%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV192+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 05:31:41 AM UTC 2025
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV192+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:31:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(leq_type, type, (
% 0.20/0.41 leq: ( $i * $i ) > $o)).
% 0.20/0.41 tff(pred_type, type, (
% 0.20/0.41 pred: $i > $i)).
% 0.20/0.41 tff(pv5_type, type, (
% 0.20/0.41 pv5: $i)).
% 0.20/0.41 tff(tptp_fun_F_13_type, type, (
% 0.20/0.41 tptp_fun_F_13: $i)).
% 0.20/0.41 tff(n2_type, type, (
% 0.20/0.41 n2: $i)).
% 0.20/0.41 tff(tptp_fun_E_14_type, type, (
% 0.20/0.41 tptp_fun_E_14: $i)).
% 0.20/0.41 tff(n0_type, type, (
% 0.20/0.41 n0: $i)).
% 0.20/0.41 tff(n1_type, type, (
% 0.20/0.41 n1: $i)).
% 0.20/0.41 tff(use_type, type, (
% 0.20/0.41 use: $i)).
% 0.20/0.41 tff(a_select3_type, type, (
% 0.20/0.41 a_select3: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(u_defuse_type, type, (
% 0.20/0.41 u_defuse: $i)).
% 0.20/0.41 tff(z_defuse_type, type, (
% 0.20/0.41 z_defuse: $i)).
% 0.20/0.41 tff(gt_type, type, (
% 0.20/0.41 gt: ( $i * $i ) > $o)).
% 0.20/0.41 tff(n998_type, type, (
% 0.20/0.41 n998: $i)).
% 0.20/0.41 tff(a_select2_type, type, (
% 0.20/0.41 a_select2: ( $i * $i ) > $i)).
% 0.20/0.41 tff(n5_type, type, (
% 0.20/0.41 n5: $i)).
% 0.20/0.41 tff(xinit_noise_defuse_type, type, (
% 0.20/0.41 xinit_noise_defuse: $i)).
% 0.20/0.41 tff(n4_type, type, (
% 0.20/0.41 n4: $i)).
% 0.20/0.41 tff(n3_type, type, (
% 0.20/0.41 n3: $i)).
% 0.20/0.41 tff(xinit_mean_defuse_type, type, (
% 0.20/0.41 xinit_mean_defuse: $i)).
% 0.20/0.41 tff(xinit_defuse_type, type, (
% 0.20/0.41 xinit_defuse: $i)).
% 0.20/0.41 tff(sigma_defuse_type, type, (
% 0.20/0.41 sigma_defuse: $i)).
% 0.20/0.41 tff(rho_defuse_type, type, (
% 0.20/0.41 rho_defuse: $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 ((~((a_select3(u_defuse, E!14, F!13) = use) | (~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pred(pv5)))) | (~((~((n0 = E!14) & (pv5 = F!13))) & (~((n1 = E!14) & (pv5 = F!13))) & (~((n2 = E!14) & (pv5 = F!13))))))) <=> (~((a_select3(u_defuse, E!14, F!13) = use) | (~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pred(pv5)))) | (~((~((n0 = E!14) & (pv5 = F!13))) & (~((n1 = E!14) & (pv5 = F!13))) & (~((n2 = E!14) & (pv5 = F!13)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 ((~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))))) <=> (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 ((~((((((((((((((((((((((((((((((((((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, pred(pv5))) => ((((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F)))) & (~((n2 = E) & (pv5 = F)))) => (a_select3(u_defuse, E, F) = use))))) <=> (~((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n0) & leq(pv5, n998) & 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(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 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, pred(pv5))) => ((((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F)))) & (~((n2 = E) & (pv5 = F)))) => (a_select3(u_defuse, E, F) = use))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_inuse_0003')).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (~((~((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(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))))),
% 0.20/0.42 inference(or_elim,[status(thm)],[5])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.20/0.42 tff(10,plain,(
% 0.20/0.42 ~((a_select3(u_defuse, E!14, F!13) = use) | (~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pred(pv5)))) | (~((~((n0 = E!14) & (pv5 = F!13))) & (~((n1 = E!14) & (pv5 = F!13))) & (~((n2 = E!14) & (pv5 = F!13))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[9])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (~((a_select3(u_defuse, E!14, F!13) = use) | (~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pred(pv5)))) | (~((~((n0 = E!14) & (pv5 = F!13))) & (~((n1 = E!14) & (pv5 = F!13))) & (~((n2 = E!14) & (pv5 = F!13))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pred(pv5))),
% 0.20/0.42 inference(or_elim,[status(thm)],[11])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (leq(F!13, pred(pv5))),
% 0.20/0.42 inference(and_elim,[status(thm)],[12])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (leq(E!14, n2)),
% 0.20/0.42 inference(and_elim,[status(thm)],[12])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (leq(n0, F!13)),
% 0.20/0.42 inference(and_elim,[status(thm)],[12])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (leq(n0, E!14)),
% 0.20/0.42 inference(and_elim,[status(thm)],[12])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (~(a_select3(u_defuse, E!14, F!13) = use)),
% 0.20/0.42 inference(or_elim,[status(thm)],[11])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (^[A: $i, B: $i] : refl(((a_select3(u_defuse, A, B) = use) | (~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5)))) <=> ((a_select3(u_defuse, A, B) = use) | (~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((a_select3(u_defuse, A, B) = use) | (~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5)))) <=> ![A: $i, B: $i] : ((a_select3(u_defuse, A, B) = use) | (~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5))) <=> (~((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5)))))), ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) <=> (~(~((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5)))))))), rewrite((~(~((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5)))))) <=> ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5))))), ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) <=> ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5)))))), (((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) <=> (((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)))), rewrite((((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) <=> ((a_select3(u_defuse, A, B) = use) | (~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5))))), (((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) <=> ((a_select3(u_defuse, A, B) = use) | (~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) <=> ![A: $i, B: $i] : ((a_select3(u_defuse, A, B) = use) | (~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) <=> ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ((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))),
% 0.20/0.42 inference(or_elim,[status(thm)],[5])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use))),
% 0.20/0.42 inference(and_elim,[status(thm)],[23])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 22])).
% 0.20/0.42 tff(26,plain,(
% 0.20/0.42 ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use))),
% 0.20/0.42 inference(skolemize,[status(sab)],[25])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((a_select3(u_defuse, A, B) = use) | (~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((a_select3(u_defuse, A, B) = use) | (~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (((~![A: $i, B: $i] : ((a_select3(u_defuse, A, B) = use) | (~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5))))) | ((a_select3(u_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, pred(pv5))))) <=> ((~![A: $i, B: $i] : ((a_select3(u_defuse, A, B) = use) | (~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5))))) | (a_select3(u_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, pred(pv5))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : ((a_select3(u_defuse, A, B) = use) | (~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5))))) | ((a_select3(u_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, pred(pv5))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : ((a_select3(u_defuse, A, B) = use) | (~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pred(pv5))))) | (a_select3(u_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, pred(pv5)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[31, 28, 17, 16, 15, 14, 13])).
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------