%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV031+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:31:22 AM UTC 2025
% Result : Theorem 170.26s 170.45s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV031+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:26:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 170.26/170.45 % SZS status Theorem
% 170.26/170.45 % SZS output start Proof
% 170.26/170.45 tff(init_type, type, (
% 170.26/170.45 init: $i)).
% 170.26/170.45 tff(a_select3_type, type, (
% 170.26/170.45 a_select3: ( $i * $i * $i ) > $i)).
% 170.26/170.45 tff(pv10_type, type, (
% 170.26/170.45 pv10: $i)).
% 170.26/170.45 tff(pv9_type, type, (
% 170.26/170.45 pv9: $i)).
% 170.26/170.45 tff(tptp_const_array2_type, type, (
% 170.26/170.45 tptp_const_array2: ( $i * $i * $i ) > $i)).
% 170.26/170.45 tff(dim_type, type, (
% 170.26/170.45 dim: ( $i * $i ) > $i)).
% 170.26/170.45 tff(minus_type, type, (
% 170.26/170.45 minus: ( $i * $i ) > $i)).
% 170.26/170.45 tff(n1_type, type, (
% 170.26/170.45 n1: $i)).
% 170.26/170.45 tff(n330_type, type, (
% 170.26/170.45 n330: $i)).
% 170.26/170.45 tff(n0_type, type, (
% 170.26/170.45 n0: $i)).
% 170.26/170.45 tff(n410_type, type, (
% 170.26/170.45 n410: $i)).
% 170.26/170.45 tff(pred_type, type, (
% 170.26/170.45 pred: $i > $i)).
% 170.26/170.45 tff(leq_type, type, (
% 170.26/170.45 leq: ( $i * $i ) > $o)).
% 170.26/170.45 tff(a_select2_type, type, (
% 170.26/170.45 a_select2: ( $i * $i ) > $i)).
% 170.26/170.45 tff(s_values7_init_type, type, (
% 170.26/170.45 s_values7_init: $i)).
% 170.26/170.45 tff(n3_type, type, (
% 170.26/170.45 n3: $i)).
% 170.26/170.45 tff(simplex7_init_type, type, (
% 170.26/170.45 simplex7_init: $i)).
% 170.26/170.45 tff(n2_type, type, (
% 170.26/170.45 n2: $i)).
% 170.26/170.45 tff(tptp_fun_F_15_type, type, (
% 170.26/170.45 tptp_fun_F_15: $i)).
% 170.26/170.45 tff(tptp_fun_D_13_type, type, (
% 170.26/170.45 tptp_fun_D_13: $i)).
% 170.26/170.45 tff(tptp_fun_E_14_type, type, (
% 170.26/170.45 tptp_fun_E_14: $i)).
% 170.26/170.45 tff(1,plain,
% 170.26/170.45 (^[X: $i] : refl((minus(X, n1) = pred(X)) <=> (minus(X, n1) = pred(X)))),
% 170.26/170.45 inference(bind,[status(th)],[])).
% 170.26/170.45 tff(2,plain,
% 170.26/170.45 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 170.26/170.45 inference(quant_intro,[status(thm)],[1])).
% 170.26/170.45 tff(3,plain,
% 170.26/170.45 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 170.26/170.45 inference(rewrite,[status(thm)],[])).
% 170.26/170.45 tff(4,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 170.26/170.45 tff(5,plain,
% 170.26/170.45 (![X: $i] : (minus(X, n1) = pred(X))),
% 170.26/170.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 170.26/170.45 tff(6,plain,(
% 170.26/170.45 ![X: $i] : (minus(X, n1) = pred(X))),
% 170.26/170.45 inference(skolemize,[status(sab)],[5])).
% 170.26/170.45 tff(7,plain,
% 170.26/170.45 (![X: $i] : (minus(X, n1) = pred(X))),
% 170.26/170.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 170.26/170.45 tff(8,plain,
% 170.26/170.45 ((~![X: $i] : (minus(X, n1) = pred(X))) | (minus(n330, n1) = pred(n330))),
% 170.26/170.45 inference(quant_inst,[status(thm)],[])).
% 170.26/170.45 tff(9,plain,
% 170.26/170.45 (minus(n330, n1) = pred(n330)),
% 170.26/170.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 170.26/170.45 tff(10,plain,
% 170.26/170.45 (pred(n330) = minus(n330, n1)),
% 170.26/170.45 inference(symmetry,[status(thm)],[9])).
% 170.26/170.45 tff(11,plain,
% 170.26/170.45 (leq(pv10, pred(n330)) <=> leq(pv10, minus(n330, n1))),
% 170.26/170.45 inference(monotonicity,[status(thm)],[10])).
% 170.26/170.45 tff(12,plain,
% 170.26/170.45 (leq(pv10, minus(n330, n1)) <=> leq(pv10, pred(n330))),
% 170.26/170.45 inference(symmetry,[status(thm)],[11])).
% 170.26/170.45 tff(13,plain,
% 170.26/170.45 (leq(pv10, minus(n330, n1)) <=> leq(pv10, minus(n330, n1))),
% 170.26/170.45 inference(rewrite,[status(thm)],[])).
% 170.26/170.45 tff(14,plain,
% 170.26/170.45 ((~((((((((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)))))),
% 170.26/170.45 inference(rewrite,[status(thm)],[])).
% 170.26/170.45 tff(15,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/sandbox2/benchmark/theBenchmark.p','gauss_init_0037')).
% 170.26/170.46 tff(16,plain,
% 170.26/170.46 (~((~(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))))),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[15, 14])).
% 170.26/170.46 tff(17,plain,
% 170.26/170.46 (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))),
% 170.26/170.46 inference(or_elim,[status(thm)],[16])).
% 170.26/170.46 tff(18,plain,
% 170.26/170.46 (leq(pv10, minus(n330, n1))),
% 170.26/170.46 inference(and_elim,[status(thm)],[17])).
% 170.26/170.46 tff(19,plain,
% 170.26/170.46 (leq(pv10, minus(n330, n1))),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[18, 13])).
% 170.26/170.46 tff(20,plain,
% 170.26/170.46 (leq(pv10, pred(n330))),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[19, 12])).
% 170.26/170.46 tff(21,plain,
% 170.26/170.46 ((~![X: $i] : (minus(X, n1) = pred(X))) | (minus(n410, n1) = pred(n410))),
% 170.26/170.46 inference(quant_inst,[status(thm)],[])).
% 170.26/170.46 tff(22,plain,
% 170.26/170.46 (minus(n410, n1) = pred(n410)),
% 170.26/170.46 inference(unit_resolution,[status(thm)],[21, 7])).
% 170.26/170.46 tff(23,plain,
% 170.26/170.46 (pred(n410) = minus(n410, n1)),
% 170.26/170.46 inference(symmetry,[status(thm)],[22])).
% 170.26/170.46 tff(24,plain,
% 170.26/170.46 (leq(pv9, pred(n410)) <=> leq(pv9, minus(n410, n1))),
% 170.26/170.46 inference(monotonicity,[status(thm)],[23])).
% 170.26/170.46 tff(25,plain,
% 170.26/170.46 (leq(pv9, minus(n410, n1)) <=> leq(pv9, pred(n410))),
% 170.26/170.46 inference(symmetry,[status(thm)],[24])).
% 170.26/170.46 tff(26,plain,
% 170.26/170.46 (leq(pv9, minus(n410, n1)) <=> leq(pv9, minus(n410, n1))),
% 170.26/170.46 inference(rewrite,[status(thm)],[])).
% 170.26/170.46 tff(27,plain,
% 170.26/170.46 (leq(pv9, minus(n410, n1))),
% 170.26/170.46 inference(and_elim,[status(thm)],[17])).
% 170.26/170.46 tff(28,plain,
% 170.26/170.46 (leq(pv9, minus(n410, n1))),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[27, 26])).
% 170.26/170.46 tff(29,plain,
% 170.26/170.46 (leq(pv9, pred(n410))),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[28, 25])).
% 170.26/170.46 tff(30,plain,
% 170.26/170.46 (leq(n0, pv10) <=> leq(n0, pv10)),
% 170.26/170.46 inference(rewrite,[status(thm)],[])).
% 170.26/170.46 tff(31,plain,
% 170.26/170.46 (leq(n0, pv10)),
% 170.26/170.46 inference(and_elim,[status(thm)],[17])).
% 170.26/170.46 tff(32,plain,
% 170.26/170.46 (leq(n0, pv10)),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[31, 30])).
% 170.26/170.46 tff(33,plain,
% 170.26/170.46 (leq(n0, pv9) <=> leq(n0, pv9)),
% 170.26/170.46 inference(rewrite,[status(thm)],[])).
% 170.26/170.46 tff(34,plain,
% 170.26/170.46 (leq(n0, pv9)),
% 170.26/170.46 inference(and_elim,[status(thm)],[17])).
% 170.26/170.46 tff(35,plain,
% 170.26/170.46 (leq(n0, pv9)),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[34, 33])).
% 170.26/170.46 tff(36,plain,
% 170.26/170.46 (^[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))))),
% 170.26/170.46 inference(bind,[status(th)],[])).
% 170.26/170.46 tff(37,plain,
% 170.26/170.46 (![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)))),
% 170.26/170.46 inference(quant_intro,[status(thm)],[36])).
% 170.26/170.46 tff(38,plain,
% 170.26/170.46 (^[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)))))),
% 170.26/170.46 inference(bind,[status(th)],[])).
% 170.26/170.46 tff(39,plain,
% 170.26/170.46 (![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)))),
% 170.26/170.46 inference(quant_intro,[status(thm)],[38])).
% 170.26/170.46 tff(40,plain,
% 170.26/170.46 (![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))),
% 170.26/170.46 inference(rewrite,[status(thm)],[])).
% 170.26/170.46 tff(41,plain,
% 170.26/170.46 (^[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))))),
% 170.26/170.46 inference(bind,[status(th)],[])).
% 170.26/170.46 tff(42,plain,
% 170.26/170.46 (![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))),
% 170.26/170.46 inference(quant_intro,[status(thm)],[41])).
% 170.26/170.46 tff(43,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/sandbox2/benchmark/Axioms/SWV003+0.ax','const_array2_select')).
% 170.26/170.46 tff(44,plain,
% 170.26/170.46 (![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))),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[43, 42])).
% 170.26/170.46 tff(45,plain,
% 170.26/170.46 (![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))),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[44, 40])).
% 170.26/170.46 tff(46,plain,(
% 170.26/170.46 ![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))),
% 170.26/170.46 inference(skolemize,[status(sab)],[45])).
% 170.26/170.46 tff(47,plain,
% 170.26/170.46 (![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)))),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[46, 39])).
% 170.26/170.46 tff(48,plain,
% 170.26/170.46 (![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)))),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[47, 37])).
% 170.26/170.46 tff(49,plain,
% 170.26/170.46 (((~![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(n0, pv9)) | (~leq(n0, pv10)) | (~leq(pv9, pred(n410))) | (~leq(pv10, pred(n330))) | (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, 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(n0, pv9)) | (~leq(n0, pv10)) | (~leq(pv9, pred(n410))) | (~leq(pv10, pred(n330))) | (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv9, pv10) = init))),
% 170.26/170.46 inference(rewrite,[status(thm)],[])).
% 170.26/170.46 tff(50,plain,
% 170.26/170.46 (((a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv9, pv10) = init) | (~leq(n0, pv10)) | (~leq(pv10, pred(n330))) | (~leq(n0, pv9)) | (~leq(pv9, pred(n410)))) <=> ((~leq(n0, pv9)) | (~leq(n0, pv10)) | (~leq(pv9, pred(n410))) | (~leq(pv10, pred(n330))) | (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv9, pv10) = init))),
% 170.26/170.46 inference(rewrite,[status(thm)],[])).
% 170.26/170.46 tff(51,plain,
% 170.26/170.46 (((~![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(n0, pred(n410)), dim(n0, pred(n330)), init), pv9, pv10) = init) | (~leq(n0, pv10)) | (~leq(pv10, pred(n330))) | (~leq(n0, 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(n0, pv9)) | (~leq(n0, pv10)) | (~leq(pv9, pred(n410))) | (~leq(pv10, pred(n330))) | (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv9, pv10) = init)))),
% 170.26/170.46 inference(monotonicity,[status(thm)],[50])).
% 170.26/170.46 tff(52,plain,
% 170.26/170.46 (((~![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(n0, pred(n410)), dim(n0, pred(n330)), init), pv9, pv10) = init) | (~leq(n0, pv10)) | (~leq(pv10, pred(n330))) | (~leq(n0, 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(n0, pv9)) | (~leq(n0, pv10)) | (~leq(pv9, pred(n410))) | (~leq(pv10, pred(n330))) | (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv9, pv10) = init))),
% 170.26/170.46 inference(transitivity,[status(thm)],[51, 49])).
% 170.26/170.46 tff(53,plain,
% 170.26/170.46 ((~![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(n0, pred(n410)), dim(n0, pred(n330)), init), pv9, pv10) = init) | (~leq(n0, pv10)) | (~leq(pv10, pred(n330))) | (~leq(n0, pv9)) | (~leq(pv9, pred(n410))))),
% 170.26/170.46 inference(quant_inst,[status(thm)],[])).
% 170.26/170.46 tff(54,plain,
% 170.26/170.46 ((~![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(n0, pv9)) | (~leq(n0, pv10)) | (~leq(pv9, pred(n410))) | (~leq(pv10, pred(n330))) | (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv9, pv10) = init)),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[53, 52])).
% 170.26/170.46 tff(55,plain,
% 170.26/170.46 (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv9, pv10) = init),
% 170.26/170.46 inference(unit_resolution,[status(thm)],[54, 48, 35, 32, 29, 20])).
% 170.26/170.46 tff(56,plain,
% 170.26/170.46 (dim(n0, pred(n330)) = dim(n0, minus(n330, n1))),
% 170.26/170.46 inference(monotonicity,[status(thm)],[10])).
% 170.26/170.46 tff(57,plain,
% 170.26/170.46 (dim(n0, pred(n410)) = dim(n0, minus(n410, n1))),
% 170.26/170.46 inference(monotonicity,[status(thm)],[23])).
% 170.26/170.46 tff(58,plain,
% 170.26/170.46 (tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init) = tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init)),
% 170.26/170.46 inference(monotonicity,[status(thm)],[57, 56])).
% 170.26/170.46 tff(59,plain,
% 170.26/170.46 (tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init) = tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init)),
% 170.26/170.46 inference(symmetry,[status(thm)],[58])).
% 170.26/170.46 tff(60,plain,
% 170.26/170.46 (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv9, pv10)),
% 170.26/170.46 inference(monotonicity,[status(thm)],[59])).
% 170.26/170.46 tff(61,plain,
% 170.26/170.46 (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv9, pv10) = init),
% 170.26/170.46 inference(transitivity,[status(thm)],[60, 55])).
% 170.26/170.46 tff(62,assumption,(~((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3)))), introduced(assumption)).
% 170.26/170.46 tff(63,plain,
% 170.26/170.46 (((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3))) | leq(F!15, n3)),
% 170.26/170.46 inference(tautology,[status(thm)],[])).
% 170.26/170.46 tff(64,plain,
% 170.26/170.46 (leq(F!15, n3)),
% 170.26/170.46 inference(unit_resolution,[status(thm)],[63, 62])).
% 170.26/170.46 tff(65,plain,
% 170.26/170.46 (((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3))) | leq(n0, F!15)),
% 170.26/170.46 inference(tautology,[status(thm)],[])).
% 170.26/170.46 tff(66,plain,
% 170.26/170.46 (leq(n0, F!15)),
% 170.26/170.46 inference(unit_resolution,[status(thm)],[65, 62])).
% 170.26/170.46 tff(67,plain,
% 170.26/170.46 (((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3))) | (~(a_select2(s_values7_init, F!15) = init))),
% 170.26/170.46 inference(tautology,[status(thm)],[])).
% 170.26/170.46 tff(68,plain,
% 170.26/170.46 (~(a_select2(s_values7_init, F!15) = init)),
% 170.26/170.46 inference(unit_resolution,[status(thm)],[67, 62])).
% 170.26/170.46 tff(69,plain,
% 170.26/170.46 (^[C: $i] : refl(((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3))) <=> ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3))))),
% 170.26/170.46 inference(bind,[status(th)],[])).
% 170.26/170.46 tff(70,plain,
% 170.26/170.46 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3))) <=> ![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))),
% 170.26/170.46 inference(quant_intro,[status(thm)],[69])).
% 170.26/170.46 tff(71,plain,
% 170.26/170.46 (^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, C) & leq(C, n3)) <=> (~((~leq(n0, C)) | (~leq(C, n3))))), ((~(leq(n0, C) & leq(C, n3))) <=> (~(~((~leq(n0, C)) | (~leq(C, n3))))))), rewrite((~(~((~leq(n0, C)) | (~leq(C, n3))))) <=> ((~leq(n0, C)) | (~leq(C, n3)))), ((~(leq(n0, C) & leq(C, n3))) <=> ((~leq(n0, C)) | (~leq(C, n3))))), (((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init)) <=> (((~leq(n0, C)) | (~leq(C, n3))) | (a_select2(s_values7_init, C) = init)))), rewrite((((~leq(n0, C)) | (~leq(C, n3))) | (a_select2(s_values7_init, C) = init)) <=> ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))), (((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init)) <=> ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))))),
% 170.26/170.46 inference(bind,[status(th)],[])).
% 170.26/170.46 tff(72,plain,
% 170.26/170.46 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init)) <=> ![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))),
% 170.26/170.46 inference(quant_intro,[status(thm)],[71])).
% 170.26/170.46 tff(73,plain,
% 170.26/170.46 (![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))),
% 170.26/170.46 inference(rewrite,[status(thm)],[])).
% 170.26/170.46 tff(74,plain,
% 170.26/170.46 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 170.26/170.46 inference(and_elim,[status(thm)],[17])).
% 170.26/170.46 tff(75,plain,
% 170.26/170.46 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[74, 73])).
% 170.26/170.46 tff(76,plain,(
% 170.26/170.46 ![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 170.26/170.46 inference(skolemize,[status(sab)],[75])).
% 170.26/170.46 tff(77,plain,
% 170.26/170.46 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[76, 72])).
% 170.26/170.46 tff(78,plain,
% 170.26/170.46 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[77, 70])).
% 170.26/170.46 tff(79,plain,
% 170.26/170.46 (((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))) | ((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3)))) <=> ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))) | (a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3)))),
% 170.26/170.46 inference(rewrite,[status(thm)],[])).
% 170.26/170.46 tff(80,plain,
% 170.26/170.46 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))) | ((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3)))),
% 170.26/170.46 inference(quant_inst,[status(thm)],[])).
% 170.26/170.46 tff(81,plain,
% 170.26/170.46 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))) | (a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3))),
% 170.26/170.46 inference(modus_ponens,[status(thm)],[80, 79])).
% 170.26/170.46 tff(82,plain,
% 170.26/170.46 ($false),
% 170.26/170.46 inference(unit_resolution,[status(thm)],[81, 78, 68, 66, 64])).
% 170.26/170.46 tff(83,plain,((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3))), inference(lemma,lemma(discharge,[]))).
% 170.26/170.46 tff(84,assumption,(~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2)))), introduced(assumption)).
% 170.26/170.47 tff(85,plain,
% 170.26/170.47 (((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2))) | leq(D!13, n2)),
% 170.26/170.47 inference(tautology,[status(thm)],[])).
% 170.26/170.47 tff(86,plain,
% 170.26/170.47 (leq(D!13, n2)),
% 170.26/170.47 inference(unit_resolution,[status(thm)],[85, 84])).
% 170.26/170.47 tff(87,plain,
% 170.26/170.47 (((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2))) | leq(n0, D!13)),
% 170.26/170.47 inference(tautology,[status(thm)],[])).
% 170.26/170.47 tff(88,plain,
% 170.26/170.47 (leq(n0, D!13)),
% 170.26/170.47 inference(unit_resolution,[status(thm)],[87, 84])).
% 170.26/170.47 tff(89,plain,
% 170.26/170.47 (^[A: $i] : refl(((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3)))) <=> ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3)))))),
% 170.26/170.47 inference(bind,[status(th)],[])).
% 170.26/170.47 tff(90,plain,
% 170.26/170.47 (![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3)))) <=> ![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 170.26/170.47 inference(quant_intro,[status(thm)],[89])).
% 170.26/170.47 tff(91,plain,
% 170.26/170.47 (^[A: $i] : rewrite(((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3)))) <=> ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3)))))),
% 170.26/170.47 inference(bind,[status(th)],[])).
% 170.26/170.47 tff(92,plain,
% 170.26/170.47 (![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3)))) <=> ![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 170.26/170.47 inference(quant_intro,[status(thm)],[91])).
% 170.26/170.47 tff(93,plain,
% 170.26/170.47 (![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3)))) <=> ![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 170.26/170.47 inference(transitivity,[status(thm)],[92, 90])).
% 170.26/170.47 tff(94,plain,
% 170.26/170.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, A) & leq(A, n2)) <=> (~((~leq(n0, A)) | (~leq(A, n2))))), ((~(leq(n0, A) & leq(A, n2))) <=> (~(~((~leq(n0, A)) | (~leq(A, n2))))))), rewrite((~(~((~leq(n0, A)) | (~leq(A, n2))))) <=> ((~leq(n0, A)) | (~leq(A, n2)))), ((~(leq(n0, A) & leq(A, n2))) <=> ((~leq(n0, A)) | (~leq(A, n2))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, B) & leq(B, n3)) <=> (~((~leq(n0, B)) | (~leq(B, n3))))), ((~(leq(n0, B) & leq(B, n3))) <=> (~(~((~leq(n0, B)) | (~leq(B, n3))))))), rewrite((~(~((~leq(n0, B)) | (~leq(B, n3))))) <=> ((~leq(n0, B)) | (~leq(B, n3)))), ((~(leq(n0, B) & leq(B, n3))) <=> ((~leq(n0, B)) | (~leq(B, n3))))), (((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)) <=> (((~leq(n0, B)) | (~leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)))), rewrite((((~leq(n0, B)) | (~leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)) <=> ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3)))), (((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)) <=> ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3)))))), (![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)) <=> ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))), (((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init))) <=> (((~leq(n0, A)) | (~leq(A, n2))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3)))))), rewrite((((~leq(n0, A)) | (~leq(A, n2))) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3)))) <=> ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))), (((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init))) <=> ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))))),
% 170.26/170.47 inference(bind,[status(th)],[])).
% 170.26/170.47 tff(95,plain,
% 170.26/170.47 (![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] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 170.26/170.47 inference(quant_intro,[status(thm)],[94])).
% 170.26/170.47 tff(96,plain,
% 170.26/170.47 (![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)))),
% 170.26/170.47 inference(rewrite,[status(thm)],[])).
% 170.26/170.47 tff(97,plain,
% 170.26/170.47 (![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)))),
% 170.26/170.47 inference(and_elim,[status(thm)],[17])).
% 170.26/170.47 tff(98,plain,
% 170.26/170.47 (![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)))),
% 170.26/170.47 inference(modus_ponens,[status(thm)],[97, 96])).
% 170.26/170.47 tff(99,plain,(
% 170.26/170.47 ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)))),
% 170.26/170.47 inference(skolemize,[status(sab)],[98])).
% 170.26/170.47 tff(100,plain,
% 170.26/170.47 (![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 170.26/170.47 inference(modus_ponens,[status(thm)],[99, 95])).
% 170.26/170.47 tff(101,plain,
% 170.26/170.47 (![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 170.26/170.47 inference(modus_ponens,[status(thm)],[100, 93])).
% 170.26/170.47 tff(102,plain,
% 170.26/170.47 (((~![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))) | ((~leq(n0, D!13)) | (~leq(D!13, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(n0, B)) | (~leq(B, n3))))) <=> ((~![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))) | (~leq(n0, D!13)) | (~leq(D!13, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 170.26/170.47 inference(rewrite,[status(thm)],[])).
% 170.26/170.47 tff(103,plain,
% 170.26/170.47 ((~![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))) | ((~leq(n0, D!13)) | (~leq(D!13, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 170.26/170.47 inference(quant_inst,[status(thm)],[])).
% 170.26/170.47 tff(104,plain,
% 170.26/170.47 ((~![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))) | (~leq(n0, D!13)) | (~leq(D!13, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))),
% 170.26/170.47 inference(modus_ponens,[status(thm)],[103, 102])).
% 170.26/170.47 tff(105,plain,
% 170.26/170.47 (![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))),
% 170.26/170.47 inference(unit_resolution,[status(thm)],[104, 101, 88, 86])).
% 170.26/170.47 tff(106,plain,
% 170.26/170.47 (((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2))) | leq(E!14, n3)),
% 170.26/170.47 inference(tautology,[status(thm)],[])).
% 170.26/170.47 tff(107,plain,
% 170.26/170.47 (leq(E!14, n3)),
% 170.26/170.47 inference(unit_resolution,[status(thm)],[106, 84])).
% 170.26/170.47 tff(108,plain,
% 170.26/170.47 (((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2))) | leq(n0, E!14)),
% 170.26/170.47 inference(tautology,[status(thm)],[])).
% 170.26/170.47 tff(109,plain,
% 170.26/170.47 (leq(n0, E!14)),
% 170.26/170.47 inference(unit_resolution,[status(thm)],[108, 84])).
% 170.26/170.47 tff(110,plain,
% 170.26/170.47 (((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2))) | (~(a_select3(simplex7_init, E!14, D!13) = init))),
% 170.26/170.47 inference(tautology,[status(thm)],[])).
% 170.26/170.47 tff(111,plain,
% 170.26/170.47 (~(a_select3(simplex7_init, E!14, D!13) = init)),
% 170.26/170.47 inference(unit_resolution,[status(thm)],[110, 84])).
% 170.26/170.47 tff(112,plain,
% 170.26/170.47 (((~![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))) | ((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)))) <=> ((~![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))) | (a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)))),
% 170.26/170.47 inference(rewrite,[status(thm)],[])).
% 170.26/170.47 tff(113,plain,
% 170.26/170.47 ((~![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))) | ((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)))),
% 170.26/170.47 inference(quant_inst,[status(thm)],[])).
% 170.26/170.47 tff(114,plain,
% 170.26/170.47 ((~![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))) | (a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3))),
% 170.26/170.47 inference(modus_ponens,[status(thm)],[113, 112])).
% 170.26/170.47 tff(115,plain,
% 170.26/170.47 ($false),
% 170.26/170.47 inference(unit_resolution,[status(thm)],[114, 111, 109, 107, 105])).
% 170.26/170.47 tff(116,plain,((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2))), inference(lemma,lemma(discharge,[]))).
% 170.26/170.47 tff(117,plain,
% 170.26/170.47 (((~(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))) | (~((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3)))) | (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2))))) <=> ((~(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))) | (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2)))) | (~((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3)))))),
% 170.26/170.47 inference(rewrite,[status(thm)],[])).
% 170.26/170.47 tff(118,plain,
% 170.26/170.47 ((leq(n0, D!13) & leq(D!13, n2) & (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3))))) <=> (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2))))),
% 170.26/170.47 inference(rewrite,[status(thm)],[])).
% 170.26/170.47 tff(119,plain,
% 170.26/170.47 ((~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init))) <=> (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3))))),
% 170.26/170.47 inference(rewrite,[status(thm)],[])).
% 170.26/170.47 tff(120,plain,
% 170.26/170.47 ((leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) <=> (leq(n0, D!13) & leq(D!13, n2) & (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)))))),
% 170.26/170.47 inference(monotonicity,[status(thm)],[119])).
% 170.26/170.47 tff(121,plain,
% 170.26/170.47 ((leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) <=> (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2))))),
% 170.26/170.47 inference(transitivity,[status(thm)],[120, 118])).
% 170.26/170.47 tff(122,plain,
% 170.26/170.47 ((~((~(leq(n0, F!15) & leq(F!15, n3))) | (a_select2(s_values7_init, F!15) = init))) <=> (~((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3))))),
% 170.26/170.47 inference(rewrite,[status(thm)],[])).
% 170.26/170.47 tff(123,plain,
% 170.26/170.47 (((~(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))) | (~((~(leq(n0, F!15) & leq(F!15, n3))) | (a_select2(s_values7_init, F!15) = init))) | (leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = 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))) | (~((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3)))) | (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2)))))),
% 170.26/170.47 inference(monotonicity,[status(thm)],[122, 121])).
% 170.26/170.47 tff(124,plain,
% 170.26/170.47 (((~(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))) | (~((~(leq(n0, F!15) & leq(F!15, n3))) | (a_select2(s_values7_init, F!15) = init))) | (leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = 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))) | (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2)))) | (~((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, n3)))))),
% 170.26/170.47 inference(transitivity,[status(thm)],[123, 117])).
% 170.26/170.47 tff(125,plain,
% 170.26/170.47 (((~(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))) | (leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) | (~((~(leq(n0, F!15) & leq(F!15, n3))) | (a_select2(s_values7_init, F!15) = 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))) | (~((~(leq(n0, F!15) & leq(F!15, n3))) | (a_select2(s_values7_init, F!15) = init))) | (leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))))),
% 170.26/170.47 inference(rewrite,[status(thm)],[])).
% 170.26/170.47 tff(126,plain,
% 170.26/170.47 (((leq(n0, D!13) & leq(D!13, n2)) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) <=> (leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init))))),
% 170.26/170.47 inference(rewrite,[status(thm)],[])).
% 170.26/170.47 tff(127,plain,
% 170.26/170.47 (((~(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))) | ((leq(n0, D!13) & leq(D!13, n2)) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) | (~((~(leq(n0, F!15) & leq(F!15, n3))) | (a_select2(s_values7_init, F!15) = 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))) | (leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) | (~((~(leq(n0, F!15) & leq(F!15, n3))) | (a_select2(s_values7_init, F!15) = init))))),
% 170.26/170.47 inference(monotonicity,[status(thm)],[126])).
% 170.26/170.47 tff(128,plain,
% 170.26/170.47 (((~(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))) | ((leq(n0, D!13) & leq(D!13, n2)) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) | (~((~(leq(n0, F!15) & leq(F!15, n3))) | (a_select2(s_values7_init, F!15) = 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))) | (~((~(leq(n0, F!15) & leq(F!15, n3))) | (a_select2(s_values7_init, F!15) = init))) | (leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))))),
% 170.26/170.48 inference(transitivity,[status(thm)],[127, 125])).
% 170.26/170.48 tff(129,plain,
% 170.26/170.48 (((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)))),
% 170.26/170.48 inference(rewrite,[status(thm)],[])).
% 170.26/170.48 tff(130,plain,
% 170.26/170.48 ((~((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))))),
% 170.26/170.48 inference(monotonicity,[status(thm)],[129])).
% 170.26/170.48 tff(131,plain,
% 170.26/170.48 ((~((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))))),
% 170.26/170.48 inference(rewrite,[status(thm)],[])).
% 170.26/170.48 tff(132,plain,
% 170.26/170.48 (~((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)))),
% 170.26/170.48 inference(or_elim,[status(thm)],[16])).
% 170.26/170.48 tff(133,plain,
% 170.26/170.48 (~((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)))),
% 170.26/170.48 inference(modus_ponens,[status(thm)],[132, 130])).
% 170.26/170.48 tff(134,plain,
% 170.26/170.48 (~((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)))),
% 170.26/170.48 inference(modus_ponens,[status(thm)],[133, 131])).
% 170.26/170.48 tff(135,plain,
% 170.26/170.48 (~((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)))),
% 170.26/170.48 inference(modus_ponens,[status(thm)],[134, 130])).
% 170.26/170.48 unexpected number of arguments: (let ((a!1 (a_select3 (tptp_const_array2
% 170.26/170.48 (dim n0 (minus n410 n1))
% 170.26/170.48 (dim n0 (minus n330 n1))
% 170.26/170.48 init)
% 170.26/170.48 pv9
% 170.26/170.48 pv10))
% 170.26/170.48 (a!3 (refl (~ (not (leq n0 pv9)) (not (leq n0 pv9)))))
% 170.26/170.48 (a!4 (~ (not (leq pv9 (minus n410 n1))) (not (leq pv9 (minus n410 n1)))))
% 170.26/170.48 (a!5 (forall ((D $i))
% 170.26/170.48 (let ((a!1 (forall ((E $i))
% 170.26/170.48 (or (not (and (leq n0 E) (leq E n3)))
% 170.26/170.48 (= (a_select3 simplex7_init E D) init)))))
% 170.26/170.48 (or (not (and (leq n0 D) (leq D n2))) a!1))))
% 170.26/170.48 (a!6 (forall ((E $i))
% 170.26/170.48 (or (not (and (leq n0 E) (leq E n3)))
% 170.26/170.48 (= (a_select3 simplex7_init E D!13) init))))
% 170.26/170.48 (a!8 (refl (~ (and (leq n0 D!13) (leq D!13 n2))
% 170.26/170.48 (and (leq n0 D!13) (leq D!13 n2)))))
% 170.26/170.48 (a!9 (or (not (and (leq n0 E!14) (leq E!14 n3)))
% 170.26/170.48 (= (a_select3 simplex7_init E!14 D!13) init)))
% 170.26/170.48 (a!13 (forall ((F $i))
% 170.26/170.48 (or (not (and (leq n0 F) (leq F n3)))
% 170.26/170.48 (= (a_select2 s_values7_init F) init))))
% 170.26/170.48 (a!14 (or (not (and (leq n0 F!15) (leq F!15 n3)))
% 170.26/170.48 (= (a_select2 s_values7_init F!15) init))))
% 170.26/170.48 (let ((a!2 (refl (~ (not (= a!1 init)) (not (= a!1 init)))))
% 170.26/170.48 (a!7 (or (not (and (leq n0 D!13) (leq D!13 n2))) a!6))
% 170.26/170.48 (a!10 (and (and (leq n0 D!13) (leq D!13 n2)) (not a!9)))
% 170.26/170.48 (a!15 (not (and (= a!1 init)
% 170.26/170.48 (leq n0 pv9)
% 170.26/170.48 (leq pv9 (minus n410 n1))
% 170.26/170.48 a!5
% 170.26/170.48 a!13))))
% 170.26/170.48 (let ((a!11 (nnf-neg a!8 (sk (~ (not a!6) (not a!9))) (~ (not a!7) a!10)))
% 170.26/170.48 (a!16 (or (not (= a!1 init))
% 170.26/170.48 (not (leq n0 pv9))
% 170.26/170.48 (not (leq pv9 (minus n410 n1)))
% 170.26/170.48 a!10
% 170.26/170.48 (not a!14))))
% 170.26/170.48 (let ((a!12 (trans (sk (~ (not a!5) (not a!7))) a!11 (~ (not a!5) a!10))))
% 170.26/170.48 (nnf-neg a!2 a!3 (refl a!4) a!12 (sk (~ (not a!13) (not a!14))) (~ a!15 a!16))))))
% 170.26/170.48 Proof display could not be completed: unexpected number of arguments
% 170.97/171.13 % E exiting
%------------------------------------------------------------------------------