TSTP Solution File: SWV204+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV204+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 15:10:22 EDT 2022
% Result : Theorem 0.61s 0.64s
% Output : Proof 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV204+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Sep 4 01:43:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.61/0.64 % SZS status Theorem
% 0.61/0.64 % SZS output start Proof
% 0.61/0.64 tff(a_select3_type, type, (
% 0.61/0.64 a_select3: ( $i * $i * $i ) > $i)).
% 0.61/0.64 tff(succ_type, type, (
% 0.61/0.64 succ: $i > $i)).
% 0.61/0.64 tff(tptp_minus_1_type, type, (
% 0.61/0.64 tptp_minus_1: $i)).
% 0.61/0.64 tff(u_defuse_type, type, (
% 0.61/0.64 u_defuse: $i)).
% 0.61/0.64 tff(a_select2_type, type, (
% 0.61/0.64 a_select2: ( $i * $i ) > $i)).
% 0.61/0.64 tff(tptp_fun_E_13_type, type, (
% 0.61/0.64 tptp_fun_E_13: $i)).
% 0.61/0.64 tff(rho_defuse_type, type, (
% 0.61/0.64 rho_defuse: $i)).
% 0.61/0.64 tff(sigma_defuse_type, type, (
% 0.61/0.64 sigma_defuse: $i)).
% 0.61/0.64 tff(use_type, type, (
% 0.61/0.64 use: $i)).
% 0.61/0.64 tff(n0_type, type, (
% 0.61/0.64 n0: $i)).
% 0.61/0.64 tff(z_defuse_type, type, (
% 0.61/0.64 z_defuse: $i)).
% 0.61/0.64 tff(leq_type, type, (
% 0.61/0.64 leq: ( $i * $i ) > $o)).
% 0.61/0.64 tff(n998_type, type, (
% 0.61/0.64 n998: $i)).
% 0.61/0.64 tff(n2_type, type, (
% 0.61/0.64 n2: $i)).
% 0.61/0.64 tff(n5_type, type, (
% 0.61/0.64 n5: $i)).
% 0.61/0.64 tff(xinit_noise_defuse_type, type, (
% 0.61/0.64 xinit_noise_defuse: $i)).
% 0.61/0.64 tff(n4_type, type, (
% 0.61/0.64 n4: $i)).
% 0.61/0.64 tff(n3_type, type, (
% 0.61/0.64 n3: $i)).
% 0.61/0.64 tff(n1_type, type, (
% 0.61/0.64 n1: $i)).
% 0.61/0.64 tff(xinit_mean_defuse_type, type, (
% 0.61/0.64 xinit_mean_defuse: $i)).
% 0.61/0.64 tff(xinit_defuse_type, type, (
% 0.61/0.64 xinit_defuse: $i)).
% 0.61/0.64 tff(1,plain,
% 0.61/0.64 ((a_select2(sigma_defuse, succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1))) <=> (a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(2,plain,
% 0.61/0.64 ((a_select2(sigma_defuse, n0) = use) <=> (a_select2(sigma_defuse, succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(3,plain,
% 0.61/0.64 ((a_select2(sigma_defuse, n0) = use) <=> (a_select2(sigma_defuse, n0) = use)),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(4,plain,
% 0.61/0.64 ((~((((((((((((((((((((((((((((((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, n2)) => (a_select2(rho_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, n2))) | (a_select2(rho_defuse, E) = use))))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(5,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, n2)) => (a_select2(rho_defuse, E) = use)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_inuse_0015')).
% 0.61/0.64 tff(6,plain,
% 0.61/0.64 (~((~((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, n2))) | (a_select2(rho_defuse, E) = use)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.61/0.64 tff(7,plain,
% 0.61/0.64 ((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))),
% 0.61/0.64 inference(or_elim,[status(thm)],[6])).
% 0.61/0.64 tff(8,plain,
% 0.61/0.64 (a_select2(sigma_defuse, n0) = use),
% 0.61/0.64 inference(and_elim,[status(thm)],[7])).
% 0.61/0.64 tff(9,plain,
% 0.61/0.64 (a_select2(sigma_defuse, n0) = use),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.61/0.64 tff(10,plain,
% 0.61/0.64 (a_select2(sigma_defuse, succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.61/0.64 tff(11,plain,
% 0.61/0.64 (a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.61/0.64 tff(12,plain,
% 0.61/0.64 (a_select2(rho_defuse, succ(tptp_minus_1)) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.61/0.64 inference(symmetry,[status(thm)],[11])).
% 0.61/0.64 tff(13,plain,
% 0.61/0.64 ((a_select2(rho_defuse, succ(succ(tptp_minus_1))) = a_select2(rho_defuse, succ(tptp_minus_1))) <=> (a_select2(rho_defuse, succ(succ(tptp_minus_1))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(14,plain,
% 0.61/0.64 ((a_select2(rho_defuse, n1) = use) <=> (a_select2(rho_defuse, succ(succ(tptp_minus_1))) = a_select2(rho_defuse, succ(tptp_minus_1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(15,plain,
% 0.61/0.64 ((a_select2(rho_defuse, n1) = use) <=> (a_select2(rho_defuse, n1) = use)),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(16,plain,
% 0.61/0.64 (a_select2(rho_defuse, n1) = use),
% 0.61/0.64 inference(and_elim,[status(thm)],[7])).
% 0.61/0.64 tff(17,plain,
% 0.61/0.64 (a_select2(rho_defuse, n1) = use),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.61/0.64 tff(18,plain,
% 0.61/0.64 (a_select2(rho_defuse, succ(succ(tptp_minus_1))) = a_select2(rho_defuse, succ(tptp_minus_1))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.61/0.64 tff(19,plain,
% 0.61/0.64 (a_select2(rho_defuse, succ(succ(tptp_minus_1))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.61/0.64 tff(20,assumption,(E!13 = succ(succ(tptp_minus_1))), introduced(assumption)).
% 0.61/0.64 tff(21,plain,
% 0.61/0.64 (a_select2(rho_defuse, E!13) = a_select2(rho_defuse, succ(succ(tptp_minus_1)))),
% 0.61/0.64 inference(monotonicity,[status(thm)],[20])).
% 0.61/0.64 tff(22,plain,
% 0.61/0.64 (a_select2(rho_defuse, E!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.61/0.64 inference(transitivity,[status(thm)],[21, 19])).
% 0.61/0.64 tff(23,plain,
% 0.61/0.64 ((~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_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(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(24,plain,
% 0.61/0.64 ((~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(25,plain,
% 0.61/0.64 ((~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(26,plain,
% 0.61/0.64 ((~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select2(rho_defuse, succ(tptp_minus_1))))) <=> (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(27,plain,
% 0.61/0.64 ((~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select2(rho_defuse, succ(tptp_minus_1))))) <=> (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(28,plain,
% 0.61/0.64 ((~![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | (a_select2(rho_defuse, E) = use))) <=> (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(29,plain,
% 0.61/0.64 ((~![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | (a_select2(rho_defuse, E) = use))) <=> (~![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | (a_select2(rho_defuse, E) = use)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(30,plain,
% 0.61/0.64 (~![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | (a_select2(rho_defuse, E) = use))),
% 0.61/0.64 inference(or_elim,[status(thm)],[6])).
% 0.61/0.64 tff(31,plain,
% 0.61/0.64 (~![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | (a_select2(rho_defuse, E) = use))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.61/0.64 tff(32,plain,
% 0.61/0.64 (~![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | (a_select2(rho_defuse, E) = use))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[31, 29])).
% 0.61/0.64 tff(33,plain,
% 0.61/0.64 (~![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | (a_select2(rho_defuse, E) = use))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.61/0.64 tff(34,plain,
% 0.61/0.64 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.61/0.64 tff(35,plain,
% 0.61/0.64 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.61/0.64 tff(36,plain,
% 0.61/0.64 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[35, 26])).
% 0.61/0.64 tff(37,plain,
% 0.61/0.64 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[36, 25])).
% 0.61/0.64 tff(38,plain,
% 0.61/0.64 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[37, 24])).
% 0.61/0.64 tff(39,plain,
% 0.61/0.64 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[38, 23])).
% 0.61/0.64 tff(40,plain,
% 0.61/0.64 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[39, 23])).
% 0.61/0.64 tff(41,plain,
% 0.61/0.64 (~![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[40, 23])).
% 0.61/0.64 tff(42,plain,(
% 0.61/0.64 ~((~(leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))))) | (a_select2(rho_defuse, E!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.61/0.64 inference(skolemize,[status(sab)],[41])).
% 0.61/0.64 tff(43,plain,
% 0.61/0.64 (~(a_select2(rho_defuse, E!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.61/0.64 inference(or_elim,[status(thm)],[42])).
% 0.61/0.64 tff(44,plain,
% 0.61/0.64 ($false),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[43, 22])).
% 0.61/0.64 tff(45,plain,(~(E!13 = succ(succ(tptp_minus_1)))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.64 tff(46,plain,
% 0.61/0.64 ((a_select2(rho_defuse, succ(succ(succ(tptp_minus_1)))) = a_select2(rho_defuse, succ(tptp_minus_1))) <=> (a_select2(rho_defuse, succ(succ(succ(tptp_minus_1)))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(47,plain,
% 0.61/0.64 ((a_select2(rho_defuse, n2) = use) <=> (a_select2(rho_defuse, succ(succ(succ(tptp_minus_1)))) = a_select2(rho_defuse, succ(tptp_minus_1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(48,plain,
% 0.61/0.64 ((a_select2(rho_defuse, n2) = use) <=> (a_select2(rho_defuse, n2) = use)),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(49,plain,
% 0.61/0.64 (a_select2(rho_defuse, n2) = use),
% 0.61/0.64 inference(and_elim,[status(thm)],[7])).
% 0.61/0.64 tff(50,plain,
% 0.61/0.64 (a_select2(rho_defuse, n2) = use),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.61/0.64 tff(51,plain,
% 0.61/0.64 (a_select2(rho_defuse, succ(succ(succ(tptp_minus_1)))) = a_select2(rho_defuse, succ(tptp_minus_1))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[50, 47])).
% 0.61/0.64 tff(52,plain,
% 0.61/0.64 (a_select2(rho_defuse, succ(succ(succ(tptp_minus_1)))) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[51, 46])).
% 0.61/0.64 tff(53,assumption,(E!13 = succ(succ(succ(tptp_minus_1)))), introduced(assumption)).
% 0.61/0.64 tff(54,plain,
% 0.61/0.64 (a_select2(rho_defuse, E!13) = a_select2(rho_defuse, succ(succ(succ(tptp_minus_1))))),
% 0.61/0.64 inference(monotonicity,[status(thm)],[53])).
% 0.61/0.64 tff(55,plain,
% 0.61/0.64 (a_select2(rho_defuse, E!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.61/0.64 inference(transitivity,[status(thm)],[54, 52])).
% 0.61/0.64 tff(56,plain,
% 0.61/0.64 ($false),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[43, 55])).
% 0.61/0.64 tff(57,plain,(~(E!13 = succ(succ(succ(tptp_minus_1))))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.64 tff(58,plain,
% 0.61/0.64 (leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1))))),
% 0.61/0.64 inference(or_elim,[status(thm)],[42])).
% 0.61/0.64 tff(59,plain,
% 0.61/0.64 (leq(E!13, succ(succ(succ(tptp_minus_1))))),
% 0.61/0.64 inference(and_elim,[status(thm)],[58])).
% 0.61/0.64 tff(60,plain,
% 0.61/0.64 (leq(succ(tptp_minus_1), E!13)),
% 0.61/0.64 inference(and_elim,[status(thm)],[58])).
% 0.61/0.64 tff(61,plain,
% 0.61/0.64 (^[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)))))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(62,plain,
% 0.61/0.64 (![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))))))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[61])).
% 0.61/0.64 tff(63,plain,
% 0.61/0.64 (^[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))))))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(64,plain,
% 0.61/0.65 (![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))))))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[63])).
% 0.61/0.65 tff(65,plain,
% 0.61/0.65 (^[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)))))))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(66,plain,
% 0.61/0.65 (![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)))))))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[65])).
% 0.61/0.65 tff(67,plain,
% 0.61/0.65 (![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))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(68,plain,
% 0.61/0.65 (^[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))))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(69,plain,
% 0.61/0.65 (![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))))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[68])).
% 0.61/0.65 tff(70,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n2)) => (((X = n0) | (X = n1)) | (X = n2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','finite_domain_2')).
% 0.61/0.65 tff(71,plain,
% 0.61/0.65 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.61/0.65 tff(72,plain,
% 0.61/0.65 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.61/0.65 tff(73,plain,
% 0.61/0.65 (![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)))))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[72, 66])).
% 0.61/0.65 tff(74,plain,(
% 0.61/0.65 ![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)))))))),
% 0.61/0.65 inference(skolemize,[status(sab)],[73])).
% 0.61/0.65 tff(75,plain,
% 0.61/0.65 (![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))))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.61/0.65 tff(76,plain,
% 0.61/0.65 (![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))))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[75, 62])).
% 0.61/0.65 tff(77,plain,
% 0.61/0.65 (((~![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!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(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))))))) | (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(tptp_minus_1))))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(78,plain,
% 0.61/0.65 ((~![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!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(tptp_minus_1))))))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(79,plain,
% 0.61/0.65 ((~![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) | (E!13 = succ(succ(succ(tptp_minus_1)))) | (E!13 = succ(succ(tptp_minus_1))) | (E!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(tptp_minus_1)))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.61/0.65 tff(80,plain,
% 0.61/0.65 ((E!13 = succ(succ(succ(tptp_minus_1)))) | (E!13 = succ(succ(tptp_minus_1))) | (E!13 = succ(tptp_minus_1))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[79, 76, 60, 59])).
% 0.61/0.65 tff(81,plain,
% 0.61/0.65 ((E!13 = succ(succ(tptp_minus_1))) | (E!13 = succ(tptp_minus_1))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[80, 57])).
% 0.61/0.65 tff(82,plain,
% 0.61/0.65 (E!13 = succ(tptp_minus_1)),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[81, 45])).
% 0.61/0.65 tff(83,plain,
% 0.61/0.65 (a_select2(rho_defuse, E!13) = a_select2(rho_defuse, succ(tptp_minus_1))),
% 0.61/0.65 inference(monotonicity,[status(thm)],[82])).
% 0.61/0.65 tff(84,plain,
% 0.61/0.65 (a_select2(rho_defuse, E!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.61/0.65 inference(transitivity,[status(thm)],[83, 12])).
% 0.65/0.65 tff(85,plain,
% 0.65/0.65 ($false),
% 0.65/0.65 inference(unit_resolution,[status(thm)],[43, 84])).
% 0.65/0.65 % SZS output end Proof
%------------------------------------------------------------------------------