TSTP Solution File: SWV092+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV092+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 15:09:57 EDT 2022
% Result : Theorem 0.16s 0.41s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV092+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.11/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n029.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun Sep 4 01:31:00 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.16/0.41 % SZS status Theorem
% 0.16/0.41 % SZS output start Proof
% 0.16/0.41 tff(gt_type, type, (
% 0.16/0.41 gt: ( $i * $i ) > $o)).
% 0.16/0.41 tff(succ_type, type, (
% 0.16/0.41 succ: $i > $i)).
% 0.16/0.41 tff(tptp_minus_1_type, type, (
% 0.16/0.41 tptp_minus_1: $i)).
% 0.16/0.41 tff(leq_type, type, (
% 0.16/0.41 leq: ( $i * $i ) > $o)).
% 0.16/0.41 tff(minus_type, type, (
% 0.16/0.41 minus: ( $i * $i ) > $i)).
% 0.16/0.41 tff(pred_type, type, (
% 0.16/0.41 pred: $i > $i)).
% 0.16/0.41 tff(n1_type, type, (
% 0.16/0.41 n1: $i)).
% 0.16/0.41 tff(tptp_fun_B_13_type, type, (
% 0.16/0.41 tptp_fun_B_13: $i)).
% 0.16/0.41 tff(tptp_fun_A_14_type, type, (
% 0.16/0.41 tptp_fun_A_14: $i)).
% 0.16/0.41 tff(a_select3_type, type, (
% 0.16/0.41 a_select3: ( $i * $i * $i ) > $i)).
% 0.16/0.41 tff(u_defuse_type, type, (
% 0.16/0.41 u_defuse: $i)).
% 0.16/0.41 tff(z_defuse_type, type, (
% 0.16/0.41 z_defuse: $i)).
% 0.16/0.41 tff(a_select2_type, type, (
% 0.16/0.41 a_select2: ( $i * $i ) > $i)).
% 0.16/0.41 tff(sigma_defuse_type, type, (
% 0.16/0.41 sigma_defuse: $i)).
% 0.16/0.41 tff(rho_defuse_type, type, (
% 0.16/0.41 rho_defuse: $i)).
% 0.16/0.41 tff(use_type, type, (
% 0.16/0.41 use: $i)).
% 0.16/0.41 tff(n0_type, type, (
% 0.16/0.41 n0: $i)).
% 0.16/0.41 tff(n2_type, type, (
% 0.16/0.41 n2: $i)).
% 0.16/0.41 tff(n5_type, type, (
% 0.16/0.41 n5: $i)).
% 0.16/0.41 tff(xinit_noise_defuse_type, type, (
% 0.16/0.41 xinit_noise_defuse: $i)).
% 0.16/0.41 tff(n4_type, type, (
% 0.16/0.41 n4: $i)).
% 0.16/0.41 tff(n3_type, type, (
% 0.16/0.41 n3: $i)).
% 0.16/0.41 tff(xinit_mean_defuse_type, type, (
% 0.16/0.41 xinit_mean_defuse: $i)).
% 0.16/0.41 tff(xinit_defuse_type, type, (
% 0.16/0.41 xinit_defuse: $i)).
% 0.16/0.41 tff(1,plain,
% 0.16/0.41 (^[X: $i, Y: $i] : refl((leq(X, Y) <=> gt(succ(Y), X)) <=> (leq(X, Y) <=> gt(succ(Y), X)))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(2,plain,
% 0.16/0.41 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.16/0.41 tff(3,plain,
% 0.16/0.41 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 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')).
% 0.16/0.41 tff(5,plain,
% 0.16/0.41 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.16/0.41 tff(6,plain,(
% 0.16/0.41 ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.16/0.41 inference(skolemize,[status(sab)],[5])).
% 0.16/0.41 tff(7,plain,
% 0.16/0.41 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.16/0.41 tff(8,plain,
% 0.16/0.41 ((~![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)))),
% 0.16/0.41 inference(quant_inst,[status(thm)],[])).
% 0.16/0.41 tff(9,plain,
% 0.16/0.41 (leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.16/0.41 tff(10,plain,
% 0.16/0.41 (^[X: $i] : refl((minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(11,plain,
% 0.16/0.41 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.16/0.41 tff(12,plain,
% 0.16/0.41 (^[X: $i] : rewrite((minus(X, n1) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(13,plain,
% 0.16/0.41 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.16/0.41 tff(14,plain,
% 0.16/0.41 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(15,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 0.16/0.41 tff(16,plain,
% 0.16/0.41 (![X: $i] : (minus(X, n1) = pred(X))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.16/0.41 tff(17,plain,
% 0.16/0.41 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.16/0.41 tff(18,plain,(
% 0.16/0.41 ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.16/0.41 inference(skolemize,[status(sab)],[17])).
% 0.16/0.41 tff(19,plain,
% 0.16/0.41 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.16/0.41 tff(20,plain,
% 0.16/0.41 ((~![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))) | (minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))) = pred(succ(tptp_minus_1)))),
% 0.16/0.42 inference(quant_inst,[status(thm)],[])).
% 0.16/0.42 tff(21,plain,
% 0.16/0.42 (minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))) = pred(succ(tptp_minus_1))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.16/0.42 tff(22,plain,
% 0.16/0.42 (pred(succ(tptp_minus_1)) = minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))),
% 0.16/0.42 inference(symmetry,[status(thm)],[21])).
% 0.16/0.42 tff(23,plain,
% 0.16/0.42 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(24,plain,
% 0.16/0.42 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(25,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 0.16/0.42 tff(26,plain,
% 0.16/0.42 (![X: $i] : (pred(succ(X)) = X)),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.16/0.42 tff(27,plain,(
% 0.16/0.42 ![X: $i] : (pred(succ(X)) = X)),
% 0.16/0.42 inference(skolemize,[status(sab)],[26])).
% 0.16/0.42 tff(28,plain,
% 0.16/0.42 (![X: $i] : (pred(succ(X)) = X)),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.16/0.42 tff(29,plain,
% 0.16/0.42 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(tptp_minus_1)) = tptp_minus_1)),
% 0.16/0.42 inference(quant_inst,[status(thm)],[])).
% 0.16/0.42 tff(30,plain,
% 0.16/0.42 (pred(succ(tptp_minus_1)) = tptp_minus_1),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.16/0.42 tff(31,plain,
% 0.16/0.42 (tptp_minus_1 = pred(succ(tptp_minus_1))),
% 0.16/0.42 inference(symmetry,[status(thm)],[30])).
% 0.16/0.42 tff(32,plain,
% 0.16/0.42 (tptp_minus_1 = minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))),
% 0.16/0.42 inference(transitivity,[status(thm)],[31, 22])).
% 0.16/0.42 tff(33,plain,
% 0.16/0.42 (leq(succ(tptp_minus_1), tptp_minus_1) <=> leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))),
% 0.16/0.42 inference(monotonicity,[status(thm)],[32])).
% 0.16/0.42 tff(34,plain,
% 0.16/0.42 (leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) <=> leq(succ(tptp_minus_1), tptp_minus_1)),
% 0.16/0.42 inference(symmetry,[status(thm)],[33])).
% 0.16/0.42 tff(35,plain,
% 0.16/0.42 ((~![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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(36,plain,
% 0.16/0.42 ((~![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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(37,plain,
% 0.16/0.42 ((~![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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(38,plain,
% 0.16/0.42 ((~![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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(39,plain,
% 0.16/0.42 ((~![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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(40,plain,
% 0.16/0.42 ((~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(41,plain,
% 0.16/0.42 ((~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))) <=> (~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(42,plain,
% 0.16/0.42 ((~((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, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))))) <=> (~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(43,plain,
% 0.16/0.42 (((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, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (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, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(44,plain,
% 0.16/0.42 ((~((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, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (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, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))))),
% 0.16/0.43 inference(monotonicity,[status(thm)],[43])).
% 0.16/0.43 tff(45,plain,
% 0.16/0.43 ((~((((((((((((((((((((((((((((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_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, minus(n0, n1))) => ((a_select3(u_defuse, A, B) = use) & (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_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, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))))))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(46,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_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, minus(n0, n1))) => ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_inuse_0004')).
% 0.16/0.43 tff(47,plain,
% 0.16/0.43 (~((~((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_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, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.16/0.43 tff(48,plain,
% 0.16/0.43 (~((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, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))))),
% 0.16/0.43 inference(or_elim,[status(thm)],[47])).
% 0.16/0.43 tff(49,plain,
% 0.16/0.43 (~((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, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.16/0.43 tff(50,plain,
% 0.16/0.43 (~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.16/0.43 tff(51,plain,
% 0.16/0.43 (~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[50, 41])).
% 0.16/0.43 tff(52,plain,
% 0.16/0.43 (~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(n0, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.16/0.43 tff(53,plain,
% 0.16/0.43 (~![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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[52, 40])).
% 0.16/0.44 tff(54,plain,
% 0.16/0.44 (~![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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[53, 39])).
% 0.16/0.44 tff(55,plain,
% 0.16/0.44 (~![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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[54, 38])).
% 0.16/0.44 tff(56,plain,
% 0.16/0.44 (~![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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[55, 37])).
% 0.16/0.44 tff(57,plain,
% 0.16/0.44 (~![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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[56, 36])).
% 0.16/0.44 tff(58,plain,
% 0.16/0.44 (~![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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[57, 35])).
% 0.16/0.44 tff(59,plain,
% 0.16/0.44 (~![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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[58, 35])).
% 0.16/0.44 tff(60,plain,
% 0.16/0.44 (~![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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[59, 35])).
% 0.16/0.44 tff(61,plain,(
% 0.16/0.44 ~((~(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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A!14, B!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, A!14, B!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.16/0.44 inference(skolemize,[status(sab)],[60])).
% 0.16/0.44 tff(62,plain,
% 0.16/0.44 (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, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))),
% 0.16/0.44 inference(or_elim,[status(thm)],[61])).
% 0.16/0.44 tff(63,plain,
% 0.16/0.44 (leq(B!13, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))),
% 0.16/0.44 inference(and_elim,[status(thm)],[62])).
% 0.16/0.44 tff(64,plain,
% 0.16/0.44 (leq(succ(tptp_minus_1), B!13)),
% 0.16/0.44 inference(and_elim,[status(thm)],[62])).
% 0.16/0.44 tff(65,plain,
% 0.16/0.44 (![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)))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(66,plain,
% 0.16/0.44 (^[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)))))),
% 0.16/0.44 inference(bind,[status(th)],[])).
% 0.16/0.44 tff(67,plain,
% 0.16/0.44 (![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)))),
% 0.16/0.44 inference(quant_intro,[status(thm)],[66])).
% 0.16/0.44 tff(68,plain,
% 0.16/0.44 (![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))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(69,plain,
% 0.16/0.44 (^[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)))),
% 0.16/0.44 inference(bind,[status(th)],[])).
% 0.16/0.44 tff(70,plain,
% 0.16/0.44 (![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))),
% 0.16/0.44 inference(quant_intro,[status(thm)],[69])).
% 0.16/0.44 tff(71,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')).
% 0.16/0.44 tff(72,plain,
% 0.16/0.44 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.16/0.44 tff(73,plain,
% 0.16/0.44 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.16/0.44 tff(74,plain,(
% 0.16/0.44 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.16/0.44 inference(skolemize,[status(sab)],[73])).
% 0.16/0.44 tff(75,plain,
% 0.16/0.44 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.16/0.44 tff(76,plain,
% 0.16/0.44 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.16/0.44 tff(77,plain,
% 0.16/0.44 (((~![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), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!13, minus(succ(tptp_minus_1), succ(succ(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), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!13, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(78,plain,
% 0.16/0.44 ((leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!13, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), B!13))) <=> ((~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!13, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(79,plain,
% 0.16/0.44 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!13, minus(succ(tptp_minus_1), succ(succ(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), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!13, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))))),
% 0.16/0.44 inference(monotonicity,[status(thm)],[78])).
% 0.16/0.44 tff(80,plain,
% 0.16/0.44 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!13, minus(succ(tptp_minus_1), succ(succ(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), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!13, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))),
% 0.16/0.44 inference(transitivity,[status(thm)],[79, 77])).
% 0.16/0.44 tff(81,plain,
% 0.16/0.44 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!13, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), B!13)))),
% 0.16/0.44 inference(quant_inst,[status(thm)],[])).
% 0.16/0.44 tff(82,plain,
% 0.16/0.44 ((~![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), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) | (~leq(B!13, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.16/0.44 tff(83,plain,
% 0.16/0.44 (leq(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))),
% 0.16/0.44 inference(unit_resolution,[status(thm)],[82, 76, 64, 63])).
% 0.16/0.44 tff(84,plain,
% 0.16/0.44 (leq(succ(tptp_minus_1), tptp_minus_1)),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[83, 34])).
% 0.16/0.44 tff(85,plain,
% 0.16/0.44 (^[X: $i] : refl((~gt(X, X)) <=> (~gt(X, X)))),
% 0.16/0.44 inference(bind,[status(th)],[])).
% 0.16/0.44 tff(86,plain,
% 0.16/0.44 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.16/0.44 inference(quant_intro,[status(thm)],[85])).
% 0.16/0.44 tff(87,plain,
% 0.16/0.44 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(88,axiom,(![X: $i] : (~gt(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','irreflexivity_gt')).
% 0.16/0.44 tff(89,plain,
% 0.16/0.44 (![X: $i] : (~gt(X, X))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.16/0.44 tff(90,plain,(
% 0.16/0.44 ![X: $i] : (~gt(X, X))),
% 0.16/0.44 inference(skolemize,[status(sab)],[89])).
% 0.16/0.44 tff(91,plain,
% 0.16/0.44 (![X: $i] : (~gt(X, X))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.16/0.44 tff(92,plain,
% 0.16/0.44 ((~![X: $i] : (~gt(X, X))) | (~gt(succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.16/0.44 inference(quant_inst,[status(thm)],[])).
% 0.16/0.44 tff(93,plain,
% 0.16/0.44 (~gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.16/0.44 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.16/0.44 tff(94,plain,
% 0.16/0.44 ((~(leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1)))) | (~leq(succ(tptp_minus_1), tptp_minus_1)) | gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.16/0.44 inference(tautology,[status(thm)],[])).
% 0.16/0.44 tff(95,plain,
% 0.16/0.44 ($false),
% 0.16/0.44 inference(unit_resolution,[status(thm)],[94, 93, 84, 9])).
% 0.16/0.44 % SZS output end Proof
%------------------------------------------------------------------------------