TSTP Solution File: SWV209+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV209+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 15:10:23 EDT 2022
% Result : Theorem 0.55s 0.59s
% Output : Proof 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV209+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 01:41:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.55/0.59 % SZS status Theorem
% 0.55/0.59 % SZS output start Proof
% 0.55/0.59 tff(a_select3_type, type, (
% 0.55/0.59 a_select3: ( $i * $i * $i ) > $i)).
% 0.55/0.59 tff(succ_type, type, (
% 0.55/0.59 succ: $i > $i)).
% 0.55/0.59 tff(tptp_minus_1_type, type, (
% 0.55/0.59 tptp_minus_1: $i)).
% 0.55/0.59 tff(u_defuse_type, type, (
% 0.55/0.59 u_defuse: $i)).
% 0.55/0.59 tff(a_select2_type, type, (
% 0.55/0.59 a_select2: ( $i * $i ) > $i)).
% 0.55/0.59 tff(tptp_fun_E_13_type, type, (
% 0.55/0.59 tptp_fun_E_13: $i)).
% 0.55/0.59 tff(xinit_noise_defuse_type, type, (
% 0.55/0.59 xinit_noise_defuse: $i)).
% 0.55/0.59 tff(sigma_defuse_type, type, (
% 0.55/0.59 sigma_defuse: $i)).
% 0.55/0.59 tff(rho_defuse_type, type, (
% 0.55/0.59 rho_defuse: $i)).
% 0.55/0.59 tff(use_type, type, (
% 0.55/0.59 use: $i)).
% 0.55/0.59 tff(n1_type, type, (
% 0.55/0.59 n1: $i)).
% 0.55/0.59 tff(z_defuse_type, type, (
% 0.55/0.59 z_defuse: $i)).
% 0.55/0.59 tff(leq_type, type, (
% 0.55/0.59 leq: ( $i * $i ) > $o)).
% 0.55/0.59 tff(n998_type, type, (
% 0.55/0.59 n998: $i)).
% 0.55/0.59 tff(n2_type, type, (
% 0.55/0.59 n2: $i)).
% 0.55/0.59 tff(n0_type, type, (
% 0.55/0.59 n0: $i)).
% 0.55/0.59 tff(n5_type, type, (
% 0.55/0.59 n5: $i)).
% 0.55/0.59 tff(n4_type, type, (
% 0.55/0.59 n4: $i)).
% 0.55/0.59 tff(n3_type, type, (
% 0.55/0.59 n3: $i)).
% 0.55/0.59 tff(xinit_mean_defuse_type, type, (
% 0.55/0.59 xinit_mean_defuse: $i)).
% 0.55/0.59 tff(xinit_defuse_type, type, (
% 0.55/0.59 xinit_defuse: $i)).
% 0.55/0.59 tff(gt_type, type, (
% 0.55/0.59 gt: ( $i * $i ) > $o)).
% 0.55/0.59 tff(1,plain,
% 0.55/0.59 ((a_select2(xinit_noise_defuse, succ(succ(tptp_minus_1))) = a_select2(sigma_defuse, succ(tptp_minus_1))) <=> (a_select2(xinit_noise_defuse, succ(succ(tptp_minus_1))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(2,plain,
% 0.55/0.59 ((a_select2(xinit_noise_defuse, succ(succ(tptp_minus_1))) = a_select2(rho_defuse, succ(tptp_minus_1))) <=> (a_select2(xinit_noise_defuse, succ(succ(tptp_minus_1))) = a_select2(sigma_defuse, succ(tptp_minus_1)))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(3,plain,
% 0.55/0.59 ((a_select2(xinit_noise_defuse, n1) = use) <=> (a_select2(xinit_noise_defuse, succ(succ(tptp_minus_1))) = a_select2(rho_defuse, succ(tptp_minus_1)))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(4,plain,
% 0.55/0.59 ((a_select2(xinit_noise_defuse, n1) = use) <=> (a_select2(xinit_noise_defuse, n1) = use)),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(5,plain,
% 0.55/0.59 ((~((((((((((((((((((((((((((((((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] : ((leq(n0, E) & leq(E, n5)) => (a_select2(xinit_noise_defuse, E) = 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] : ((~(leq(n0, E) & leq(E, n5))) | (a_select2(xinit_noise_defuse, E) = use))))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(6,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] : ((leq(n0, E) & leq(E, n5)) => (a_select2(xinit_noise_defuse, E) = use)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_inuse_0020')).
% 0.55/0.60 tff(7,plain,
% 0.55/0.60 (~((~((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] : ((~(leq(n0, E) & leq(E, n5))) | (a_select2(xinit_noise_defuse, E) = use)))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.55/0.60 tff(8,plain,
% 0.55/0.60 ((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))),
% 0.55/0.60 inference(or_elim,[status(thm)],[7])).
% 0.55/0.60 tff(9,plain,
% 0.55/0.60 (a_select2(xinit_noise_defuse, n1) = use),
% 0.55/0.60 inference(and_elim,[status(thm)],[8])).
% 0.55/0.60 tff(10,plain,
% 0.55/0.60 (a_select2(xinit_noise_defuse, n1) = use),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.55/0.60 tff(11,plain,
% 0.55/0.60 (a_select2(xinit_noise_defuse, succ(succ(tptp_minus_1))) = a_select2(rho_defuse, succ(tptp_minus_1))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.55/0.60 tff(12,plain,
% 0.55/0.60 (a_select2(xinit_noise_defuse, succ(succ(tptp_minus_1))) = a_select2(sigma_defuse, succ(tptp_minus_1))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.55/0.60 tff(13,plain,
% 0.55/0.60 (a_select2(xinit_noise_defuse, succ(succ(tptp_minus_1))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.55/0.60 tff(14,plain,
% 0.55/0.60 ((a_select2(xinit_noise_defuse, succ(tptp_minus_1)) = a_select2(sigma_defuse, succ(tptp_minus_1))) <=> (a_select2(xinit_noise_defuse, succ(tptp_minus_1)) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(15,plain,
% 0.55/0.60 ((a_select2(xinit_noise_defuse, succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1))) <=> (a_select2(xinit_noise_defuse, succ(tptp_minus_1)) = a_select2(sigma_defuse, succ(tptp_minus_1)))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(16,plain,
% 0.55/0.60 ((a_select2(xinit_noise_defuse, n0) = use) <=> (a_select2(xinit_noise_defuse, succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1)))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(17,plain,
% 0.55/0.60 ((a_select2(xinit_noise_defuse, n0) = use) <=> (a_select2(xinit_noise_defuse, n0) = use)),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(18,plain,
% 0.55/0.60 (a_select2(xinit_noise_defuse, n0) = use),
% 0.55/0.60 inference(and_elim,[status(thm)],[8])).
% 0.55/0.60 tff(19,plain,
% 0.55/0.60 (a_select2(xinit_noise_defuse, n0) = use),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.55/0.60 tff(20,plain,
% 0.55/0.60 (a_select2(xinit_noise_defuse, succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.55/0.60 tff(21,plain,
% 0.55/0.60 (a_select2(xinit_noise_defuse, succ(tptp_minus_1)) = a_select2(sigma_defuse, succ(tptp_minus_1))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.55/0.60 tff(22,plain,
% 0.55/0.60 (a_select2(xinit_noise_defuse, succ(tptp_minus_1)) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.55/0.60 tff(23,assumption,(E!13 = succ(tptp_minus_1)), introduced(assumption)).
% 0.55/0.60 tff(24,plain,
% 0.55/0.60 (a_select2(xinit_noise_defuse, E!13) = a_select2(xinit_noise_defuse, succ(tptp_minus_1))),
% 0.55/0.60 inference(monotonicity,[status(thm)],[23])).
% 0.55/0.60 tff(25,plain,
% 0.55/0.60 (a_select2(xinit_noise_defuse, E!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.55/0.60 inference(transitivity,[status(thm)],[24, 22])).
% 0.55/0.60 tff(26,plain,
% 0.55/0.60 ((~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))) <=> (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(27,plain,
% 0.55/0.60 ((~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(28,plain,
% 0.55/0.60 ((~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(29,plain,
% 0.55/0.60 ((~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select2(rho_defuse, succ(tptp_minus_1))))) <=> (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(30,plain,
% 0.55/0.60 ((~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select2(rho_defuse, succ(tptp_minus_1))))) <=> (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(31,plain,
% 0.55/0.60 ((~![E: $i] : ((~(leq(n0, E) & leq(E, n5))) | (a_select2(xinit_noise_defuse, E) = use))) <=> (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(32,plain,
% 0.55/0.60 ((~![E: $i] : ((~(leq(n0, E) & leq(E, n5))) | (a_select2(xinit_noise_defuse, E) = use))) <=> (~![E: $i] : ((~(leq(n0, E) & leq(E, n5))) | (a_select2(xinit_noise_defuse, E) = use)))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(33,plain,
% 0.55/0.60 (~![E: $i] : ((~(leq(n0, E) & leq(E, n5))) | (a_select2(xinit_noise_defuse, E) = use))),
% 0.55/0.60 inference(or_elim,[status(thm)],[7])).
% 0.55/0.60 tff(34,plain,
% 0.55/0.60 (~![E: $i] : ((~(leq(n0, E) & leq(E, n5))) | (a_select2(xinit_noise_defuse, E) = use))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.55/0.60 tff(35,plain,
% 0.55/0.60 (~![E: $i] : ((~(leq(n0, E) & leq(E, n5))) | (a_select2(xinit_noise_defuse, E) = use))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[34, 32])).
% 0.55/0.60 tff(36,plain,
% 0.55/0.60 (~![E: $i] : ((~(leq(n0, E) & leq(E, n5))) | (a_select2(xinit_noise_defuse, E) = use))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.55/0.60 tff(37,plain,
% 0.55/0.60 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.55/0.60 tff(38,plain,
% 0.55/0.60 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.55/0.60 tff(39,plain,
% 0.55/0.60 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[38, 29])).
% 0.58/0.60 tff(40,plain,
% 0.58/0.60 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[39, 28])).
% 0.58/0.60 tff(41,plain,
% 0.58/0.60 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[40, 27])).
% 0.58/0.60 tff(42,plain,
% 0.58/0.60 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[41, 26])).
% 0.58/0.60 tff(43,plain,
% 0.58/0.60 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[42, 26])).
% 0.58/0.60 tff(44,plain,
% 0.58/0.60 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[43, 26])).
% 0.58/0.60 tff(45,plain,(
% 0.58/0.60 ~((~(leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select2(xinit_noise_defuse, E!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.58/0.60 inference(skolemize,[status(sab)],[44])).
% 0.58/0.60 tff(46,plain,
% 0.58/0.60 (~(a_select2(xinit_noise_defuse, E!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.58/0.60 inference(or_elim,[status(thm)],[45])).
% 0.58/0.60 tff(47,plain,
% 0.58/0.60 ($false),
% 0.58/0.60 inference(unit_resolution,[status(thm)],[46, 25])).
% 0.58/0.60 tff(48,plain,(~(E!13 = succ(tptp_minus_1))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.60 tff(49,plain,
% 0.58/0.60 ((a_select2(xinit_noise_defuse, succ(succ(succ(tptp_minus_1)))) = a_select2(sigma_defuse, succ(tptp_minus_1))) <=> (a_select2(xinit_noise_defuse, succ(succ(succ(tptp_minus_1)))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(50,plain,
% 0.58/0.60 ((a_select2(xinit_noise_defuse, succ(succ(succ(tptp_minus_1)))) = a_select2(rho_defuse, succ(tptp_minus_1))) <=> (a_select2(xinit_noise_defuse, succ(succ(succ(tptp_minus_1)))) = a_select2(sigma_defuse, succ(tptp_minus_1)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(51,plain,
% 0.58/0.60 ((a_select2(xinit_noise_defuse, n2) = use) <=> (a_select2(xinit_noise_defuse, succ(succ(succ(tptp_minus_1)))) = a_select2(rho_defuse, succ(tptp_minus_1)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(52,plain,
% 0.58/0.60 ((a_select2(xinit_noise_defuse, n2) = use) <=> (a_select2(xinit_noise_defuse, n2) = use)),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(53,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, n2) = use),
% 0.58/0.60 inference(and_elim,[status(thm)],[8])).
% 0.58/0.60 tff(54,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, n2) = use),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.58/0.60 tff(55,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, succ(succ(succ(tptp_minus_1)))) = a_select2(rho_defuse, succ(tptp_minus_1))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.58/0.60 tff(56,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, succ(succ(succ(tptp_minus_1)))) = a_select2(sigma_defuse, succ(tptp_minus_1))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[55, 50])).
% 0.58/0.60 tff(57,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, succ(succ(succ(tptp_minus_1)))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.58/0.60 tff(58,assumption,(E!13 = succ(succ(succ(tptp_minus_1)))), introduced(assumption)).
% 0.58/0.60 tff(59,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, E!13) = a_select2(xinit_noise_defuse, succ(succ(succ(tptp_minus_1))))),
% 0.58/0.60 inference(monotonicity,[status(thm)],[58])).
% 0.58/0.60 tff(60,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, E!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.58/0.60 inference(transitivity,[status(thm)],[59, 57])).
% 0.58/0.60 tff(61,plain,
% 0.58/0.60 ($false),
% 0.58/0.60 inference(unit_resolution,[status(thm)],[46, 60])).
% 0.58/0.60 tff(62,plain,(~(E!13 = succ(succ(succ(tptp_minus_1))))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.60 tff(63,plain,
% 0.58/0.60 (^[X: $i, Y: $i] : refl((leq(X, Y) <=> gt(succ(Y), X)) <=> (leq(X, Y) <=> gt(succ(Y), X)))),
% 0.58/0.60 inference(bind,[status(th)],[])).
% 0.58/0.60 tff(64,plain,
% 0.58/0.60 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.58/0.60 inference(quant_intro,[status(thm)],[63])).
% 0.58/0.60 tff(65,plain,
% 0.58/0.60 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(66,axiom,(![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_succ_gt_equiv')).
% 0.58/0.60 tff(67,plain,
% 0.58/0.60 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.58/0.60 tff(68,plain,(
% 0.58/0.60 ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.58/0.60 inference(skolemize,[status(sab)],[67])).
% 0.58/0.60 tff(69,plain,
% 0.58/0.60 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.58/0.60 tff(70,plain,
% 0.58/0.60 ((~![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))) | (leq(E!13, succ(succ(succ(succ(tptp_minus_1))))) <=> gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13))),
% 0.58/0.60 inference(quant_inst,[status(thm)],[])).
% 0.58/0.60 tff(71,plain,
% 0.58/0.60 (leq(E!13, succ(succ(succ(succ(tptp_minus_1))))) <=> gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13)),
% 0.58/0.60 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.58/0.60 tff(72,plain,
% 0.58/0.60 ((a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(tptp_minus_1)))))) = a_select2(sigma_defuse, succ(tptp_minus_1))) <=> (a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(tptp_minus_1)))))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(73,plain,
% 0.58/0.60 ((a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(tptp_minus_1)))))) = a_select2(rho_defuse, succ(tptp_minus_1))) <=> (a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(tptp_minus_1)))))) = a_select2(sigma_defuse, succ(tptp_minus_1)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(74,plain,
% 0.58/0.60 ((a_select2(xinit_noise_defuse, n4) = use) <=> (a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(tptp_minus_1)))))) = a_select2(rho_defuse, succ(tptp_minus_1)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(75,plain,
% 0.58/0.60 ((a_select2(xinit_noise_defuse, n4) = use) <=> (a_select2(xinit_noise_defuse, n4) = use)),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(76,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, n4) = use),
% 0.58/0.60 inference(and_elim,[status(thm)],[8])).
% 0.58/0.60 tff(77,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, n4) = use),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.58/0.60 tff(78,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(tptp_minus_1)))))) = a_select2(rho_defuse, succ(tptp_minus_1))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[77, 74])).
% 0.58/0.60 tff(79,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(tptp_minus_1)))))) = a_select2(sigma_defuse, succ(tptp_minus_1))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[78, 73])).
% 0.58/0.60 tff(80,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(tptp_minus_1)))))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.58/0.60 tff(81,assumption,(E!13 = succ(succ(succ(succ(succ(tptp_minus_1)))))), introduced(assumption)).
% 0.58/0.60 tff(82,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, E!13) = a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.58/0.60 inference(monotonicity,[status(thm)],[81])).
% 0.58/0.60 tff(83,plain,
% 0.58/0.60 (a_select2(xinit_noise_defuse, E!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.58/0.60 inference(transitivity,[status(thm)],[82, 80])).
% 0.58/0.60 tff(84,plain,
% 0.58/0.60 ($false),
% 0.58/0.60 inference(unit_resolution,[status(thm)],[46, 83])).
% 0.58/0.60 tff(85,plain,(~(E!13 = succ(succ(succ(succ(succ(tptp_minus_1))))))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.61 tff(86,plain,
% 0.58/0.61 ((~![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))) | (leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1)))))) <=> gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13))),
% 0.58/0.61 inference(quant_inst,[status(thm)],[])).
% 0.58/0.61 tff(87,plain,
% 0.58/0.61 (leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1)))))) <=> gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13)),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[86, 69])).
% 0.58/0.61 tff(88,plain,
% 0.58/0.61 ((a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = a_select2(sigma_defuse, succ(tptp_minus_1))) <=> (a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(89,plain,
% 0.58/0.61 ((a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = a_select2(rho_defuse, succ(tptp_minus_1))) <=> (a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = a_select2(sigma_defuse, succ(tptp_minus_1)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(90,plain,
% 0.58/0.61 ((a_select2(xinit_noise_defuse, n5) = use) <=> (a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = a_select2(rho_defuse, succ(tptp_minus_1)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(91,plain,
% 0.58/0.61 ((a_select2(xinit_noise_defuse, n5) = use) <=> (a_select2(xinit_noise_defuse, n5) = use)),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(92,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, n5) = use),
% 0.58/0.61 inference(and_elim,[status(thm)],[8])).
% 0.58/0.61 tff(93,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, n5) = use),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.58/0.61 tff(94,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = a_select2(rho_defuse, succ(tptp_minus_1))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[93, 90])).
% 0.58/0.61 tff(95,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = a_select2(sigma_defuse, succ(tptp_minus_1))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[94, 89])).
% 0.58/0.61 tff(96,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.58/0.61 tff(97,assumption,(E!13 = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.58/0.61 tff(98,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, E!13) = a_select2(xinit_noise_defuse, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.58/0.61 inference(monotonicity,[status(thm)],[97])).
% 0.58/0.61 tff(99,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, E!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.58/0.61 inference(transitivity,[status(thm)],[98, 96])).
% 0.58/0.61 tff(100,plain,
% 0.58/0.61 ($false),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[46, 99])).
% 0.58/0.61 tff(101,plain,(~(E!13 = succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.61 tff(102,plain,
% 0.58/0.61 (leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.58/0.61 inference(or_elim,[status(thm)],[45])).
% 0.58/0.61 tff(103,plain,
% 0.58/0.61 (leq(E!13, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.58/0.61 inference(and_elim,[status(thm)],[102])).
% 0.58/0.61 tff(104,plain,
% 0.58/0.61 (^[X: $i, Y: $i] : refl(((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y))))),
% 0.58/0.61 inference(bind,[status(th)],[])).
% 0.58/0.61 tff(105,plain,
% 0.58/0.61 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.58/0.61 inference(quant_intro,[status(thm)],[104])).
% 0.58/0.61 tff(106,plain,
% 0.58/0.61 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & (~(X = Y))) <=> (~((~leq(X, Y)) | (X = Y)))), ((~(leq(X, Y) & (~(X = Y)))) <=> (~(~((~leq(X, Y)) | (X = Y)))))), rewrite((~(~((~leq(X, Y)) | (X = Y)))) <=> ((~leq(X, Y)) | (X = Y))), ((~(leq(X, Y) & (~(X = Y)))) <=> ((~leq(X, Y)) | (X = Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> (((~leq(X, Y)) | (X = Y)) | gt(Y, X)))), rewrite((((~leq(X, Y)) | (X = Y)) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))))),
% 0.58/0.61 inference(bind,[status(th)],[])).
% 0.58/0.61 tff(107,plain,
% 0.58/0.61 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.58/0.61 inference(quant_intro,[status(thm)],[106])).
% 0.58/0.61 tff(108,plain,
% 0.58/0.61 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(109,plain,
% 0.58/0.61 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)))),
% 0.58/0.61 inference(bind,[status(th)],[])).
% 0.58/0.61 tff(110,plain,
% 0.58/0.61 (![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.58/0.61 inference(quant_intro,[status(thm)],[109])).
% 0.58/0.61 tff(111,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt2')).
% 0.58/0.61 tff(112,plain,
% 0.58/0.61 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.58/0.61 tff(113,plain,
% 0.58/0.61 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.58/0.61 tff(114,plain,(
% 0.58/0.61 ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.58/0.61 inference(skolemize,[status(sab)],[113])).
% 0.58/0.61 tff(115,plain,
% 0.58/0.61 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.58/0.61 tff(116,plain,
% 0.58/0.61 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[115, 105])).
% 0.58/0.61 tff(117,plain,
% 0.58/0.61 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((E!13 = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | (~leq(E!13, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (E!13 = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | (~leq(E!13, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(118,plain,
% 0.58/0.61 (((E!13 = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13) | (~leq(E!13, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((E!13 = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | (~leq(E!13, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(119,plain,
% 0.58/0.61 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((E!13 = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13) | (~leq(E!13, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((E!13 = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | (~leq(E!13, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13)))),
% 0.58/0.61 inference(monotonicity,[status(thm)],[118])).
% 0.58/0.61 tff(120,plain,
% 0.58/0.61 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((E!13 = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13) | (~leq(E!13, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (E!13 = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | (~leq(E!13, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13))),
% 0.58/0.61 inference(transitivity,[status(thm)],[119, 117])).
% 0.58/0.61 tff(121,plain,
% 0.58/0.61 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((E!13 = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13) | (~leq(E!13, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.58/0.61 inference(quant_inst,[status(thm)],[])).
% 0.58/0.61 tff(122,plain,
% 0.58/0.61 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (E!13 = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | (~leq(E!13, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13)),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.58/0.61 tff(123,plain,
% 0.58/0.61 ((E!13 = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13)),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[122, 116, 103])).
% 0.58/0.61 tff(124,plain,
% 0.58/0.61 (gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13)),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[123, 101])).
% 0.58/0.61 tff(125,plain,
% 0.58/0.61 ((~(leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1)))))) <=> gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13))) | leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1)))))) | (~gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13))),
% 0.58/0.61 inference(tautology,[status(thm)],[])).
% 0.58/0.61 tff(126,plain,
% 0.58/0.61 ((~(leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1)))))) <=> gt(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), E!13))) | leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.58/0.61 tff(127,plain,
% 0.58/0.61 (leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[126, 87])).
% 0.58/0.61 tff(128,plain,
% 0.58/0.61 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((E!13 = succ(succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))) | gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (E!13 = succ(succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))) | gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(129,plain,
% 0.58/0.61 (((E!13 = succ(succ(succ(succ(succ(tptp_minus_1)))))) | gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> ((E!13 = succ(succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))) | gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(130,plain,
% 0.58/0.61 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((E!13 = succ(succ(succ(succ(succ(tptp_minus_1)))))) | gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((E!13 = succ(succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))) | gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13)))),
% 0.58/0.61 inference(monotonicity,[status(thm)],[129])).
% 0.58/0.61 tff(131,plain,
% 0.58/0.61 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((E!13 = succ(succ(succ(succ(succ(tptp_minus_1)))))) | gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (E!13 = succ(succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))) | gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13))),
% 0.58/0.61 inference(transitivity,[status(thm)],[130, 128])).
% 0.58/0.61 tff(132,plain,
% 0.58/0.61 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((E!13 = succ(succ(succ(succ(succ(tptp_minus_1)))))) | gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.58/0.61 inference(quant_inst,[status(thm)],[])).
% 0.58/0.61 tff(133,plain,
% 0.58/0.61 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (E!13 = succ(succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(E!13, succ(succ(succ(succ(succ(tptp_minus_1))))))) | gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13)),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.58/0.61 tff(134,plain,
% 0.58/0.61 ((E!13 = succ(succ(succ(succ(succ(tptp_minus_1)))))) | gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13)),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[133, 116, 127])).
% 0.58/0.61 tff(135,plain,
% 0.58/0.61 (gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13)),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[134, 85])).
% 0.58/0.61 tff(136,plain,
% 0.58/0.61 ((~(leq(E!13, succ(succ(succ(succ(tptp_minus_1))))) <=> gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13))) | leq(E!13, succ(succ(succ(succ(tptp_minus_1))))) | (~gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13))),
% 0.58/0.61 inference(tautology,[status(thm)],[])).
% 0.58/0.61 tff(137,plain,
% 0.58/0.61 ((~(leq(E!13, succ(succ(succ(succ(tptp_minus_1))))) <=> gt(succ(succ(succ(succ(succ(tptp_minus_1))))), E!13))) | leq(E!13, succ(succ(succ(succ(tptp_minus_1)))))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.58/0.61 tff(138,plain,
% 0.58/0.61 (leq(E!13, succ(succ(succ(succ(tptp_minus_1)))))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[137, 71])).
% 0.58/0.61 tff(139,plain,
% 0.58/0.61 ((a_select2(xinit_noise_defuse, succ(succ(succ(succ(tptp_minus_1))))) = a_select2(sigma_defuse, succ(tptp_minus_1))) <=> (a_select2(xinit_noise_defuse, succ(succ(succ(succ(tptp_minus_1))))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(140,plain,
% 0.58/0.61 ((a_select2(xinit_noise_defuse, succ(succ(succ(succ(tptp_minus_1))))) = a_select2(rho_defuse, succ(tptp_minus_1))) <=> (a_select2(xinit_noise_defuse, succ(succ(succ(succ(tptp_minus_1))))) = a_select2(sigma_defuse, succ(tptp_minus_1)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(141,plain,
% 0.58/0.61 ((a_select2(xinit_noise_defuse, n3) = use) <=> (a_select2(xinit_noise_defuse, succ(succ(succ(succ(tptp_minus_1))))) = a_select2(rho_defuse, succ(tptp_minus_1)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(142,plain,
% 0.58/0.61 ((a_select2(xinit_noise_defuse, n3) = use) <=> (a_select2(xinit_noise_defuse, n3) = use)),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(143,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, n3) = use),
% 0.58/0.61 inference(and_elim,[status(thm)],[8])).
% 0.58/0.61 tff(144,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, n3) = use),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.58/0.61 tff(145,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, succ(succ(succ(succ(tptp_minus_1))))) = a_select2(rho_defuse, succ(tptp_minus_1))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[144, 141])).
% 0.58/0.61 tff(146,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, succ(succ(succ(succ(tptp_minus_1))))) = a_select2(sigma_defuse, succ(tptp_minus_1))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[145, 140])).
% 0.58/0.61 tff(147,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, succ(succ(succ(succ(tptp_minus_1))))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.58/0.61 tff(148,assumption,(E!13 = succ(succ(succ(succ(tptp_minus_1))))), introduced(assumption)).
% 0.58/0.61 tff(149,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, E!13) = a_select2(xinit_noise_defuse, succ(succ(succ(succ(tptp_minus_1)))))),
% 0.58/0.61 inference(monotonicity,[status(thm)],[148])).
% 0.58/0.61 tff(150,plain,
% 0.58/0.61 (a_select2(xinit_noise_defuse, E!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.58/0.61 inference(transitivity,[status(thm)],[149, 147])).
% 0.58/0.61 tff(151,plain,
% 0.58/0.61 ($false),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[46, 150])).
% 0.58/0.61 tff(152,plain,(~(E!13 = succ(succ(succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.61 tff(153,plain,
% 0.58/0.61 (leq(succ(tptp_minus_1), E!13)),
% 0.58/0.61 inference(and_elim,[status(thm)],[102])).
% 0.58/0.61 tff(154,plain,
% 0.58/0.61 (^[X: $i] : refl(((X = succ(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(succ(tptp_minus_1))))))) <=> ((X = succ(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(succ(tptp_minus_1))))))))),
% 0.58/0.61 inference(bind,[status(th)],[])).
% 0.58/0.61 tff(155,plain,
% 0.58/0.61 (![X: $i] : ((X = succ(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(succ(tptp_minus_1))))))) <=> ![X: $i] : ((X = succ(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(succ(tptp_minus_1)))))))),
% 0.58/0.61 inference(quant_intro,[status(thm)],[154])).
% 0.58/0.61 tff(156,plain,
% 0.58/0.61 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(succ(tptp_minus_1)))))) <=> (~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(succ(tptp_minus_1))))))))), ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(succ(tptp_minus_1))))))) <=> (~(~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(succ(tptp_minus_1))))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(succ(tptp_minus_1))))))) <=> ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(succ(tptp_minus_1))))))))), (((X = succ(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(succ(tptp_minus_1)))))))) <=> ((X = succ(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(succ(tptp_minus_1)))))))))), rewrite(((X = succ(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(succ(tptp_minus_1)))))))) <=> ((X = succ(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(succ(tptp_minus_1)))))))), (((X = succ(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(succ(tptp_minus_1)))))))) <=> ((X = succ(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(succ(tptp_minus_1)))))))))),
% 0.58/0.61 inference(bind,[status(th)],[])).
% 0.58/0.61 tff(157,plain,
% 0.58/0.61 (![X: $i] : ((X = succ(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(succ(tptp_minus_1)))))))) <=> ![X: $i] : ((X = succ(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(succ(tptp_minus_1)))))))),
% 0.58/0.61 inference(quant_intro,[status(thm)],[156])).
% 0.58/0.61 tff(158,plain,
% 0.58/0.61 (^[X: $i] : trans(monotonicity(rewrite((X = n3) <=> (X = succ(succ(succ(succ(tptp_minus_1)))))), 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, n3))) <=> (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(succ(tptp_minus_1)))))))), (((X = n3) | (X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n3)))) <=> ((X = succ(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(succ(tptp_minus_1)))))))))), rewrite(((X = succ(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(succ(tptp_minus_1)))))))) <=> ((X = succ(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(succ(tptp_minus_1))))))))), (((X = n3) | (X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n3)))) <=> ((X = succ(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(succ(tptp_minus_1))))))))))),
% 0.58/0.61 inference(bind,[status(th)],[])).
% 0.58/0.61 tff(159,plain,
% 0.58/0.61 (![X: $i] : ((X = n3) | (X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n3)))) <=> ![X: $i] : ((X = succ(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(succ(tptp_minus_1))))))))),
% 0.58/0.61 inference(quant_intro,[status(thm)],[158])).
% 0.58/0.61 tff(160,plain,
% 0.58/0.61 (![X: $i] : ((X = n3) | (X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n3)))) <=> ![X: $i] : ((X = n3) | (X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n3))))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(161,plain,
% 0.58/0.61 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((X = n0) | (X = n1)) | (X = n2)) <=> ((X = n2) | (X = n1) | (X = n0))), (((((X = n0) | (X = n1)) | (X = n2)) | (X = n3)) <=> (((X = n2) | (X = n1) | (X = n0)) | (X = n3)))), rewrite((((X = n2) | (X = n1) | (X = n0)) | (X = n3)) <=> ((X = n3) | (X = n2) | (X = n1) | (X = n0))), (((((X = n0) | (X = n1)) | (X = n2)) | (X = n3)) <=> ((X = n3) | (X = n2) | (X = n1) | (X = n0)))), (((leq(n0, X) & leq(X, n3)) => ((((X = n0) | (X = n1)) | (X = n2)) | (X = n3))) <=> ((leq(n0, X) & leq(X, n3)) => ((X = n3) | (X = n2) | (X = n1) | (X = n0))))), rewrite(((leq(n0, X) & leq(X, n3)) => ((X = n3) | (X = n2) | (X = n1) | (X = n0))) <=> ((X = n3) | (X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n3))))), (((leq(n0, X) & leq(X, n3)) => ((((X = n0) | (X = n1)) | (X = n2)) | (X = n3))) <=> ((X = n3) | (X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n3))))))),
% 0.58/0.61 inference(bind,[status(th)],[])).
% 0.58/0.61 tff(162,plain,
% 0.58/0.61 (![X: $i] : ((leq(n0, X) & leq(X, n3)) => ((((X = n0) | (X = n1)) | (X = n2)) | (X = n3))) <=> ![X: $i] : ((X = n3) | (X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n3))))),
% 0.58/0.61 inference(quant_intro,[status(thm)],[161])).
% 0.58/0.61 tff(163,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n3)) => ((((X = n0) | (X = n1)) | (X = n2)) | (X = n3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','finite_domain_3')).
% 0.58/0.61 tff(164,plain,
% 0.58/0.61 (![X: $i] : ((X = n3) | (X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n3))))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.58/0.61 tff(165,plain,
% 0.58/0.61 (![X: $i] : ((X = n3) | (X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n3))))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.58/0.61 tff(166,plain,
% 0.58/0.61 (![X: $i] : ((X = succ(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(succ(tptp_minus_1))))))))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[165, 159])).
% 0.58/0.61 tff(167,plain,(
% 0.58/0.61 ![X: $i] : ((X = succ(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(succ(tptp_minus_1))))))))),
% 0.58/0.61 inference(skolemize,[status(sab)],[166])).
% 0.58/0.61 tff(168,plain,
% 0.58/0.61 (![X: $i] : ((X = succ(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(succ(tptp_minus_1)))))))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[167, 157])).
% 0.58/0.61 tff(169,plain,
% 0.58/0.61 (![X: $i] : ((X = succ(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(succ(tptp_minus_1)))))))),
% 0.58/0.62 inference(modus_ponens,[status(thm)],[168, 155])).
% 0.58/0.62 tff(170,plain,
% 0.58/0.62 (((~![X: $i] : ((X = succ(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(succ(tptp_minus_1)))))))) | ((E!13 = succ(succ(succ(succ(tptp_minus_1))))) | (E!13 = succ(succ(succ(tptp_minus_1)))) | (E!13 = succ(succ(tptp_minus_1))) | (E!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(succ(tptp_minus_1)))))))) <=> ((~![X: $i] : ((X = succ(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(succ(tptp_minus_1)))))))) | (E!13 = succ(succ(succ(succ(tptp_minus_1))))) | (E!13 = succ(succ(succ(tptp_minus_1)))) | (E!13 = succ(succ(tptp_minus_1))) | (E!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.58/0.62 inference(rewrite,[status(thm)],[])).
% 0.58/0.62 tff(171,plain,
% 0.58/0.62 ((~![X: $i] : ((X = succ(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(succ(tptp_minus_1)))))))) | ((E!13 = succ(succ(succ(succ(tptp_minus_1))))) | (E!13 = succ(succ(succ(tptp_minus_1)))) | (E!13 = succ(succ(tptp_minus_1))) | (E!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.58/0.62 inference(quant_inst,[status(thm)],[])).
% 0.58/0.62 tff(172,plain,
% 0.58/0.62 ((~![X: $i] : ((X = succ(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(succ(tptp_minus_1)))))))) | (E!13 = succ(succ(succ(succ(tptp_minus_1))))) | (E!13 = succ(succ(succ(tptp_minus_1)))) | (E!13 = succ(succ(tptp_minus_1))) | (E!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(succ(tptp_minus_1))))))),
% 0.58/0.62 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.58/0.62 tff(173,plain,
% 0.58/0.62 ((E!13 = succ(succ(succ(succ(tptp_minus_1))))) | (E!13 = succ(succ(succ(tptp_minus_1)))) | (E!13 = succ(succ(tptp_minus_1))) | (E!13 = succ(tptp_minus_1)) | (~leq(E!13, succ(succ(succ(succ(tptp_minus_1))))))),
% 0.58/0.62 inference(unit_resolution,[status(thm)],[172, 169, 153])).
% 0.58/0.62 tff(174,plain,
% 0.58/0.62 ((E!13 = succ(succ(succ(tptp_minus_1)))) | (E!13 = succ(succ(tptp_minus_1))) | (E!13 = succ(tptp_minus_1)) | (~leq(E!13, succ(succ(succ(succ(tptp_minus_1))))))),
% 0.58/0.62 inference(unit_resolution,[status(thm)],[173, 152])).
% 0.58/0.62 tff(175,plain,
% 0.58/0.62 ((E!13 = succ(succ(succ(tptp_minus_1)))) | (E!13 = succ(succ(tptp_minus_1))) | (E!13 = succ(tptp_minus_1))),
% 0.58/0.62 inference(unit_resolution,[status(thm)],[174, 138])).
% 0.58/0.62 tff(176,plain,
% 0.58/0.62 ((E!13 = succ(succ(tptp_minus_1))) | (E!13 = succ(tptp_minus_1))),
% 0.58/0.62 inference(unit_resolution,[status(thm)],[175, 62])).
% 0.58/0.62 tff(177,plain,
% 0.58/0.62 (E!13 = succ(succ(tptp_minus_1))),
% 0.58/0.62 inference(unit_resolution,[status(thm)],[176, 48])).
% 0.58/0.62 tff(178,plain,
% 0.58/0.62 (a_select2(xinit_noise_defuse, E!13) = a_select2(xinit_noise_defuse, succ(succ(tptp_minus_1)))),
% 0.58/0.62 inference(monotonicity,[status(thm)],[177])).
% 0.58/0.62 tff(179,plain,
% 0.58/0.62 (a_select2(xinit_noise_defuse, E!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.58/0.62 inference(transitivity,[status(thm)],[178, 13])).
% 0.58/0.62 tff(180,plain,
% 0.58/0.62 ($false),
% 0.58/0.62 inference(unit_resolution,[status(thm)],[46, 179])).
% 0.58/0.62 % SZS output end Proof
%------------------------------------------------------------------------------