TSTP Solution File: SWV191+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV191+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 15:10:19 EDT 2022
% Result : Theorem 0.11s 0.30s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SWV191+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.00/0.07 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.06/0.26 % Computer : n001.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Sun Sep 4 02:02:56 EDT 2022
% 0.06/0.26 % CPUTime :
% 0.06/0.26 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.06/0.26 Usage: tptp [options] [-file:]file
% 0.06/0.26 -h, -? prints this message.
% 0.06/0.26 -smt2 print SMT-LIB2 benchmark.
% 0.06/0.26 -m, -model generate model.
% 0.06/0.26 -p, -proof generate proof.
% 0.06/0.26 -c, -core generate unsat core of named formulas.
% 0.06/0.26 -st, -statistics display statistics.
% 0.06/0.26 -t:timeout set timeout (in second).
% 0.06/0.26 -smt2status display status in smt2 format instead of SZS.
% 0.06/0.26 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.06/0.26 -<param>:<value> configuration parameter and value.
% 0.06/0.26 -o:<output-file> file to place output in.
% 0.11/0.30 % SZS status Theorem
% 0.11/0.30 % SZS output start Proof
% 0.11/0.30 tff(gt_type, type, (
% 0.11/0.30 gt: ( $i * $i ) > $o)).
% 0.11/0.30 tff(succ_type, type, (
% 0.11/0.30 succ: $i > $i)).
% 0.11/0.30 tff(tptp_minus_1_type, type, (
% 0.11/0.30 tptp_minus_1: $i)).
% 0.11/0.30 tff(leq_type, type, (
% 0.11/0.30 leq: ( $i * $i ) > $o)).
% 0.11/0.30 tff(tptp_fun_B_13_type, type, (
% 0.11/0.30 tptp_fun_B_13: $i)).
% 0.11/0.30 tff(tptp_fun_A_14_type, type, (
% 0.11/0.30 tptp_fun_A_14: $i)).
% 0.11/0.30 tff(a_select3_type, type, (
% 0.11/0.30 a_select3: ( $i * $i * $i ) > $i)).
% 0.11/0.30 tff(u_defuse_type, type, (
% 0.11/0.30 u_defuse: $i)).
% 0.11/0.30 tff(z_defuse_type, type, (
% 0.11/0.30 z_defuse: $i)).
% 0.11/0.30 tff(a_select2_type, type, (
% 0.11/0.30 a_select2: ( $i * $i ) > $i)).
% 0.11/0.30 tff(sigma_defuse_type, type, (
% 0.11/0.30 sigma_defuse: $i)).
% 0.11/0.30 tff(rho_defuse_type, type, (
% 0.11/0.30 rho_defuse: $i)).
% 0.11/0.30 tff(use_type, type, (
% 0.11/0.30 use: $i)).
% 0.11/0.30 tff(n2_type, type, (
% 0.11/0.30 n2: $i)).
% 0.11/0.30 tff(n0_type, type, (
% 0.11/0.30 n0: $i)).
% 0.11/0.30 tff(n5_type, type, (
% 0.11/0.30 n5: $i)).
% 0.11/0.30 tff(xinit_noise_defuse_type, type, (
% 0.11/0.30 xinit_noise_defuse: $i)).
% 0.11/0.30 tff(n4_type, type, (
% 0.11/0.30 n4: $i)).
% 0.11/0.30 tff(n3_type, type, (
% 0.11/0.30 n3: $i)).
% 0.11/0.30 tff(n1_type, type, (
% 0.11/0.30 n1: $i)).
% 0.11/0.30 tff(xinit_mean_defuse_type, type, (
% 0.11/0.30 xinit_mean_defuse: $i)).
% 0.11/0.30 tff(xinit_defuse_type, type, (
% 0.11/0.30 xinit_defuse: $i)).
% 0.11/0.30 tff(1,plain,
% 0.11/0.30 (^[X: $i, Y: $i] : refl((leq(X, Y) <=> gt(succ(Y), X)) <=> (leq(X, Y) <=> gt(succ(Y), X)))),
% 0.11/0.30 inference(bind,[status(th)],[])).
% 0.11/0.30 tff(2,plain,
% 0.11/0.30 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.11/0.30 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.30 tff(3,plain,
% 0.11/0.30 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(4,axiom,(![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_succ_gt_equiv')).
% 0.11/0.30 tff(5,plain,
% 0.11/0.30 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.30 tff(6,plain,(
% 0.11/0.30 ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.11/0.30 inference(skolemize,[status(sab)],[5])).
% 0.11/0.30 tff(7,plain,
% 0.11/0.30 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.30 tff(8,plain,
% 0.11/0.30 ((~![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))) | (leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.11/0.30 inference(quant_inst,[status(thm)],[])).
% 0.11/0.30 tff(9,plain,
% 0.11/0.30 (leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.11/0.30 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.30 tff(10,plain,
% 0.11/0.30 ((~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))) <=> (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(11,plain,
% 0.11/0.30 ((~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(12,plain,
% 0.11/0.30 ((~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(13,plain,
% 0.11/0.30 ((~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))))) <=> (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(14,plain,
% 0.11/0.30 ((~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))))) <=> (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(15,plain,
% 0.11/0.30 ((~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = use))) <=> (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(16,plain,
% 0.11/0.30 ((~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = use))) <=> (~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = use)))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(17,plain,
% 0.11/0.30 ((~((((((((((((((((((((((((((((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, tptp_minus_1)) => (a_select3(z_defuse, A, B) = 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, tptp_minus_1))) | (a_select3(z_defuse, A, B) = use))))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(18,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, tptp_minus_1)) => (a_select3(z_defuse, A, B) = use)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_inuse_0002')).
% 0.11/0.31 tff(19,plain,
% 0.11/0.31 (~((~((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, tptp_minus_1))) | (a_select3(z_defuse, A, B) = use)))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.31 tff(20,plain,
% 0.11/0.31 (~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = use))),
% 0.11/0.31 inference(or_elim,[status(thm)],[19])).
% 0.11/0.31 tff(21,plain,
% 0.11/0.31 (~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = use))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.11/0.31 tff(22,plain,
% 0.11/0.31 (~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = use))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.11/0.31 tff(23,plain,
% 0.11/0.31 (~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = use))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[22, 16])).
% 0.11/0.31 tff(24,plain,
% 0.11/0.31 (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[23, 15])).
% 0.11/0.31 tff(25,plain,
% 0.11/0.31 (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.11/0.31 tff(26,plain,
% 0.11/0.31 (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[25, 13])).
% 0.11/0.31 tff(27,plain,
% 0.11/0.31 (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[26, 12])).
% 0.11/0.31 tff(28,plain,
% 0.11/0.31 (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[27, 11])).
% 0.11/0.31 tff(29,plain,
% 0.11/0.31 (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[28, 10])).
% 0.11/0.31 tff(30,plain,
% 0.11/0.31 (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[29, 10])).
% 0.11/0.31 tff(31,plain,
% 0.11/0.31 (~![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, tptp_minus_1))) | (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[30, 10])).
% 0.11/0.31 tff(32,plain,(
% 0.11/0.31 ~((~(leq(succ(tptp_minus_1), A!14) & leq(succ(tptp_minus_1), B!13) & leq(A!14, succ(succ(succ(tptp_minus_1)))) & leq(B!13, tptp_minus_1))) | (a_select3(z_defuse, A!14, B!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.11/0.31 inference(skolemize,[status(sab)],[31])).
% 0.11/0.31 tff(33,plain,
% 0.11/0.31 (leq(succ(tptp_minus_1), A!14) & leq(succ(tptp_minus_1), B!13) & leq(A!14, succ(succ(succ(tptp_minus_1)))) & leq(B!13, tptp_minus_1)),
% 0.11/0.31 inference(or_elim,[status(thm)],[32])).
% 0.11/0.31 tff(34,plain,
% 0.11/0.31 (leq(B!13, tptp_minus_1)),
% 0.11/0.31 inference(and_elim,[status(thm)],[33])).
% 0.11/0.31 tff(35,plain,
% 0.11/0.31 (leq(succ(tptp_minus_1), B!13)),
% 0.11/0.31 inference(and_elim,[status(thm)],[33])).
% 0.11/0.31 tff(36,plain,
% 0.11/0.31 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(37,plain,
% 0.11/0.31 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 0.11/0.31 inference(bind,[status(th)],[])).
% 0.11/0.31 tff(38,plain,
% 0.11/0.31 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.11/0.31 inference(quant_intro,[status(thm)],[37])).
% 0.11/0.31 tff(39,plain,
% 0.11/0.31 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(40,plain,
% 0.11/0.31 (^[X: $i, Y: $i, Z: $i] : rewrite(((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)))),
% 0.11/0.31 inference(bind,[status(th)],[])).
% 0.11/0.31 tff(41,plain,
% 0.11/0.31 (![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.11/0.31 inference(quant_intro,[status(thm)],[40])).
% 0.11/0.31 tff(42,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 0.11/0.31 tff(43,plain,
% 0.11/0.31 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.11/0.31 tff(44,plain,
% 0.11/0.31 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.11/0.31 tff(45,plain,(
% 0.11/0.31 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.11/0.31 inference(skolemize,[status(sab)],[44])).
% 0.11/0.31 tff(46,plain,
% 0.11/0.31 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.11/0.31 tff(47,plain,
% 0.11/0.31 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.11/0.31 tff(48,plain,
% 0.11/0.31 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(49,plain,
% 0.11/0.31 ((leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)) | (~leq(succ(tptp_minus_1), B!13))) <=> ((~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(50,plain,
% 0.11/0.31 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)) | (~leq(succ(tptp_minus_1), B!13)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1))))),
% 0.11/0.31 inference(monotonicity,[status(thm)],[49])).
% 0.11/0.31 tff(51,plain,
% 0.11/0.31 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)) | (~leq(succ(tptp_minus_1), B!13)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)))),
% 0.11/0.31 inference(transitivity,[status(thm)],[50, 48])).
% 0.11/0.31 tff(52,plain,
% 0.11/0.31 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)) | (~leq(succ(tptp_minus_1), B!13)))),
% 0.11/0.31 inference(quant_inst,[status(thm)],[])).
% 0.11/0.31 tff(53,plain,
% 0.11/0.31 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.11/0.31 tff(54,plain,
% 0.11/0.31 (leq(succ(tptp_minus_1), tptp_minus_1)),
% 0.11/0.31 inference(unit_resolution,[status(thm)],[53, 47, 35, 34])).
% 0.11/0.31 tff(55,plain,
% 0.11/0.31 ((~(leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1)))) | (~leq(succ(tptp_minus_1), tptp_minus_1)) | gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.11/0.31 inference(tautology,[status(thm)],[])).
% 0.11/0.31 tff(56,plain,
% 0.11/0.31 ((~(leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1)))) | gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.11/0.31 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.11/0.31 tff(57,plain,
% 0.11/0.31 (gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.11/0.31 inference(unit_resolution,[status(thm)],[56, 9])).
% 0.11/0.31 tff(58,plain,
% 0.11/0.31 (^[X: $i] : refl((~gt(X, X)) <=> (~gt(X, X)))),
% 0.11/0.31 inference(bind,[status(th)],[])).
% 0.11/0.31 tff(59,plain,
% 0.11/0.31 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.11/0.31 inference(quant_intro,[status(thm)],[58])).
% 0.11/0.31 tff(60,plain,
% 0.11/0.31 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(61,axiom,(![X: $i] : (~gt(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','irreflexivity_gt')).
% 0.11/0.31 tff(62,plain,
% 0.11/0.31 (![X: $i] : (~gt(X, X))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.11/0.31 tff(63,plain,(
% 0.11/0.31 ![X: $i] : (~gt(X, X))),
% 0.11/0.31 inference(skolemize,[status(sab)],[62])).
% 0.11/0.31 tff(64,plain,
% 0.11/0.31 (![X: $i] : (~gt(X, X))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.11/0.31 tff(65,plain,
% 0.11/0.31 ((~![X: $i] : (~gt(X, X))) | (~gt(succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.11/0.31 inference(quant_inst,[status(thm)],[])).
% 0.11/0.31 tff(66,plain,
% 0.11/0.31 ($false),
% 0.11/0.31 inference(unit_resolution,[status(thm)],[65, 64, 57])).
% 0.11/0.31 % SZS output end Proof
%------------------------------------------------------------------------------