TSTP Solution File: SWV203+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV203+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:10:21 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV203+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 01:27:36 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(succ_type, type, (
% 0.20/0.46 succ: $i > $i)).
% 0.20/0.46 tff(tptp_minus_1_type, type, (
% 0.20/0.46 tptp_minus_1: $i)).
% 0.20/0.46 tff(tptp_fun_E_14_type, type, (
% 0.20/0.46 tptp_fun_E_14: $i)).
% 0.20/0.46 tff(tptp_fun_F_13_type, type, (
% 0.20/0.46 tptp_fun_F_13: $i)).
% 0.20/0.46 tff(pv5_type, type, (
% 0.20/0.46 pv5: $i)).
% 0.20/0.46 tff(gt_type, type, (
% 0.20/0.46 gt: ( $i * $i ) > $o)).
% 0.20/0.46 tff(leq_type, type, (
% 0.20/0.46 leq: ( $i * $i ) > $o)).
% 0.20/0.46 tff(pred_type, type, (
% 0.20/0.46 pred: $i > $i)).
% 0.20/0.46 tff(a_select3_type, type, (
% 0.20/0.46 a_select3: ( $i * $i * $i ) > $i)).
% 0.20/0.46 tff(u_defuse_type, type, (
% 0.20/0.46 u_defuse: $i)).
% 0.20/0.46 tff(z_defuse_type, type, (
% 0.20/0.46 z_defuse: $i)).
% 0.20/0.46 tff(a_select2_type, type, (
% 0.20/0.46 a_select2: ( $i * $i ) > $i)).
% 0.20/0.46 tff(sigma_defuse_type, type, (
% 0.20/0.46 sigma_defuse: $i)).
% 0.20/0.46 tff(rho_defuse_type, type, (
% 0.20/0.46 rho_defuse: $i)).
% 0.20/0.46 tff(n2_type, type, (
% 0.20/0.46 n2: $i)).
% 0.20/0.46 tff(n0_type, type, (
% 0.20/0.46 n0: $i)).
% 0.20/0.46 tff(n1_type, type, (
% 0.20/0.46 n1: $i)).
% 0.20/0.46 tff(use_type, type, (
% 0.20/0.46 use: $i)).
% 0.20/0.46 tff(n998_type, type, (
% 0.20/0.46 n998: $i)).
% 0.20/0.46 tff(n5_type, type, (
% 0.20/0.46 n5: $i)).
% 0.20/0.46 tff(xinit_noise_defuse_type, type, (
% 0.20/0.46 xinit_noise_defuse: $i)).
% 0.20/0.46 tff(n4_type, type, (
% 0.20/0.46 n4: $i)).
% 0.20/0.46 tff(n3_type, type, (
% 0.20/0.46 n3: $i)).
% 0.20/0.46 tff(xinit_mean_defuse_type, type, (
% 0.20/0.46 xinit_mean_defuse: $i)).
% 0.20/0.46 tff(xinit_defuse_type, type, (
% 0.20/0.46 xinit_defuse: $i)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 ((E!14 = succ(tptp_minus_1)) <=> (succ(tptp_minus_1) = E!14)),
% 0.20/0.46 inference(commutativity,[status(thm)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 ((succ(tptp_minus_1) = E!14) <=> (E!14 = succ(tptp_minus_1))),
% 0.20/0.46 inference(symmetry,[status(thm)],[1])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 ((~(succ(tptp_minus_1) = E!14)) <=> (~(E!14 = succ(tptp_minus_1)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 ((F!13 = pv5) <=> (pv5 = F!13)),
% 0.20/0.46 inference(commutativity,[status(thm)],[])).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(6,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(8,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.46 tff(10,plain,(
% 0.20/0.46 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.46 inference(skolemize,[status(sab)],[9])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(F!13, pred(pv5)) <=> gt(pv5, F!13))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (leq(F!13, pred(pv5)) <=> gt(pv5, F!13)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 ((~((~((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) & (~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) & (~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))))) | (~(leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))) <=> (~((~((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) & (~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) & (~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))))) | (~(leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 ((~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 ((~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 ((~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 ((~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))))) <=> (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 ((~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))))) <=> (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 ((~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))) <=> (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 ((~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))) <=> (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 ((~(((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, n998)) & gt(pv5, n0)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pred(pv5))) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, pred(pv5))) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pv5)) => ((((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F)))) & (~((n2 = E) & (pv5 = F)))) => (a_select3(z_defuse, E, F) = use))))) <=> (~((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n998) & gt(pv5, n0) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)))) | ![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(23,axiom,(~(((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, n998)) & gt(pv5, n0)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pred(pv5))) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, pred(pv5))) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pv5)) => ((((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F)))) & (~((n2 = E) & (pv5 = F)))) => (a_select3(z_defuse, E, F) = use))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_inuse_0014')).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (~((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n998) & gt(pv5, n0) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)))) | ![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.20/0.47 inference(or_elim,[status(thm)],[24])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[30, 18])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[31, 17])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[32, 16])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[33, 15])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[34, 15])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[35, 15])).
% 0.20/0.47 tff(37,plain,(
% 0.20/0.47 ~((~((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) & (~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) & (~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))))) | (~(leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[36])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (~((~((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) & (~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) & (~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))))) | (~(leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[37, 14])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 (~(a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.20/0.47 inference(or_elim,[status(thm)],[38])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 (leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5)),
% 0.20/0.47 inference(or_elim,[status(thm)],[38])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (leq(E!14, succ(succ(succ(tptp_minus_1))))),
% 0.20/0.47 inference(and_elim,[status(thm)],[40])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 (leq(succ(tptp_minus_1), F!13)),
% 0.20/0.47 inference(and_elim,[status(thm)],[40])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 (leq(succ(tptp_minus_1), E!14)),
% 0.20/0.47 inference(and_elim,[status(thm)],[40])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 (^[C: $i, D: $i] : refl(((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))) <=> ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 (![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))) <=> ![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 (^[C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5))) <=> (~((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))))), ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) <=> (~(~((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))))))), rewrite((~(~((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))), ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))))), (((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) <=> (((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))), rewrite((((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))), (((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) <=> ![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (^[C: $i, D: $i] : rewrite(((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1)))) <=> ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1)))) <=> ![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (^[C: $i, D: $i] : rewrite(((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1)))) <=> ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 (![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1)))) <=> ![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (^[C: $i, D: $i] : rewrite(((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)) <=> ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)) <=> ![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)) <=> ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 ((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n998) & gt(pv5, n0) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 0.20/0.48 inference(or_elim,[status(thm)],[24])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 0.20/0.48 inference(and_elim,[status(thm)],[55])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[56, 54])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 (![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 (![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 (![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.20/0.48 tff(61,plain,(
% 0.20/0.48 ![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[60])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[61, 47])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 (![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[62, 45])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 (((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | ((a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, pred(pv5))))) <=> ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, pred(pv5))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 (((~leq(succ(tptp_minus_1), E!14)) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5)))) <=> ((a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, pred(pv5))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 (((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | ((~leq(succ(tptp_minus_1), E!14)) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5))))) <=> ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | ((a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, pred(pv5)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[65])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 (((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | ((~leq(succ(tptp_minus_1), E!14)) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5))))) <=> ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, pred(pv5))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[66, 64])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | ((~leq(succ(tptp_minus_1), E!14)) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, pred(pv5)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 (~leq(F!13, pred(pv5))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[69, 63, 43, 42, 41, 39])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 ((~(leq(F!13, pred(pv5)) <=> gt(pv5, F!13))) | leq(F!13, pred(pv5)) | (~gt(pv5, F!13))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 ((~(leq(F!13, pred(pv5)) <=> gt(pv5, F!13))) | (~gt(pv5, F!13))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 (~gt(pv5, F!13)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[72, 13])).
% 0.20/0.48 tff(74,plain,
% 0.20/0.48 (leq(F!13, pv5)),
% 0.20/0.48 inference(and_elim,[status(thm)],[40])).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 (^[X: $i, Y: $i] : refl(((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(76,plain,
% 0.20/0.48 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.48 tff(77,plain,
% 0.20/0.48 (^[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)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(78,plain,
% 0.20/0.48 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.48 tff(79,plain,
% 0.20/0.48 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(80,plain,
% 0.20/0.48 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(81,plain,
% 0.20/0.48 (![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.48 tff(82,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt2')).
% 0.20/0.48 tff(83,plain,
% 0.20/0.48 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.48 tff(84,plain,
% 0.20/0.48 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.48 tff(85,plain,(
% 0.20/0.48 ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.20/0.48 inference(skolemize,[status(sab)],[84])).
% 0.20/0.48 tff(86,plain,
% 0.20/0.48 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.20/0.48 tff(87,plain,
% 0.20/0.48 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((F!13 = pv5) | gt(pv5, F!13) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (F!13 = pv5) | gt(pv5, F!13) | (~leq(F!13, pv5)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((F!13 = pv5) | gt(pv5, F!13) | (~leq(F!13, pv5)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(90,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (F!13 = pv5) | gt(pv5, F!13) | (~leq(F!13, pv5))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 ((F!13 = pv5) | gt(pv5, F!13)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[90, 87, 74])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 (F!13 = pv5),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[91, 73])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 (pv5 = F!13),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[92, 4])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 ((~(~((~(succ(tptp_minus_1) = E!14)) | (~(pv5 = F!13))))) <=> ((~(succ(tptp_minus_1) = E!14)) | (~(pv5 = F!13)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 (((succ(tptp_minus_1) = E!14) & (pv5 = F!13)) <=> (~((~(succ(tptp_minus_1) = E!14)) | (~(pv5 = F!13))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 ((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) <=> (~(~((~(succ(tptp_minus_1) = E!14)) | (~(pv5 = F!13)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[95])).
% 0.20/0.48 tff(97,plain,
% 0.20/0.48 ((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) <=> ((~(succ(tptp_minus_1) = E!14)) | (~(pv5 = F!13)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[96, 94])).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 ((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) & (~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) & (~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13)))),
% 0.20/0.48 inference(or_elim,[status(thm)],[38])).
% 0.20/0.48 tff(99,plain,
% 0.20/0.48 (~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))),
% 0.20/0.48 inference(and_elim,[status(thm)],[98])).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 ((~(succ(tptp_minus_1) = E!14)) | (~(pv5 = F!13))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[99, 97])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 (~(succ(tptp_minus_1) = E!14)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[100, 93])).
% 0.20/0.48 tff(102,plain,
% 0.20/0.48 (~(E!14 = succ(tptp_minus_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[101, 3])).
% 0.20/0.48 tff(103,plain,
% 0.20/0.48 ((E!14 = succ(succ(tptp_minus_1))) <=> (succ(succ(tptp_minus_1)) = E!14)),
% 0.20/0.48 inference(commutativity,[status(thm)],[])).
% 0.20/0.48 tff(104,plain,
% 0.20/0.48 ((succ(succ(tptp_minus_1)) = E!14) <=> (E!14 = succ(succ(tptp_minus_1)))),
% 0.20/0.48 inference(symmetry,[status(thm)],[103])).
% 0.20/0.48 tff(105,plain,
% 0.20/0.48 ((~(succ(succ(tptp_minus_1)) = E!14)) <=> (~(E!14 = succ(succ(tptp_minus_1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[104])).
% 0.20/0.48 tff(106,plain,
% 0.20/0.48 ((~(~((~(pv5 = F!13)) | (~(succ(succ(tptp_minus_1)) = E!14))))) <=> ((~(pv5 = F!13)) | (~(succ(succ(tptp_minus_1)) = E!14)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(107,plain,
% 0.20/0.48 (((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13)) <=> (~((~(pv5 = F!13)) | (~(succ(succ(tptp_minus_1)) = E!14))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(108,plain,
% 0.20/0.48 ((~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) <=> (~(~((~(pv5 = F!13)) | (~(succ(succ(tptp_minus_1)) = E!14)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[107])).
% 0.20/0.48 tff(109,plain,
% 0.20/0.48 ((~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) <=> ((~(pv5 = F!13)) | (~(succ(succ(tptp_minus_1)) = E!14)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[108, 106])).
% 0.20/0.48 tff(110,plain,
% 0.20/0.48 (~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))),
% 0.20/0.48 inference(and_elim,[status(thm)],[98])).
% 0.20/0.48 tff(111,plain,
% 0.20/0.48 ((~(pv5 = F!13)) | (~(succ(succ(tptp_minus_1)) = E!14))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.48 tff(112,plain,
% 0.20/0.48 (~(succ(succ(tptp_minus_1)) = E!14)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[111, 93])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 (~(E!14 = succ(succ(tptp_minus_1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.20/0.48 tff(114,plain,
% 0.20/0.48 ((E!14 = succ(succ(succ(tptp_minus_1)))) <=> (succ(succ(succ(tptp_minus_1))) = E!14)),
% 0.20/0.48 inference(commutativity,[status(thm)],[])).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 ((succ(succ(succ(tptp_minus_1))) = E!14) <=> (E!14 = succ(succ(succ(tptp_minus_1))))),
% 0.20/0.48 inference(symmetry,[status(thm)],[114])).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 ((~(succ(succ(succ(tptp_minus_1))) = E!14)) <=> (~(E!14 = succ(succ(succ(tptp_minus_1)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 ((~(~((~(pv5 = F!13)) | (~(succ(succ(succ(tptp_minus_1))) = E!14))))) <=> ((~(pv5 = F!13)) | (~(succ(succ(succ(tptp_minus_1))) = E!14)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 (((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13)) <=> (~((~(pv5 = F!13)) | (~(succ(succ(succ(tptp_minus_1))) = E!14))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 ((~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))) <=> (~(~((~(pv5 = F!13)) | (~(succ(succ(succ(tptp_minus_1))) = E!14)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[118])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 ((~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))) <=> ((~(pv5 = F!13)) | (~(succ(succ(succ(tptp_minus_1))) = E!14)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[119, 117])).
% 0.20/0.48 tff(121,plain,
% 0.20/0.48 (~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))),
% 0.20/0.48 inference(and_elim,[status(thm)],[98])).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 ((~(pv5 = F!13)) | (~(succ(succ(succ(tptp_minus_1))) = E!14))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 (~(succ(succ(succ(tptp_minus_1))) = E!14)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[122, 93])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 (~(E!14 = succ(succ(succ(tptp_minus_1))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 (^[X: $i] : refl(((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 (![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))) <=> ![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1)))))))), (((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))))), rewrite(((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))), (((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))))) <=> ![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 (^[X: $i] : trans(monotonicity(rewrite((X = n2) <=> (X = succ(succ(succ(tptp_minus_1))))), rewrite((X = n1) <=> (X = succ(succ(tptp_minus_1)))), rewrite((X = n0) <=> (X = succ(tptp_minus_1))), rewrite((~(leq(n0, X) & leq(X, n2))) <=> (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))))), (((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2)))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))))))), rewrite(((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1))))))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))))), (((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2)))) <=> ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(130,plain,
% 0.20/0.48 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2)))) <=> ![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2)))) <=> ![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 (^[X: $i] : trans(monotonicity(rewrite((((X = n0) | (X = n1)) | (X = n2)) <=> ((X = n2) | (X = n1) | (X = n0))), (((leq(n0, X) & leq(X, n2)) => (((X = n0) | (X = n1)) | (X = n2))) <=> ((leq(n0, X) & leq(X, n2)) => ((X = n2) | (X = n1) | (X = n0))))), rewrite(((leq(n0, X) & leq(X, n2)) => ((X = n2) | (X = n1) | (X = n0))) <=> ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))), (((leq(n0, X) & leq(X, n2)) => (((X = n0) | (X = n1)) | (X = n2))) <=> ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 (![X: $i] : ((leq(n0, X) & leq(X, n2)) => (((X = n0) | (X = n1)) | (X = n2))) <=> ![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.48 tff(134,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n2)) => (((X = n0) | (X = n1)) | (X = n2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','finite_domain_2')).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (![X: $i] : ((X = n2) | (X = n1) | (X = n0) | (~(leq(n0, X) & leq(X, n2))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 (![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[136, 130])).
% 0.20/0.48 tff(138,plain,(
% 0.20/0.48 ![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~(leq(succ(tptp_minus_1), X) & leq(X, succ(succ(succ(tptp_minus_1)))))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[137])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 (![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[138, 128])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 (![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[139, 126])).
% 0.20/0.49 tff(141,plain,
% 0.20/0.49 (((~![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) | ((E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))))) <=> ((~![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) | (E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(142,plain,
% 0.20/0.49 ((~![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) | ((E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(143,plain,
% 0.20/0.49 ((~![X: $i] : ((X = succ(succ(succ(tptp_minus_1)))) | (X = succ(succ(tptp_minus_1))) | (X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(succ(succ(tptp_minus_1))))))) | (E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(tptp_minus_1)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.49 tff(144,plain,
% 0.20/0.49 ((E!14 = succ(succ(succ(tptp_minus_1)))) | (E!14 = succ(succ(tptp_minus_1))) | (E!14 = succ(tptp_minus_1))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[143, 140, 43, 41])).
% 0.20/0.49 tff(145,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[144, 124, 113, 102])).
% 0.20/0.49 % SZS output end Proof
%------------------------------------------------------------------------------