%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV198+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 05:31:41 AM UTC 2025
% Result : Theorem 9.67s 9.89s
% Output : Proof 9.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV198+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:35:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 9.67/9.89 % SZS status Theorem
% 9.67/9.89 % SZS output start Proof
% 9.67/9.89 tff(use_type, type, (
% 9.67/9.89 use: $i)).
% 9.67/9.89 tff(a_select3_type, type, (
% 9.67/9.89 a_select3: ( $i * $i * $i ) > $i)).
% 9.67/9.89 tff(tptp_fun_F_13_type, type, (
% 9.67/9.89 tptp_fun_F_13: $i)).
% 9.67/9.89 tff(tptp_fun_E_14_type, type, (
% 9.67/9.89 tptp_fun_E_14: $i)).
% 9.67/9.89 tff(u_defuse_type, type, (
% 9.67/9.89 u_defuse: $i)).
% 9.67/9.89 tff(n0_type, type, (
% 9.67/9.89 n0: $i)).
% 9.67/9.89 tff(z_defuse_type, type, (
% 9.67/9.89 z_defuse: $i)).
% 9.67/9.89 tff(leq_type, type, (
% 9.67/9.89 leq: ( $i * $i ) > $o)).
% 9.67/9.89 tff(pred_type, type, (
% 9.67/9.89 pred: $i > $i)).
% 9.67/9.89 tff(pv5_type, type, (
% 9.67/9.89 pv5: $i)).
% 9.67/9.89 tff(n2_type, type, (
% 9.67/9.89 n2: $i)).
% 9.67/9.89 tff(n998_type, type, (
% 9.67/9.89 n998: $i)).
% 9.67/9.89 tff(a_select2_type, type, (
% 9.67/9.89 a_select2: ( $i * $i ) > $i)).
% 9.67/9.89 tff(n5_type, type, (
% 9.67/9.89 n5: $i)).
% 9.67/9.89 tff(xinit_noise_defuse_type, type, (
% 9.67/9.89 xinit_noise_defuse: $i)).
% 9.67/9.89 tff(n4_type, type, (
% 9.67/9.89 n4: $i)).
% 9.67/9.89 tff(n3_type, type, (
% 9.67/9.89 n3: $i)).
% 9.67/9.89 tff(n1_type, type, (
% 9.67/9.89 n1: $i)).
% 9.67/9.89 tff(xinit_mean_defuse_type, type, (
% 9.67/9.89 xinit_mean_defuse: $i)).
% 9.67/9.89 tff(xinit_defuse_type, type, (
% 9.67/9.89 xinit_defuse: $i)).
% 9.67/9.89 tff(sigma_defuse_type, type, (
% 9.67/9.89 sigma_defuse: $i)).
% 9.67/9.89 tff(rho_defuse_type, type, (
% 9.67/9.89 rho_defuse: $i)).
% 9.67/9.89 tff(succ_type, type, (
% 9.67/9.89 succ: $i > $i)).
% 9.67/9.89 tff(gt_type, type, (
% 9.67/9.89 gt: ( $i * $i ) > $o)).
% 9.67/9.89 tff(1,plain,
% 9.67/9.89 ((a_select3(u_defuse, n0, n0) = use) <=> (a_select3(u_defuse, n0, n0) = use)),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(2,plain,
% 9.67/9.89 ((~(((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, n0)) & leq(pv5, n998)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pred(pv5))) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, pred(pv5))) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pv5)) => (a_select3(u_defuse, E, F) = use)))) <=> (~((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n0) & leq(pv5, n998) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)))) | ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))))),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(3,axiom,(~(((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, n0)) & leq(pv5, n998)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pred(pv5))) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, pred(pv5))) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pv5)) => (a_select3(u_defuse, E, F) = use)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_inuse_0009')).
% 9.67/9.89 tff(4,plain,
% 9.67/9.89 (~((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n0) & leq(pv5, n998) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)))) | ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use)))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[3, 2])).
% 9.67/9.89 tff(5,plain,
% 9.67/9.89 ((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n0) & leq(pv5, n998) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 9.67/9.89 inference(or_elim,[status(thm)],[4])).
% 9.67/9.89 tff(6,plain,
% 9.67/9.89 (a_select3(u_defuse, n0, n0) = use),
% 9.67/9.89 inference(and_elim,[status(thm)],[5])).
% 9.67/9.89 tff(7,plain,
% 9.67/9.89 (a_select3(u_defuse, n0, n0) = use),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[6, 1])).
% 9.67/9.89 tff(8,plain,
% 9.67/9.89 ((~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))) <=> (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use)))),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(9,plain,
% 9.67/9.89 (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))),
% 9.67/9.89 inference(or_elim,[status(thm)],[4])).
% 9.67/9.89 tff(10,plain,
% 9.67/9.89 (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[9, 8])).
% 9.67/9.89 tff(11,plain,
% 9.67/9.89 (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[10, 8])).
% 9.67/9.89 tff(12,plain,
% 9.67/9.89 (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[11, 8])).
% 9.67/9.89 tff(13,plain,(
% 9.67/9.89 ~((~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5))) | (a_select3(u_defuse, E!14, F!13) = use))),
% 9.67/9.89 inference(skolemize,[status(sab)],[12])).
% 9.67/9.89 tff(14,plain,
% 9.67/9.89 (leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5)),
% 9.67/9.89 inference(or_elim,[status(thm)],[13])).
% 9.67/9.89 tff(15,plain,
% 9.67/9.89 (leq(F!13, pv5)),
% 9.67/9.89 inference(and_elim,[status(thm)],[14])).
% 9.67/9.89 tff(16,plain,
% 9.67/9.89 (leq(pv5, n0) <=> leq(pv5, n0)),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(17,plain,
% 9.67/9.89 (leq(pv5, n0)),
% 9.67/9.89 inference(and_elim,[status(thm)],[5])).
% 9.67/9.89 tff(18,plain,
% 9.67/9.89 (leq(pv5, n0)),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[17, 16])).
% 9.67/9.89 tff(19,plain,
% 9.67/9.89 (![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)))),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(20,plain,
% 9.67/9.89 (^[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)))))),
% 9.67/9.89 inference(bind,[status(th)],[])).
% 9.67/9.89 tff(21,plain,
% 9.67/9.89 (![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)))),
% 9.67/9.89 inference(quant_intro,[status(thm)],[20])).
% 9.67/9.89 tff(22,plain,
% 9.67/9.89 (![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))),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(23,plain,
% 9.67/9.89 (^[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)))),
% 9.67/9.89 inference(bind,[status(th)],[])).
% 9.67/9.89 tff(24,plain,
% 9.67/9.89 (![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))),
% 9.67/9.89 inference(quant_intro,[status(thm)],[23])).
% 9.67/9.89 tff(25,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')).
% 9.67/9.89 tff(26,plain,
% 9.67/9.89 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[25, 24])).
% 9.67/9.89 tff(27,plain,
% 9.67/9.89 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[26, 22])).
% 9.67/9.89 tff(28,plain,(
% 9.67/9.89 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 9.67/9.89 inference(skolemize,[status(sab)],[27])).
% 9.67/9.89 tff(29,plain,
% 9.67/9.89 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[28, 21])).
% 9.67/9.89 tff(30,plain,
% 9.67/9.89 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[29, 19])).
% 9.67/9.89 tff(31,plain,
% 9.67/9.89 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(pv5, n0)) | leq(F!13, n0) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pv5, n0)) | leq(F!13, n0) | (~leq(F!13, pv5)))),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(32,plain,
% 9.67/9.89 ((leq(F!13, n0) | (~leq(pv5, n0)) | (~leq(F!13, pv5))) <=> ((~leq(pv5, n0)) | leq(F!13, n0) | (~leq(F!13, pv5)))),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(33,plain,
% 9.67/9.89 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(F!13, n0) | (~leq(pv5, n0)) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(pv5, n0)) | leq(F!13, n0) | (~leq(F!13, pv5))))),
% 9.67/9.89 inference(monotonicity,[status(thm)],[32])).
% 9.67/9.89 tff(34,plain,
% 9.67/9.89 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(F!13, n0) | (~leq(pv5, n0)) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pv5, n0)) | leq(F!13, n0) | (~leq(F!13, pv5)))),
% 9.67/9.89 inference(transitivity,[status(thm)],[33, 31])).
% 9.67/9.89 tff(35,plain,
% 9.67/9.89 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(F!13, n0) | (~leq(pv5, n0)) | (~leq(F!13, pv5)))),
% 9.67/9.89 inference(quant_inst,[status(thm)],[])).
% 9.67/9.89 tff(36,plain,
% 9.67/9.89 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pv5, n0)) | leq(F!13, n0) | (~leq(F!13, pv5))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[35, 34])).
% 9.67/9.89 tff(37,plain,
% 9.67/9.89 (leq(F!13, n0)),
% 9.67/9.89 inference(unit_resolution,[status(thm)],[36, 30, 18, 15])).
% 9.67/9.89 tff(38,plain,
% 9.67/9.89 (leq(n0, F!13)),
% 9.67/9.89 inference(and_elim,[status(thm)],[14])).
% 9.67/9.89 tff(39,plain,
% 9.67/9.89 (^[X: $i] : refl(((X = n0) | (~leq(n0, X)) | (~leq(X, n0))) <=> ((X = n0) | (~leq(n0, X)) | (~leq(X, n0))))),
% 9.67/9.89 inference(bind,[status(th)],[])).
% 9.67/9.89 tff(40,plain,
% 9.67/9.89 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0))) <=> ![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 9.67/9.89 inference(quant_intro,[status(thm)],[39])).
% 9.67/9.89 tff(41,plain,
% 9.67/9.89 (^[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)))))),
% 9.67/9.89 inference(bind,[status(th)],[])).
% 9.67/9.89 tff(42,plain,
% 9.67/9.89 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 9.67/9.89 inference(quant_intro,[status(thm)],[41])).
% 9.67/9.89 tff(43,plain,
% 9.67/9.89 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(44,plain,
% 9.67/9.89 (^[X: $i] : rewrite(((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ((~(leq(n0, X) & leq(X, n0))) | (X = n0)))),
% 9.67/9.89 inference(bind,[status(th)],[])).
% 9.67/9.89 tff(45,plain,
% 9.67/9.89 (![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 9.67/9.89 inference(quant_intro,[status(thm)],[44])).
% 9.67/9.89 tff(46,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','finite_domain_0')).
% 9.67/9.89 tff(47,plain,
% 9.67/9.89 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[46, 45])).
% 9.67/9.89 tff(48,plain,
% 9.67/9.89 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[47, 43])).
% 9.67/9.89 tff(49,plain,(
% 9.67/9.89 ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 9.67/9.89 inference(skolemize,[status(sab)],[48])).
% 9.67/9.89 tff(50,plain,
% 9.67/9.89 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[49, 42])).
% 9.67/9.89 tff(51,plain,
% 9.67/9.89 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[50, 40])).
% 9.67/9.89 tff(52,plain,
% 9.67/9.89 (((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((~leq(n0, F!13)) | (F!13 = n0) | (~leq(F!13, n0)))) <=> ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | (~leq(n0, F!13)) | (F!13 = n0) | (~leq(F!13, n0)))),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(53,plain,
% 9.67/9.89 (((F!13 = n0) | (~leq(n0, F!13)) | (~leq(F!13, n0))) <=> ((~leq(n0, F!13)) | (F!13 = n0) | (~leq(F!13, n0)))),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(54,plain,
% 9.67/9.89 (((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((F!13 = n0) | (~leq(n0, F!13)) | (~leq(F!13, n0)))) <=> ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((~leq(n0, F!13)) | (F!13 = n0) | (~leq(F!13, n0))))),
% 9.67/9.89 inference(monotonicity,[status(thm)],[53])).
% 9.67/9.89 tff(55,plain,
% 9.67/9.89 (((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((F!13 = n0) | (~leq(n0, F!13)) | (~leq(F!13, n0)))) <=> ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | (~leq(n0, F!13)) | (F!13 = n0) | (~leq(F!13, n0)))),
% 9.67/9.89 inference(transitivity,[status(thm)],[54, 52])).
% 9.67/9.89 tff(56,plain,
% 9.67/9.89 ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((F!13 = n0) | (~leq(n0, F!13)) | (~leq(F!13, n0)))),
% 9.67/9.89 inference(quant_inst,[status(thm)],[])).
% 9.67/9.89 tff(57,plain,
% 9.67/9.89 ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | (~leq(n0, F!13)) | (F!13 = n0) | (~leq(F!13, n0))),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[56, 55])).
% 9.67/9.89 tff(58,plain,
% 9.67/9.89 ((F!13 = n0) | (~leq(F!13, n0))),
% 9.67/9.89 inference(unit_resolution,[status(thm)],[57, 51, 38])).
% 9.67/9.89 tff(59,plain,
% 9.67/9.89 (F!13 = n0),
% 9.67/9.89 inference(unit_resolution,[status(thm)],[58, 37])).
% 9.67/9.89 tff(60,plain,
% 9.67/9.89 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(61,plain,
% 9.67/9.89 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(62,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 9.67/9.89 tff(63,plain,
% 9.67/9.89 (![X: $i] : (pred(succ(X)) = X)),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[62, 61])).
% 9.67/9.89 tff(64,plain,(
% 9.67/9.89 ![X: $i] : (pred(succ(X)) = X)),
% 9.67/9.89 inference(skolemize,[status(sab)],[63])).
% 9.67/9.89 tff(65,plain,
% 9.67/9.89 (![X: $i] : (pred(succ(X)) = X)),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[64, 60])).
% 9.67/9.89 tff(66,plain,
% 9.67/9.89 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(n0)) = n0)),
% 9.67/9.89 inference(quant_inst,[status(thm)],[])).
% 9.67/9.89 tff(67,plain,
% 9.67/9.89 (pred(succ(n0)) = n0),
% 9.67/9.89 inference(unit_resolution,[status(thm)],[66, 65])).
% 9.67/9.89 tff(68,plain,
% 9.67/9.89 ((succ(n0) = n1) <=> (succ(n0) = n1)),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(69,axiom,(succ(n0) = n1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','successor_1')).
% 9.67/9.89 tff(70,plain,
% 9.67/9.89 (succ(n0) = n1),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[69, 68])).
% 9.67/9.89 tff(71,plain,
% 9.67/9.89 (n1 = succ(n0)),
% 9.67/9.89 inference(symmetry,[status(thm)],[70])).
% 9.67/9.89 tff(72,plain,
% 9.67/9.89 (pred(n1) = pred(succ(n0))),
% 9.67/9.89 inference(monotonicity,[status(thm)],[71])).
% 9.67/9.89 tff(73,plain,
% 9.67/9.89 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(n1)) = n1)),
% 9.67/9.89 inference(quant_inst,[status(thm)],[])).
% 9.67/9.89 tff(74,plain,
% 9.67/9.89 (pred(succ(n1)) = n1),
% 9.67/9.89 inference(unit_resolution,[status(thm)],[73, 65])).
% 9.67/9.89 tff(75,plain,
% 9.67/9.89 (succ(n1) = succ(succ(n0))),
% 9.67/9.89 inference(monotonicity,[status(thm)],[71])).
% 9.67/9.89 tff(76,plain,
% 9.67/9.89 (succ(succ(n0)) = succ(n1)),
% 9.67/9.89 inference(symmetry,[status(thm)],[75])).
% 9.67/9.89 tff(77,plain,
% 9.67/9.89 ((succ(succ(n0)) = n2) <=> (succ(succ(n0)) = n2)),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(78,axiom,(succ(succ(n0)) = n2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','successor_2')).
% 9.67/9.89 tff(79,plain,
% 9.67/9.89 (succ(succ(n0)) = n2),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[78, 77])).
% 9.67/9.89 tff(80,plain,
% 9.67/9.89 (n2 = succ(succ(n0))),
% 9.67/9.89 inference(symmetry,[status(thm)],[79])).
% 9.67/9.89 tff(81,plain,
% 9.67/9.89 (n2 = succ(n1)),
% 9.67/9.89 inference(transitivity,[status(thm)],[80, 76])).
% 9.67/9.89 tff(82,plain,
% 9.67/9.89 (pred(n2) = pred(succ(n1))),
% 9.67/9.89 inference(monotonicity,[status(thm)],[81])).
% 9.67/9.89 tff(83,plain,
% 9.67/9.89 ((a_select3(u_defuse, n1, n0) = use) <=> (a_select3(u_defuse, n1, n0) = use)),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(84,plain,
% 9.67/9.89 (a_select3(u_defuse, n1, n0) = use),
% 9.67/9.89 inference(and_elim,[status(thm)],[5])).
% 9.67/9.89 tff(85,plain,
% 9.67/9.89 (a_select3(u_defuse, n1, n0) = use),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[84, 83])).
% 9.67/9.89 tff(86,assumption,(n2 = succ(E!14)), introduced(assumption)).
% 9.67/9.89 tff(87,plain,
% 9.67/9.89 (succ(E!14) = n2),
% 9.67/9.89 inference(symmetry,[status(thm)],[86])).
% 9.67/9.89 tff(88,plain,
% 9.67/9.89 (pred(succ(E!14)) = pred(n2)),
% 9.67/9.89 inference(monotonicity,[status(thm)],[87])).
% 9.67/9.89 tff(89,plain,
% 9.67/9.89 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(E!14)) = E!14)),
% 9.67/9.89 inference(quant_inst,[status(thm)],[])).
% 9.67/9.89 tff(90,plain,
% 9.67/9.89 (pred(succ(E!14)) = E!14),
% 9.67/9.89 inference(unit_resolution,[status(thm)],[89, 65])).
% 9.67/9.89 tff(91,plain,
% 9.67/9.89 (E!14 = pred(succ(E!14))),
% 9.67/9.89 inference(symmetry,[status(thm)],[90])).
% 9.67/9.89 tff(92,plain,
% 9.67/9.89 (E!14 = n1),
% 9.67/9.89 inference(transitivity,[status(thm)],[91, 88, 82, 74])).
% 9.67/9.89 tff(93,plain,
% 9.67/9.89 (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, n1, n0)),
% 9.67/9.89 inference(monotonicity,[status(thm)],[92, 59])).
% 9.67/9.89 tff(94,plain,
% 9.67/9.89 (a_select3(u_defuse, E!14, F!13) = use),
% 9.67/9.89 inference(transitivity,[status(thm)],[93, 85])).
% 9.67/9.89 tff(95,plain,
% 9.67/9.89 (~(a_select3(u_defuse, E!14, F!13) = use)),
% 9.67/9.89 inference(or_elim,[status(thm)],[13])).
% 9.67/9.89 tff(96,plain,
% 9.67/9.89 ($false),
% 9.67/9.89 inference(unit_resolution,[status(thm)],[95, 94])).
% 9.67/9.89 tff(97,plain,(~(n2 = succ(E!14))), inference(lemma,lemma(discharge,[]))).
% 9.67/9.89 tff(98,plain,
% 9.67/9.89 ((a_select3(u_defuse, n2, n0) = use) <=> (a_select3(u_defuse, n2, n0) = use)),
% 9.67/9.89 inference(rewrite,[status(thm)],[])).
% 9.67/9.89 tff(99,plain,
% 9.67/9.89 (a_select3(u_defuse, n2, n0) = use),
% 9.67/9.89 inference(and_elim,[status(thm)],[5])).
% 9.67/9.89 tff(100,plain,
% 9.67/9.89 (a_select3(u_defuse, n2, n0) = use),
% 9.67/9.89 inference(modus_ponens,[status(thm)],[99, 98])).
% 9.67/9.89 tff(101,assumption,(n2 = E!14), introduced(assumption)).
% 9.67/9.89 tff(102,plain,
% 9.67/9.89 (E!14 = n2),
% 9.67/9.89 inference(symmetry,[status(thm)],[101])).
% 9.67/9.89 tff(103,plain,
% 9.67/9.89 (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, n2, n0)),
% 9.67/9.89 inference(monotonicity,[status(thm)],[102, 59])).
% 9.67/9.89 tff(104,plain,
% 9.67/9.89 (a_select3(u_defuse, E!14, F!13) = use),
% 9.67/9.89 inference(transitivity,[status(thm)],[103, 100])).
% 9.67/9.89 tff(105,plain,
% 9.67/9.89 ($false),
% 9.67/9.89 inference(unit_resolution,[status(thm)],[95, 104])).
% 9.67/9.89 tff(106,plain,(~(n2 = E!14)), inference(lemma,lemma(discharge,[]))).
% 9.67/9.89 tff(107,plain,
% 9.67/9.89 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 9.67/9.89 inference(bind,[status(th)],[])).
% 9.67/9.89 tff(108,plain,
% 9.67/9.89 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 9.67/9.89 inference(quant_intro,[status(thm)],[107])).
% 9.67/9.89 tff(109,plain,
% 9.67/9.89 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 9.67/9.90 inference(rewrite,[status(thm)],[])).
% 9.67/9.90 tff(110,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 9.67/9.90 tff(111,plain,
% 9.67/9.90 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 9.67/9.90 inference(modus_ponens,[status(thm)],[110, 109])).
% 9.67/9.90 tff(112,plain,(
% 9.67/9.90 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 9.67/9.90 inference(skolemize,[status(sab)],[111])).
% 9.67/9.90 tff(113,plain,
% 9.67/9.90 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 9.67/9.90 inference(modus_ponens,[status(thm)],[112, 108])).
% 9.67/9.90 tff(114,plain,
% 9.67/9.90 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(n2, pred(E!14)) <=> gt(E!14, n2))),
% 9.67/9.90 inference(quant_inst,[status(thm)],[])).
% 9.67/9.90 tff(115,plain,
% 9.67/9.90 (leq(n2, pred(E!14)) <=> gt(E!14, n2)),
% 9.67/9.90 inference(unit_resolution,[status(thm)],[114, 113])).
% 9.67/9.90 tff(116,plain,
% 9.67/9.90 (^[X: $i, Y: $i] : refl((leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> (leq(succ(X), succ(Y)) <=> leq(X, Y)))),
% 9.67/9.90 inference(bind,[status(th)],[])).
% 9.67/9.90 tff(117,plain,
% 9.67/9.90 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 9.67/9.90 inference(quant_intro,[status(thm)],[116])).
% 9.67/9.90 tff(118,plain,
% 9.67/9.90 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 9.67/9.90 inference(rewrite,[status(thm)],[])).
% 9.67/9.90 tff(119,axiom,(![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_succ_succ')).
% 9.67/9.90 tff(120,plain,
% 9.67/9.90 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 9.67/9.90 inference(modus_ponens,[status(thm)],[119, 118])).
% 9.67/9.90 tff(121,plain,(
% 9.67/9.90 ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 9.67/9.90 inference(skolemize,[status(sab)],[120])).
% 9.67/9.90 tff(122,plain,
% 9.67/9.90 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 9.67/9.90 inference(modus_ponens,[status(thm)],[121, 117])).
% 9.67/9.90 tff(123,plain,
% 9.67/9.90 ((~![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))) | (leq(succ(n2), succ(pred(E!14))) <=> leq(n2, pred(E!14)))),
% 9.67/9.90 inference(quant_inst,[status(thm)],[])).
% 9.67/9.90 tff(124,plain,
% 9.67/9.90 (leq(succ(n2), succ(pred(E!14))) <=> leq(n2, pred(E!14))),
% 9.67/9.90 inference(unit_resolution,[status(thm)],[123, 122])).
% 9.67/9.90 tff(125,plain,
% 9.67/9.90 (![X: $i] : (succ(pred(X)) = X) <=> ![X: $i] : (succ(pred(X)) = X)),
% 9.67/9.90 inference(rewrite,[status(thm)],[])).
% 9.67/9.90 tff(126,plain,
% 9.67/9.90 (![X: $i] : (succ(pred(X)) = X) <=> ![X: $i] : (succ(pred(X)) = X)),
% 9.67/9.90 inference(rewrite,[status(thm)],[])).
% 9.67/9.90 tff(127,axiom,(![X: $i] : (succ(pred(X)) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','succ_pred')).
% 9.67/9.90 tff(128,plain,
% 9.67/9.90 (![X: $i] : (succ(pred(X)) = X)),
% 9.67/9.90 inference(modus_ponens,[status(thm)],[127, 126])).
% 9.67/9.90 tff(129,plain,(
% 9.67/9.90 ![X: $i] : (succ(pred(X)) = X)),
% 9.67/9.90 inference(skolemize,[status(sab)],[128])).
% 9.67/9.90 tff(130,plain,
% 9.67/9.90 (![X: $i] : (succ(pred(X)) = X)),
% 9.67/9.90 inference(modus_ponens,[status(thm)],[129, 125])).
% 9.67/9.90 tff(131,plain,
% 9.67/9.90 ((~![X: $i] : (succ(pred(X)) = X)) | (succ(pred(E!14)) = E!14)),
% 9.67/9.90 inference(quant_inst,[status(thm)],[])).
% 9.67/9.90 tff(132,plain,
% 9.67/9.90 (succ(pred(E!14)) = E!14),
% 9.67/9.90 inference(unit_resolution,[status(thm)],[131, 130])).
% 9.67/9.90 tff(133,plain,
% 9.67/9.90 ((succ(succ(succ(n0))) = n3) <=> (succ(succ(succ(n0))) = n3)),
% 9.67/9.90 inference(rewrite,[status(thm)],[])).
% 9.67/9.90 tff(134,axiom,(succ(succ(succ(n0))) = n3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','successor_3')).
% 9.67/9.90 tff(135,plain,
% 9.67/9.90 (succ(succ(succ(n0))) = n3),
% 9.67/9.90 inference(modus_ponens,[status(thm)],[134, 133])).
% 9.67/9.90 tff(136,plain,
% 9.67/9.90 (succ(n2) = succ(succ(succ(n0)))),
% 9.67/9.90 inference(monotonicity,[status(thm)],[80])).
% 9.67/9.90 tff(137,plain,
% 9.67/9.90 (succ(n2) = n3),
% 9.67/9.90 inference(transitivity,[status(thm)],[136, 135])).
% 9.67/9.90 tff(138,plain,
% 9.67/9.90 (leq(succ(n2), succ(pred(E!14))) <=> leq(n3, E!14)),
% 9.67/9.90 inference(monotonicity,[status(thm)],[137, 132])).
% 9.67/9.90 tff(139,plain,
% 9.67/9.90 (leq(n3, E!14) <=> leq(succ(n2), succ(pred(E!14)))),
% 9.67/9.90 inference(symmetry,[status(thm)],[138])).
% 9.67/9.90 tff(140,plain,
% 9.67/9.90 ((~leq(n3, E!14)) <=> (~leq(succ(n2), succ(pred(E!14))))),
% 9.67/9.90 inference(monotonicity,[status(thm)],[139])).
% 9.67/9.90 tff(141,plain,
% 9.74/9.90 (leq(succ(n2), n2) <=> leq(n3, n2)),
% 9.74/9.90 inference(monotonicity,[status(thm)],[137])).
% 9.74/9.90 tff(142,plain,
% 9.74/9.90 ((~leq(succ(n2), n2)) <=> (~leq(n3, n2))),
% 9.74/9.90 inference(monotonicity,[status(thm)],[141])).
% 9.74/9.90 tff(143,plain,
% 9.74/9.90 (^[X: $i] : refl((~gt(X, X)) <=> (~gt(X, X)))),
% 9.74/9.90 inference(bind,[status(th)],[])).
% 9.74/9.90 tff(144,plain,
% 9.74/9.90 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 9.74/9.90 inference(quant_intro,[status(thm)],[143])).
% 9.74/9.90 tff(145,plain,
% 9.74/9.90 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 9.74/9.90 inference(rewrite,[status(thm)],[])).
% 9.74/9.90 tff(146,axiom,(![X: $i] : (~gt(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','irreflexivity_gt')).
% 9.74/9.90 tff(147,plain,
% 9.74/9.90 (![X: $i] : (~gt(X, X))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[146, 145])).
% 9.74/9.90 tff(148,plain,(
% 9.74/9.90 ![X: $i] : (~gt(X, X))),
% 9.74/9.90 inference(skolemize,[status(sab)],[147])).
% 9.74/9.90 tff(149,plain,
% 9.74/9.90 (![X: $i] : (~gt(X, X))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[148, 144])).
% 9.74/9.90 tff(150,plain,
% 9.74/9.90 ((~![X: $i] : (~gt(X, X))) | (~gt(n2, n2))),
% 9.74/9.90 inference(quant_inst,[status(thm)],[])).
% 9.74/9.90 tff(151,plain,
% 9.74/9.90 (~gt(n2, n2)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[150, 149])).
% 9.74/9.90 tff(152,plain,
% 9.74/9.90 (^[X: $i, Y: $i] : refl(((~leq(succ(X), Y)) | gt(Y, X)) <=> ((~leq(succ(X), Y)) | gt(Y, X)))),
% 9.74/9.90 inference(bind,[status(th)],[])).
% 9.74/9.90 tff(153,plain,
% 9.74/9.90 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 9.74/9.90 inference(quant_intro,[status(thm)],[152])).
% 9.74/9.90 tff(154,plain,
% 9.74/9.90 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 9.74/9.90 inference(rewrite,[status(thm)],[])).
% 9.74/9.90 tff(155,plain,
% 9.74/9.90 (^[X: $i, Y: $i] : rewrite((leq(succ(X), Y) => gt(Y, X)) <=> ((~leq(succ(X), Y)) | gt(Y, X)))),
% 9.74/9.90 inference(bind,[status(th)],[])).
% 9.74/9.90 tff(156,plain,
% 9.74/9.90 (![X: $i, Y: $i] : (leq(succ(X), Y) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 9.74/9.90 inference(quant_intro,[status(thm)],[155])).
% 9.74/9.90 tff(157,axiom,(![X: $i, Y: $i] : (leq(succ(X), Y) => gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_succ_gt')).
% 9.74/9.90 tff(158,plain,
% 9.74/9.90 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[157, 156])).
% 9.74/9.90 tff(159,plain,
% 9.74/9.90 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[158, 154])).
% 9.74/9.90 tff(160,plain,(
% 9.74/9.90 ![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 9.74/9.90 inference(skolemize,[status(sab)],[159])).
% 9.74/9.90 tff(161,plain,
% 9.74/9.90 (![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[160, 153])).
% 9.74/9.90 tff(162,plain,
% 9.74/9.90 (((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | ((~leq(succ(n2), n2)) | gt(n2, n2))) <=> ((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | (~leq(succ(n2), n2)) | gt(n2, n2))),
% 9.74/9.90 inference(rewrite,[status(thm)],[])).
% 9.74/9.90 tff(163,plain,
% 9.74/9.90 ((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | ((~leq(succ(n2), n2)) | gt(n2, n2))),
% 9.74/9.90 inference(quant_inst,[status(thm)],[])).
% 9.74/9.90 tff(164,plain,
% 9.74/9.90 ((~![X: $i, Y: $i] : ((~leq(succ(X), Y)) | gt(Y, X))) | (~leq(succ(n2), n2)) | gt(n2, n2)),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[163, 162])).
% 9.74/9.90 tff(165,plain,
% 9.74/9.90 ((~leq(succ(n2), n2)) | gt(n2, n2)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[164, 161])).
% 9.74/9.90 tff(166,plain,
% 9.74/9.90 (~leq(succ(n2), n2)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[165, 151])).
% 9.74/9.90 tff(167,plain,
% 9.74/9.90 (~leq(n3, n2)),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[166, 142])).
% 9.74/9.90 tff(168,plain,
% 9.74/9.90 (leq(E!14, n2)),
% 9.74/9.90 inference(and_elim,[status(thm)],[14])).
% 9.74/9.90 tff(169,plain,
% 9.74/9.90 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(E!14, n2)) | leq(n3, n2) | (~leq(n3, E!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(E!14, n2)) | leq(n3, n2) | (~leq(n3, E!14)))),
% 9.74/9.90 inference(rewrite,[status(thm)],[])).
% 9.74/9.90 tff(170,plain,
% 9.74/9.90 ((leq(n3, n2) | (~leq(E!14, n2)) | (~leq(n3, E!14))) <=> ((~leq(E!14, n2)) | leq(n3, n2) | (~leq(n3, E!14)))),
% 9.74/9.90 inference(rewrite,[status(thm)],[])).
% 9.74/9.90 tff(171,plain,
% 9.74/9.90 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n3, n2) | (~leq(E!14, n2)) | (~leq(n3, E!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(E!14, n2)) | leq(n3, n2) | (~leq(n3, E!14))))),
% 9.74/9.90 inference(monotonicity,[status(thm)],[170])).
% 9.74/9.90 tff(172,plain,
% 9.74/9.90 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n3, n2) | (~leq(E!14, n2)) | (~leq(n3, E!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(E!14, n2)) | leq(n3, n2) | (~leq(n3, E!14)))),
% 9.74/9.90 inference(transitivity,[status(thm)],[171, 169])).
% 9.74/9.90 tff(173,plain,
% 9.74/9.90 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n3, n2) | (~leq(E!14, n2)) | (~leq(n3, E!14)))),
% 9.74/9.90 inference(quant_inst,[status(thm)],[])).
% 9.74/9.90 tff(174,plain,
% 9.74/9.90 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(E!14, n2)) | leq(n3, n2) | (~leq(n3, E!14))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[173, 172])).
% 9.74/9.90 tff(175,plain,
% 9.74/9.90 (leq(n3, n2) | (~leq(n3, E!14))),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[174, 30, 168])).
% 9.74/9.90 tff(176,plain,
% 9.74/9.90 (~leq(n3, E!14)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[175, 167])).
% 9.74/9.90 tff(177,plain,
% 9.74/9.90 (~leq(succ(n2), succ(pred(E!14)))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[176, 140])).
% 9.74/9.90 tff(178,plain,
% 9.74/9.90 ((~(leq(succ(n2), succ(pred(E!14))) <=> leq(n2, pred(E!14)))) | leq(succ(n2), succ(pred(E!14))) | (~leq(n2, pred(E!14)))),
% 9.74/9.90 inference(tautology,[status(thm)],[])).
% 9.74/9.90 tff(179,plain,
% 9.74/9.90 (~leq(n2, pred(E!14))),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[178, 177, 124])).
% 9.74/9.90 tff(180,plain,
% 9.74/9.90 ((~(leq(n2, pred(E!14)) <=> gt(E!14, n2))) | leq(n2, pred(E!14)) | (~gt(E!14, n2))),
% 9.74/9.90 inference(tautology,[status(thm)],[])).
% 9.74/9.90 tff(181,plain,
% 9.74/9.90 (~gt(E!14, n2)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[180, 179, 115])).
% 9.74/9.90 tff(182,plain,
% 9.74/9.90 (^[X: $i, Y: $i] : refl(((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y))))),
% 9.74/9.90 inference(bind,[status(th)],[])).
% 9.74/9.90 tff(183,plain,
% 9.74/9.90 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 9.74/9.90 inference(quant_intro,[status(thm)],[182])).
% 9.74/9.90 tff(184,plain,
% 9.74/9.90 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & (~(X = Y))) <=> (~((~leq(X, Y)) | (X = Y)))), ((~(leq(X, Y) & (~(X = Y)))) <=> (~(~((~leq(X, Y)) | (X = Y)))))), rewrite((~(~((~leq(X, Y)) | (X = Y)))) <=> ((~leq(X, Y)) | (X = Y))), ((~(leq(X, Y) & (~(X = Y)))) <=> ((~leq(X, Y)) | (X = Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> (((~leq(X, Y)) | (X = Y)) | gt(Y, X)))), rewrite((((~leq(X, Y)) | (X = Y)) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))))),
% 9.74/9.90 inference(bind,[status(th)],[])).
% 9.74/9.90 tff(185,plain,
% 9.74/9.90 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 9.74/9.90 inference(quant_intro,[status(thm)],[184])).
% 9.74/9.90 tff(186,plain,
% 9.74/9.90 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 9.74/9.90 inference(rewrite,[status(thm)],[])).
% 9.74/9.90 tff(187,plain,
% 9.74/9.90 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)))),
% 9.74/9.90 inference(bind,[status(th)],[])).
% 9.74/9.90 tff(188,plain,
% 9.74/9.90 (![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 9.74/9.90 inference(quant_intro,[status(thm)],[187])).
% 9.74/9.90 tff(189,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt2')).
% 9.74/9.90 tff(190,plain,
% 9.74/9.90 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[189, 188])).
% 9.74/9.90 tff(191,plain,
% 9.74/9.90 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[190, 186])).
% 9.74/9.90 tff(192,plain,(
% 9.74/9.90 ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 9.74/9.90 inference(skolemize,[status(sab)],[191])).
% 9.74/9.90 tff(193,plain,
% 9.74/9.90 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[192, 185])).
% 9.74/9.90 tff(194,plain,
% 9.74/9.90 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[193, 183])).
% 9.74/9.90 tff(195,plain,
% 9.74/9.90 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((~leq(n2, E!14)) | (n2 = E!14) | gt(E!14, n2))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(n2, E!14)) | (n2 = E!14) | gt(E!14, n2))),
% 9.74/9.90 inference(rewrite,[status(thm)],[])).
% 9.74/9.90 tff(196,plain,
% 9.74/9.90 (((n2 = E!14) | gt(E!14, n2) | (~leq(n2, E!14))) <=> ((~leq(n2, E!14)) | (n2 = E!14) | gt(E!14, n2))),
% 9.74/9.90 inference(rewrite,[status(thm)],[])).
% 9.74/9.90 tff(197,plain,
% 9.74/9.90 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((n2 = E!14) | gt(E!14, n2) | (~leq(n2, E!14)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((~leq(n2, E!14)) | (n2 = E!14) | gt(E!14, n2)))),
% 9.74/9.90 inference(monotonicity,[status(thm)],[196])).
% 9.74/9.90 tff(198,plain,
% 9.74/9.90 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((n2 = E!14) | gt(E!14, n2) | (~leq(n2, E!14)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(n2, E!14)) | (n2 = E!14) | gt(E!14, n2))),
% 9.74/9.90 inference(transitivity,[status(thm)],[197, 195])).
% 9.74/9.90 tff(199,plain,
% 9.74/9.90 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((n2 = E!14) | gt(E!14, n2) | (~leq(n2, E!14)))),
% 9.74/9.90 inference(quant_inst,[status(thm)],[])).
% 9.74/9.90 tff(200,plain,
% 9.74/9.90 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(n2, E!14)) | (n2 = E!14) | gt(E!14, n2)),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[199, 198])).
% 9.74/9.90 tff(201,plain,
% 9.74/9.90 ((~leq(n2, E!14)) | (n2 = E!14) | gt(E!14, n2)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[200, 194])).
% 9.74/9.90 tff(202,plain,
% 9.74/9.90 ((~leq(n2, E!14)) | (n2 = E!14)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[201, 181])).
% 9.74/9.90 tff(203,plain,
% 9.74/9.90 (~leq(n2, E!14)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[202, 106])).
% 9.74/9.90 tff(204,plain,
% 9.74/9.90 (^[X: $i, Y: $i] : refl((leq(X, Y) <=> gt(succ(Y), X)) <=> (leq(X, Y) <=> gt(succ(Y), X)))),
% 9.74/9.90 inference(bind,[status(th)],[])).
% 9.74/9.90 tff(205,plain,
% 9.74/9.90 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 9.74/9.90 inference(quant_intro,[status(thm)],[204])).
% 9.74/9.90 tff(206,plain,
% 9.74/9.90 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 9.74/9.90 inference(rewrite,[status(thm)],[])).
% 9.74/9.90 tff(207,axiom,(![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_succ_gt_equiv')).
% 9.74/9.90 tff(208,plain,
% 9.74/9.90 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[207, 206])).
% 9.74/9.90 tff(209,plain,(
% 9.74/9.90 ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 9.74/9.90 inference(skolemize,[status(sab)],[208])).
% 9.74/9.90 tff(210,plain,
% 9.74/9.90 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[209, 205])).
% 9.74/9.90 tff(211,plain,
% 9.74/9.90 ((~![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))) | (leq(n2, E!14) <=> gt(succ(E!14), n2))),
% 9.74/9.90 inference(quant_inst,[status(thm)],[])).
% 9.74/9.90 tff(212,plain,
% 9.74/9.90 (leq(n2, E!14) <=> gt(succ(E!14), n2)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[211, 210])).
% 9.74/9.90 tff(213,plain,
% 9.74/9.90 ((~(leq(n2, E!14) <=> gt(succ(E!14), n2))) | leq(n2, E!14) | (~gt(succ(E!14), n2))),
% 9.74/9.90 inference(tautology,[status(thm)],[])).
% 9.74/9.90 tff(214,plain,
% 9.74/9.90 (leq(n2, E!14) | (~gt(succ(E!14), n2))),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[213, 212])).
% 9.74/9.90 tff(215,plain,
% 9.74/9.90 (~gt(succ(E!14), n2)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[214, 203])).
% 9.74/9.90 tff(216,plain,
% 9.74/9.90 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((~leq(n2, succ(E!14))) | (n2 = succ(E!14)) | gt(succ(E!14), n2))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(n2, succ(E!14))) | (n2 = succ(E!14)) | gt(succ(E!14), n2))),
% 9.74/9.90 inference(rewrite,[status(thm)],[])).
% 9.74/9.90 tff(217,plain,
% 9.74/9.90 (((n2 = succ(E!14)) | gt(succ(E!14), n2) | (~leq(n2, succ(E!14)))) <=> ((~leq(n2, succ(E!14))) | (n2 = succ(E!14)) | gt(succ(E!14), n2))),
% 9.74/9.90 inference(rewrite,[status(thm)],[])).
% 9.74/9.90 tff(218,plain,
% 9.74/9.90 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((n2 = succ(E!14)) | gt(succ(E!14), n2) | (~leq(n2, succ(E!14))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((~leq(n2, succ(E!14))) | (n2 = succ(E!14)) | gt(succ(E!14), n2)))),
% 9.74/9.90 inference(monotonicity,[status(thm)],[217])).
% 9.74/9.90 tff(219,plain,
% 9.74/9.90 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((n2 = succ(E!14)) | gt(succ(E!14), n2) | (~leq(n2, succ(E!14))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(n2, succ(E!14))) | (n2 = succ(E!14)) | gt(succ(E!14), n2))),
% 9.74/9.90 inference(transitivity,[status(thm)],[218, 216])).
% 9.74/9.90 tff(220,plain,
% 9.74/9.90 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((n2 = succ(E!14)) | gt(succ(E!14), n2) | (~leq(n2, succ(E!14))))),
% 9.74/9.90 inference(quant_inst,[status(thm)],[])).
% 9.74/9.90 tff(221,plain,
% 9.74/9.90 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(n2, succ(E!14))) | (n2 = succ(E!14)) | gt(succ(E!14), n2)),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[220, 219])).
% 9.74/9.90 tff(222,plain,
% 9.74/9.90 ((~leq(n2, succ(E!14))) | (n2 = succ(E!14)) | gt(succ(E!14), n2)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[221, 194])).
% 9.74/9.90 tff(223,plain,
% 9.74/9.90 (~leq(n2, succ(E!14))),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[222, 215, 97])).
% 9.74/9.90 tff(224,plain,
% 9.74/9.90 ((~![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))) | (leq(n2, succ(E!14)) <=> gt(succ(succ(E!14)), n2))),
% 9.74/9.90 inference(quant_inst,[status(thm)],[])).
% 9.74/9.90 tff(225,plain,
% 9.74/9.90 (leq(n2, succ(E!14)) <=> gt(succ(succ(E!14)), n2)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[224, 210])).
% 9.74/9.90 tff(226,plain,
% 9.74/9.90 ((~(leq(n2, succ(E!14)) <=> gt(succ(succ(E!14)), n2))) | leq(n2, succ(E!14)) | (~gt(succ(succ(E!14)), n2))),
% 9.74/9.90 inference(tautology,[status(thm)],[])).
% 9.74/9.90 tff(227,plain,
% 9.74/9.90 (leq(n2, succ(E!14)) | (~gt(succ(succ(E!14)), n2))),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[226, 225])).
% 9.74/9.90 tff(228,plain,
% 9.74/9.90 (~gt(succ(succ(E!14)), n2)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[227, 223])).
% 9.74/9.90 tff(229,plain,
% 9.74/9.90 (succ(n1) = n2),
% 9.74/9.90 inference(transitivity,[status(thm)],[75, 79])).
% 9.74/9.90 tff(230,plain,
% 9.74/9.90 (leq(succ(n1), succ(succ(E!14))) <=> leq(n2, succ(succ(E!14)))),
% 9.74/9.90 inference(monotonicity,[status(thm)],[229])).
% 9.74/9.90 tff(231,plain,
% 9.74/9.90 ((~![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))) | (leq(succ(n1), succ(succ(E!14))) <=> leq(n1, succ(E!14)))),
% 9.74/9.90 inference(quant_inst,[status(thm)],[])).
% 9.74/9.90 tff(232,plain,
% 9.74/9.90 (leq(succ(n1), succ(succ(E!14))) <=> leq(n1, succ(E!14))),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[231, 122])).
% 9.74/9.90 tff(233,plain,
% 9.74/9.90 (leq(n1, succ(E!14)) <=> leq(succ(n0), succ(E!14))),
% 9.74/9.90 inference(monotonicity,[status(thm)],[71])).
% 9.74/9.90 tff(234,plain,
% 9.74/9.90 (leq(succ(n0), succ(E!14)) <=> leq(n1, succ(E!14))),
% 9.74/9.90 inference(symmetry,[status(thm)],[233])).
% 9.74/9.90 tff(235,plain,
% 9.74/9.90 ((~![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))) | (leq(succ(n0), succ(E!14)) <=> leq(n0, E!14))),
% 9.74/9.90 inference(quant_inst,[status(thm)],[])).
% 9.74/9.90 tff(236,plain,
% 9.74/9.90 (leq(succ(n0), succ(E!14)) <=> leq(n0, E!14)),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[235, 122])).
% 9.74/9.90 tff(237,plain,
% 9.74/9.90 (leq(n0, E!14)),
% 9.74/9.90 inference(and_elim,[status(thm)],[14])).
% 9.74/9.90 tff(238,plain,
% 9.74/9.90 ((~(leq(succ(n0), succ(E!14)) <=> leq(n0, E!14))) | leq(succ(n0), succ(E!14)) | (~leq(n0, E!14))),
% 9.74/9.90 inference(tautology,[status(thm)],[])).
% 9.74/9.90 tff(239,plain,
% 9.74/9.90 ((~(leq(succ(n0), succ(E!14)) <=> leq(n0, E!14))) | leq(succ(n0), succ(E!14))),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[238, 237])).
% 9.74/9.90 tff(240,plain,
% 9.74/9.90 (leq(succ(n0), succ(E!14))),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[239, 236])).
% 9.74/9.90 tff(241,plain,
% 9.74/9.90 (leq(n1, succ(E!14))),
% 9.74/9.90 inference(modus_ponens,[status(thm)],[240, 234])).
% 9.74/9.90 tff(242,plain,
% 9.74/9.90 ((~(leq(succ(n1), succ(succ(E!14))) <=> leq(n1, succ(E!14)))) | leq(succ(n1), succ(succ(E!14))) | (~leq(n1, succ(E!14)))),
% 9.74/9.90 inference(tautology,[status(thm)],[])).
% 9.74/9.90 tff(243,plain,
% 9.74/9.90 (leq(succ(n1), succ(succ(E!14)))),
% 9.74/9.90 inference(unit_resolution,[status(thm)],[242, 241, 232])).
% 9.74/9.95 tff(244,plain,
% 9.74/9.95 (leq(n2, succ(succ(E!14)))),
% 9.74/9.95 inference(modus_ponens,[status(thm)],[243, 230])).
% 9.74/9.95 tff(245,plain,
% 9.74/9.95 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (gt(succ(succ(E!14)), n2) | (~leq(n2, succ(succ(E!14)))) | (n2 = succ(succ(E!14))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | gt(succ(succ(E!14)), n2) | (~leq(n2, succ(succ(E!14)))) | (n2 = succ(succ(E!14))))),
% 9.74/9.95 inference(rewrite,[status(thm)],[])).
% 9.74/9.95 tff(246,plain,
% 9.74/9.95 (((n2 = succ(succ(E!14))) | gt(succ(succ(E!14)), n2) | (~leq(n2, succ(succ(E!14))))) <=> (gt(succ(succ(E!14)), n2) | (~leq(n2, succ(succ(E!14)))) | (n2 = succ(succ(E!14))))),
% 9.74/9.95 inference(rewrite,[status(thm)],[])).
% 9.74/9.95 tff(247,plain,
% 9.74/9.95 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((n2 = succ(succ(E!14))) | gt(succ(succ(E!14)), n2) | (~leq(n2, succ(succ(E!14)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (gt(succ(succ(E!14)), n2) | (~leq(n2, succ(succ(E!14)))) | (n2 = succ(succ(E!14)))))),
% 9.74/9.95 inference(monotonicity,[status(thm)],[246])).
% 9.74/9.95 tff(248,plain,
% 9.74/9.95 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((n2 = succ(succ(E!14))) | gt(succ(succ(E!14)), n2) | (~leq(n2, succ(succ(E!14)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | gt(succ(succ(E!14)), n2) | (~leq(n2, succ(succ(E!14)))) | (n2 = succ(succ(E!14))))),
% 9.74/9.95 inference(transitivity,[status(thm)],[247, 245])).
% 9.74/9.95 tff(249,plain,
% 9.74/9.95 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((n2 = succ(succ(E!14))) | gt(succ(succ(E!14)), n2) | (~leq(n2, succ(succ(E!14)))))),
% 9.74/9.95 inference(quant_inst,[status(thm)],[])).
% 9.74/9.95 tff(250,plain,
% 9.74/9.95 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | gt(succ(succ(E!14)), n2) | (~leq(n2, succ(succ(E!14)))) | (n2 = succ(succ(E!14)))),
% 9.74/9.95 inference(modus_ponens,[status(thm)],[249, 248])).
% 9.74/9.95 tff(251,plain,
% 9.74/9.95 (gt(succ(succ(E!14)), n2) | (~leq(n2, succ(succ(E!14)))) | (n2 = succ(succ(E!14)))),
% 9.74/9.95 inference(unit_resolution,[status(thm)],[250, 194])).
% 9.74/9.95 tff(252,plain,
% 9.74/9.95 (gt(succ(succ(E!14)), n2) | (n2 = succ(succ(E!14)))),
% 9.74/9.95 inference(unit_resolution,[status(thm)],[251, 244])).
% 9.74/9.95 tff(253,plain,
% 9.74/9.95 (n2 = succ(succ(E!14))),
% 9.74/9.95 inference(unit_resolution,[status(thm)],[252, 228])).
% 9.74/9.95 tff(254,plain,
% 9.74/9.95 (succ(succ(E!14)) = n2),
% 9.74/9.95 inference(symmetry,[status(thm)],[253])).
% 9.74/9.95 tff(255,plain,
% 9.74/9.95 (pred(succ(succ(E!14))) = pred(n2)),
% 9.74/9.95 inference(monotonicity,[status(thm)],[254])).
% 9.74/9.95 tff(256,plain,
% 9.74/9.95 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(succ(E!14))) = succ(E!14))),
% 9.74/9.95 inference(quant_inst,[status(thm)],[])).
% 9.74/9.95 tff(257,plain,
% 9.74/9.95 (pred(succ(succ(E!14))) = succ(E!14)),
% 9.74/9.95 inference(unit_resolution,[status(thm)],[256, 65])).
% 9.74/9.95 tff(258,plain,
% 9.74/9.95 (succ(E!14) = pred(succ(succ(E!14)))),
% 9.74/9.95 inference(symmetry,[status(thm)],[257])).
% 9.74/9.95 tff(259,plain,
% 9.74/9.95 (succ(E!14) = n1),
% 9.74/9.95 inference(transitivity,[status(thm)],[258, 255, 82, 74])).
% 9.74/9.95 tff(260,plain,
% 9.74/9.95 (pred(succ(E!14)) = pred(n1)),
% 9.74/9.95 inference(monotonicity,[status(thm)],[259])).
% 9.74/9.95 tff(261,plain,
% 9.74/9.95 (E!14 = n0),
% 9.74/9.95 inference(transitivity,[status(thm)],[91, 260, 72, 67])).
% 9.74/9.95 tff(262,plain,
% 9.74/9.95 (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, n0, n0)),
% 9.74/9.95 inference(monotonicity,[status(thm)],[261, 59])).
% 9.74/9.95 tff(263,plain,
% 9.74/9.95 (a_select3(u_defuse, E!14, F!13) = use),
% 9.74/9.95 inference(transitivity,[status(thm)],[262, 7])).
% 9.74/9.95 tff(264,plain,
% 9.74/9.95 ($false),
% 9.74/9.95 inference(unit_resolution,[status(thm)],[95, 263])).
% 9.74/9.95 % SZS output end Proof
% 9.74/9.95 % E exiting
%------------------------------------------------------------------------------