%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV210+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:31:43 AM UTC 2025
% Result : Theorem 0.23s 0.43s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SWV210+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 09:33:16 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.23/0.43 % SZS status Theorem
% 0.23/0.43 % SZS output start Proof
% 0.23/0.43 tff(use_type, type, (
% 0.23/0.43 use: $i)).
% 0.23/0.43 tff(a_select3_type, type, (
% 0.23/0.43 a_select3: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_F_13_type, type, (
% 0.23/0.43 tptp_fun_F_13: $i)).
% 0.23/0.43 tff(tptp_fun_E_14_type, type, (
% 0.23/0.43 tptp_fun_E_14: $i)).
% 0.23/0.43 tff(z_defuse_type, type, (
% 0.23/0.43 z_defuse: $i)).
% 0.23/0.43 tff(leq_type, type, (
% 0.23/0.43 leq: ( $i * $i ) > $o)).
% 0.23/0.43 tff(n998_type, type, (
% 0.23/0.43 n998: $i)).
% 0.23/0.43 tff(n2_type, type, (
% 0.23/0.43 n2: $i)).
% 0.23/0.43 tff(n0_type, type, (
% 0.23/0.43 n0: $i)).
% 0.23/0.43 tff(u_defuse_type, type, (
% 0.23/0.43 u_defuse: $i)).
% 0.23/0.43 tff(a_select2_type, type, (
% 0.23/0.43 a_select2: ( $i * $i ) > $i)).
% 0.23/0.43 tff(n5_type, type, (
% 0.23/0.43 n5: $i)).
% 0.23/0.43 tff(xinit_noise_defuse_type, type, (
% 0.23/0.43 xinit_noise_defuse: $i)).
% 0.23/0.43 tff(n4_type, type, (
% 0.23/0.43 n4: $i)).
% 0.23/0.43 tff(n3_type, type, (
% 0.23/0.43 n3: $i)).
% 0.23/0.43 tff(n1_type, type, (
% 0.23/0.43 n1: $i)).
% 0.23/0.43 tff(xinit_mean_defuse_type, type, (
% 0.23/0.43 xinit_mean_defuse: $i)).
% 0.23/0.43 tff(xinit_defuse_type, type, (
% 0.23/0.43 xinit_defuse: $i)).
% 0.23/0.43 tff(sigma_defuse_type, type, (
% 0.23/0.43 sigma_defuse: $i)).
% 0.23/0.43 tff(rho_defuse_type, type, (
% 0.23/0.43 rho_defuse: $i)).
% 0.23/0.43 tff(1,plain,
% 0.23/0.43 ((~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, n998))) | (a_select3(z_defuse, E, F) = use))) <=> (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, n998))) | (a_select3(z_defuse, E, F) = use)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(2,plain,
% 0.23/0.43 ((~((((((((((((((((((((((((((((((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)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, n998)) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, n998)) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, n998)) => (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) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, n998))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998))) | (a_select3(z_defuse, C, D) = use)))) | ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, n998))) | (a_select3(z_defuse, E, F) = use))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(3,axiom,(~((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, n998)) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, n998)) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, n998)) => (a_select3(z_defuse, E, F) = use)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_inuse_0021')).
% 0.23/0.44 tff(4,plain,
% 0.23/0.44 (~((~((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) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, n998))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998))) | (a_select3(z_defuse, C, D) = use)))) | ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, n998))) | (a_select3(z_defuse, E, F) = use)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.23/0.44 tff(5,plain,
% 0.23/0.44 (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, n998))) | (a_select3(z_defuse, E, F) = use))),
% 0.23/0.44 inference(or_elim,[status(thm)],[4])).
% 0.23/0.44 tff(6,plain,
% 0.23/0.44 (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, n998))) | (a_select3(z_defuse, E, F) = use))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.23/0.44 tff(7,plain,
% 0.23/0.44 (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, n998))) | (a_select3(z_defuse, E, F) = use))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.23/0.44 tff(8,plain,
% 0.23/0.44 (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, n998))) | (a_select3(z_defuse, E, F) = use))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.23/0.44 tff(9,plain,(
% 0.23/0.44 ~((~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, n998))) | (a_select3(z_defuse, E!14, F!13) = use))),
% 0.23/0.44 inference(skolemize,[status(sab)],[8])).
% 0.23/0.44 tff(10,plain,
% 0.23/0.44 (~(a_select3(z_defuse, E!14, F!13) = use)),
% 0.23/0.44 inference(or_elim,[status(thm)],[9])).
% 0.23/0.44 tff(11,plain,
% 0.23/0.44 (leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, n998)),
% 0.23/0.44 inference(or_elim,[status(thm)],[9])).
% 0.23/0.44 tff(12,plain,
% 0.23/0.44 (leq(F!13, n998)),
% 0.23/0.44 inference(and_elim,[status(thm)],[11])).
% 0.23/0.44 tff(13,plain,
% 0.23/0.44 (leq(E!14, n2)),
% 0.23/0.44 inference(and_elim,[status(thm)],[11])).
% 0.23/0.44 tff(14,plain,
% 0.23/0.44 (leq(n0, F!13)),
% 0.23/0.44 inference(and_elim,[status(thm)],[11])).
% 0.23/0.44 tff(15,plain,
% 0.23/0.44 (leq(n0, E!14)),
% 0.23/0.44 inference(and_elim,[status(thm)],[11])).
% 0.23/0.44 tff(16,plain,
% 0.23/0.44 (^[C: $i, D: $i] : refl(((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998))) <=> ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(17,plain,
% 0.23/0.44 (![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998))) <=> ![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[16])).
% 0.23/0.44 tff(18,plain,
% 0.23/0.44 (^[C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998)) <=> (~((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998))))), ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998))) <=> (~(~((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998))))))), rewrite((~(~((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998))))) <=> ((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998)))), ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998))) <=> ((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998))))), (((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998))) | (a_select3(z_defuse, C, D) = use)) <=> (((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998))) | (a_select3(z_defuse, C, D) = use)))), rewrite((((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998))) | (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, n998)))), (((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998))) | (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, n998)))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(19,plain,
% 0.23/0.44 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998))) | (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, n998)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[18])).
% 0.23/0.44 tff(20,plain,
% 0.23/0.44 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998))) | (a_select3(z_defuse, C, D) = use)) <=> ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998))) | (a_select3(z_defuse, C, D) = use))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(21,plain,
% 0.23/0.44 ((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) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, n998))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998))) | (a_select3(z_defuse, C, D) = use))),
% 0.23/0.45 inference(or_elim,[status(thm)],[4])).
% 0.23/0.45 tff(22,plain,
% 0.23/0.45 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998))) | (a_select3(z_defuse, C, D) = use))),
% 0.23/0.45 inference(and_elim,[status(thm)],[21])).
% 0.23/0.45 tff(23,plain,
% 0.23/0.45 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998))) | (a_select3(z_defuse, C, D) = use))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.23/0.45 tff(24,plain,(
% 0.23/0.45 ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n998))) | (a_select3(z_defuse, C, D) = use))),
% 0.23/0.45 inference(skolemize,[status(sab)],[23])).
% 0.23/0.45 tff(25,plain,
% 0.23/0.45 (![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.23/0.45 tff(26,plain,
% 0.23/0.45 (![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[25, 17])).
% 0.23/0.45 tff(27,plain,
% 0.23/0.45 (((~![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998)))) | ((a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(E!14, n2)) | (~leq(n0, F!13)) | (~leq(F!13, n998)))) <=> ((~![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998)))) | (a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(E!14, n2)) | (~leq(n0, F!13)) | (~leq(F!13, n998)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(28,plain,
% 0.23/0.45 (((a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, n998))) <=> ((a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(E!14, n2)) | (~leq(n0, F!13)) | (~leq(F!13, n998)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(29,plain,
% 0.23/0.45 (((~![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998)))) | ((a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, n998)))) <=> ((~![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998)))) | ((a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(E!14, n2)) | (~leq(n0, F!13)) | (~leq(F!13, n998))))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[28])).
% 0.23/0.45 tff(30,plain,
% 0.23/0.45 (((~![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998)))) | ((a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, n998)))) <=> ((~![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998)))) | (a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(E!14, n2)) | (~leq(n0, F!13)) | (~leq(F!13, n998)))),
% 0.23/0.45 inference(transitivity,[status(thm)],[29, 27])).
% 0.23/0.45 tff(31,plain,
% 0.23/0.45 ((~![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998)))) | ((a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, n998)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(32,plain,
% 0.23/0.45 ((~![C: $i, D: $i] : ((a_select3(z_defuse, C, D) = use) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, n2)) | (~leq(D, n998)))) | (a_select3(z_defuse, E!14, F!13) = use) | (~leq(n0, E!14)) | (~leq(E!14, n2)) | (~leq(n0, F!13)) | (~leq(F!13, n998))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.23/0.45 tff(33,plain,
% 0.23/0.45 ($false),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[32, 26, 15, 14, 13, 12, 10])).
% 0.23/0.45 % SZS output end Proof
% 0.23/0.46 % E exiting
%------------------------------------------------------------------------------