(succ(succ(n0))) = n3)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(2,axiom,(succ(succ(succ(n0))) = n3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','successor_3')).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (succ(succ(succ(n0))) = n3),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (n3 = succ(succ(succ(n0)))),
% 0.20/0.43 inference(symmetry,[status(thm)],[3])).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (succ(n3) = succ(succ(succ(succ(n0))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[4])).
% 0.20/0.43 tff(6,plain,
% 0.20/0.43 (succ(succ(succ(succ(n0)))) = succ(n3)),
% 0.20/0.43 inference(symmetry,[status(thm)],[5])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 ((succ(succ(succ(succ(n0)))) = n4) <=> (succ(succ(succ(succ(n0)))) = n4)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(8,axiom,(succ(succ(succ(succ(n0)))) = n4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','successor_4')).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (succ(succ(succ(succ(n0)))) = n4),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (n4 = succ(succ(succ(succ(n0))))),
% 0.20/0.43 inference(symmetry,[status(thm)],[9])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 (n4 = succ(n3)),
% 0.20/0.43 inference(transitivity,[status(thm)],[10, 6])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 (gt(n4, n4) <=> gt(succ(n3), n4)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[11])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 (gt(succ(n3), n4) <=> gt(n4, n4)),
% 0.20/0.43 inference(symmetry,[status(thm)],[12])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 ((succ(tptp_minus_1) = n0) <=> (succ(tptp_minus_1) = n0)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(15,axiom,(succ(tptp_minus_1) = n0), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','succ_tptp_minus_1')).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (succ(tptp_minus_1) = n0),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (n0 = succ(tptp_minus_1)),
% 0.20/0.43 inference(symmetry,[status(thm)],[16])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (succ(n0) = succ(succ(tptp_minus_1))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[17])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (succ(succ(n0)) = succ(succ(succ(tptp_minus_1)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (succ(succ(succ(n0))) = succ(succ(succ(succ(tptp_minus_1))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (succ(succ(succ(succ(tptp_minus_1)))) = succ(succ(succ(n0)))),
% 0.20/0.43 inference(symmetry,[status(thm)],[20])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (succ(succ(succ(succ(succ(tptp_minus_1))))) = succ(succ(succ(succ(n0))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 (^[X: $i] : refl((plus(n5, X) = succ(succ(succ(succ(succ(X)))))) <=> (plus(n5, X) = succ(succ(succ(succ(succ(X)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X)))))) <=> ![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X)))))) <=> ![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(26,axiom,(![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','succ_plus_5_l')).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.44 tff(28,plain,(
% 0.20/0.44 ![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[27])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 ((~![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))) | (plus(n5, tptp_minus_1) = succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (plus(n5, tptp_minus_1) = succ(succ(succ(succ(succ(tptp_minus_1)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 ((~![H: $i] : ((~(leq(n0, H) & leq(H, tptp_minus_1))) | (a_select2(mu_init, H) = init))) <=> (~![H: $i] : ((~(leq(n0, H) & leq(H, tptp_minus_1))) | (a_select2(mu_init, H) = init)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 ((~((((((![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, n4)) => (a_select3(center_init, D, n0) = init))) & (gt(loopcounter, n1) => ![E: $i] : ((leq(n0, E) & leq(E, n4)) => (a_select2(muold_init, E) = init)))) & (gt(loopcounter, n1) => ![F: $i] : ((leq(n0, F) & leq(F, n4)) => (a_select2(rhoold_init, F) = init)))) & (gt(loopcounter, n1) => ![G: $i] : ((leq(n0, G) & leq(G, n4)) => (a_select2(sigmaold_init, G) = init)))) => ![H: $i] : ((leq(n0, H) & leq(H, tptp_minus_1)) => (a_select2(mu_init, H) = init)))) <=> (~((~(![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, n4))) | (a_select3(center_init, D, n0) = init)) & ((~gt(loopcounter, n1)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(muold_init, E) = init))) & ((~gt(loopcounter, n1)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(rhoold_init, F) = init))) & ((~gt(loopcounter, n1)) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(sigmaold_init, G) = init))))) | ![H: $i] : ((~(leq(n0, H) & leq(H, tptp_minus_1))) | (a_select2(mu_init, H) = init))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(34,axiom,(~((((((![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, n4)) => (a_select3(center_init, D, n0) = init))) & (gt(loopcounter, n1) => ![E: $i] : ((leq(n0, E) & leq(E, n4)) => (a_select2(muold_init, E) = init)))) & (gt(loopcounter, n1) => ![F: $i] : ((leq(n0, F) & leq(F, n4)) => (a_select2(rhoold_init, F) = init)))) & (gt(loopcounter, n1) => ![G: $i] : ((leq(n0, G) & leq(G, n4)) => (a_select2(sigmaold_init, G) = init)))) => ![H: $i] : ((leq(n0, H) & leq(H, tptp_minus_1)) => (a_select2(mu_init, H) = init)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cl5_nebula_init_0116')).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 (~((~(![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, n4))) | (a_select3(center_init, D, n0) = init)) & ((~gt(loopcounter, n1)) | ![E: $i] : ((~(leq(n0, E) & leq(E, n4))) | (a_select2(muold_init, E) = init))) & ((~gt(loopcounter, n1)) | ![F: $i] : ((~(leq(n0, F) & leq(F, n4))) | (a_select2(rhoold_init, F) = init))) & ((~gt(loopcounter, n1)) | ![G: $i] : ((~(leq(n0, G) & leq(G, n4))) | (a_select2(sigmaold_init, G) = init))))) | ![H: $i] : ((~(leq(n0, H) & leq(H, tptp_minus_1))) | (a_select2(mu_init, H) = init)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (~![H: $i] : ((~(leq(n0, H) & leq(H, tptp_minus_1))) | (a_select2(mu_init, H) = init))),
% 0.20/0.44 inference(or_elim,[status(thm)],[35])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (~![H: $i] : ((~(leq(n0, H) & leq(H, tptp_minus_1))) | (a_select2(mu_init, H) = init))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (~![H: $i] : ((~(leq(n0, H) & leq(H, tptp_minus_1))) | (a_select2(mu_init, H) = init))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[37, 32])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 (~![H: $i] : ((~(leq(n0, H) & leq(H, tptp_minus_1))) | (a_select2(mu_init, H) = init))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[38, 32])).
% 0.20/0.44 tff(40,plain,(
% 0.20/0.44 ~((~(leq(n0, H!13) & leq(H!13, tptp_minus_1))) | (a_select2(mu_init, H!13) = init))),
% 0.20/0.44 inference(skolemize,[status(sab)],[39])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (leq(n0, H!13) & leq(H!13, tptp_minus_1)),
% 0.20/0.44 inference(or_elim,[status(thm)],[40])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (leq(H!13, tptp_minus_1)),
% 0.20/0.44 inference(and_elim,[status(thm)],[41])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (leq(n0, H!13)),
% 0.20/0.44 inference(and_elim,[status(thm)],[41])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (^[X: $i, Y: $i, Z: $i] : rewrite(((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.44 tff(50,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.44 tff(53,plain,(
% 0.20/0.44 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.20/0.44 inference(skolemize,[status(sab)],[52])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(n0, H!13)) | leq(n0, tptp_minus_1) | (~leq(H!13, tptp_minus_1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(n0, H!13)) | leq(n0, tptp_minus_1) | (~leq(H!13, tptp_minus_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 ((leq(n0, tptp_minus_1) | (~leq(H!13, tptp_minus_1)) | (~leq(n0, H!13))) <=> ((~leq(n0, H!13)) | leq(n0, tptp_minus_1) | (~leq(H!13, tptp_minus_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n0, tptp_minus_1) | (~leq(H!13, tptp_minus_1)) | (~leq(n0, H!13)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(n0, H!13)) | leq(n0, tptp_minus_1) | (~leq(H!13, tptp_minus_1))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[57])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n0, tptp_minus_1) | (~leq(H!13, tptp_minus_1)) | (~leq(n0, H!13)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(n0, H!13)) | leq(n0, tptp_minus_1) | (~leq(H!13, tptp_minus_1)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[58, 56])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n0, tptp_minus_1) | (~leq(H!13, tptp_minus_1)) | (~leq(n0, H!13)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(n0, H!13)) | leq(n0, tptp_minus_1) | (~leq(H!13, tptp_minus_1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (leq(n0, tptp_minus_1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[61, 55, 43, 42])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 (gt(n0, tptp_minus_1) <=> gt(n0, tptp_minus_1)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(64,axiom,(gt(n0, tptp_minus_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_0_tptp_minus_1')).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (gt(n0, tptp_minus_1)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : refl(((~gt(Y, X)) | leq(X, Y)) <=> ((~gt(Y, X)) | leq(X, Y)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y)) <=> ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y)) <=> ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : rewrite((gt(Y, X) => leq(X, Y)) <=> ((~gt(Y, X)) | leq(X, Y)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (gt(Y, X) => leq(X, Y)) <=> ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.44 tff(71,axiom,(![X: $i, Y: $i] : (gt(Y, X) => leq(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt1')).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.20/0.44 tff(74,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.20/0.44 inference(skolemize,[status(sab)],[73])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | ((~gt(n0, tptp_minus_1)) | leq(tptp_minus_1, n0))) <=> ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | (~gt(n0, tptp_minus_1)) | leq(tptp_minus_1, n0))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | ((~gt(n0, tptp_minus_1)) | leq(tptp_minus_1, n0))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | (~gt(n0, tptp_minus_1)) | leq(tptp_minus_1, n0)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (leq(tptp_minus_1, n0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[78, 75, 65])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (^[X: $i] : refl(((X = n0) | (~leq(n0, X)) | (~leq(X, n0))) <=> ((X = n0) | (~leq(n0, X)) | (~leq(X, n0))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0))) <=> ![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, X) & leq(X, n0)) <=> (~((~leq(n0, X)) | (~leq(X, n0))))), ((~(leq(n0, X) & leq(X, n0))) <=> (~(~((~leq(n0, X)) | (~leq(X, n0))))))), rewrite((~(~((~leq(n0, X)) | (~leq(X, n0))))) <=> ((~leq(n0, X)) | (~leq(X, n0)))), ((~(leq(n0, X) & leq(X, n0))) <=> ((~leq(n0, X)) | (~leq(X, n0))))), (((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> (((~leq(n0, X)) | (~leq(X, n0))) | (X = n0)))), rewrite((((~leq(n0, X)) | (~leq(X, n0))) | (X = n0)) <=> ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))), (((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (^[X: $i] : rewrite(((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ((~(leq(n0, X) & leq(X, n0))) | (X = n0)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 (![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.45 tff(87,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','finite_domain_0')).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.20/0.45 tff(90,plain,(
% 0.20/0.45 ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.20/0.45 inference(skolemize,[status(sab)],[89])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[91, 81])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 (((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((~leq(tptp_minus_1, n0)) | (~leq(n0, tptp_minus_1)) | (tptp_minus_1 = n0))) <=> ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | (~leq(tptp_minus_1, n0)) | (~leq(n0, tptp_minus_1)) | (tptp_minus_1 = n0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 (((tptp_minus_1 = n0) | (~leq(n0, tptp_minus_1)) | (~leq(tptp_minus_1, n0))) <=> ((~leq(tptp_minus_1, n0)) | (~leq(n0, tptp_minus_1)) | (tptp_minus_1 = n0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((tptp_minus_1 = n0) | (~leq(n0, tptp_minus_1)) | (~leq(tptp_minus_1, n0)))) <=> ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((~leq(tptp_minus_1, n0)) | (~leq(n0, tptp_minus_1)) | (tptp_minus_1 = n0)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[94])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 (((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((tptp_minus_1 = n0) | (~leq(n0, tptp_minus_1)) | (~leq(tptp_minus_1, n0)))) <=> ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | (~leq(tptp_minus_1, n0)) | (~leq(n0, tptp_minus_1)) | (tptp_minus_1 = n0))),
% 0.20/0.45 inference(transitivity,[status(thm)],[95, 93])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((tptp_minus_1 = n0) | (~leq(n0, tptp_minus_1)) | (~leq(tptp_minus_1, n0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | (~leq(tptp_minus_1, n0)) | (~leq(n0, tptp_minus_1)) | (tptp_minus_1 = n0)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 (tptp_minus_1 = n0),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[98, 92, 79, 62])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 (n0 = tptp_minus_1),
% 0.20/0.45 inference(symmetry,[status(thm)],[99])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 (plus(n5, n0) = plus(n5, tptp_minus_1)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[100])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 ((~![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))) | (plus(n5, n0) = succ(succ(succ(succ(succ(n0))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 (plus(n5, n0) = succ(succ(succ(succ(succ(n0)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[102, 29])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 (succ(succ(succ(succ(succ(n0))))) = plus(n5, n0)),
% 0.20/0.45 inference(symmetry,[status(thm)],[103])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 ((succ(succ(succ(succ(succ(n0))))) = n5) <=> (succ(succ(succ(succ(succ(n0))))) = n5)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(106,axiom,(succ(succ(succ(succ(succ(n0))))) = n5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','successor_5')).
% 0.20/0.45 tff(107,plain,
% 0.20/0.45 (succ(succ(succ(succ(succ(n0))))) = n5),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 (n5 = succ(succ(succ(succ(succ(n0)))))),
% 0.20/0.45 inference(symmetry,[status(thm)],[107])).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 (n5 = succ(n3)),
% 0.20/0.45 inference(transitivity,[status(thm)],[108, 104, 101, 31, 22, 6])).
% 0.20/0.45 tff(110,plain,
% 0.20/0.45 (gt(n5, n4) <=> gt(succ(n3), n4)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[109])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (gt(n5, n4) <=> gt(n4, n4)),
% 0.20/0.45 inference(transitivity,[status(thm)],[110, 13])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (gt(n5, n4) <=> gt(n5, n4)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(113,axiom,(gt(n5, n4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_5_4')).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (gt(n5, n4)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 (gt(n4, n4)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[114, 111])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (^[X: $i] : refl((~gt(X, X)) <=> (~gt(X, X)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[116])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(119,axiom,(![X: $i] : (~gt(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','irreflexivity_gt')).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 (![X: $i] : (~gt(X, X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.45 tff(121,plain,(
% 0.20/0.45 ![X: $i] : (~gt(X, X))),
% 0.20/0.45 inference(skolemize,[status(sab)],[120])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (![X: $i] : (~gt(X, X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 ((~![X: $i] : (~gt(X, X))) | (~gt(n4, n4))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[123, 122, 115])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------