%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV203+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.87s 1.07s
% Output : Proof 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV203+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.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 09:31:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.87/1.07 % SZS status Theorem
% 0.87/1.07 % SZS output start Proof
% 0.87/1.07 tff(n0_type, type, (
% 0.87/1.07 n0: $i)).
% 0.87/1.07 tff(tptp_fun_E_14_type, type, (
% 0.87/1.07 tptp_fun_E_14: $i)).
% 0.87/1.07 tff(tptp_fun_F_13_type, type, (
% 0.87/1.07 tptp_fun_F_13: $i)).
% 0.87/1.07 tff(pv5_type, type, (
% 0.87/1.07 pv5: $i)).
% 0.87/1.07 tff(gt_type, type, (
% 0.87/1.07 gt: ( $i * $i ) > $o)).
% 0.87/1.07 tff(leq_type, type, (
% 0.87/1.07 leq: ( $i * $i ) > $o)).
% 0.87/1.07 tff(pred_type, type, (
% 0.87/1.07 pred: $i > $i)).
% 0.87/1.07 tff(n2_type, type, (
% 0.87/1.07 n2: $i)).
% 0.87/1.07 tff(n1_type, type, (
% 0.87/1.07 n1: $i)).
% 0.87/1.07 tff(use_type, type, (
% 0.87/1.07 use: $i)).
% 0.87/1.07 tff(a_select3_type, type, (
% 0.87/1.07 a_select3: ( $i * $i * $i ) > $i)).
% 0.87/1.07 tff(z_defuse_type, type, (
% 0.87/1.07 z_defuse: $i)).
% 0.87/1.07 tff(u_defuse_type, type, (
% 0.87/1.07 u_defuse: $i)).
% 0.87/1.07 tff(n998_type, type, (
% 0.87/1.07 n998: $i)).
% 0.87/1.07 tff(a_select2_type, type, (
% 0.87/1.07 a_select2: ( $i * $i ) > $i)).
% 0.87/1.07 tff(n5_type, type, (
% 0.87/1.07 n5: $i)).
% 0.87/1.07 tff(xinit_noise_defuse_type, type, (
% 0.87/1.07 xinit_noise_defuse: $i)).
% 0.87/1.07 tff(n4_type, type, (
% 0.87/1.07 n4: $i)).
% 0.87/1.07 tff(n3_type, type, (
% 0.87/1.07 n3: $i)).
% 0.87/1.07 tff(xinit_mean_defuse_type, type, (
% 0.87/1.07 xinit_mean_defuse: $i)).
% 0.87/1.07 tff(xinit_defuse_type, type, (
% 0.87/1.07 xinit_defuse: $i)).
% 0.87/1.07 tff(sigma_defuse_type, type, (
% 0.87/1.07 sigma_defuse: $i)).
% 0.87/1.07 tff(rho_defuse_type, type, (
% 0.87/1.07 rho_defuse: $i)).
% 0.87/1.07 tff(1,plain,
% 0.87/1.07 ((E!14 = n0) <=> (n0 = E!14)),
% 0.87/1.07 inference(commutativity,[status(thm)],[])).
% 0.87/1.07 tff(2,plain,
% 0.87/1.07 ((n0 = E!14) <=> (E!14 = n0)),
% 0.87/1.07 inference(symmetry,[status(thm)],[1])).
% 0.87/1.07 tff(3,plain,
% 0.87/1.07 ((~(n0 = E!14)) <=> (~(E!14 = n0))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2])).
% 0.87/1.07 tff(4,plain,
% 0.87/1.07 ((F!13 = pv5) <=> (pv5 = F!13)),
% 0.87/1.07 inference(commutativity,[status(thm)],[])).
% 0.87/1.07 tff(5,plain,
% 0.87/1.07 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(6,plain,
% 0.87/1.07 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[5])).
% 0.87/1.07 tff(7,plain,
% 0.87/1.07 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(8,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 0.87/1.07 tff(9,plain,
% 0.87/1.07 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.87/1.07 tff(10,plain,(
% 0.87/1.07 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.87/1.07 inference(skolemize,[status(sab)],[9])).
% 0.87/1.07 tff(11,plain,
% 0.87/1.07 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.87/1.07 tff(12,plain,
% 0.87/1.07 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(F!13, pred(pv5)) <=> gt(pv5, F!13))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(13,plain,
% 0.87/1.07 (leq(F!13, pred(pv5)) <=> gt(pv5, F!13)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.87/1.07 tff(14,plain,
% 0.87/1.07 ((~((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)))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(15,plain,
% 0.87/1.07 ((~![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)))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(16,plain,
% 0.87/1.07 ((~(((((((((((((((((((((((((((((((((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, 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, 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))))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(17,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, 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/sandbox/benchmark/theBenchmark.p','quaternion_ds1_inuse_0014')).
% 0.87/1.08 tff(18,plain,
% 0.87/1.08 (~((~((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, 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)))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.87/1.08 tff(19,plain,
% 0.87/1.08 (~![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))))),
% 0.87/1.08 inference(or_elim,[status(thm)],[18])).
% 0.87/1.08 tff(20,plain,
% 0.87/1.08 (~![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))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.87/1.08 tff(21,plain,
% 0.87/1.08 (~![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))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.87/1.08 tff(22,plain,
% 0.87/1.08 (~![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))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.87/1.08 tff(23,plain,(
% 0.87/1.08 ~((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))))),
% 0.87/1.08 inference(skolemize,[status(sab)],[22])).
% 0.87/1.08 tff(24,plain,
% 0.87/1.08 (~((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))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[23, 14])).
% 0.87/1.08 tff(25,plain,
% 0.87/1.08 (leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5)),
% 0.87/1.08 inference(or_elim,[status(thm)],[24])).
% 0.87/1.08 tff(26,plain,
% 0.87/1.08 (leq(E!14, n2)),
% 0.87/1.08 inference(and_elim,[status(thm)],[25])).
% 0.87/1.08 tff(27,plain,
% 0.87/1.08 (leq(n0, F!13)),
% 0.87/1.08 inference(and_elim,[status(thm)],[25])).
% 0.87/1.08 tff(28,plain,
% 0.87/1.08 (leq(n0, E!14)),
% 0.87/1.08 inference(and_elim,[status(thm)],[25])).
% 0.87/1.08 tff(29,plain,
% 0.87/1.08 (~(a_select3(z_defuse, E!14, F!13) = use)),
% 0.87/1.08 inference(or_elim,[status(thm)],[24])).
% 0.87/1.08 tff(30,plain,
% 0.87/1.08 (^[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)))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(31,plain,
% 0.87/1.08 (![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))))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[30])).
% 0.87/1.08 tff(32,plain,
% 0.87/1.08 (^[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))))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(33,plain,
% 0.87/1.08 (![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))))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[32])).
% 0.87/1.08 tff(34,plain,
% 0.87/1.08 (![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))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(35,plain,
% 0.87/1.08 ((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, 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))),
% 0.87/1.08 inference(or_elim,[status(thm)],[18])).
% 0.87/1.08 tff(36,plain,
% 0.87/1.08 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 0.87/1.08 inference(and_elim,[status(thm)],[35])).
% 0.87/1.08 tff(37,plain,
% 0.87/1.08 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.87/1.08 tff(38,plain,(
% 0.87/1.08 ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 0.87/1.08 inference(skolemize,[status(sab)],[37])).
% 0.87/1.08 tff(39,plain,
% 0.87/1.08 (![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.87/1.08 tff(40,plain,
% 0.87/1.08 (![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, pred(pv5))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[39, 31])).
% 0.87/1.08 tff(41,plain,
% 0.87/1.08 (((~![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(E!14, n2)) | (~leq(n0, F!13)) | (~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(E!14, n2)) | (~leq(n0, F!13)) | (~leq(F!13, pred(pv5))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(42,plain,
% 0.87/1.08 (((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)))) <=> ((a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(E!14, n2)) | (~leq(n0, F!13)) | (~leq(F!13, pred(pv5))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(43,plain,
% 0.87/1.08 (((~![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(E!14, n2)) | (~leq(n0, F!13)) | (~leq(F!13, pred(pv5)))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[42])).
% 0.87/1.08 tff(44,plain,
% 0.87/1.08 (((~![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(E!14, n2)) | (~leq(n0, F!13)) | (~leq(F!13, pred(pv5))))),
% 0.87/1.08 inference(transitivity,[status(thm)],[43, 41])).
% 0.87/1.08 tff(45,plain,
% 0.87/1.08 ((~![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))))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(46,plain,
% 0.87/1.08 ((~![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(E!14, n2)) | (~leq(n0, F!13)) | (~leq(F!13, pred(pv5)))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.87/1.08 tff(47,plain,
% 0.87/1.08 (~leq(F!13, pred(pv5))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[46, 40, 29, 28, 27, 26])).
% 0.87/1.08 tff(48,plain,
% 0.87/1.08 ((~(leq(F!13, pred(pv5)) <=> gt(pv5, F!13))) | leq(F!13, pred(pv5)) | (~gt(pv5, F!13))),
% 0.87/1.08 inference(tautology,[status(thm)],[])).
% 0.87/1.08 tff(49,plain,
% 0.87/1.08 ((~(leq(F!13, pred(pv5)) <=> gt(pv5, F!13))) | (~gt(pv5, F!13))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.87/1.08 tff(50,plain,
% 0.87/1.08 (~gt(pv5, F!13)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[49, 13])).
% 0.87/1.08 tff(51,plain,
% 0.87/1.08 (leq(F!13, pv5)),
% 0.87/1.08 inference(and_elim,[status(thm)],[25])).
% 0.87/1.08 tff(52,plain,
% 0.87/1.08 (^[X: $i, Y: $i] : refl(((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(53,plain,
% 0.87/1.08 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[52])).
% 0.87/1.08 tff(54,plain,
% 0.87/1.08 (^[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)))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(55,plain,
% 0.87/1.08 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[54])).
% 0.87/1.08 tff(56,plain,
% 0.87/1.08 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(57,plain,
% 0.87/1.08 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(58,plain,
% 0.87/1.08 (![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[57])).
% 0.87/1.08 tff(59,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt2')).
% 0.87/1.08 tff(60,plain,
% 0.87/1.08 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.87/1.08 tff(61,plain,
% 0.87/1.08 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.87/1.08 tff(62,plain,(
% 0.87/1.08 ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.87/1.08 inference(skolemize,[status(sab)],[61])).
% 0.87/1.08 tff(63,plain,
% 0.87/1.08 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.87/1.08 tff(64,plain,
% 0.87/1.08 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.87/1.08 tff(65,plain,
% 0.87/1.08 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((F!13 = pv5) | gt(pv5, F!13) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (F!13 = pv5) | gt(pv5, F!13) | (~leq(F!13, pv5)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(66,plain,
% 0.87/1.08 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((F!13 = pv5) | gt(pv5, F!13) | (~leq(F!13, pv5)))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(67,plain,
% 0.87/1.08 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (F!13 = pv5) | gt(pv5, F!13) | (~leq(F!13, pv5))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.87/1.08 tff(68,plain,
% 0.87/1.08 ((F!13 = pv5) | gt(pv5, F!13)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[67, 64, 51])).
% 0.87/1.08 tff(69,plain,
% 0.87/1.08 (F!13 = pv5),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[68, 50])).
% 0.87/1.08 tff(70,plain,
% 0.87/1.08 (pv5 = F!13),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[69, 4])).
% 0.87/1.08 tff(71,plain,
% 0.87/1.08 ((~(~((~(n0 = E!14)) | (~(pv5 = F!13))))) <=> ((~(n0 = E!14)) | (~(pv5 = F!13)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(72,plain,
% 0.87/1.08 (((n0 = E!14) & (pv5 = F!13)) <=> (~((~(n0 = E!14)) | (~(pv5 = F!13))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(73,plain,
% 0.87/1.08 ((~((n0 = E!14) & (pv5 = F!13))) <=> (~(~((~(n0 = E!14)) | (~(pv5 = F!13)))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[72])).
% 0.87/1.08 tff(74,plain,
% 0.87/1.08 ((~((n0 = E!14) & (pv5 = F!13))) <=> ((~(n0 = E!14)) | (~(pv5 = F!13)))),
% 0.87/1.08 inference(transitivity,[status(thm)],[73, 71])).
% 0.87/1.08 tff(75,plain,
% 0.87/1.08 ((~((n0 = E!14) & (pv5 = F!13))) & (~((n1 = E!14) & (pv5 = F!13))) & (~((n2 = E!14) & (pv5 = F!13)))),
% 0.87/1.08 inference(or_elim,[status(thm)],[24])).
% 0.87/1.08 tff(76,plain,
% 0.87/1.08 (~((n0 = E!14) & (pv5 = F!13))),
% 0.87/1.08 inference(and_elim,[status(thm)],[75])).
% 0.87/1.08 tff(77,plain,
% 0.87/1.08 ((~(n0 = E!14)) | (~(pv5 = F!13))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[76, 74])).
% 0.87/1.08 tff(78,plain,
% 0.87/1.08 (~(n0 = E!14)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[77, 70])).
% 0.87/1.08 tff(79,plain,
% 0.87/1.08 (~(E!14 = n0)),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[78, 3])).
% 0.87/1.08 tff(80,plain,
% 0.87/1.08 ((E!14 = n1) <=> (n1 = E!14)),
% 0.87/1.08 inference(commutativity,[status(thm)],[])).
% 0.87/1.08 tff(81,plain,
% 0.87/1.08 ((n1 = E!14) <=> (E!14 = n1)),
% 0.87/1.08 inference(symmetry,[status(thm)],[80])).
% 0.87/1.08 tff(82,plain,
% 0.87/1.08 ((~(n1 = E!14)) <=> (~(E!14 = n1))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[81])).
% 0.87/1.08 tff(83,plain,
% 0.87/1.08 ((~(~((~(n1 = E!14)) | (~(pv5 = F!13))))) <=> ((~(n1 = E!14)) | (~(pv5 = F!13)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(84,plain,
% 0.87/1.08 (((n1 = E!14) & (pv5 = F!13)) <=> (~((~(n1 = E!14)) | (~(pv5 = F!13))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(85,plain,
% 0.87/1.08 ((~((n1 = E!14) & (pv5 = F!13))) <=> (~(~((~(n1 = E!14)) | (~(pv5 = F!13)))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[84])).
% 0.87/1.08 tff(86,plain,
% 0.87/1.08 ((~((n1 = E!14) & (pv5 = F!13))) <=> ((~(n1 = E!14)) | (~(pv5 = F!13)))),
% 0.87/1.08 inference(transitivity,[status(thm)],[85, 83])).
% 0.87/1.08 tff(87,plain,
% 0.87/1.08 (~((n1 = E!14) & (pv5 = F!13))),
% 0.87/1.08 inference(and_elim,[status(thm)],[75])).
% 0.87/1.08 tff(88,plain,
% 0.87/1.08 ((~(n1 = E!14)) | (~(pv5 = F!13))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.87/1.08 tff(89,plain,
% 0.87/1.08 (~(n1 = E!14)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[88, 70])).
% 0.87/1.08 tff(90,plain,
% 0.87/1.08 (~(E!14 = n1)),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.87/1.08 tff(91,plain,
% 0.87/1.08 ((E!14 = n2) <=> (n2 = E!14)),
% 0.87/1.08 inference(commutativity,[status(thm)],[])).
% 0.87/1.08 tff(92,plain,
% 0.87/1.08 ((n2 = E!14) <=> (E!14 = n2)),
% 0.87/1.08 inference(symmetry,[status(thm)],[91])).
% 0.87/1.08 tff(93,plain,
% 0.87/1.08 ((~(n2 = E!14)) <=> (~(E!14 = n2))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[92])).
% 0.87/1.08 tff(94,plain,
% 0.87/1.08 ((~(~((~(n2 = E!14)) | (~(pv5 = F!13))))) <=> ((~(n2 = E!14)) | (~(pv5 = F!13)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(95,plain,
% 0.87/1.08 (((n2 = E!14) & (pv5 = F!13)) <=> (~((~(n2 = E!14)) | (~(pv5 = F!13))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(96,plain,
% 0.87/1.08 ((~((n2 = E!14) & (pv5 = F!13))) <=> (~(~((~(n2 = E!14)) | (~(pv5 = F!13)))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[95])).
% 0.87/1.08 tff(97,plain,
% 0.87/1.08 ((~((n2 = E!14) & (pv5 = F!13))) <=> ((~(n2 = E!14)) | (~(pv5 = F!13)))),
% 0.87/1.08 inference(transitivity,[status(thm)],[96, 94])).
% 0.87/1.08 tff(98,plain,
% 0.87/1.08 (~((n2 = E!14) & (pv5 = F!13))),
% 0.87/1.08 inference(and_elim,[status(thm)],[75])).
% 0.87/1.08 tff(99,plain,
% 0.87/1.08 ((~(n2 = E!14)) | (~(pv5 = F!13))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.87/1.08 tff(100,plain,
% 0.87/1.08 (~(n2 = E!14)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[99, 70])).
% 0.87/1.08 tff(101,plain,
% 0.87/1.08 (~(E!14 = n2)),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.87/1.08 tff(102,plain,
% 0.87/1.08 (^[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))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(103,plain,
% 0.87/1.08 (![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)))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[102])).
% 0.87/1.08 tff(104,plain,
% 0.87/1.08 (^[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)))))),
% 0.87/1.09 inference(bind,[status(th)],[])).
% 0.87/1.09 tff(105,plain,
% 0.87/1.09 (![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)))),
% 0.87/1.09 inference(quant_intro,[status(thm)],[104])).
% 0.87/1.09 tff(106,plain,
% 0.87/1.09 (![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))))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(107,plain,
% 0.87/1.09 (^[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))))))),
% 0.87/1.09 inference(bind,[status(th)],[])).
% 0.87/1.09 tff(108,plain,
% 0.87/1.09 (![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))))),
% 0.87/1.09 inference(quant_intro,[status(thm)],[107])).
% 0.87/1.09 tff(109,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n2)) => (((X = n0) | (X = n1)) | (X = n2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','finite_domain_2')).
% 0.87/1.09 tff(110,plain,
% 0.87/1.09 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.87/1.09 tff(111,plain,
% 0.87/1.09 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.87/1.09 tff(112,plain,(
% 0.87/1.09 ![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.87/1.09 inference(skolemize,[status(sab)],[111])).
% 0.87/1.09 tff(113,plain,
% 0.87/1.09 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.87/1.09 tff(114,plain,
% 0.87/1.09 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.87/1.09 tff(115,plain,
% 0.87/1.09 (((~![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)))) | (E!14 = n2) | (E!14 = n1) | (E!14 = n0) | (~leq(n0, E!14)) | (~leq(E!14, n2)))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(116,plain,
% 0.87/1.09 ((~![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)))),
% 0.87/1.09 inference(quant_inst,[status(thm)],[])).
% 0.87/1.09 tff(117,plain,
% 0.87/1.09 ((~![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~leq(n0, X)) | (~leq(X, n2)))) | (E!14 = n2) | (E!14 = n1) | (E!14 = n0) | (~leq(n0, E!14)) | (~leq(E!14, n2))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.87/1.09 tff(118,plain,
% 0.87/1.09 ((E!14 = n2) | (E!14 = n1) | (E!14 = n0)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[117, 114, 28, 26])).
% 0.87/1.09 tff(119,plain,
% 0.87/1.09 ($false),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[118, 101, 90, 79])).
% 0.87/1.09 % SZS output end Proof
% 0.92/1.10 % E exiting
%------------------------------------------------------------------------------