%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV196+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:31:41 AM UTC 2025
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV196+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:31:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(leq_type, type, (
% 0.21/0.41 leq: ( $i * $i ) > $o)).
% 0.21/0.41 tff(pred_type, type, (
% 0.21/0.41 pred: $i > $i)).
% 0.21/0.41 tff(pv5_type, type, (
% 0.21/0.41 pv5: $i)).
% 0.21/0.41 tff(tptp_fun_F_13_type, type, (
% 0.21/0.41 tptp_fun_F_13: $i)).
% 0.21/0.41 tff(n0_type, type, (
% 0.21/0.41 n0: $i)).
% 0.21/0.41 tff(n2_type, type, (
% 0.21/0.41 n2: $i)).
% 0.21/0.41 tff(tptp_fun_E_14_type, type, (
% 0.21/0.41 tptp_fun_E_14: $i)).
% 0.21/0.41 tff(n1_type, type, (
% 0.21/0.41 n1: $i)).
% 0.21/0.41 tff(use_type, type, (
% 0.21/0.41 use: $i)).
% 0.21/0.41 tff(a_select3_type, type, (
% 0.21/0.41 a_select3: ( $i * $i * $i ) > $i)).
% 0.21/0.41 tff(z_defuse_type, type, (
% 0.21/0.41 z_defuse: $i)).
% 0.21/0.41 tff(u_defuse_type, type, (
% 0.21/0.41 u_defuse: $i)).
% 0.21/0.41 tff(gt_type, type, (
% 0.21/0.41 gt: ( $i * $i ) > $o)).
% 0.21/0.41 tff(n998_type, type, (
% 0.21/0.41 n998: $i)).
% 0.21/0.41 tff(a_select2_type, type, (
% 0.21/0.41 a_select2: ( $i * $i ) > $i)).
% 0.21/0.41 tff(n5_type, type, (
% 0.21/0.41 n5: $i)).
% 0.21/0.41 tff(xinit_noise_defuse_type, type, (
% 0.21/0.41 xinit_noise_defuse: $i)).
% 0.21/0.41 tff(n4_type, type, (
% 0.21/0.41 n4: $i)).
% 0.21/0.41 tff(n3_type, type, (
% 0.21/0.41 n3: $i)).
% 0.21/0.41 tff(xinit_mean_defuse_type, type, (
% 0.21/0.41 xinit_mean_defuse: $i)).
% 0.21/0.41 tff(xinit_defuse_type, type, (
% 0.21/0.41 xinit_defuse: $i)).
% 0.21/0.41 tff(sigma_defuse_type, type, (
% 0.21/0.42 sigma_defuse: $i)).
% 0.21/0.42 tff(rho_defuse_type, type, (
% 0.21/0.42 rho_defuse: $i)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 ((~((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)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 ((~![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)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 ((~((((((((((((((((((((((((((((((((((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)) & gt(pv5, n0)) & ![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) & gt(pv5, n0) & ![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))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(4,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)) & gt(pv5, n0)) & ![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_0007')).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (~((~((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) & gt(pv5, n0) & ![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)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 (~![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))))),
% 0.21/0.43 inference(or_elim,[status(thm)],[5])).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 (~![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))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 (~![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))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.21/0.43 tff(9,plain,
% 0.21/0.43 (~![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))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.21/0.43 tff(10,plain,(
% 0.21/0.43 ~((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))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[9])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (~((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))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 (leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5)),
% 0.21/0.43 inference(or_elim,[status(thm)],[11])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 (leq(F!13, pv5)),
% 0.21/0.43 inference(and_elim,[status(thm)],[12])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (leq(pv5, n0) <=> leq(pv5, n0)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 ((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) & gt(pv5, n0) & ![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))),
% 0.21/0.43 inference(or_elim,[status(thm)],[5])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (leq(pv5, n0)),
% 0.21/0.43 inference(and_elim,[status(thm)],[15])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (leq(pv5, n0)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[16, 14])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (![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))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (^[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)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (![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))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.43 tff(24,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')).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.43 tff(27,plain,(
% 0.21/0.43 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.21/0.43 inference(skolemize,[status(sab)],[26])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (((~![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 ((leq(F!13, n0) | (~leq(pv5, n0)) | (~leq(F!13, pv5))) <=> ((~leq(pv5, n0)) | leq(F!13, n0) | (~leq(F!13, pv5)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 (((~![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))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[31])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (((~![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)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[32, 30])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 ((~![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)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 ((~![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))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (leq(F!13, n0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[35, 29, 17, 13])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 (leq(n0, F!13)),
% 0.21/0.43 inference(and_elim,[status(thm)],[12])).
% 0.21/0.43 tff(38,plain,
% 0.21/0.43 (^[X: $i] : refl(((X = n0) | (~leq(n0, X)) | (~leq(X, n0))) <=> ((X = n0) | (~leq(n0, X)) | (~leq(X, n0))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0))) <=> ![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (^[X: $i] : rewrite(((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ((~(leq(n0, X) & leq(X, n0))) | (X = n0)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.43 tff(45,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','finite_domain_0')).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.21/0.43 tff(48,plain,(
% 0.21/0.43 ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.21/0.43 inference(skolemize,[status(sab)],[47])).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.21/0.43 tff(50,plain,
% 0.21/0.43 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (((~![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (((F!13 = n0) | (~leq(n0, F!13)) | (~leq(F!13, n0))) <=> ((~leq(n0, F!13)) | (F!13 = n0) | (~leq(F!13, n0)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (((~![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))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[52])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (((~![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)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[53, 51])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((F!13 = n0) | (~leq(n0, F!13)) | (~leq(F!13, n0)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.44 ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | (~leq(n0, F!13)) | (F!13 = n0) | (~leq(F!13, n0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 ((F!13 = n0) | (~leq(F!13, n0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[56, 50, 37])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (F!13 = n0),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[57, 36])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 (leq(F!13, pred(pv5)) <=> leq(n0, pred(pv5))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 (leq(n0, pred(pv5)) <=> leq(F!13, pred(pv5))),
% 0.21/0.44 inference(symmetry,[status(thm)],[59])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(64,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.44 tff(66,plain,(
% 0.21/0.44 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(skolemize,[status(sab)],[65])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(n0, pred(pv5)) <=> gt(pv5, n0))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (leq(n0, pred(pv5)) <=> gt(pv5, n0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 (gt(pv5, n0) <=> gt(pv5, n0)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 (gt(pv5, n0)),
% 0.21/0.44 inference(and_elim,[status(thm)],[15])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 (gt(pv5, n0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.44 tff(73,plain,
% 0.21/0.44 ((~(leq(n0, pred(pv5)) <=> gt(pv5, n0))) | leq(n0, pred(pv5)) | (~gt(pv5, n0))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(74,plain,
% 0.21/0.44 ((~(leq(n0, pred(pv5)) <=> gt(pv5, n0))) | leq(n0, pred(pv5))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 (leq(n0, pred(pv5))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[74, 69])).
% 0.21/0.44 tff(76,plain,
% 0.21/0.44 (leq(F!13, pred(pv5))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[75, 60])).
% 0.21/0.44 tff(77,plain,
% 0.21/0.44 (leq(E!14, n2)),
% 0.21/0.44 inference(and_elim,[status(thm)],[12])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 (leq(n0, E!14)),
% 0.21/0.44 inference(and_elim,[status(thm)],[12])).
% 0.21/0.44 tff(79,plain,
% 0.21/0.44 (~(a_select3(z_defuse, E!14, F!13) = use)),
% 0.21/0.44 inference(or_elim,[status(thm)],[11])).
% 0.21/0.44 tff(80,plain,
% 0.21/0.44 (^[C: $i, D: $i] : refl(((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5)))) <=> ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(81,plain,
% 0.21/0.44 (![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5)))) <=> ![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.44 tff(82,plain,
% 0.21/0.44 (^[C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5))) <=> (~((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5)))))), ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) <=> (~(~((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5)))))))), rewrite((~(~((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5)))))) <=> ((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5))))), ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) <=> ((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5)))))), (((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)) <=> (((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)))), rewrite((((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)) <=> ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5))))), (((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)) <=> ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)) <=> ![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[82])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = 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))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 0.21/0.45 inference(and_elim,[status(thm)],[15])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.45 tff(87,plain,(
% 0.21/0.45 ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 0.21/0.45 inference(skolemize,[status(sab)],[86])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 (![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 (((~![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5))))) | ((a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, pred(pv5))))) <=> ((~![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5))))) | (a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, pred(pv5))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 ((~![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5))))) | ((a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, pred(pv5))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 ((~![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5))))) | (a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, pred(pv5)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 (~leq(F!13, pred(pv5))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[92, 89, 79, 78, 37, 77])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[93, 76])).
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------