TSTP Solution File: SWV031+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV031+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 15:09:42 EDT 2022
% Result : Theorem 0.11s 0.35s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : SWV031+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.02/0.07 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.07/0.26 % Computer : n016.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Sun Sep 4 01:30:07 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.07/0.26 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.07/0.26 Usage: tptp [options] [-file:]file
% 0.07/0.26 -h, -? prints this message.
% 0.07/0.26 -smt2 print SMT-LIB2 benchmark.
% 0.07/0.26 -m, -model generate model.
% 0.07/0.26 -p, -proof generate proof.
% 0.07/0.26 -c, -core generate unsat core of named formulas.
% 0.07/0.26 -st, -statistics display statistics.
% 0.07/0.26 -t:timeout set timeout (in second).
% 0.07/0.26 -smt2status display status in smt2 format instead of SZS.
% 0.07/0.26 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.07/0.26 -<param>:<value> configuration parameter and value.
% 0.07/0.26 -o:<output-file> file to place output in.
% 0.11/0.35 % SZS status Theorem
% 0.11/0.35 % SZS output start Proof
% 0.11/0.35 tff(init_type, type, (
% 0.11/0.35 init: $i)).
% 0.11/0.35 tff(a_select3_type, type, (
% 0.11/0.35 a_select3: ( $i * $i * $i ) > $i)).
% 0.11/0.35 tff(pv10_type, type, (
% 0.11/0.35 pv10: $i)).
% 0.11/0.35 tff(pv9_type, type, (
% 0.11/0.35 pv9: $i)).
% 0.11/0.35 tff(tptp_const_array2_type, type, (
% 0.11/0.35 tptp_const_array2: ( $i * $i * $i ) > $i)).
% 0.11/0.35 tff(dim_type, type, (
% 0.11/0.35 dim: ( $i * $i ) > $i)).
% 0.11/0.35 tff(minus_type, type, (
% 0.11/0.35 minus: ( $i * $i ) > $i)).
% 0.11/0.35 tff(succ_type, type, (
% 0.11/0.35 succ: $i > $i)).
% 0.11/0.35 tff(tptp_minus_1_type, type, (
% 0.11/0.35 tptp_minus_1: $i)).
% 0.11/0.35 tff(n330_type, type, (
% 0.11/0.35 n330: $i)).
% 0.11/0.35 tff(n410_type, type, (
% 0.11/0.35 n410: $i)).
% 0.11/0.35 tff(pred_type, type, (
% 0.11/0.35 pred: $i > $i)).
% 0.11/0.35 tff(leq_type, type, (
% 0.11/0.35 leq: ( $i * $i ) > $o)).
% 0.11/0.35 tff(n1_type, type, (
% 0.11/0.35 n1: $i)).
% 0.11/0.35 tff(a_select2_type, type, (
% 0.11/0.35 a_select2: ( $i * $i ) > $i)).
% 0.11/0.35 tff(s_values7_init_type, type, (
% 0.11/0.35 s_values7_init: $i)).
% 0.11/0.35 tff(n3_type, type, (
% 0.11/0.35 n3: $i)).
% 0.11/0.35 tff(n0_type, type, (
% 0.11/0.35 n0: $i)).
% 0.11/0.35 tff(simplex7_init_type, type, (
% 0.11/0.35 simplex7_init: $i)).
% 0.11/0.35 tff(n2_type, type, (
% 0.11/0.35 n2: $i)).
% 0.11/0.35 tff(tptp_fun_D_13_type, type, (
% 0.11/0.35 tptp_fun_D_13: $i)).
% 0.11/0.35 tff(tptp_fun_E_14_type, type, (
% 0.11/0.35 tptp_fun_E_14: $i)).
% 0.11/0.35 tff(tptp_fun_F_15_type, type, (
% 0.11/0.35 tptp_fun_F_15: $i)).
% 0.11/0.35 tff(1,plain,
% 0.11/0.35 (^[X: $i] : refl((minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.11/0.35 inference(bind,[status(th)],[])).
% 0.11/0.35 tff(2,plain,
% 0.11/0.35 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.11/0.35 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.35 tff(3,plain,
% 0.11/0.35 (^[X: $i] : rewrite((minus(X, n1) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.11/0.35 inference(bind,[status(th)],[])).
% 0.11/0.35 tff(4,plain,
% 0.11/0.35 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.11/0.35 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.35 tff(5,plain,
% 0.11/0.35 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(6,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 0.11/0.35 tff(7,plain,
% 0.11/0.35 (![X: $i] : (minus(X, n1) = pred(X))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.11/0.35 tff(8,plain,
% 0.11/0.35 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.11/0.35 tff(9,plain,(
% 0.11/0.35 ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.11/0.35 inference(skolemize,[status(sab)],[8])).
% 0.11/0.35 tff(10,plain,
% 0.11/0.35 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.11/0.35 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.11/0.35 tff(11,plain,
% 0.11/0.35 ((~![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))) | (minus(n330, succ(succ(tptp_minus_1))) = pred(n330))),
% 0.11/0.35 inference(quant_inst,[status(thm)],[])).
% 0.11/0.35 tff(12,plain,
% 0.11/0.35 (minus(n330, succ(succ(tptp_minus_1))) = pred(n330)),
% 0.11/0.35 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.11/0.35 tff(13,plain,
% 0.11/0.35 (pred(n330) = minus(n330, succ(succ(tptp_minus_1)))),
% 0.11/0.35 inference(symmetry,[status(thm)],[12])).
% 0.11/0.35 tff(14,plain,
% 0.11/0.35 (leq(pv10, pred(n330)) <=> leq(pv10, minus(n330, succ(succ(tptp_minus_1))))),
% 0.11/0.35 inference(monotonicity,[status(thm)],[13])).
% 0.11/0.35 tff(15,plain,
% 0.11/0.35 (leq(pv10, minus(n330, succ(succ(tptp_minus_1)))) <=> leq(pv10, pred(n330))),
% 0.11/0.35 inference(symmetry,[status(thm)],[14])).
% 0.11/0.35 tff(16,plain,
% 0.11/0.35 (leq(pv10, minus(n330, n1)) <=> leq(pv10, minus(n330, succ(succ(tptp_minus_1))))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(17,plain,
% 0.11/0.35 (leq(pv10, minus(n330, n1)) <=> leq(pv10, minus(n330, n1))),
% 0.11/0.35 inference(rewrite,[status(thm)],[])).
% 0.11/0.35 tff(18,plain,
% 0.11/0.35 ((~((((((((init = init) & leq(n0, pv9)) & leq(n0, pv10)) & leq(pv9, minus(n410, n1))) & leq(pv10, minus(n330, n1))) & ![A: $i] : ((leq(n0, A) & leq(A, n2)) => ![B: $i] : ((leq(n0, B) & leq(B, n3)) => (a_select3(simplex7_init, B, A) = init)))) & ![C: $i] : ((leq(n0, C) & leq(C, n3)) => (a_select2(s_values7_init, C) = init))) => ((((((init = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init)) & leq(n0, pv9)) & leq(pv9, minus(n410, n1))) & ![D: $i] : ((leq(n0, D) & leq(D, n2)) => ![E: $i] : ((leq(n0, E) & leq(E, n3)) => (a_select3(simplex7_init, E, D) = init)))) & ![F: $i] : ((leq(n0, F) & leq(F, n3)) => (a_select2(s_values7_init, F) = init))))) <=> (~((~(leq(n0, pv9) & leq(n0, pv10) & leq(pv9, minus(n410, n1)) & leq(pv10, minus(n330, n1)) & ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init))) & ![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init)))) | ((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & leq(n0, pv9) & leq(pv9, minus(n410, n1)) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(19,axiom,(~((((((((init = init) & leq(n0, pv9)) & leq(n0, pv10)) & leq(pv9, minus(n410, n1))) & leq(pv10, minus(n330, n1))) & ![A: $i] : ((leq(n0, A) & leq(A, n2)) => ![B: $i] : ((leq(n0, B) & leq(B, n3)) => (a_select3(simplex7_init, B, A) = init)))) & ![C: $i] : ((leq(n0, C) & leq(C, n3)) => (a_select2(s_values7_init, C) = init))) => ((((((init = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init)) & leq(n0, pv9)) & leq(pv9, minus(n410, n1))) & ![D: $i] : ((leq(n0, D) & leq(D, n2)) => ![E: $i] : ((leq(n0, E) & leq(E, n3)) => (a_select3(simplex7_init, E, D) = init)))) & ![F: $i] : ((leq(n0, F) & leq(F, n3)) => (a_select2(s_values7_init, F) = init))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gauss_init_0037')).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (~((~(leq(n0, pv9) & leq(n0, pv10) & leq(pv9, minus(n410, n1)) & leq(pv10, minus(n330, n1)) & ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init))) & ![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init)))) | ((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & leq(n0, pv9) & leq(pv9, minus(n410, n1)) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (leq(n0, pv9) & leq(n0, pv10) & leq(pv9, minus(n410, n1)) & leq(pv10, minus(n330, n1)) & ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init))) & ![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 0.11/0.36 inference(or_elim,[status(thm)],[20])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (leq(pv10, minus(n330, n1))),
% 0.11/0.36 inference(and_elim,[status(thm)],[21])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (leq(pv10, minus(n330, n1))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (leq(pv10, minus(n330, succ(succ(tptp_minus_1))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (leq(pv10, pred(n330))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 15])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 ((~![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))) | (minus(n410, succ(succ(tptp_minus_1))) = pred(n410))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (minus(n410, succ(succ(tptp_minus_1))) = pred(n410)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[26, 10])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 (pred(n410) = minus(n410, succ(succ(tptp_minus_1)))),
% 0.11/0.36 inference(symmetry,[status(thm)],[27])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 (leq(pv9, pred(n410)) <=> leq(pv9, minus(n410, succ(succ(tptp_minus_1))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[28])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 (leq(pv9, minus(n410, succ(succ(tptp_minus_1)))) <=> leq(pv9, pred(n410))),
% 0.11/0.36 inference(symmetry,[status(thm)],[29])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 (leq(pv9, minus(n410, n1)) <=> leq(pv9, minus(n410, succ(succ(tptp_minus_1))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 (leq(pv9, minus(n410, n1)) <=> leq(pv9, minus(n410, n1))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 (leq(pv9, minus(n410, n1))),
% 0.11/0.36 inference(and_elim,[status(thm)],[21])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 (leq(pv9, minus(n410, n1))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 (leq(pv9, minus(n410, succ(succ(tptp_minus_1))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 (leq(pv9, pred(n410))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[35, 30])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 (leq(n0, pv10) <=> leq(succ(tptp_minus_1), pv10)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(38,plain,
% 0.11/0.36 (leq(n0, pv10) <=> leq(n0, pv10)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(39,plain,
% 0.11/0.36 (leq(n0, pv10)),
% 0.11/0.36 inference(and_elim,[status(thm)],[21])).
% 0.11/0.36 tff(40,plain,
% 0.11/0.36 (leq(n0, pv10)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.11/0.36 tff(41,plain,
% 0.11/0.36 (leq(succ(tptp_minus_1), pv10)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.11/0.36 tff(42,plain,
% 0.11/0.36 (leq(n0, pv9) <=> leq(succ(tptp_minus_1), pv9)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(43,plain,
% 0.11/0.36 (leq(n0, pv9) <=> leq(n0, pv9)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(44,plain,
% 0.11/0.36 (leq(n0, pv9)),
% 0.11/0.36 inference(and_elim,[status(thm)],[21])).
% 0.11/0.36 tff(45,plain,
% 0.11/0.36 (leq(n0, pv9)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.11/0.36 tff(46,plain,
% 0.11/0.36 (leq(succ(tptp_minus_1), pv9)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[45, 42])).
% 0.11/0.36 tff(47,plain,
% 0.11/0.36 (^[I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : refl(((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1))) <=> ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(48,plain,
% 0.11/0.36 (![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1))) <=> ![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[47])).
% 0.11/0.36 tff(49,plain,
% 0.11/0.36 (^[I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2)) <=> (~((~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1))))), ((~(leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))) <=> (~(~((~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1))))))), rewrite((~(~((~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1))))) <=> ((~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))), ((~(leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))) <=> ((~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1))))), (((~(leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))) | (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val)) <=> (((~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1))) | (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val)))), rewrite((((~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1))) | (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val)) <=> ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))), (((~(leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))) | (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val)) <=> ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(50,plain,
% 0.11/0.36 (![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((~(leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))) | (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val)) <=> ![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[49])).
% 0.11/0.36 tff(51,plain,
% 0.11/0.36 (![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((~(leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))) | (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val)) <=> ![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((~(leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))) | (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(52,plain,
% 0.11/0.36 (^[I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : trans(monotonicity(trans(monotonicity(rewrite(((leq(L1, I) & leq(I, U1)) & leq(L2, J)) <=> (leq(L1, I) & leq(I, U1) & leq(L2, J))), ((((leq(L1, I) & leq(I, U1)) & leq(L2, J)) & leq(J, U2)) <=> ((leq(L1, I) & leq(I, U1) & leq(L2, J)) & leq(J, U2)))), rewrite(((leq(L1, I) & leq(I, U1) & leq(L2, J)) & leq(J, U2)) <=> (leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))), ((((leq(L1, I) & leq(I, U1)) & leq(L2, J)) & leq(J, U2)) <=> (leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2)))), (((((leq(L1, I) & leq(I, U1)) & leq(L2, J)) & leq(J, U2)) => (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val)) <=> ((leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2)) => (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val)))), rewrite(((leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2)) => (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val)) <=> ((~(leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))) | (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val))), (((((leq(L1, I) & leq(I, U1)) & leq(L2, J)) & leq(J, U2)) => (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val)) <=> ((~(leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))) | (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(53,plain,
% 0.11/0.36 (![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((((leq(L1, I) & leq(I, U1)) & leq(L2, J)) & leq(J, U2)) => (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val)) <=> ![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((~(leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))) | (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[52])).
% 0.11/0.36 tff(54,axiom,(![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((((leq(L1, I) & leq(I, U1)) & leq(L2, J)) & leq(J, U2)) => (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','const_array2_select')).
% 0.11/0.36 tff(55,plain,
% 0.11/0.36 (![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((~(leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))) | (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.11/0.36 tff(56,plain,
% 0.11/0.36 (![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((~(leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))) | (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.11/0.36 tff(57,plain,(
% 0.11/0.36 ![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((~(leq(L1, I) & leq(I, U1) & leq(L2, J) & leq(J, U2))) | (a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val))),
% 0.11/0.36 inference(skolemize,[status(sab)],[56])).
% 0.11/0.36 tff(58,plain,
% 0.11/0.36 (![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.11/0.36 tff(59,plain,
% 0.11/0.36 (![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.11/0.36 tff(60,plain,
% 0.11/0.36 (((~![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))) | ((~leq(succ(tptp_minus_1), pv9)) | (~leq(succ(tptp_minus_1), pv10)) | (~leq(pv9, pred(n410))) | (~leq(pv10, pred(n330))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init), pv9, pv10) = init))) <=> ((~![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))) | (~leq(succ(tptp_minus_1), pv9)) | (~leq(succ(tptp_minus_1), pv10)) | (~leq(pv9, pred(n410))) | (~leq(pv10, pred(n330))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init), pv9, pv10) = init))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(61,plain,
% 0.11/0.36 (((a_select3(tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init), pv9, pv10) = init) | (~leq(succ(tptp_minus_1), pv10)) | (~leq(pv10, pred(n330))) | (~leq(succ(tptp_minus_1), pv9)) | (~leq(pv9, pred(n410)))) <=> ((~leq(succ(tptp_minus_1), pv9)) | (~leq(succ(tptp_minus_1), pv10)) | (~leq(pv9, pred(n410))) | (~leq(pv10, pred(n330))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init), pv9, pv10) = init))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(62,plain,
% 0.11/0.36 (((~![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))) | ((a_select3(tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init), pv9, pv10) = init) | (~leq(succ(tptp_minus_1), pv10)) | (~leq(pv10, pred(n330))) | (~leq(succ(tptp_minus_1), pv9)) | (~leq(pv9, pred(n410))))) <=> ((~![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))) | ((~leq(succ(tptp_minus_1), pv9)) | (~leq(succ(tptp_minus_1), pv10)) | (~leq(pv9, pred(n410))) | (~leq(pv10, pred(n330))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init), pv9, pv10) = init)))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[61])).
% 0.11/0.36 tff(63,plain,
% 0.11/0.36 (((~![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))) | ((a_select3(tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init), pv9, pv10) = init) | (~leq(succ(tptp_minus_1), pv10)) | (~leq(pv10, pred(n330))) | (~leq(succ(tptp_minus_1), pv9)) | (~leq(pv9, pred(n410))))) <=> ((~![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))) | (~leq(succ(tptp_minus_1), pv9)) | (~leq(succ(tptp_minus_1), pv10)) | (~leq(pv9, pred(n410))) | (~leq(pv10, pred(n330))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init), pv9, pv10) = init))),
% 0.11/0.36 inference(transitivity,[status(thm)],[62, 60])).
% 0.11/0.36 tff(64,plain,
% 0.11/0.36 ((~![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))) | ((a_select3(tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init), pv9, pv10) = init) | (~leq(succ(tptp_minus_1), pv10)) | (~leq(pv10, pred(n330))) | (~leq(succ(tptp_minus_1), pv9)) | (~leq(pv9, pred(n410))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(65,plain,
% 0.11/0.37 ((~![I: $i, L1: $i, U1: $i, J: $i, L2: $i, U2: $i, Val: $i] : ((a_select3(tptp_const_array2(dim(L1, U1), dim(L2, U2), Val), I, J) = Val) | (~leq(L2, J)) | (~leq(J, U2)) | (~leq(L1, I)) | (~leq(I, U1)))) | (~leq(succ(tptp_minus_1), pv9)) | (~leq(succ(tptp_minus_1), pv10)) | (~leq(pv9, pred(n410))) | (~leq(pv10, pred(n330))) | (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init), pv9, pv10) = init)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.11/0.37 tff(66,plain,
% 0.11/0.37 (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init), pv9, pv10) = init),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[65, 59, 46, 41, 36, 25])).
% 0.11/0.37 tff(67,plain,
% 0.11/0.37 (dim(succ(tptp_minus_1), pred(n330)) = dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[13])).
% 0.11/0.37 tff(68,plain,
% 0.11/0.37 (dim(succ(tptp_minus_1), pred(n410)) = dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[28])).
% 0.11/0.37 tff(69,plain,
% 0.11/0.37 (tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init) = tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[68, 67])).
% 0.11/0.37 tff(70,plain,
% 0.11/0.37 (tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init) = tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init)),
% 0.11/0.37 inference(symmetry,[status(thm)],[69])).
% 0.11/0.37 tff(71,plain,
% 0.11/0.37 (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = a_select3(tptp_const_array2(dim(succ(tptp_minus_1), pred(n410)), dim(succ(tptp_minus_1), pred(n330)), init), pv9, pv10)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[70])).
% 0.11/0.37 tff(72,plain,
% 0.11/0.37 (a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init),
% 0.11/0.37 inference(transitivity,[status(thm)],[71, 66])).
% 0.11/0.37 tff(73,assumption,(~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(D!13, succ(succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.11/0.37 tff(74,plain,
% 0.11/0.37 (((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(D!13, succ(succ(succ(tptp_minus_1)))))) | leq(D!13, succ(succ(succ(tptp_minus_1))))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(75,plain,
% 0.11/0.37 (leq(D!13, succ(succ(succ(tptp_minus_1))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.11/0.37 tff(76,plain,
% 0.11/0.37 (((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(D!13, succ(succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), D!13)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(77,plain,
% 0.11/0.37 (leq(succ(tptp_minus_1), D!13)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.11/0.37 tff(78,plain,
% 0.11/0.37 (^[A: $i] : refl(((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(79,plain,
% 0.11/0.37 (![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))) <=> ![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[78])).
% 0.11/0.37 tff(80,plain,
% 0.11/0.37 (^[A: $i] : rewrite(((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(81,plain,
% 0.11/0.37 (![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))) <=> ![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[80])).
% 0.11/0.37 tff(82,plain,
% 0.11/0.37 (![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))) <=> ![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[81, 79])).
% 0.11/0.37 tff(83,plain,
% 0.11/0.37 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1)))))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(tptp_minus_1)))))) <=> (~((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))), ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(tptp_minus_1))))))) <=> (~(~((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(tptp_minus_1))))))) <=> ((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))), (((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, B, A) = init)) <=> (((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, B, A) = init)))), rewrite((((~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, B, A) = init)) <=> ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, B, A) = init)) <=> ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))))), (![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, B, A) = init)) <=> ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))), (((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, B, A) = init))) <=> (((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))))), rewrite((((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))), (((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, B, A) = init))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(84,plain,
% 0.11/0.37 (![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, B, A) = init))) <=> ![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[83])).
% 0.11/0.37 tff(85,plain,
% 0.11/0.37 (^[A: $i] : rewrite(((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init))) <=> ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, B, A) = init))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(86,plain,
% 0.11/0.37 (![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init))) <=> ![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, B, A) = init)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[85])).
% 0.11/0.37 tff(87,plain,
% 0.11/0.37 (![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init))) <=> ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(88,plain,
% 0.11/0.37 (![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)))),
% 0.11/0.37 inference(and_elim,[status(thm)],[21])).
% 0.11/0.37 tff(89,plain,
% 0.11/0.37 (![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.11/0.37 tff(90,plain,
% 0.11/0.37 (![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, B, A) = init)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[89, 86])).
% 0.11/0.37 tff(91,plain,(
% 0.11/0.37 ![A: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, succ(succ(succ(tptp_minus_1)))))) | ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, B, A) = init)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[90])).
% 0.11/0.37 tff(92,plain,
% 0.11/0.37 (![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.11/0.37 tff(93,plain,
% 0.11/0.37 (![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.11/0.37 tff(94,plain,
% 0.11/0.37 (((~![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))) | ((~leq(succ(tptp_minus_1), D!13)) | (~leq(D!13, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(D!13, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(95,plain,
% 0.11/0.37 ((~![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))) | ((~leq(succ(tptp_minus_1), D!13)) | (~leq(D!13, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(96,plain,
% 0.11/0.37 ((~![A: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1))))))))) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(D!13, succ(succ(succ(tptp_minus_1))))) | ![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.11/0.37 tff(97,plain,
% 0.11/0.37 (![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[96, 93, 77, 75])).
% 0.11/0.37 tff(98,plain,
% 0.11/0.37 (((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(D!13, succ(succ(succ(tptp_minus_1)))))) | leq(E!14, succ(succ(succ(succ(tptp_minus_1)))))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(99,plain,
% 0.11/0.37 (leq(E!14, succ(succ(succ(succ(tptp_minus_1)))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[98, 73])).
% 0.11/0.37 tff(100,plain,
% 0.11/0.37 (((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(D!13, succ(succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), E!14)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(101,plain,
% 0.11/0.38 (leq(succ(tptp_minus_1), E!14)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[100, 73])).
% 0.11/0.38 tff(102,plain,
% 0.11/0.38 (((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(D!13, succ(succ(succ(tptp_minus_1)))))) | (~(a_select3(simplex7_init, E!14, D!13) = init))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(103,plain,
% 0.11/0.38 (~(a_select3(simplex7_init, E!14, D!13) = init)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[102, 73])).
% 0.11/0.38 tff(104,plain,
% 0.11/0.38 (((~![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))) | ((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(succ(tptp_minus_1)))))))) <=> ((~![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(simplex7_init, E!14, D!13) = init) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(105,plain,
% 0.11/0.38 ((~![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))) | ((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(106,plain,
% 0.11/0.38 ((~![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select3(simplex7_init, E!14, D!13) = init) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.11/0.38 tff(107,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[106, 103, 101, 99, 97])).
% 0.11/0.38 tff(108,plain,((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(D!13, succ(succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(109,assumption,(~((a_select2(s_values7_init, F!15) = init) | (~leq(succ(tptp_minus_1), F!15)) | (~leq(F!15, succ(succ(succ(succ(tptp_minus_1)))))))), introduced(assumption)).
% 0.11/0.38 tff(110,plain,
% 0.11/0.38 (((a_select2(s_values7_init, F!15) = init) | (~leq(succ(tptp_minus_1), F!15)) | (~leq(F!15, succ(succ(succ(succ(tptp_minus_1))))))) | leq(F!15, succ(succ(succ(succ(tptp_minus_1)))))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(111,plain,
% 0.11/0.38 (leq(F!15, succ(succ(succ(succ(tptp_minus_1)))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.11/0.38 tff(112,plain,
% 0.11/0.38 (((a_select2(s_values7_init, F!15) = init) | (~leq(succ(tptp_minus_1), F!15)) | (~leq(F!15, succ(succ(succ(succ(tptp_minus_1))))))) | leq(succ(tptp_minus_1), F!15)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(113,plain,
% 0.11/0.38 (leq(succ(tptp_minus_1), F!15)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[112, 109])).
% 0.11/0.38 tff(114,plain,
% 0.11/0.38 (((a_select2(s_values7_init, F!15) = init) | (~leq(succ(tptp_minus_1), F!15)) | (~leq(F!15, succ(succ(succ(succ(tptp_minus_1))))))) | (~(a_select2(s_values7_init, F!15) = init))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(115,plain,
% 0.11/0.38 (~(a_select2(s_values7_init, F!15) = init)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[114, 109])).
% 0.11/0.38 tff(116,plain,
% 0.11/0.38 (^[C: $i] : refl(((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))) <=> ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(117,plain,
% 0.11/0.38 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))) <=> ![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[116])).
% 0.11/0.38 tff(118,plain,
% 0.11/0.38 (^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1)))))) <=> (~((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))))), ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) <=> (~(~((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))))), (((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init)) <=> (((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init)))), rewrite((((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init)) <=> ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init)) <=> ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(119,plain,
% 0.11/0.38 (![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init)) <=> ![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[118])).
% 0.11/0.38 tff(120,plain,
% 0.11/0.38 (^[C: $i] : rewrite(((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init)) <=> ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(121,plain,
% 0.11/0.38 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init)) <=> ![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[120])).
% 0.11/0.38 tff(122,plain,
% 0.11/0.38 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init)) <=> ![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(123,plain,
% 0.11/0.38 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 0.11/0.38 inference(and_elim,[status(thm)],[21])).
% 0.11/0.38 tff(124,plain,
% 0.11/0.38 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.11/0.38 tff(125,plain,
% 0.11/0.38 (![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[124, 121])).
% 0.11/0.38 tff(126,plain,(
% 0.11/0.38 ![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init))),
% 0.11/0.38 inference(skolemize,[status(sab)],[125])).
% 0.11/0.38 tff(127,plain,
% 0.11/0.38 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.11/0.38 tff(128,plain,
% 0.11/0.38 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[127, 117])).
% 0.11/0.38 tff(129,plain,
% 0.11/0.38 (((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))) | ((a_select2(s_values7_init, F!15) = init) | (~leq(succ(tptp_minus_1), F!15)) | (~leq(F!15, succ(succ(succ(succ(tptp_minus_1)))))))) <=> ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(s_values7_init, F!15) = init) | (~leq(succ(tptp_minus_1), F!15)) | (~leq(F!15, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(130,plain,
% 0.11/0.38 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))) | ((a_select2(s_values7_init, F!15) = init) | (~leq(succ(tptp_minus_1), F!15)) | (~leq(F!15, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(131,plain,
% 0.11/0.38 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(s_values7_init, F!15) = init) | (~leq(succ(tptp_minus_1), F!15)) | (~leq(F!15, succ(succ(succ(succ(tptp_minus_1))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.11/0.38 tff(132,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[131, 128, 115, 113, 111])).
% 0.11/0.38 tff(133,plain,((a_select2(s_values7_init, F!15) = init) | (~leq(succ(tptp_minus_1), F!15)) | (~leq(F!15, succ(succ(succ(succ(tptp_minus_1))))))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(134,plain,
% 0.11/0.38 (((~(a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init)) | (~((~(leq(succ(tptp_minus_1), F!15) & leq(F!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F!15) = init))) | (leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E!14, D!13) = init))))) <=> ((~(a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init)) | (~((a_select2(s_values7_init, F!15) = init) | (~leq(succ(tptp_minus_1), F!15)) | (~leq(F!15, succ(succ(succ(succ(tptp_minus_1)))))))) | (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(D!13, succ(succ(succ(tptp_minus_1))))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(135,plain,
% 0.11/0.38 (((~(a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init)) | (leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E!14, D!13) = init)))) | (~((~(leq(succ(tptp_minus_1), F!15) & leq(F!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F!15) = init)))) <=> ((~(a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init)) | (~((~(leq(succ(tptp_minus_1), F!15) & leq(F!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F!15) = init))) | (leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E!14, D!13) = init)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(136,plain,
% 0.11/0.38 (((leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E!14, D!13) = init)))) <=> (leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E!14, D!13) = init))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(137,plain,
% 0.11/0.39 ((~(~(leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1))))))) <=> (leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1)))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(138,plain,
% 0.11/0.39 (((~(~(leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E!14, D!13) = init)))) <=> ((leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E!14, D!13) = init))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[137])).
% 0.11/0.39 tff(139,plain,
% 0.11/0.39 (((~(~(leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E!14, D!13) = init)))) <=> (leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E!14, D!13) = init))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[138, 136])).
% 0.11/0.39 tff(140,plain,
% 0.11/0.39 (((~(a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init)) | ((~(~(leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E!14, D!13) = init)))) | (~((~(leq(succ(tptp_minus_1), F!15) & leq(F!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F!15) = init)))) <=> ((~(a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init)) | (leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E!14, D!13) = init)))) | (~((~(leq(succ(tptp_minus_1), F!15) & leq(F!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F!15) = init))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[139])).
% 0.11/0.39 tff(141,plain,
% 0.11/0.39 (((~(a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init)) | ((~(~(leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E!14, D!13) = init)))) | (~((~(leq(succ(tptp_minus_1), F!15) & leq(F!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F!15) = init)))) <=> ((~(a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init)) | (~((~(leq(succ(tptp_minus_1), F!15) & leq(F!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F!15) = init))) | (leq(succ(tptp_minus_1), D!13) & leq(D!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E!14, D!13) = init)))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[140, 135])).
% 0.11/0.39 tff(142,plain,
% 0.11/0.39 (((a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, succ(succ(succ(tptp_minus_1)))))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F) = init))) <=> ((a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, succ(succ(succ(tptp_minus_1)))))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F) = init)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(143,plain,
% 0.11/0.39 ((~((a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, succ(succ(succ(tptp_minus_1)))))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F) = init)))) <=> (~((a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, succ(succ(succ(tptp_minus_1)))))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F) = init))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[142])).
% 0.11/0.39 tff(144,plain,
% 0.11/0.39 ((~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init)))) <=> (~((a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, succ(succ(succ(tptp_minus_1)))))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F) = init))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(145,plain,
% 0.11/0.39 (((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init))) <=> ((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(146,plain,
% 0.11/0.39 ((~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init)))) <=> (~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[145])).
% 0.11/0.39 tff(147,plain,
% 0.11/0.39 ((~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init)))) <=> (~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(148,plain,
% 0.11/0.39 ((~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & leq(n0, pv9) & leq(pv9, minus(n410, n1)) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init)))) <=> (~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(149,plain,
% 0.11/0.39 (((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & leq(n0, pv9) & leq(pv9, minus(n410, n1)) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init))) <=> ((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & leq(n0, pv9) & leq(pv9, minus(n410, n1)) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(150,plain,
% 0.11/0.39 ((~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & leq(n0, pv9) & leq(pv9, minus(n410, n1)) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init)))) <=> (~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & leq(n0, pv9) & leq(pv9, minus(n410, n1)) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[149])).
% 0.11/0.39 tff(151,plain,
% 0.11/0.39 (~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & leq(n0, pv9) & leq(pv9, minus(n410, n1)) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init)))),
% 0.11/0.39 inference(or_elim,[status(thm)],[20])).
% 0.11/0.39 tff(152,plain,
% 0.11/0.39 (~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & leq(n0, pv9) & leq(pv9, minus(n410, n1)) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.11/0.40 tff(153,plain,
% 0.11/0.40 (~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.11/0.40 tff(154,plain,
% 0.11/0.40 (~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[153, 147])).
% 0.11/0.40 tff(155,plain,
% 0.11/0.40 (~((a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select2(s_values7_init, F) = init)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[154, 146])).
% 0.11/0.40 tff(156,plain,
% 0.11/0.40 (~((a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, succ(succ(succ(tptp_minus_1)))))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F) = init)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[155, 144])).
% 0.11/0.40 tff(157,plain,
% 0.11/0.40 (~((a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, succ(succ(succ(tptp_minus_1)))))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F) = init)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[156, 143])).
% 0.11/0.40 tff(158,plain,
% 0.11/0.40 (~((a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, succ(succ(succ(tptp_minus_1)))))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F) = init)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[157, 143])).
% 0.11/0.40 tff(159,plain,
% 0.11/0.40 (~((a_select3(tptp_const_array2(dim(succ(tptp_minus_1), minus(n410, succ(succ(tptp_minus_1)))), dim(succ(tptp_minus_1), minus(n330, succ(succ(tptp_minus_1)))), init), pv9, pv10) = init) & ![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, succ(succ(succ(tptp_minus_1)))))) | ![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, F) = init)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[158, 143])).
% 0.11/0.40 unexpected number of arguments: (let ((a!1 (dim (succ tptp_minus_1) (minus n410 (succ (succ tptp_minus_1)))))
% 0.11/0.40 (a!2 (dim (succ tptp_minus_1) (minus n330 (succ (succ tptp_minus_1)))))
% 0.11/0.40 (a!4 (forall ((D $i))
% 0.11/0.40 (let ((a!1 (leq D (succ (succ (succ tptp_minus_1)))))
% 0.11/0.40 (a!3 (forall ((E $i))
% 0.11/0.40 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.11/0.40 (let ((a!2 (not (and (leq (succ tptp_minus_1) E)
% 0.11/0.40 (leq E a!1)))))
% 0.11/0.40 (or a!2 (= (a_select3 simplex7_init E D) init)))))))
% 0.11/0.40 (let ((a!2 (not (and (leq (succ tptp_minus_1) D) a!1))))
% 0.11/0.40 (or a!2 a!3)))))
% 0.11/0.40 (a!5 (leq D!13 (succ (succ (succ tptp_minus_1)))))
% 0.11/0.40 (a!7 (forall ((E $i))
% 0.11/0.40 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.11/0.40 (let ((a!2 (not (and (leq (succ tptp_minus_1) E) (leq E a!1)))))
% 0.11/0.40 (or a!2 (= (a_select3 simplex7_init E D!13) init))))))
% 0.11/0.40 (a!9 (succ (succ (succ (succ tptp_minus_1)))))
% 0.11/0.40 (a!14 (forall ((F $i))
% 0.11/0.40 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.11/0.40 (let ((a!2 (not (and (leq (succ tptp_minus_1) F) (leq F a!1)))))
% 0.11/0.40 (or a!2 (= (a_select2 s_values7_init F) init)))))))
% 0.11/0.40 (let ((a!3 (not (= (a_select3 (tptp_const_array2 a!1 a!2 init) pv9 pv10) init)))
% 0.11/0.40 (a!6 (not (and (leq (succ tptp_minus_1) D!13) a!5)))
% 0.11/0.40 (a!10 (not (and (leq (succ tptp_minus_1) E!14) (leq E!14 a!9))))
% 0.11/0.40 (a!15 (not (and (leq (succ tptp_minus_1) F!15) (leq F!15 a!9))))
% 0.11/0.40 (a!17 (and (= (a_select3 (tptp_const_array2 a!1 a!2 init) pv9 pv10) init)
% 0.11/0.40 a!4
% 0.11/0.40 a!14)))
% 0.11/0.40 (let ((a!8 (sk (~ (not a!4) (not (or a!6 a!7)))))
% 0.11/0.40 (a!11 (not (or a!10 (= (a_select3 simplex7_init E!14 D!13) init))))
% 0.11/0.40 (a!16 (not (or a!15 (= (a_select2 s_values7_init F!15) init)))))
% 0.11/0.40 (let ((a!12 (nnf-neg (refl (~ (not a!6) (not a!6)))
% 0.11/0.40 (sk (~ (not a!7) a!11))
% 0.11/0.40 (~ (not (or a!6 a!7)) (and (not a!6) a!11))))
% 0.11/0.40 (a!18 (~ (not a!17) (or a!3 (and (not a!6) a!11) a!16))))
% 0.11/0.40 (let ((a!13 (trans a!8 a!12 (~ (not a!4) (and (not a!6) a!11)))))
% 0.11/0.40 (nnf-neg (refl (~ a!3 a!3)) a!13 (sk (~ (not a!14) a!16)) a!18))))))
% 0.11/0.40 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------