%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV199+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:31:42 AM UTC 2025
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV199+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 09:31:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 tff(n0_type, type, (
% 0.19/0.48 n0: $i)).
% 0.19/0.48 tff(tptp_fun_E_14_type, type, (
% 0.19/0.48 tptp_fun_E_14: $i)).
% 0.19/0.48 tff(tptp_fun_F_13_type, type, (
% 0.19/0.48 tptp_fun_F_13: $i)).
% 0.19/0.48 tff(pv5_type, type, (
% 0.19/0.48 pv5: $i)).
% 0.19/0.48 tff(leq_type, type, (
% 0.19/0.48 leq: ( $i * $i ) > $o)).
% 0.19/0.48 tff(use_type, type, (
% 0.19/0.48 use: $i)).
% 0.19/0.48 tff(a_select3_type, type, (
% 0.19/0.48 a_select3: ( $i * $i * $i ) > $i)).
% 0.19/0.48 tff(z_defuse_type, type, (
% 0.19/0.48 z_defuse: $i)).
% 0.19/0.48 tff(pred_type, type, (
% 0.19/0.48 pred: $i > $i)).
% 0.19/0.48 tff(n2_type, type, (
% 0.19/0.48 n2: $i)).
% 0.19/0.48 tff(u_defuse_type, type, (
% 0.19/0.48 u_defuse: $i)).
% 0.19/0.48 tff(n998_type, type, (
% 0.19/0.48 n998: $i)).
% 0.19/0.48 tff(a_select2_type, type, (
% 0.19/0.48 a_select2: ( $i * $i ) > $i)).
% 0.19/0.48 tff(n5_type, type, (
% 0.19/0.48 n5: $i)).
% 0.19/0.48 tff(xinit_noise_defuse_type, type, (
% 0.19/0.48 xinit_noise_defuse: $i)).
% 0.19/0.48 tff(n4_type, type, (
% 0.19/0.48 n4: $i)).
% 0.19/0.48 tff(n3_type, type, (
% 0.19/0.48 n3: $i)).
% 0.19/0.48 tff(n1_type, type, (
% 0.19/0.48 n1: $i)).
% 0.19/0.48 tff(xinit_mean_defuse_type, type, (
% 0.19/0.48 xinit_mean_defuse: $i)).
% 0.19/0.48 tff(xinit_defuse_type, type, (
% 0.19/0.48 xinit_defuse: $i)).
% 0.19/0.48 tff(sigma_defuse_type, type, (
% 0.19/0.48 sigma_defuse: $i)).
% 0.19/0.48 tff(rho_defuse_type, type, (
% 0.19/0.48 rho_defuse: $i)).
% 0.19/0.48 tff(1,plain,
% 0.19/0.48 ((E!14 = n0) <=> (n0 = E!14)),
% 0.19/0.48 inference(commutativity,[status(thm)],[])).
% 0.19/0.48 tff(2,plain,
% 0.19/0.48 ((n0 = E!14) <=> (E!14 = n0)),
% 0.19/0.48 inference(symmetry,[status(thm)],[1])).
% 0.19/0.48 tff(3,plain,
% 0.19/0.48 ((~(n0 = E!14)) <=> (~(E!14 = n0))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[2])).
% 0.19/0.48 tff(4,plain,
% 0.19/0.48 ((n0 = F!13) <=> (F!13 = n0)),
% 0.19/0.48 inference(commutativity,[status(thm)],[])).
% 0.19/0.48 tff(5,plain,
% 0.19/0.48 (leq(pv5, n0) <=> leq(pv5, n0)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(6,plain,
% 0.19/0.48 ((~(((((((((((((((((((((((((((((((((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)) => ((((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F)))) & (~((n2 = E) & (pv5 = F)))) => (a_select3(z_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] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(7,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)) => ((((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F)))) & (~((n2 = E) & (pv5 = F)))) => (a_select3(z_defuse, E, F) = use))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_inuse_0010')).
% 0.19/0.49 tff(8,plain,
% 0.19/0.49 (~((~((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] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.49 tff(9,plain,
% 0.19/0.49 ((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))),
% 0.19/0.49 inference(or_elim,[status(thm)],[8])).
% 0.19/0.49 tff(10,plain,
% 0.19/0.49 (leq(pv5, n0)),
% 0.19/0.49 inference(and_elim,[status(thm)],[9])).
% 0.19/0.49 tff(11,plain,
% 0.19/0.49 (leq(pv5, n0)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.19/0.49 tff(12,plain,
% 0.19/0.49 (leq(n0, pv5) <=> leq(n0, pv5)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(13,plain,
% 0.19/0.49 (leq(n0, pv5)),
% 0.19/0.49 inference(and_elim,[status(thm)],[9])).
% 0.19/0.49 tff(14,plain,
% 0.19/0.49 (leq(n0, pv5)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.49 tff(15,plain,
% 0.19/0.49 (^[X: $i] : refl(((X = n0) | (~leq(n0, X)) | (~leq(X, n0))) <=> ((X = n0) | (~leq(n0, X)) | (~leq(X, n0))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(16,plain,
% 0.19/0.49 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0))) <=> ![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.49 tff(17,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(18,plain,
% 0.19/0.49 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.49 tff(19,plain,
% 0.19/0.49 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(20,plain,
% 0.19/0.49 (^[X: $i] : rewrite(((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ((~(leq(n0, X) & leq(X, n0))) | (X = n0)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(21,plain,
% 0.19/0.49 (![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.49 tff(22,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','finite_domain_0')).
% 0.19/0.49 tff(23,plain,
% 0.19/0.49 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.49 tff(24,plain,
% 0.19/0.49 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.49 tff(25,plain,(
% 0.19/0.49 ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.49 inference(skolemize,[status(sab)],[24])).
% 0.19/0.49 tff(26,plain,
% 0.19/0.49 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.19/0.49 tff(27,plain,
% 0.19/0.49 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.19/0.49 tff(28,plain,
% 0.19/0.49 (((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((pv5 = n0) | (~leq(n0, pv5)) | (~leq(pv5, n0)))) <=> ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | (pv5 = n0) | (~leq(n0, pv5)) | (~leq(pv5, n0)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(29,plain,
% 0.19/0.49 ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((pv5 = n0) | (~leq(n0, pv5)) | (~leq(pv5, n0)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(30,plain,
% 0.19/0.49 ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | (pv5 = n0) | (~leq(n0, pv5)) | (~leq(pv5, n0))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.49 tff(31,plain,
% 0.19/0.49 (pv5 = n0),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[30, 27, 14, 11])).
% 0.19/0.49 tff(32,plain,
% 0.19/0.49 ((pv5 = F!13) <=> (n0 = F!13)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.49 tff(33,plain,
% 0.19/0.49 ((pv5 = F!13) <=> (F!13 = n0)),
% 0.19/0.49 inference(transitivity,[status(thm)],[32, 4])).
% 0.19/0.49 tff(34,plain,
% 0.19/0.49 ((F!13 = n0) <=> (pv5 = F!13)),
% 0.19/0.49 inference(symmetry,[status(thm)],[33])).
% 0.19/0.49 tff(35,plain,
% 0.19/0.49 ((~((a_select3(z_defuse, E!14, F!13) = use) | (~((~((n0 = E!14) & (pv5 = F!13))) & (~((n1 = E!14) & (pv5 = F!13))) & (~((n2 = E!14) & (pv5 = F!13))))) | (~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5))))) <=> (~((a_select3(z_defuse, E!14, F!13) = use) | (~((~((n0 = E!14) & (pv5 = F!13))) & (~((n1 = E!14) & (pv5 = F!13))) & (~((n2 = E!14) & (pv5 = F!13))))) | (~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(36,plain,
% 0.19/0.49 ((~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))) <=> (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(37,plain,
% 0.19/0.49 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.19/0.49 inference(or_elim,[status(thm)],[8])).
% 0.19/0.49 tff(38,plain,
% 0.19/0.49 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.49 tff(39,plain,
% 0.19/0.49 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[38, 36])).
% 0.19/0.49 tff(40,plain,
% 0.19/0.49 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.19/0.49 tff(41,plain,(
% 0.19/0.49 ~((a_select3(z_defuse, E!14, F!13) = use) | (~((~((n0 = E!14) & (pv5 = F!13))) & (~((n1 = E!14) & (pv5 = F!13))) & (~((n2 = E!14) & (pv5 = F!13))))) | (~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[40])).
% 0.19/0.49 tff(42,plain,
% 0.19/0.49 (~((a_select3(z_defuse, E!14, F!13) = use) | (~((~((n0 = E!14) & (pv5 = F!13))) & (~((n1 = E!14) & (pv5 = F!13))) & (~((n2 = E!14) & (pv5 = F!13))))) | (~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.19/0.49 tff(43,plain,
% 0.19/0.49 (leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5)),
% 0.19/0.49 inference(or_elim,[status(thm)],[42])).
% 0.19/0.49 tff(44,plain,
% 0.19/0.49 (leq(F!13, pv5)),
% 0.19/0.49 inference(and_elim,[status(thm)],[43])).
% 0.19/0.49 tff(45,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(46,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(47,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.49 tff(48,plain,
% 0.19/0.49 (![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))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(49,plain,
% 0.19/0.49 (^[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)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(50,plain,
% 0.19/0.49 (![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))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.49 tff(51,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')).
% 0.19/0.49 tff(52,plain,
% 0.19/0.49 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.49 tff(53,plain,
% 0.19/0.49 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.49 tff(54,plain,(
% 0.19/0.49 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.49 inference(skolemize,[status(sab)],[53])).
% 0.19/0.49 tff(55,plain,
% 0.19/0.49 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.19/0.49 tff(56,plain,
% 0.19/0.49 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.19/0.49 tff(57,plain,
% 0.19/0.49 (((~![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(58,plain,
% 0.19/0.49 ((leq(F!13, n0) | (~leq(pv5, n0)) | (~leq(F!13, pv5))) <=> ((~leq(pv5, n0)) | leq(F!13, n0) | (~leq(F!13, pv5)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(59,plain,
% 0.19/0.49 (((~![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))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[58])).
% 0.19/0.49 tff(60,plain,
% 0.19/0.49 (((~![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)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[59, 57])).
% 0.19/0.49 tff(61,plain,
% 0.19/0.49 ((~![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)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(62,plain,
% 0.19/0.49 ((~![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))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.50 tff(63,plain,
% 0.19/0.50 (leq(F!13, n0)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[62, 56, 11, 44])).
% 0.19/0.50 tff(64,plain,
% 0.19/0.50 (leq(n0, F!13)),
% 0.19/0.50 inference(and_elim,[status(thm)],[43])).
% 0.19/0.50 tff(65,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(66,plain,
% 0.19/0.50 (((F!13 = n0) | (~leq(n0, F!13)) | (~leq(F!13, n0))) <=> ((~leq(n0, F!13)) | (F!13 = n0) | (~leq(F!13, n0)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(67,plain,
% 0.19/0.50 (((~![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))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.50 tff(68,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.50 tff(69,plain,
% 0.19/0.50 ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((F!13 = n0) | (~leq(n0, F!13)) | (~leq(F!13, n0)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(70,plain,
% 0.19/0.50 ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | (~leq(n0, F!13)) | (F!13 = n0) | (~leq(F!13, n0))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.50 tff(71,plain,
% 0.19/0.50 ((F!13 = n0) | (~leq(F!13, n0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[70, 27, 64])).
% 0.19/0.50 tff(72,plain,
% 0.19/0.50 (F!13 = n0),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[71, 63])).
% 0.19/0.50 tff(73,plain,
% 0.19/0.50 (pv5 = F!13),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[72, 34])).
% 0.19/0.50 tff(74,plain,
% 0.19/0.50 ((~(~((~(n0 = E!14)) | (~(pv5 = F!13))))) <=> ((~(n0 = E!14)) | (~(pv5 = F!13)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(75,plain,
% 0.19/0.50 (((n0 = E!14) & (pv5 = F!13)) <=> (~((~(n0 = E!14)) | (~(pv5 = F!13))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(76,plain,
% 0.19/0.50 ((~((n0 = E!14) & (pv5 = F!13))) <=> (~(~((~(n0 = E!14)) | (~(pv5 = F!13)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.50 tff(77,plain,
% 0.19/0.50 ((~((n0 = E!14) & (pv5 = F!13))) <=> ((~(n0 = E!14)) | (~(pv5 = F!13)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[76, 74])).
% 0.19/0.50 tff(78,plain,
% 0.19/0.50 ((~((n0 = E!14) & (pv5 = F!13))) & (~((n1 = E!14) & (pv5 = F!13))) & (~((n2 = E!14) & (pv5 = F!13)))),
% 0.19/0.50 inference(or_elim,[status(thm)],[42])).
% 0.19/0.50 tff(79,plain,
% 0.19/0.50 (~((n0 = E!14) & (pv5 = F!13))),
% 0.19/0.50 inference(and_elim,[status(thm)],[78])).
% 0.19/0.50 tff(80,plain,
% 0.19/0.50 ((~(n0 = E!14)) | (~(pv5 = F!13))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[79, 77])).
% 0.19/0.50 tff(81,plain,
% 0.19/0.50 (~(n0 = E!14)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[80, 73])).
% 0.19/0.50 tff(82,plain,
% 0.19/0.50 (~(E!14 = n0)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[81, 3])).
% 0.19/0.50 tff(83,plain,
% 0.19/0.50 ((E!14 = n1) <=> (n1 = E!14)),
% 0.19/0.50 inference(commutativity,[status(thm)],[])).
% 0.19/0.50 tff(84,plain,
% 0.19/0.50 ((n1 = E!14) <=> (E!14 = n1)),
% 0.19/0.50 inference(symmetry,[status(thm)],[83])).
% 0.19/0.50 tff(85,plain,
% 0.19/0.50 ((~(n1 = E!14)) <=> (~(E!14 = n1))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[84])).
% 0.19/0.50 tff(86,plain,
% 0.19/0.50 ((~(~((~(n1 = E!14)) | (~(pv5 = F!13))))) <=> ((~(n1 = E!14)) | (~(pv5 = F!13)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(87,plain,
% 0.19/0.50 (((n1 = E!14) & (pv5 = F!13)) <=> (~((~(n1 = E!14)) | (~(pv5 = F!13))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(88,plain,
% 0.19/0.50 ((~((n1 = E!14) & (pv5 = F!13))) <=> (~(~((~(n1 = E!14)) | (~(pv5 = F!13)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[87])).
% 0.19/0.50 tff(89,plain,
% 0.19/0.50 ((~((n1 = E!14) & (pv5 = F!13))) <=> ((~(n1 = E!14)) | (~(pv5 = F!13)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[88, 86])).
% 0.19/0.50 tff(90,plain,
% 0.19/0.50 (~((n1 = E!14) & (pv5 = F!13))),
% 0.19/0.50 inference(and_elim,[status(thm)],[78])).
% 0.19/0.50 tff(91,plain,
% 0.19/0.50 ((~(n1 = E!14)) | (~(pv5 = F!13))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.50 tff(92,plain,
% 0.19/0.50 (~(n1 = E!14)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[91, 73])).
% 0.19/0.50 tff(93,plain,
% 0.19/0.50 (~(E!14 = n1)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.19/0.50 tff(94,plain,
% 0.19/0.50 ((E!14 = n2) <=> (n2 = E!14)),
% 0.19/0.50 inference(commutativity,[status(thm)],[])).
% 0.19/0.50 tff(95,plain,
% 0.19/0.50 ((n2 = E!14) <=> (E!14 = n2)),
% 0.19/0.50 inference(symmetry,[status(thm)],[94])).
% 0.19/0.50 tff(96,plain,
% 0.19/0.50 ((~(n2 = E!14)) <=> (~(E!14 = n2))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.50 tff(97,plain,
% 0.19/0.50 ((~(~((~(n2 = E!14)) | (~(pv5 = F!13))))) <=> ((~(n2 = E!14)) | (~(pv5 = F!13)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(98,plain,
% 0.19/0.50 (((n2 = E!14) & (pv5 = F!13)) <=> (~((~(n2 = E!14)) | (~(pv5 = F!13))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(99,plain,
% 0.19/0.50 ((~((n2 = E!14) & (pv5 = F!13))) <=> (~(~((~(n2 = E!14)) | (~(pv5 = F!13)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[98])).
% 0.19/0.50 tff(100,plain,
% 0.19/0.50 ((~((n2 = E!14) & (pv5 = F!13))) <=> ((~(n2 = E!14)) | (~(pv5 = F!13)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[99, 97])).
% 0.19/0.50 tff(101,plain,
% 0.19/0.50 (~((n2 = E!14) & (pv5 = F!13))),
% 0.19/0.50 inference(and_elim,[status(thm)],[78])).
% 0.19/0.50 tff(102,plain,
% 0.19/0.50 ((~(n2 = E!14)) | (~(pv5 = F!13))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.50 tff(103,plain,
% 0.19/0.50 (~(n2 = E!14)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[102, 73])).
% 0.19/0.50 tff(104,plain,
% 0.19/0.50 (~(E!14 = n2)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.19/0.50 tff(105,plain,
% 0.19/0.50 (leq(E!14, n2)),
% 0.19/0.50 inference(and_elim,[status(thm)],[43])).
% 0.19/0.50 tff(106,plain,
% 0.19/0.50 (leq(n0, E!14)),
% 0.19/0.50 inference(and_elim,[status(thm)],[43])).
% 0.19/0.50 tff(107,plain,
% 0.19/0.50 (^[X: $i] : refl(((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2))) <=> ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(108,plain,
% 0.19/0.50 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2))) <=> ![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.50 tff(109,plain,
% 0.19/0.50 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, X) & leq(X, n2)) <=> (~((~leq(n0, X)) | (~leq(X, n2))))), ((~(leq(n0, X) & leq(X, n2))) <=> (~(~((~leq(n0, X)) | (~leq(X, n2))))))), rewrite((~(~((~leq(n0, X)) | (~leq(X, n2))))) <=> ((~leq(n0, X)) | (~leq(X, n2)))), ((~(leq(n0, X) & leq(X, n2))) <=> ((~leq(n0, X)) | (~leq(X, n2))))), (((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2)))) <=> ((X = n2) | (X = n1) | (X = n0) | ((~leq(n0, X)) | (~leq(X, n2)))))), rewrite(((X = n2) | (X = n1) | (X = n0) | ((~leq(n0, X)) | (~leq(X, n2)))) <=> ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))), (((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2)))) <=> ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(110,plain,
% 0.19/0.50 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2)))) <=> ![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.50 tff(111,plain,
% 0.19/0.50 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2)))) <=> ![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(112,plain,
% 0.19/0.50 (^[X: $i] : trans(monotonicity(rewrite((((X = n0) | (X = n1)) | (X = n2)) <=> ((X = n2) | (X = n1) | (X = n0))), (((leq(n0, X) & leq(X, n2)) => (((X = n0) | (X = n1)) | (X = n2))) <=> ((leq(n0, X) & leq(X, n2)) => ((X = n2) | (X = n1) | (X = n0))))), rewrite(((leq(n0, X) & leq(X, n2)) => ((X = n2) | (X = n1) | (X = n0))) <=> ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))), (((leq(n0, X) & leq(X, n2)) => (((X = n0) | (X = n1)) | (X = n2))) <=> ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(113,plain,
% 0.19/0.50 (![X: $i] : ((leq(n0, X) & leq(X, n2)) => (((X = n0) | (X = n1)) | (X = n2))) <=> ![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.50 tff(114,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n2)) => (((X = n0) | (X = n1)) | (X = n2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','finite_domain_2')).
% 0.19/0.50 tff(115,plain,
% 0.19/0.50 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.50 tff(116,plain,
% 0.19/0.50 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.19/0.50 tff(117,plain,(
% 0.19/0.50 ![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[116])).
% 0.19/0.50 tff(118,plain,
% 0.19/0.50 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.19/0.50 tff(119,plain,
% 0.19/0.50 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[118, 108])).
% 0.19/0.50 tff(120,plain,
% 0.19/0.50 (((~![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))) | ((~leq(n0, E!14)) | (E!14 = n2) | (E!14 = n1) | (E!14 = n0) | (~leq(E!14, n2)))) <=> ((~![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))) | (~leq(n0, E!14)) | (E!14 = n2) | (E!14 = n1) | (E!14 = n0) | (~leq(E!14, n2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(121,plain,
% 0.19/0.50 (((E!14 = n2) | (E!14 = n1) | (E!14 = n0) | (~leq(n0, E!14)) | (~leq(E!14, n2))) <=> ((~leq(n0, E!14)) | (E!14 = n2) | (E!14 = n1) | (E!14 = n0) | (~leq(E!14, n2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(122,plain,
% 0.19/0.50 (((~![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))) | ((E!14 = n2) | (E!14 = n1) | (E!14 = n0) | (~leq(n0, E!14)) | (~leq(E!14, n2)))) <=> ((~![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))) | ((~leq(n0, E!14)) | (E!14 = n2) | (E!14 = n1) | (E!14 = n0) | (~leq(E!14, n2))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[121])).
% 0.19/0.50 tff(123,plain,
% 0.19/0.50 (((~![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))) | ((E!14 = n2) | (E!14 = n1) | (E!14 = n0) | (~leq(n0, E!14)) | (~leq(E!14, n2)))) <=> ((~![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))) | (~leq(n0, E!14)) | (E!14 = n2) | (E!14 = n1) | (E!14 = n0) | (~leq(E!14, n2)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[122, 120])).
% 0.19/0.50 tff(124,plain,
% 0.19/0.50 ((~![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))) | ((E!14 = n2) | (E!14 = n1) | (E!14 = n0) | (~leq(n0, E!14)) | (~leq(E!14, n2)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(125,plain,
% 0.19/0.50 ((~![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))) | (~leq(n0, E!14)) | (E!14 = n2) | (E!14 = n1) | (E!14 = n0) | (~leq(E!14, n2))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.50 tff(126,plain,
% 0.19/0.50 ((E!14 = n2) | (E!14 = n1) | (E!14 = n0)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[125, 119, 106, 105])).
% 0.19/0.51 tff(127,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[126, 104, 93, 82])).
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------