TSTP Solution File: SWV199+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV199+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 : Thu Sep 29 15:10:21 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV199+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 01:44:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(succ_type, type, (
% 0.20/0.47 succ: $i > $i)).
% 0.20/0.47 tff(tptp_minus_1_type, type, (
% 0.20/0.47 tptp_minus_1: $i)).
% 0.20/0.47 tff(tptp_fun_E_14_type, type, (
% 0.20/0.47 tptp_fun_E_14: $i)).
% 0.20/0.47 tff(tptp_fun_F_13_type, type, (
% 0.20/0.47 tptp_fun_F_13: $i)).
% 0.20/0.47 tff(pv5_type, type, (
% 0.20/0.47 pv5: $i)).
% 0.20/0.47 tff(leq_type, type, (
% 0.20/0.47 leq: ( $i * $i ) > $o)).
% 0.20/0.47 tff(n0_type, type, (
% 0.20/0.47 n0: $i)).
% 0.20/0.47 tff(use_type, type, (
% 0.20/0.47 use: $i)).
% 0.20/0.47 tff(a_select3_type, type, (
% 0.20/0.47 a_select3: ( $i * $i * $i ) > $i)).
% 0.20/0.47 tff(z_defuse_type, type, (
% 0.20/0.47 z_defuse: $i)).
% 0.20/0.47 tff(pred_type, type, (
% 0.20/0.47 pred: $i > $i)).
% 0.20/0.47 tff(n2_type, type, (
% 0.20/0.47 n2: $i)).
% 0.20/0.47 tff(u_defuse_type, type, (
% 0.20/0.47 u_defuse: $i)).
% 0.20/0.47 tff(n998_type, type, (
% 0.20/0.47 n998: $i)).
% 0.20/0.47 tff(a_select2_type, type, (
% 0.20/0.47 a_select2: ( $i * $i ) > $i)).
% 0.20/0.47 tff(n5_type, type, (
% 0.20/0.47 n5: $i)).
% 0.20/0.47 tff(xinit_noise_defuse_type, type, (
% 0.20/0.47 xinit_noise_defuse: $i)).
% 0.20/0.47 tff(n4_type, type, (
% 0.20/0.47 n4: $i)).
% 0.20/0.47 tff(n3_type, type, (
% 0.20/0.47 n3: $i)).
% 0.20/0.47 tff(n1_type, type, (
% 0.20/0.47 n1: $i)).
% 0.20/0.47 tff(xinit_mean_defuse_type, type, (
% 0.20/0.47 xinit_mean_defuse: $i)).
% 0.20/0.47 tff(xinit_defuse_type, type, (
% 0.20/0.47 xinit_defuse: $i)).
% 0.20/0.47 tff(sigma_defuse_type, type, (
% 0.20/0.47 sigma_defuse: $i)).
% 0.20/0.47 tff(rho_defuse_type, type, (
% 0.20/0.47 rho_defuse: $i)).
% 0.20/0.47 tff(1,plain,
% 0.20/0.47 ((E!14 = succ(tptp_minus_1)) <=> (succ(tptp_minus_1) = E!14)),
% 0.20/0.47 inference(commutativity,[status(thm)],[])).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 ((succ(tptp_minus_1) = E!14) <=> (E!14 = succ(tptp_minus_1))),
% 0.20/0.47 inference(symmetry,[status(thm)],[1])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 ((~(succ(tptp_minus_1) = E!14)) <=> (~(E!14 = succ(tptp_minus_1)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.47 tff(4,plain,
% 0.20/0.47 ((succ(tptp_minus_1) = F!13) <=> (F!13 = succ(tptp_minus_1))),
% 0.20/0.47 inference(commutativity,[status(thm)],[])).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (leq(pv5, n0) <=> leq(pv5, succ(tptp_minus_1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(6,plain,
% 0.20/0.47 (leq(pv5, n0) <=> leq(pv5, n0)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(7,plain,
% 0.20/0.47 ((~(((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, n0)) & leq(pv5, n998)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pred(pv5))) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, pred(pv5))) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pv5)) => ((((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F)))) & (~((n2 = E) & (pv5 = F)))) => (a_select3(z_defuse, E, F) = use))))) <=> (~((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n0) & leq(pv5, n998) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)))) | ![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(8,axiom,(~(((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, n0)) & leq(pv5, n998)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pred(pv5))) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, pred(pv5))) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pv5)) => ((((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F)))) & (~((n2 = E) & (pv5 = F)))) => (a_select3(z_defuse, E, F) = use))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_inuse_0010')).
% 0.20/0.47 tff(9,plain,
% 0.20/0.47 (~((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n0) & leq(pv5, n998) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)))) | ![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 ((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n0) & leq(pv5, n998) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 0.20/0.48 inference(or_elim,[status(thm)],[9])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (leq(pv5, n0)),
% 0.20/0.48 inference(and_elim,[status(thm)],[10])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (leq(pv5, n0)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (leq(pv5, succ(tptp_minus_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 (leq(n0, pv5) <=> leq(succ(tptp_minus_1), pv5)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 (leq(n0, pv5) <=> leq(n0, pv5)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (leq(n0, pv5)),
% 0.20/0.48 inference(and_elim,[status(thm)],[10])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (leq(n0, pv5)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (leq(succ(tptp_minus_1), pv5)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (^[X: $i] : refl(((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))) <=> ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 (![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))) <=> ![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1))) <=> (~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))), ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) <=> (~(~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))))), rewrite((~(~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))), ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))), (((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))) <=> (((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))))), rewrite((((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))) <=> ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))), (((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))) <=> ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))) <=> ![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 (^[X: $i] : rewrite(((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (^[X: $i] : rewrite(((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ((~(leq(n0, X) & leq(X, n0))) | (X = n0)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.48 tff(28,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','finite_domain_0')).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.20/0.48 tff(32,plain,(
% 0.20/0.48 ![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[31])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[33, 20])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((pv5 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), pv5)) | (~leq(pv5, succ(tptp_minus_1))))) <=> ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | (pv5 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), pv5)) | (~leq(pv5, succ(tptp_minus_1))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((pv5 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), pv5)) | (~leq(pv5, succ(tptp_minus_1))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | (pv5 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), pv5)) | (~leq(pv5, succ(tptp_minus_1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (pv5 = succ(tptp_minus_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[37, 34, 18, 13])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 ((pv5 = F!13) <=> (succ(tptp_minus_1) = F!13)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 ((pv5 = F!13) <=> (F!13 = succ(tptp_minus_1))),
% 0.20/0.48 inference(transitivity,[status(thm)],[39, 4])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 ((F!13 = succ(tptp_minus_1)) <=> (pv5 = F!13)),
% 0.20/0.48 inference(symmetry,[status(thm)],[40])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 ((~((~((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) & (~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) & (~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))))) | (~(leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))) <=> (~((~((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) & (~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) & (~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))))) | (~(leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 ((~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 ((~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 ((~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 ((~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))))) <=> (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 ((~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))))) <=> (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 ((~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))) <=> (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 ((~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))) <=> (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(50,plain,
% 0.20/0.49 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.20/0.49 inference(or_elim,[status(thm)],[9])).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.49 tff(52,plain,
% 0.20/0.49 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[51, 49])).
% 0.20/0.49 tff(53,plain,
% 0.20/0.49 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.20/0.49 tff(54,plain,
% 0.20/0.49 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[53, 48])).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.20/0.49 tff(56,plain,
% 0.20/0.49 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[55, 46])).
% 0.20/0.49 tff(57,plain,
% 0.20/0.49 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[56, 45])).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[57, 44])).
% 0.20/0.49 tff(59,plain,
% 0.20/0.49 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[58, 43])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[59, 43])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[60, 43])).
% 0.20/0.49 tff(62,plain,(
% 0.20/0.49 ~((~((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) & (~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) & (~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))))) | (~(leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[61])).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (~((~((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) & (~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) & (~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))))) | (~(leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[62, 42])).
% 0.20/0.49 tff(64,plain,
% 0.20/0.49 (leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5)),
% 0.20/0.49 inference(or_elim,[status(thm)],[63])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 (leq(F!13, pv5)),
% 0.20/0.49 inference(and_elim,[status(thm)],[64])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(68,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(70,plain,
% 0.20/0.50 (^[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)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(71,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.50 tff(72,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 0.20/0.50 tff(73,plain,
% 0.20/0.50 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.50 tff(74,plain,
% 0.20/0.50 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.50 tff(75,plain,(
% 0.20/0.50 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.20/0.50 inference(skolemize,[status(sab)],[74])).
% 0.20/0.50 tff(76,plain,
% 0.20/0.50 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.20/0.50 tff(77,plain,
% 0.20/0.50 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[76, 66])).
% 0.20/0.50 tff(78,plain,
% 0.20/0.50 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(79,plain,
% 0.20/0.50 ((leq(F!13, succ(tptp_minus_1)) | (~leq(pv5, succ(tptp_minus_1))) | (~leq(F!13, pv5))) <=> ((~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(80,plain,
% 0.20/0.50 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(F!13, succ(tptp_minus_1)) | (~leq(pv5, succ(tptp_minus_1))) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.50 tff(81,plain,
% 0.20/0.50 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(F!13, succ(tptp_minus_1)) | (~leq(pv5, succ(tptp_minus_1))) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[80, 78])).
% 0.20/0.50 tff(82,plain,
% 0.20/0.50 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(F!13, succ(tptp_minus_1)) | (~leq(pv5, succ(tptp_minus_1))) | (~leq(F!13, pv5)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(83,plain,
% 0.20/0.50 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.50 tff(84,plain,
% 0.20/0.50 (leq(F!13, succ(tptp_minus_1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[83, 77, 13, 65])).
% 0.20/0.50 tff(85,plain,
% 0.20/0.50 (leq(succ(tptp_minus_1), F!13)),
% 0.20/0.50 inference(and_elim,[status(thm)],[64])).
% 0.20/0.50 tff(86,plain,
% 0.20/0.50 (((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1))))) <=> ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(87,plain,
% 0.20/0.50 (((F!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(88,plain,
% 0.20/0.50 (((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((F!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, succ(tptp_minus_1))))) <=> ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[87])).
% 0.20/0.50 tff(89,plain,
% 0.20/0.50 (((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((F!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, succ(tptp_minus_1))))) <=> ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[88, 86])).
% 0.20/0.50 tff(90,plain,
% 0.20/0.50 ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((F!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, succ(tptp_minus_1))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(91,plain,
% 0.20/0.50 ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.50 tff(92,plain,
% 0.20/0.50 ((F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[91, 34, 85])).
% 0.20/0.50 tff(93,plain,
% 0.20/0.50 (F!13 = succ(tptp_minus_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[92, 84])).
% 0.20/0.50 tff(94,plain,
% 0.20/0.50 (pv5 = F!13),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[93, 41])).
% 0.20/0.50 tff(95,plain,
% 0.20/0.50 ((~(~((~(succ(tptp_minus_1) = E!14)) | (~(pv5 = F!13))))) <=> ((~(succ(tptp_minus_1) = E!14)) | (~(pv5 = F!13)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(96,plain,
% 0.20/0.50 (((succ(tptp_minus_1) = E!14) & (pv5 = F!13)) <=> (~((~(succ(tptp_minus_1) = E!14)) | (~(pv5 = F!13))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(97,plain,
% 0.20/0.50 ((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) <=> (~(~((~(succ(tptp_minus_1) = E!14)) | (~(pv5 = F!13)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.50 tff(98,plain,
% 0.20/0.50 ((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) <=> ((~(succ(tptp_minus_1) = E!14)) | (~(pv5 = F!13)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[97, 95])).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 ((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) & (~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) & (~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13)))),
% 0.20/0.50 inference(or_elim,[status(thm)],[63])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 (~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))),
% 0.20/0.50 inference(and_elim,[status(thm)],[99])).
% 0.20/0.50 tff(101,plain,
% 0.20/0.50 ((~(succ(tptp_minus_1) = E!14)) | (~(pv5 = F!13))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[100, 98])).
% 0.20/0.50 tff(102,plain,
% 0.20/0.50 (~(succ(tptp_minus_1) = E!14)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[101, 94])).
% 0.20/0.50 tff(103,plain,
% 0.20/0.50 (~(E!14 = succ(tptp_minus_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[102, 3])).
% 0.20/0.50 tff(104,plain,
% 0.20/0.50 ((E!14 = succ(succ(tptp_minus_1))) <=> (succ(succ(tptp_minus_1)) = E!14)),
% 0.20/0.50 inference(commutativity,[status(thm)],[])).
% 0.20/0.50 tff(105,plain,
% 0.20/0.50 ((succ(succ(tptp_minus_1)) = E!14) <=> (E!14 = succ(succ(tptp_minus_1)))),
% 0.20/0.50 inference(symmetry,[status(thm)],[104])).
% 0.20/0.50 tff(106,plain,
% 0.20/0.50 ((~(succ(succ(tptp_minus_1)) = E!14)) <=> (~(E!14 = succ(succ(tptp_minus_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[105])).
% 0.20/0.50 tff(107,plain,
% 0.20/0.50 ((~(~((~(pv5 = F!13)) | (~(succ(succ(tptp_minus_1)) = E!14))))) <=> ((~(pv5 = F!13)) | (~(succ(succ(tptp_minus_1)) = E!14)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(108,plain,
% 0.20/0.50 (((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13)) <=> (~((~(pv5 = F!13)) | (~(succ(succ(tptp_minus_1)) = E!14))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(109,plain,
% 0.20/0.50 ((~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) <=> (~(~((~(pv5 = F!13)) | (~(succ(succ(tptp_minus_1)) = E!14)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[108])).
% 0.20/0.50 tff(110,plain,
% 0.20/0.50 ((~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) <=> ((~(pv5 = F!13)) | (~(succ(succ(tptp_minus_1)) = E!14)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[109, 107])).
% 0.20/0.50 tff(111,plain,
% 0.20/0.50 (~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))),
% 0.20/0.50 inference(and_elim,[status(thm)],[99])).
% 0.20/0.50 tff(112,plain,
% 0.20/0.50 ((~(pv5 = F!13)) | (~(succ(succ(tptp_minus_1)) = E!14))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.50 tff(113,plain,
% 0.20/0.50 (~(succ(succ(tptp_minus_1)) = E!14)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[112, 94])).
% 0.20/0.50 tff(114,plain,
% 0.20/0.50 (~(E!14 = succ(succ(tptp_minus_1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.20/0.50 tff(115,plain,
% 0.20/0.50 ((E!14 = succ(succ(succ(tptp_minus_1)))) <=> (succ(succ(succ(tptp_minus_1))) = E!14)),
% 0.20/0.50 inference(commutativity,[status(thm)],[])).
% 0.20/0.50 tff(116,plain,
% 0.20/0.50 ((succ(succ(succ(tptp_minus_1))) = E!14) <=> (E!14 = succ(succ(succ(tptp_minus_1))))),
% 0.20/0.50 inference(symmetry,[status(thm)],[115])).
% 0.20/0.50 tff(117,plain,
% 0.20/0.50 ((~(succ(succ(succ(tptp_minus_1))) = E!14)) <=> (~(E!14 = succ(succ(succ(tptp_minus_1)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[116])).
% 0.20/0.50 tff(118,plain,
% 0.20/0.50 ((~(~((~(pv5 = F!13)) | (~(succ(succ(succ(tptp_minus_1))) = E!14))))) <=> ((~(pv5 = F!13)) | (~(succ(succ(succ(tptp_minus_1))) = E!14)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(119,plain,
% 0.20/0.50 (((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13)) <=> (~((~(pv5 = F!13)) | (~(succ(succ(succ(tptp_minus_1))) = E!14))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(120,plain,
% 0.20/0.50 ((~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))) <=> (~(~((~(pv5 = F!13)) | (~(succ(succ(succ(tptp_minus_1))) = E!14)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[119])).
% 0.20/0.50 tff(121,plain,
% 0.20/0.50 ((~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))) <=> ((~(pv5 = F!13)) | (~(succ(succ(succ(tptp_minus_1))) = E!14)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[120, 118])).
% 0.20/0.50 tff(122,plain,
% 0.20/0.50 (~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))),
% 0.20/0.50 inference(and_elim,[status(thm)],[99])).
% 0.20/0.50 tff(123,plain,
% 0.20/0.50 ((~(pv5 = F!13)) | (~(succ(succ(succ(tptp_minus_1))) = E!14))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.50 tff(124,plain,
% 0.20/0.50 (~(succ(succ(succ(tptp_minus_1))) = E!14)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[123, 94])).
% 0.20/0.50 tff(125,plain,
% 0.20/0.50 (~(E!14 = succ(succ(succ(tptp_minus_1))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.20/0.50 tff(126,plain,
% 0.20/0.50 (leq(E!14, succ(succ(succ(tptp_minus_1))))),
% 0.20/0.50 inference(and_elim,[status(thm)],[64])).
% 0.20/0.50 tff(127,plain,
% 0.20/0.50 (leq(succ(tptp_minus_1), E!14)),
% 0.20/0.50 inference(and_elim,[status(thm)],[64])).
% 0.20/0.50 tff(128,plain,
% 0.20/0.50 (^[X: $i] : refl(((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(129,plain,
% 0.20/0.51 (![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))) <=> ![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.51 tff(130,plain,
% 0.20/0.51 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))))), (((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))))), rewrite(((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))), (((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(131,plain,
% 0.20/0.51 (![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))))) <=> ![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.51 tff(132,plain,
% 0.20/0.51 (^[X: $i] : trans(monotonicity(rewrite((X = n2) <=> (X = succ(succ(succ(tptp_minus_1))))), rewrite((X = n1) <=> (X = succ(succ(tptp_minus_1)))), rewrite((X = n0) <=> (X = succ(tptp_minus_1))), rewrite((~(leq(n0, X) & leq(X, n2))) <=> (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))))), (((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2)))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))))))), rewrite(((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))))), (((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2)))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(133,plain,
% 0.20/0.51 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2)))) <=> ![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.52 tff(134,plain,
% 0.20/0.52 (![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))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(135,plain,
% 0.20/0.52 (^[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))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(136,plain,
% 0.20/0.52 (![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))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.52 tff(137,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')).
% 0.20/0.52 tff(138,plain,
% 0.20/0.52 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.52 tff(139,plain,
% 0.20/0.52 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.20/0.52 tff(140,plain,
% 0.20/0.52 (![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[139, 133])).
% 0.20/0.52 tff(141,plain,(
% 0.20/0.52 ![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[140])).
% 0.20/0.52 tff(142,plain,
% 0.20/0.52 (![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.20/0.52 tff(143,plain,
% 0.20/0.52 (![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[142, 129])).
% 0.20/0.52 tff(144,plain,
% 0.20/0.52 (((~![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) | ((~leq(succ(tptp_minus_1), E!14)) | (E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))))) <=> ((~![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) | (~leq(succ(tptp_minus_1), E!14)) | (E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(145,plain,
% 0.20/0.52 (((E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), E!14)) | (E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(146,plain,
% 0.20/0.52 (((~![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) | ((E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))))) <=> ((~![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) | ((~leq(succ(tptp_minus_1), E!14)) | (E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(E!14, succ(succ(succ(tptp_minus_1)))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[145])).
% 0.20/0.53 tff(147,plain,
% 0.20/0.53 (((~![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) | ((E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))))) <=> ((~![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) | (~leq(succ(tptp_minus_1), E!14)) | (E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[146, 144])).
% 0.20/0.53 tff(148,plain,
% 0.20/0.53 ((~![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) | ((E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(149,plain,
% 0.20/0.53 ((~![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) | (~leq(succ(tptp_minus_1), E!14)) | (E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(E!14, succ(succ(succ(tptp_minus_1)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.53 tff(150,plain,
% 0.20/0.53 ((E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[149, 143, 127, 126])).
% 0.20/0.53 tff(151,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[150, 125, 114, 103])).
% 0.20/0.53 % SZS output end Proof
%------------------------------------------------------------------------------