%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV032+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 176.15s 176.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV032+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:22:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 176.15/176.36 % SZS status Theorem
% 176.15/176.36 % SZS output start Proof
% 176.15/176.36 tff(init_type, type, (
% 176.15/176.36 init: $i)).
% 176.15/176.36 tff(a_select3_type, type, (
% 176.15/176.36 a_select3: ( $i * $i * $i ) > $i)).
% 176.15/176.36 tff(pv20_type, type, (
% 176.15/176.36 pv20: $i)).
% 176.15/176.36 tff(pv19_type, type, (
% 176.15/176.36 pv19: $i)).
% 176.15/176.36 tff(tptp_const_array2_type, type, (
% 176.15/176.36 tptp_const_array2: ( $i * $i * $i ) > $i)).
% 176.15/176.36 tff(dim_type, type, (
% 176.15/176.36 dim: ( $i * $i ) > $i)).
% 176.15/176.36 tff(minus_type, type, (
% 176.15/176.36 minus: ( $i * $i ) > $i)).
% 176.15/176.36 tff(n1_type, type, (
% 176.15/176.36 n1: $i)).
% 176.15/176.36 tff(n330_type, type, (
% 176.15/176.36 n330: $i)).
% 176.15/176.36 tff(n0_type, type, (
% 176.15/176.36 n0: $i)).
% 176.15/176.36 tff(n410_type, type, (
% 176.15/176.36 n410: $i)).
% 176.15/176.36 tff(pred_type, type, (
% 176.15/176.36 pred: $i > $i)).
% 176.15/176.36 tff(leq_type, type, (
% 176.15/176.36 leq: ( $i * $i ) > $o)).
% 176.15/176.36 tff(a_select2_type, type, (
% 176.15/176.36 a_select2: ( $i * $i ) > $i)).
% 176.15/176.36 tff(s_values7_init_type, type, (
% 176.15/176.36 s_values7_init: $i)).
% 176.15/176.36 tff(pv1376_type, type, (
% 176.15/176.36 pv1376: $i)).
% 176.15/176.36 tff(simplex7_init_type, type, (
% 176.15/176.36 simplex7_init: $i)).
% 176.15/176.36 tff(n3_type, type, (
% 176.15/176.36 n3: $i)).
% 176.15/176.36 tff(n2_type, type, (
% 176.15/176.36 n2: $i)).
% 176.15/176.36 tff(tptp_fun_F_15_type, type, (
% 176.15/176.36 tptp_fun_F_15: $i)).
% 176.15/176.36 tff(tptp_fun_D_13_type, type, (
% 176.15/176.36 tptp_fun_D_13: $i)).
% 176.15/176.36 tff(tptp_fun_E_14_type, type, (
% 176.15/176.36 tptp_fun_E_14: $i)).
% 176.15/176.36 tff(gt_type, type, (
% 176.15/176.36 gt: ( $i * $i ) > $o)).
% 176.15/176.36 tff(succ_type, type, (
% 176.15/176.36 succ: $i > $i)).
% 176.15/176.36 tff(1,plain,
% 176.15/176.36 (^[X: $i] : refl((minus(X, n1) = pred(X)) <=> (minus(X, n1) = pred(X)))),
% 176.15/176.36 inference(bind,[status(th)],[])).
% 176.15/176.36 tff(2,plain,
% 176.15/176.36 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 176.15/176.36 inference(quant_intro,[status(thm)],[1])).
% 176.15/176.36 tff(3,plain,
% 176.15/176.36 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 176.15/176.36 inference(rewrite,[status(thm)],[])).
% 176.15/176.36 tff(4,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 176.15/176.36 tff(5,plain,
% 176.15/176.36 (![X: $i] : (minus(X, n1) = pred(X))),
% 176.15/176.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 176.15/176.36 tff(6,plain,(
% 176.15/176.36 ![X: $i] : (minus(X, n1) = pred(X))),
% 176.15/176.36 inference(skolemize,[status(sab)],[5])).
% 176.15/176.36 tff(7,plain,
% 176.15/176.36 (![X: $i] : (minus(X, n1) = pred(X))),
% 176.15/176.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 176.15/176.36 tff(8,plain,
% 176.15/176.36 ((~![X: $i] : (minus(X, n1) = pred(X))) | (minus(n330, n1) = pred(n330))),
% 176.15/176.36 inference(quant_inst,[status(thm)],[])).
% 176.15/176.36 tff(9,plain,
% 176.15/176.36 (minus(n330, n1) = pred(n330)),
% 176.15/176.36 inference(unit_resolution,[status(thm)],[8, 7])).
% 176.15/176.36 tff(10,plain,
% 176.15/176.36 (pred(n330) = minus(n330, n1)),
% 176.15/176.36 inference(symmetry,[status(thm)],[9])).
% 176.15/176.36 tff(11,plain,
% 176.15/176.36 (leq(pv20, pred(n330)) <=> leq(pv20, minus(n330, n1))),
% 176.15/176.36 inference(monotonicity,[status(thm)],[10])).
% 176.15/176.36 tff(12,plain,
% 176.15/176.36 (leq(pv20, minus(n330, n1)) <=> leq(pv20, pred(n330))),
% 176.15/176.36 inference(symmetry,[status(thm)],[11])).
% 176.15/176.36 tff(13,plain,
% 176.15/176.36 (leq(pv20, minus(n330, n1)) <=> leq(pv20, minus(n330, n1))),
% 176.15/176.36 inference(rewrite,[status(thm)],[])).
% 176.15/176.36 tff(14,plain,
% 176.15/176.36 ((~((((((((((init = init) & leq(n0, pv19)) & leq(n0, pv20)) & leq(n0, pv1376)) & leq(pv19, minus(n410, n1))) & leq(pv20, minus(n330, n1))) & leq(pv1376, n3)) & ![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, minus(pv1376, n1))) => (a_select2(s_values7_init, C) = init))) => (((((((((((init = init) & (a_select3(simplex7_init, pv1376, n0) = init)) & (a_select3(simplex7_init, pv1376, n1) = init)) & (a_select3(simplex7_init, pv1376, n2) = init)) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) & leq(n0, pv19)) & leq(n0, pv1376)) & leq(pv19, minus(n410, n1))) & leq(pv1376, n3)) & ![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, minus(pv1376, n1))) => (a_select2(s_values7_init, F) = init))))) <=> (~((~(leq(n0, pv19) & leq(n0, pv20) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv20, minus(n330, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)))) | ((a_select3(simplex7_init, pv1376, n0) = init) & (a_select3(simplex7_init, pv1376, n1) = init) & (a_select3(simplex7_init, pv1376, n2) = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init) & leq(n0, pv19) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F) = init)))))),
% 176.15/176.36 inference(rewrite,[status(thm)],[])).
% 176.15/176.36 tff(15,axiom,(~((((((((((init = init) & leq(n0, pv19)) & leq(n0, pv20)) & leq(n0, pv1376)) & leq(pv19, minus(n410, n1))) & leq(pv20, minus(n330, n1))) & leq(pv1376, n3)) & ![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, minus(pv1376, n1))) => (a_select2(s_values7_init, C) = init))) => (((((((((((init = init) & (a_select3(simplex7_init, pv1376, n0) = init)) & (a_select3(simplex7_init, pv1376, n1) = init)) & (a_select3(simplex7_init, pv1376, n2) = init)) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) & leq(n0, pv19)) & leq(n0, pv1376)) & leq(pv19, minus(n410, n1))) & leq(pv1376, n3)) & ![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, minus(pv1376, n1))) => (a_select2(s_values7_init, F) = init))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gauss_init_0041')).
% 176.15/176.36 tff(16,plain,
% 176.15/176.36 (~((~(leq(n0, pv19) & leq(n0, pv20) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv20, minus(n330, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)))) | ((a_select3(simplex7_init, pv1376, n0) = init) & (a_select3(simplex7_init, pv1376, n1) = init) & (a_select3(simplex7_init, pv1376, n2) = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init) & leq(n0, pv19) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F) = init))))),
% 176.15/176.36 inference(modus_ponens,[status(thm)],[15, 14])).
% 176.15/176.36 tff(17,plain,
% 176.15/176.36 (leq(n0, pv19) & leq(n0, pv20) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv20, minus(n330, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init))),
% 176.15/176.36 inference(or_elim,[status(thm)],[16])).
% 176.15/176.36 tff(18,plain,
% 176.15/176.36 (leq(pv20, minus(n330, n1))),
% 176.15/176.36 inference(and_elim,[status(thm)],[17])).
% 176.15/176.36 tff(19,plain,
% 176.15/176.36 (leq(pv20, minus(n330, n1))),
% 176.15/176.36 inference(modus_ponens,[status(thm)],[18, 13])).
% 176.15/176.36 tff(20,plain,
% 176.15/176.36 (leq(pv20, pred(n330))),
% 176.15/176.36 inference(modus_ponens,[status(thm)],[19, 12])).
% 176.15/176.36 tff(21,plain,
% 176.15/176.36 ((~![X: $i] : (minus(X, n1) = pred(X))) | (minus(n410, n1) = pred(n410))),
% 176.15/176.36 inference(quant_inst,[status(thm)],[])).
% 176.15/176.36 tff(22,plain,
% 176.15/176.36 (minus(n410, n1) = pred(n410)),
% 176.15/176.36 inference(unit_resolution,[status(thm)],[21, 7])).
% 176.15/176.36 tff(23,plain,
% 176.15/176.36 (pred(n410) = minus(n410, n1)),
% 176.15/176.36 inference(symmetry,[status(thm)],[22])).
% 176.15/176.36 tff(24,plain,
% 176.15/176.36 (leq(pv19, pred(n410)) <=> leq(pv19, minus(n410, n1))),
% 176.15/176.36 inference(monotonicity,[status(thm)],[23])).
% 176.15/176.36 tff(25,plain,
% 176.15/176.36 (leq(pv19, minus(n410, n1)) <=> leq(pv19, pred(n410))),
% 176.15/176.36 inference(symmetry,[status(thm)],[24])).
% 176.15/176.36 tff(26,plain,
% 176.15/176.36 (leq(pv19, minus(n410, n1)) <=> leq(pv19, minus(n410, n1))),
% 176.15/176.36 inference(rewrite,[status(thm)],[])).
% 176.15/176.36 tff(27,plain,
% 176.15/176.36 (leq(pv19, minus(n410, n1))),
% 176.15/176.36 inference(and_elim,[status(thm)],[17])).
% 176.15/176.36 tff(28,plain,
% 176.15/176.36 (leq(pv19, minus(n410, n1))),
% 176.15/176.36 inference(modus_ponens,[status(thm)],[27, 26])).
% 176.15/176.36 tff(29,plain,
% 176.15/176.36 (leq(pv19, pred(n410))),
% 176.15/176.36 inference(modus_ponens,[status(thm)],[28, 25])).
% 176.15/176.36 tff(30,plain,
% 176.15/176.36 (leq(n0, pv20) <=> leq(n0, pv20)),
% 176.15/176.36 inference(rewrite,[status(thm)],[])).
% 176.15/176.36 tff(31,plain,
% 176.15/176.36 (leq(n0, pv20)),
% 176.15/176.36 inference(and_elim,[status(thm)],[17])).
% 176.15/176.36 tff(32,plain,
% 176.15/176.36 (leq(n0, pv20)),
% 176.15/176.36 inference(modus_ponens,[status(thm)],[31, 30])).
% 176.15/176.36 tff(33,plain,
% 176.15/176.36 (leq(n0, pv19) <=> leq(n0, pv19)),
% 176.15/176.36 inference(rewrite,[status(thm)],[])).
% 176.15/176.36 tff(34,plain,
% 176.15/176.36 (leq(n0, pv19)),
% 176.15/176.36 inference(and_elim,[status(thm)],[17])).
% 176.15/176.36 tff(35,plain,
% 176.15/176.36 (leq(n0, pv19)),
% 176.15/176.36 inference(modus_ponens,[status(thm)],[34, 33])).
% 176.15/176.36 tff(36,plain,
% 176.15/176.36 (^[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))))),
% 176.15/176.36 inference(bind,[status(th)],[])).
% 176.15/176.36 tff(37,plain,
% 176.15/176.36 (![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)))),
% 176.15/176.36 inference(quant_intro,[status(thm)],[36])).
% 176.15/176.36 tff(38,plain,
% 176.15/176.36 (^[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)))))),
% 176.15/176.36 inference(bind,[status(th)],[])).
% 176.15/176.36 tff(39,plain,
% 176.15/176.36 (![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)))),
% 176.15/176.36 inference(quant_intro,[status(thm)],[38])).
% 176.15/176.36 tff(40,plain,
% 176.15/176.36 (![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))),
% 176.15/176.36 inference(rewrite,[status(thm)],[])).
% 176.15/176.36 tff(41,plain,
% 176.15/176.36 (^[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))))),
% 176.15/176.36 inference(bind,[status(th)],[])).
% 176.15/176.36 tff(42,plain,
% 176.15/176.36 (![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))),
% 176.15/176.36 inference(quant_intro,[status(thm)],[41])).
% 176.15/176.36 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/sandbox/benchmark/Axioms/SWV003+0.ax','const_array2_select')).
% 176.15/176.36 tff(44,plain,
% 176.15/176.36 (![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))),
% 176.15/176.36 inference(modus_ponens,[status(thm)],[43, 42])).
% 176.15/176.36 tff(45,plain,
% 176.15/176.36 (![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))),
% 176.15/176.36 inference(modus_ponens,[status(thm)],[44, 40])).
% 176.15/176.36 tff(46,plain,(
% 176.15/176.36 ![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))),
% 176.15/176.36 inference(skolemize,[status(sab)],[45])).
% 176.15/176.36 tff(47,plain,
% 176.15/176.36 (![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)))),
% 176.15/176.36 inference(modus_ponens,[status(thm)],[46, 39])).
% 176.15/176.36 tff(48,plain,
% 176.15/176.36 (![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)))),
% 176.15/176.36 inference(modus_ponens,[status(thm)],[47, 37])).
% 176.15/176.36 tff(49,plain,
% 176.15/176.36 (((~![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(n0, pv19)) | (~leq(n0, pv20)) | (~leq(pv19, pred(n410))) | (~leq(pv20, pred(n330))) | (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv19, pv20) = 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, pv19)) | (~leq(n0, pv20)) | (~leq(pv19, pred(n410))) | (~leq(pv20, pred(n330))) | (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv19, pv20) = init))),
% 176.15/176.37 inference(rewrite,[status(thm)],[])).
% 176.15/176.37 tff(50,plain,
% 176.15/176.37 (((a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv19, pv20) = init) | (~leq(n0, pv20)) | (~leq(pv20, pred(n330))) | (~leq(n0, pv19)) | (~leq(pv19, pred(n410)))) <=> ((~leq(n0, pv19)) | (~leq(n0, pv20)) | (~leq(pv19, pred(n410))) | (~leq(pv20, pred(n330))) | (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv19, pv20) = init))),
% 176.15/176.37 inference(rewrite,[status(thm)],[])).
% 176.15/176.37 tff(51,plain,
% 176.15/176.37 (((~![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)))) | ((a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv19, pv20) = init) | (~leq(n0, pv20)) | (~leq(pv20, pred(n330))) | (~leq(n0, pv19)) | (~leq(pv19, 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, pv19)) | (~leq(n0, pv20)) | (~leq(pv19, pred(n410))) | (~leq(pv20, pred(n330))) | (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv19, pv20) = init)))),
% 176.15/176.37 inference(monotonicity,[status(thm)],[50])).
% 176.15/176.37 tff(52,plain,
% 176.15/176.37 (((~![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)))) | ((a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv19, pv20) = init) | (~leq(n0, pv20)) | (~leq(pv20, pred(n330))) | (~leq(n0, pv19)) | (~leq(pv19, 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, pv19)) | (~leq(n0, pv20)) | (~leq(pv19, pred(n410))) | (~leq(pv20, pred(n330))) | (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv19, pv20) = init))),
% 176.15/176.37 inference(transitivity,[status(thm)],[51, 49])).
% 176.15/176.37 tff(53,plain,
% 176.15/176.37 ((~![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)))) | ((a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv19, pv20) = init) | (~leq(n0, pv20)) | (~leq(pv20, pred(n330))) | (~leq(n0, pv19)) | (~leq(pv19, pred(n410))))),
% 176.15/176.37 inference(quant_inst,[status(thm)],[])).
% 176.15/176.37 tff(54,plain,
% 176.15/176.37 ((~![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(n0, pv19)) | (~leq(n0, pv20)) | (~leq(pv19, pred(n410))) | (~leq(pv20, pred(n330))) | (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv19, pv20) = init)),
% 176.15/176.37 inference(modus_ponens,[status(thm)],[53, 52])).
% 176.15/176.37 tff(55,plain,
% 176.15/176.37 (a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv19, pv20) = init),
% 176.15/176.37 inference(unit_resolution,[status(thm)],[54, 48, 35, 32, 29, 20])).
% 176.15/176.37 tff(56,plain,
% 176.15/176.37 (dim(n0, pred(n330)) = dim(n0, minus(n330, n1))),
% 176.15/176.37 inference(monotonicity,[status(thm)],[10])).
% 176.15/176.37 tff(57,plain,
% 176.15/176.37 (dim(n0, pred(n410)) = dim(n0, minus(n410, n1))),
% 176.15/176.37 inference(monotonicity,[status(thm)],[23])).
% 176.15/176.37 tff(58,plain,
% 176.15/176.37 (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)),
% 176.15/176.37 inference(monotonicity,[status(thm)],[57, 56])).
% 176.15/176.37 tff(59,plain,
% 176.15/176.37 (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)),
% 176.15/176.37 inference(symmetry,[status(thm)],[58])).
% 176.15/176.37 tff(60,plain,
% 176.15/176.37 (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = a_select3(tptp_const_array2(dim(n0, pred(n410)), dim(n0, pred(n330)), init), pv19, pv20)),
% 176.15/176.37 inference(monotonicity,[status(thm)],[59])).
% 176.15/176.37 tff(61,plain,
% 176.15/176.37 (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init),
% 176.15/176.37 inference(transitivity,[status(thm)],[60, 55])).
% 176.15/176.37 tff(62,assumption,(~((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1))))), introduced(assumption)).
% 176.15/176.37 tff(63,plain,
% 176.15/176.37 (((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1)))) | leq(F!15, minus(pv1376, n1))),
% 176.15/176.37 inference(tautology,[status(thm)],[])).
% 176.15/176.37 tff(64,plain,
% 176.15/176.37 (leq(F!15, minus(pv1376, n1))),
% 176.15/176.37 inference(unit_resolution,[status(thm)],[63, 62])).
% 176.15/176.37 tff(65,plain,
% 176.15/176.37 (((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1)))) | leq(n0, F!15)),
% 176.15/176.37 inference(tautology,[status(thm)],[])).
% 176.15/176.37 tff(66,plain,
% 176.15/176.37 (leq(n0, F!15)),
% 176.15/176.37 inference(unit_resolution,[status(thm)],[65, 62])).
% 176.15/176.37 tff(67,plain,
% 176.15/176.37 (((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1)))) | (~(a_select2(s_values7_init, F!15) = init))),
% 176.15/176.37 inference(tautology,[status(thm)],[])).
% 176.15/176.37 tff(68,plain,
% 176.15/176.37 (~(a_select2(s_values7_init, F!15) = init)),
% 176.15/176.37 inference(unit_resolution,[status(thm)],[67, 62])).
% 176.15/176.37 tff(69,plain,
% 176.15/176.37 (^[C: $i] : refl(((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))) <=> ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))))),
% 176.15/176.37 inference(bind,[status(th)],[])).
% 176.15/176.37 tff(70,plain,
% 176.15/176.37 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))) <=> ![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))),
% 176.15/176.37 inference(quant_intro,[status(thm)],[69])).
% 176.15/176.37 tff(71,plain,
% 176.15/176.37 (^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, C) & leq(C, minus(pv1376, n1))) <=> (~((~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))))), ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) <=> (~(~((~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))))))), rewrite((~(~((~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))))) <=> ((~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))), ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) <=> ((~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))))), (((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)) <=> (((~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)))), rewrite((((~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)) <=> ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))), (((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)) <=> ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))))),
% 176.15/176.37 inference(bind,[status(th)],[])).
% 176.15/176.37 tff(72,plain,
% 176.15/176.37 (![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)) <=> ![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))),
% 176.15/176.37 inference(quant_intro,[status(thm)],[71])).
% 176.15/176.37 tff(73,plain,
% 176.15/176.37 (![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)) <=> ![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init))),
% 176.15/176.37 inference(rewrite,[status(thm)],[])).
% 176.15/176.37 tff(74,plain,
% 176.15/176.37 (![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init))),
% 176.15/176.37 inference(and_elim,[status(thm)],[17])).
% 176.15/176.37 tff(75,plain,
% 176.15/176.37 (![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init))),
% 176.15/176.37 inference(modus_ponens,[status(thm)],[74, 73])).
% 176.15/176.37 tff(76,plain,(
% 176.15/176.37 ![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init))),
% 176.15/176.37 inference(skolemize,[status(sab)],[75])).
% 176.15/176.37 tff(77,plain,
% 176.15/176.37 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))),
% 176.15/176.37 inference(modus_ponens,[status(thm)],[76, 72])).
% 176.15/176.37 tff(78,plain,
% 176.15/176.37 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))),
% 176.15/176.37 inference(modus_ponens,[status(thm)],[77, 70])).
% 176.15/176.37 tff(79,plain,
% 176.15/176.37 (((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))) | ((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1))))) <=> ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))) | (a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1))))),
% 176.15/176.37 inference(rewrite,[status(thm)],[])).
% 176.15/176.37 tff(80,plain,
% 176.15/176.37 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))) | ((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1))))),
% 176.15/176.37 inference(quant_inst,[status(thm)],[])).
% 176.15/176.37 tff(81,plain,
% 176.15/176.37 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))) | (a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1)))),
% 176.15/176.37 inference(modus_ponens,[status(thm)],[80, 79])).
% 176.15/176.37 tff(82,plain,
% 176.15/176.37 ($false),
% 176.15/176.37 inference(unit_resolution,[status(thm)],[81, 78, 68, 66, 64])).
% 176.15/176.37 tff(83,plain,((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1)))), inference(lemma,lemma(discharge,[]))).
% 176.15/176.37 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)).
% 176.15/176.37 tff(85,plain,
% 176.15/176.37 (((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)),
% 176.15/176.37 inference(tautology,[status(thm)],[])).
% 176.15/176.37 tff(86,plain,
% 176.15/176.37 (leq(D!13, n2)),
% 176.15/176.37 inference(unit_resolution,[status(thm)],[85, 84])).
% 176.15/176.37 tff(87,plain,
% 176.15/176.37 (((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)),
% 176.15/176.37 inference(tautology,[status(thm)],[])).
% 176.15/176.37 tff(88,plain,
% 176.15/176.37 (leq(n0, D!13)),
% 176.15/176.37 inference(unit_resolution,[status(thm)],[87, 84])).
% 176.15/176.37 tff(89,plain,
% 176.15/176.37 (^[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)))))),
% 176.15/176.37 inference(bind,[status(th)],[])).
% 176.15/176.37 tff(90,plain,
% 176.15/176.37 (![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))))),
% 176.15/176.37 inference(quant_intro,[status(thm)],[89])).
% 176.15/176.37 tff(91,plain,
% 176.15/176.37 (^[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)))))),
% 176.15/176.37 inference(bind,[status(th)],[])).
% 176.15/176.37 tff(92,plain,
% 176.15/176.37 (![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))))),
% 176.15/176.37 inference(quant_intro,[status(thm)],[91])).
% 176.15/176.37 tff(93,plain,
% 176.15/176.37 (![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))))),
% 176.15/176.37 inference(transitivity,[status(thm)],[92, 90])).
% 176.15/176.37 tff(94,plain,
% 176.15/176.37 (^[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))))))),
% 176.15/176.37 inference(bind,[status(th)],[])).
% 176.15/176.37 tff(95,plain,
% 176.15/176.37 (![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] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 176.15/176.37 inference(quant_intro,[status(thm)],[94])).
% 176.15/176.37 tff(96,plain,
% 176.15/176.37 (![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)))),
% 176.15/176.37 inference(rewrite,[status(thm)],[])).
% 176.15/176.37 tff(97,plain,
% 176.15/176.37 (![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)))),
% 176.15/176.37 inference(and_elim,[status(thm)],[17])).
% 176.15/176.37 tff(98,plain,
% 176.15/176.37 (![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)))),
% 176.15/176.37 inference(modus_ponens,[status(thm)],[97, 96])).
% 176.15/176.37 tff(99,plain,(
% 176.15/176.37 ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)))),
% 176.15/176.37 inference(skolemize,[status(sab)],[98])).
% 176.15/176.37 tff(100,plain,
% 176.15/176.37 (![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 176.15/176.37 inference(modus_ponens,[status(thm)],[99, 95])).
% 176.15/176.37 tff(101,plain,
% 176.15/176.37 (![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 176.15/176.37 inference(modus_ponens,[status(thm)],[100, 93])).
% 176.15/176.37 tff(102,plain,
% 176.15/176.37 (((~![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))))),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(103,plain,
% 176.15/176.38 ((~![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))))),
% 176.15/176.38 inference(quant_inst,[status(thm)],[])).
% 176.15/176.38 tff(104,plain,
% 176.15/176.38 ((~![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)))),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[103, 102])).
% 176.15/176.38 tff(105,plain,
% 176.15/176.38 (![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[104, 101, 88, 86])).
% 176.15/176.38 tff(106,plain,
% 176.15/176.38 (((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)),
% 176.15/176.38 inference(tautology,[status(thm)],[])).
% 176.15/176.38 tff(107,plain,
% 176.15/176.38 (leq(E!14, n3)),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[106, 84])).
% 176.15/176.38 tff(108,plain,
% 176.15/176.38 (((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)),
% 176.15/176.38 inference(tautology,[status(thm)],[])).
% 176.15/176.38 tff(109,plain,
% 176.15/176.38 (leq(n0, E!14)),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[108, 84])).
% 176.15/176.38 tff(110,plain,
% 176.15/176.38 (((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))),
% 176.15/176.38 inference(tautology,[status(thm)],[])).
% 176.15/176.38 tff(111,plain,
% 176.15/176.38 (~(a_select3(simplex7_init, E!14, D!13) = init)),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[110, 84])).
% 176.15/176.38 tff(112,plain,
% 176.15/176.38 (((~![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)))),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(113,plain,
% 176.15/176.38 ((~![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)))),
% 176.15/176.38 inference(quant_inst,[status(thm)],[])).
% 176.15/176.38 tff(114,plain,
% 176.15/176.38 ((~![B: $i] : ((a_select3(simplex7_init, B, D!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))) | (a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3))),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[113, 112])).
% 176.15/176.38 tff(115,plain,
% 176.15/176.38 ($false),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[114, 111, 109, 107, 105])).
% 176.15/176.38 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,[]))).
% 176.15/176.38 tff(117,plain,
% 176.15/176.38 (gt(n2, n1) <=> gt(n2, n1)),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(118,axiom,(gt(n2, n1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gt_2_1')).
% 176.15/176.38 tff(119,plain,
% 176.15/176.38 (gt(n2, n1)),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[118, 117])).
% 176.15/176.38 tff(120,plain,
% 176.15/176.38 (^[X: $i, Y: $i] : refl(((~gt(Y, X)) | leq(X, Y)) <=> ((~gt(Y, X)) | leq(X, Y)))),
% 176.15/176.38 inference(bind,[status(th)],[])).
% 176.15/176.38 tff(121,plain,
% 176.15/176.38 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y)) <=> ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 176.15/176.38 inference(quant_intro,[status(thm)],[120])).
% 176.15/176.38 tff(122,plain,
% 176.15/176.38 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y)) <=> ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(123,plain,
% 176.15/176.38 (^[X: $i, Y: $i] : rewrite((gt(Y, X) => leq(X, Y)) <=> ((~gt(Y, X)) | leq(X, Y)))),
% 176.15/176.38 inference(bind,[status(th)],[])).
% 176.15/176.38 tff(124,plain,
% 176.15/176.38 (![X: $i, Y: $i] : (gt(Y, X) => leq(X, Y)) <=> ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 176.15/176.38 inference(quant_intro,[status(thm)],[123])).
% 176.15/176.38 tff(125,axiom,(![X: $i, Y: $i] : (gt(Y, X) => leq(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt1')).
% 176.15/176.38 tff(126,plain,
% 176.15/176.38 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[125, 124])).
% 176.15/176.38 tff(127,plain,
% 176.15/176.38 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[126, 122])).
% 176.15/176.38 tff(128,plain,(
% 176.15/176.38 ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 176.15/176.38 inference(skolemize,[status(sab)],[127])).
% 176.15/176.38 tff(129,plain,
% 176.15/176.38 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[128, 121])).
% 176.15/176.38 tff(130,plain,
% 176.15/176.38 (((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | ((~gt(n2, n1)) | leq(n1, n2))) <=> ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | (~gt(n2, n1)) | leq(n1, n2))),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(131,plain,
% 176.15/176.38 ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | ((~gt(n2, n1)) | leq(n1, n2))),
% 176.15/176.38 inference(quant_inst,[status(thm)],[])).
% 176.15/176.38 tff(132,plain,
% 176.15/176.38 ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | (~gt(n2, n1)) | leq(n1, n2)),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[131, 130])).
% 176.15/176.38 tff(133,plain,
% 176.15/176.38 (leq(n1, n2)),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[132, 129, 119])).
% 176.15/176.38 tff(134,plain,
% 176.15/176.38 (gt(n1, n0) <=> gt(n1, n0)),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(135,axiom,(gt(n1, n0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gt_1_0')).
% 176.15/176.38 tff(136,plain,
% 176.15/176.38 (gt(n1, n0)),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[135, 134])).
% 176.15/176.38 tff(137,plain,
% 176.15/176.38 (((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | ((~gt(n1, n0)) | leq(n0, n1))) <=> ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | (~gt(n1, n0)) | leq(n0, n1))),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(138,plain,
% 176.15/176.38 ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | ((~gt(n1, n0)) | leq(n0, n1))),
% 176.15/176.38 inference(quant_inst,[status(thm)],[])).
% 176.15/176.38 tff(139,plain,
% 176.15/176.38 ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | (~gt(n1, n0)) | leq(n0, n1)),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[138, 137])).
% 176.15/176.38 tff(140,plain,
% 176.15/176.38 (leq(n0, n1)),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[139, 129, 136])).
% 176.15/176.38 tff(141,plain,
% 176.15/176.38 (((~![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, n1)) | (~leq(n1, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n1) = init)))) <=> ((~![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, n1)) | (~leq(n1, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n1) = init)))),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(142,plain,
% 176.15/176.38 (((~leq(n0, n1)) | (~leq(n1, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, n1) = init) | (~leq(n0, B)) | (~leq(B, n3)))) <=> ((~leq(n0, n1)) | (~leq(n1, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n1) = init)))),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(143,plain,
% 176.15/176.38 (((~![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, n1)) | (~leq(n1, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, n1) = 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, n1)) | (~leq(n1, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n1) = init))))),
% 176.15/176.38 inference(monotonicity,[status(thm)],[142])).
% 176.15/176.38 tff(144,plain,
% 176.15/176.38 (((~![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, n1)) | (~leq(n1, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, n1) = 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, n1)) | (~leq(n1, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n1) = init)))),
% 176.15/176.38 inference(transitivity,[status(thm)],[143, 141])).
% 176.15/176.38 tff(145,plain,
% 176.15/176.38 ((~![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, n1)) | (~leq(n1, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, n1) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 176.15/176.38 inference(quant_inst,[status(thm)],[])).
% 176.15/176.38 tff(146,plain,
% 176.15/176.38 ((~![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, n1)) | (~leq(n1, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n1) = init))),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[145, 144])).
% 176.15/176.38 tff(147,plain,
% 176.15/176.38 (![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n1) = init))),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[146, 101, 140, 133])).
% 176.15/176.38 tff(148,plain,
% 176.15/176.38 (leq(pv1376, n3) <=> leq(pv1376, n3)),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(149,plain,
% 176.15/176.38 (leq(pv1376, n3)),
% 176.15/176.38 inference(and_elim,[status(thm)],[17])).
% 176.15/176.38 tff(150,plain,
% 176.15/176.38 (leq(pv1376, n3)),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[149, 148])).
% 176.15/176.38 tff(151,plain,
% 176.15/176.38 (leq(n0, pv1376) <=> leq(n0, pv1376)),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(152,plain,
% 176.15/176.38 (leq(n0, pv1376)),
% 176.15/176.38 inference(and_elim,[status(thm)],[17])).
% 176.15/176.38 tff(153,plain,
% 176.15/176.38 (leq(n0, pv1376)),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[152, 151])).
% 176.15/176.38 tff(154,plain,
% 176.15/176.38 (((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n1) = init))) | ((~leq(n0, pv1376)) | (~leq(pv1376, n3)) | (a_select3(simplex7_init, pv1376, n1) = init))) <=> ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n1) = init))) | (~leq(n0, pv1376)) | (~leq(pv1376, n3)) | (a_select3(simplex7_init, pv1376, n1) = init))),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(155,plain,
% 176.15/176.38 ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n1) = init))) | ((~leq(n0, pv1376)) | (~leq(pv1376, n3)) | (a_select3(simplex7_init, pv1376, n1) = init))),
% 176.15/176.38 inference(quant_inst,[status(thm)],[])).
% 176.15/176.38 tff(156,plain,
% 176.15/176.38 ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n1) = init))) | (~leq(n0, pv1376)) | (~leq(pv1376, n3)) | (a_select3(simplex7_init, pv1376, n1) = init)),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[155, 154])).
% 176.15/176.38 tff(157,plain,
% 176.15/176.38 (a_select3(simplex7_init, pv1376, n1) = init),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[156, 153, 150, 147])).
% 176.15/176.38 tff(158,plain,
% 176.15/176.38 (gt(n2, n0) <=> gt(n2, n0)),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(159,axiom,(gt(n2, n0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gt_2_0')).
% 176.15/176.38 tff(160,plain,
% 176.15/176.38 (gt(n2, n0)),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[159, 158])).
% 176.15/176.38 tff(161,plain,
% 176.15/176.38 (((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | ((~gt(n2, n0)) | leq(n0, n2))) <=> ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | (~gt(n2, n0)) | leq(n0, n2))),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(162,plain,
% 176.15/176.38 ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | ((~gt(n2, n0)) | leq(n0, n2))),
% 176.15/176.38 inference(quant_inst,[status(thm)],[])).
% 176.15/176.38 tff(163,plain,
% 176.15/176.38 ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | (~gt(n2, n0)) | leq(n0, n2)),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[162, 161])).
% 176.15/176.38 tff(164,plain,
% 176.15/176.38 (leq(n0, n2)),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[163, 129, 160])).
% 176.15/176.38 tff(165,plain,
% 176.15/176.38 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(166,plain,
% 176.15/176.38 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(167,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 176.15/176.38 tff(168,plain,
% 176.15/176.38 (![X: $i] : (pred(succ(X)) = X)),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[167, 166])).
% 176.15/176.38 tff(169,plain,(
% 176.15/176.38 ![X: $i] : (pred(succ(X)) = X)),
% 176.15/176.38 inference(skolemize,[status(sab)],[168])).
% 176.15/176.38 tff(170,plain,
% 176.15/176.38 (![X: $i] : (pred(succ(X)) = X)),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[169, 165])).
% 176.15/176.38 tff(171,plain,
% 176.15/176.38 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(n0)) = n0)),
% 176.15/176.38 inference(quant_inst,[status(thm)],[])).
% 176.15/176.38 tff(172,plain,
% 176.15/176.38 (pred(succ(n0)) = n0),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[171, 170])).
% 176.15/176.38 tff(173,plain,
% 176.15/176.38 ((succ(n0) = n1) <=> (succ(n0) = n1)),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(174,axiom,(succ(n0) = n1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','successor_1')).
% 176.15/176.38 tff(175,plain,
% 176.15/176.38 (succ(n0) = n1),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[174, 173])).
% 176.15/176.38 tff(176,plain,
% 176.15/176.38 (n1 = succ(n0)),
% 176.15/176.38 inference(symmetry,[status(thm)],[175])).
% 176.15/176.38 tff(177,plain,
% 176.15/176.38 (pred(n1) = pred(succ(n0))),
% 176.15/176.38 inference(monotonicity,[status(thm)],[176])).
% 176.15/176.38 tff(178,plain,
% 176.15/176.38 (pred(n1) = n0),
% 176.15/176.38 inference(transitivity,[status(thm)],[177, 172])).
% 176.15/176.38 tff(179,plain,
% 176.15/176.38 (leq(n0, pred(n1)) <=> leq(n0, n0)),
% 176.15/176.38 inference(monotonicity,[status(thm)],[178])).
% 176.15/176.38 tff(180,plain,
% 176.15/176.38 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 176.15/176.38 inference(bind,[status(th)],[])).
% 176.15/176.38 tff(181,plain,
% 176.15/176.38 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 176.15/176.38 inference(quant_intro,[status(thm)],[180])).
% 176.15/176.38 tff(182,plain,
% 176.15/176.38 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(183,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 176.15/176.38 tff(184,plain,
% 176.15/176.38 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[183, 182])).
% 176.15/176.38 tff(185,plain,(
% 176.15/176.38 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 176.15/176.38 inference(skolemize,[status(sab)],[184])).
% 176.15/176.38 tff(186,plain,
% 176.15/176.38 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[185, 181])).
% 176.15/176.38 tff(187,plain,
% 176.15/176.38 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(n0, pred(n1)) <=> gt(n1, n0))),
% 176.15/176.38 inference(quant_inst,[status(thm)],[])).
% 176.15/176.38 tff(188,plain,
% 176.15/176.38 (leq(n0, pred(n1)) <=> gt(n1, n0)),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[187, 186])).
% 176.15/176.38 tff(189,plain,
% 176.15/176.38 ((~(leq(n0, pred(n1)) <=> gt(n1, n0))) | leq(n0, pred(n1)) | (~gt(n1, n0))),
% 176.15/176.38 inference(tautology,[status(thm)],[])).
% 176.15/176.38 tff(190,plain,
% 176.15/176.38 ((~(leq(n0, pred(n1)) <=> gt(n1, n0))) | leq(n0, pred(n1))),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[189, 136])).
% 176.15/176.38 tff(191,plain,
% 176.15/176.38 (leq(n0, pred(n1))),
% 176.15/176.38 inference(unit_resolution,[status(thm)],[190, 188])).
% 176.15/176.38 tff(192,plain,
% 176.15/176.38 (leq(n0, n0)),
% 176.15/176.38 inference(modus_ponens,[status(thm)],[191, 179])).
% 176.15/176.38 tff(193,plain,
% 176.15/176.38 (((~![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, n0)) | (~leq(n0, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n0) = init)))) <=> ((~![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, n0)) | (~leq(n0, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n0) = init)))),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(194,plain,
% 176.15/176.38 (((~leq(n0, n0)) | (~leq(n0, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, n0) = init) | (~leq(n0, B)) | (~leq(B, n3)))) <=> ((~leq(n0, n0)) | (~leq(n0, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n0) = init)))),
% 176.15/176.38 inference(rewrite,[status(thm)],[])).
% 176.15/176.38 tff(195,plain,
% 176.15/176.38 (((~![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, n0)) | (~leq(n0, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, n0) = 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, n0)) | (~leq(n0, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n0) = init))))),
% 176.15/176.39 inference(monotonicity,[status(thm)],[194])).
% 176.15/176.39 tff(196,plain,
% 176.15/176.39 (((~![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, n0)) | (~leq(n0, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, n0) = 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, n0)) | (~leq(n0, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n0) = init)))),
% 176.15/176.39 inference(transitivity,[status(thm)],[195, 193])).
% 176.15/176.39 tff(197,plain,
% 176.15/176.39 ((~![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, n0)) | (~leq(n0, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, n0) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 176.15/176.39 inference(quant_inst,[status(thm)],[])).
% 176.15/176.39 tff(198,plain,
% 176.15/176.39 ((~![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, n0)) | (~leq(n0, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n0) = init))),
% 176.15/176.39 inference(modus_ponens,[status(thm)],[197, 196])).
% 176.15/176.39 tff(199,plain,
% 176.15/176.39 (![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n0) = init))),
% 176.15/176.39 inference(unit_resolution,[status(thm)],[198, 101, 192, 164])).
% 176.15/176.39 tff(200,plain,
% 176.15/176.39 (((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n0) = init))) | ((~leq(n0, pv1376)) | (~leq(pv1376, n3)) | (a_select3(simplex7_init, pv1376, n0) = init))) <=> ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n0) = init))) | (~leq(n0, pv1376)) | (~leq(pv1376, n3)) | (a_select3(simplex7_init, pv1376, n0) = init))),
% 176.15/176.39 inference(rewrite,[status(thm)],[])).
% 176.15/176.39 tff(201,plain,
% 176.15/176.39 ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n0) = init))) | ((~leq(n0, pv1376)) | (~leq(pv1376, n3)) | (a_select3(simplex7_init, pv1376, n0) = init))),
% 176.15/176.39 inference(quant_inst,[status(thm)],[])).
% 176.15/176.39 tff(202,plain,
% 176.15/176.39 ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n0) = init))) | (~leq(n0, pv1376)) | (~leq(pv1376, n3)) | (a_select3(simplex7_init, pv1376, n0) = init)),
% 176.15/176.39 inference(modus_ponens,[status(thm)],[201, 200])).
% 176.15/176.39 tff(203,plain,
% 176.15/176.39 (a_select3(simplex7_init, pv1376, n0) = init),
% 176.15/176.39 inference(unit_resolution,[status(thm)],[202, 153, 150, 199])).
% 176.15/176.39 tff(204,plain,
% 176.15/176.39 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(n2)) = n2)),
% 176.15/176.39 inference(quant_inst,[status(thm)],[])).
% 176.15/176.39 tff(205,plain,
% 176.15/176.39 (pred(succ(n2)) = n2),
% 176.15/176.39 inference(unit_resolution,[status(thm)],[204, 170])).
% 176.15/176.39 tff(206,plain,
% 176.15/176.39 ((succ(succ(n0)) = n2) <=> (succ(succ(n0)) = n2)),
% 176.15/176.39 inference(rewrite,[status(thm)],[])).
% 176.15/176.39 tff(207,axiom,(succ(succ(n0)) = n2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','successor_2')).
% 176.15/176.39 tff(208,plain,
% 176.15/176.39 (succ(succ(n0)) = n2),
% 176.15/176.39 inference(modus_ponens,[status(thm)],[207, 206])).
% 176.15/176.39 tff(209,plain,
% 176.15/176.39 (n2 = succ(succ(n0))),
% 176.15/176.39 inference(symmetry,[status(thm)],[208])).
% 176.15/176.39 tff(210,plain,
% 176.15/176.39 (succ(n2) = succ(succ(succ(n0)))),
% 176.15/176.39 inference(monotonicity,[status(thm)],[209])).
% 176.15/176.39 tff(211,plain,
% 176.15/176.39 (succ(succ(succ(n0))) = succ(n2)),
% 176.15/176.39 inference(symmetry,[status(thm)],[210])).
% 176.15/176.39 tff(212,plain,
% 176.15/176.39 ((succ(succ(succ(n0))) = n3) <=> (succ(succ(succ(n0))) = n3)),
% 176.15/176.39 inference(rewrite,[status(thm)],[])).
% 176.15/176.39 tff(213,axiom,(succ(succ(succ(n0))) = n3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','successor_3')).
% 176.15/176.39 tff(214,plain,
% 176.15/176.39 (succ(succ(succ(n0))) = n3),
% 176.15/176.39 inference(modus_ponens,[status(thm)],[213, 212])).
% 176.15/176.39 tff(215,plain,
% 176.15/176.39 (n3 = succ(succ(succ(n0)))),
% 176.15/176.39 inference(symmetry,[status(thm)],[214])).
% 176.15/176.39 tff(216,plain,
% 176.15/176.39 (n3 = succ(n2)),
% 176.15/176.39 inference(transitivity,[status(thm)],[215, 211])).
% 176.15/176.39 tff(217,plain,
% 176.15/176.39 (pred(n3) = pred(succ(n2))),
% 176.15/176.39 inference(monotonicity,[status(thm)],[216])).
% 176.15/176.39 tff(218,plain,
% 176.15/176.39 (pred(n3) = n2),
% 176.15/176.39 inference(transitivity,[status(thm)],[217, 205])).
% 176.15/176.39 tff(219,plain,
% 176.15/176.39 (leq(n2, pred(n3)) <=> leq(n2, n2)),
% 176.15/176.39 inference(monotonicity,[status(thm)],[218])).
% 176.15/176.39 tff(220,plain,
% 176.15/176.39 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(n2, pred(n3)) <=> gt(n3, n2))),
% 176.15/176.39 inference(quant_inst,[status(thm)],[])).
% 176.15/176.39 tff(221,plain,
% 176.15/176.39 (leq(n2, pred(n3)) <=> gt(n3, n2)),
% 176.15/176.39 inference(unit_resolution,[status(thm)],[220, 186])).
% 176.15/176.39 tff(222,plain,
% 176.15/176.39 (gt(n3, n2) <=> gt(n3, n2)),
% 176.15/176.39 inference(rewrite,[status(thm)],[])).
% 176.15/176.39 tff(223,axiom,(gt(n3, n2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gt_3_2')).
% 176.15/176.39 tff(224,plain,
% 176.15/176.39 (gt(n3, n2)),
% 176.15/176.39 inference(modus_ponens,[status(thm)],[223, 222])).
% 176.15/176.39 tff(225,plain,
% 176.15/176.39 ((~(leq(n2, pred(n3)) <=> gt(n3, n2))) | leq(n2, pred(n3)) | (~gt(n3, n2))),
% 176.15/176.39 inference(tautology,[status(thm)],[])).
% 176.15/176.39 tff(226,plain,
% 176.15/176.39 ((~(leq(n2, pred(n3)) <=> gt(n3, n2))) | leq(n2, pred(n3))),
% 176.15/176.39 inference(unit_resolution,[status(thm)],[225, 224])).
% 176.15/176.39 tff(227,plain,
% 176.15/176.39 (leq(n2, pred(n3))),
% 176.15/176.39 inference(unit_resolution,[status(thm)],[226, 221])).
% 176.15/176.39 tff(228,plain,
% 176.15/176.39 (leq(n2, n2)),
% 176.15/176.39 inference(modus_ponens,[status(thm)],[227, 219])).
% 176.15/176.39 tff(229,plain,
% 176.15/176.39 (((~![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, n2)) | (~leq(n2, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n2) = init)))) <=> ((~![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, n2)) | (~leq(n2, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n2) = init)))),
% 176.15/176.39 inference(rewrite,[status(thm)],[])).
% 176.15/176.39 tff(230,plain,
% 176.15/176.39 (((~leq(n0, n2)) | (~leq(n2, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, n2) = init) | (~leq(n0, B)) | (~leq(B, n3)))) <=> ((~leq(n0, n2)) | (~leq(n2, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n2) = init)))),
% 176.15/176.39 inference(rewrite,[status(thm)],[])).
% 176.15/176.39 tff(231,plain,
% 176.15/176.39 (((~![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, n2)) | (~leq(n2, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, n2) = 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, n2)) | (~leq(n2, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n2) = init))))),
% 176.15/176.39 inference(monotonicity,[status(thm)],[230])).
% 176.15/176.39 tff(232,plain,
% 176.15/176.39 (((~![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, n2)) | (~leq(n2, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, n2) = 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, n2)) | (~leq(n2, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n2) = init)))),
% 176.15/176.39 inference(transitivity,[status(thm)],[231, 229])).
% 176.15/176.39 tff(233,plain,
% 176.15/176.39 ((~![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, n2)) | (~leq(n2, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, n2) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 176.15/176.39 inference(quant_inst,[status(thm)],[])).
% 176.15/176.39 tff(234,plain,
% 176.15/176.39 ((~![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, n2)) | (~leq(n2, n2)) | ![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n2) = init))),
% 176.24/176.39 inference(modus_ponens,[status(thm)],[233, 232])).
% 176.24/176.39 tff(235,plain,
% 176.24/176.39 (![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n2) = init))),
% 176.24/176.39 inference(unit_resolution,[status(thm)],[234, 101, 164, 228])).
% 176.24/176.39 tff(236,plain,
% 176.24/176.39 (((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n2) = init))) | ((~leq(n0, pv1376)) | (~leq(pv1376, n3)) | (a_select3(simplex7_init, pv1376, n2) = init))) <=> ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n2) = init))) | (~leq(n0, pv1376)) | (~leq(pv1376, n3)) | (a_select3(simplex7_init, pv1376, n2) = init))),
% 176.24/176.39 inference(rewrite,[status(thm)],[])).
% 176.24/176.39 tff(237,plain,
% 176.24/176.39 ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n2) = init))) | ((~leq(n0, pv1376)) | (~leq(pv1376, n3)) | (a_select3(simplex7_init, pv1376, n2) = init))),
% 176.24/176.39 inference(quant_inst,[status(thm)],[])).
% 176.24/176.39 tff(238,plain,
% 176.24/176.39 ((~![B: $i] : ((~leq(n0, B)) | (~leq(B, n3)) | (a_select3(simplex7_init, B, n2) = init))) | (~leq(n0, pv1376)) | (~leq(pv1376, n3)) | (a_select3(simplex7_init, pv1376, n2) = init)),
% 176.24/176.39 inference(modus_ponens,[status(thm)],[237, 236])).
% 176.24/176.39 tff(239,plain,
% 176.24/176.39 (a_select3(simplex7_init, pv1376, n2) = init),
% 176.24/176.39 inference(unit_resolution,[status(thm)],[238, 153, 150, 235])).
% 176.24/176.39 tff(240,plain,
% 176.24/176.39 (((~(a_select3(simplex7_init, pv1376, n0) = init)) | (~(a_select3(simplex7_init, pv1376, n1) = init)) | (~(a_select3(simplex7_init, pv1376, n2) = init)) | (~(a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) | (~leq(n0, pv19)) | (~leq(n0, pv1376)) | (~leq(pv19, minus(n410, n1))) | (~leq(pv1376, n3)) | (~((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, 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_select3(simplex7_init, pv1376, n0) = init)) | (~(a_select3(simplex7_init, pv1376, n1) = init)) | (~(a_select3(simplex7_init, pv1376, n2) = init)) | (~(a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) | (~leq(n0, pv19)) | (~leq(n0, pv1376)) | (~leq(pv19, minus(n410, n1))) | (~leq(pv1376, 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_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1))))))),
% 176.24/176.39 inference(rewrite,[status(thm)],[])).
% 176.24/176.39 tff(241,plain,
% 176.24/176.39 ((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))))),
% 176.24/176.39 inference(rewrite,[status(thm)],[])).
% 176.24/176.39 tff(242,plain,
% 176.24/176.39 ((~((~(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))))),
% 176.24/176.39 inference(rewrite,[status(thm)],[])).
% 176.24/176.39 tff(243,plain,
% 176.24/176.39 ((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)))))),
% 176.24/176.39 inference(monotonicity,[status(thm)],[242])).
% 176.24/176.39 tff(244,plain,
% 176.24/176.39 ((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))))),
% 176.24/176.39 inference(transitivity,[status(thm)],[243, 241])).
% 176.24/176.39 tff(245,plain,
% 176.24/176.39 ((~((~(leq(n0, F!15) & leq(F!15, minus(pv1376, n1)))) | (a_select2(s_values7_init, F!15) = init))) <=> (~((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1)))))),
% 176.24/176.39 inference(rewrite,[status(thm)],[])).
% 176.24/176.39 tff(246,plain,
% 176.24/176.39 (((~(a_select3(simplex7_init, pv1376, n0) = init)) | (~(a_select3(simplex7_init, pv1376, n1) = init)) | (~(a_select3(simplex7_init, pv1376, n2) = init)) | (~(a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) | (~leq(n0, pv19)) | (~leq(n0, pv1376)) | (~leq(pv19, minus(n410, n1))) | (~leq(pv1376, n3)) | (~((~(leq(n0, F!15) & leq(F!15, minus(pv1376, n1)))) | (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(simplex7_init, pv1376, n0) = init)) | (~(a_select3(simplex7_init, pv1376, n1) = init)) | (~(a_select3(simplex7_init, pv1376, n2) = init)) | (~(a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) | (~leq(n0, pv19)) | (~leq(n0, pv1376)) | (~leq(pv19, minus(n410, n1))) | (~leq(pv1376, n3)) | (~((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, 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)))))),
% 176.24/176.39 inference(monotonicity,[status(thm)],[245, 244])).
% 176.24/176.39 tff(247,plain,
% 176.24/176.39 (((~(a_select3(simplex7_init, pv1376, n0) = init)) | (~(a_select3(simplex7_init, pv1376, n1) = init)) | (~(a_select3(simplex7_init, pv1376, n2) = init)) | (~(a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) | (~leq(n0, pv19)) | (~leq(n0, pv1376)) | (~leq(pv19, minus(n410, n1))) | (~leq(pv1376, n3)) | (~((~(leq(n0, F!15) & leq(F!15, minus(pv1376, n1)))) | (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(simplex7_init, pv1376, n0) = init)) | (~(a_select3(simplex7_init, pv1376, n1) = init)) | (~(a_select3(simplex7_init, pv1376, n2) = init)) | (~(a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) | (~leq(n0, pv19)) | (~leq(n0, pv1376)) | (~leq(pv19, minus(n410, n1))) | (~leq(pv1376, 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_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1))))))),
% 176.24/176.39 inference(transitivity,[status(thm)],[246, 240])).
% 176.24/176.39 tff(248,plain,
% 176.24/176.39 (((~(a_select3(simplex7_init, pv1376, n0) = init)) | (~(a_select3(simplex7_init, pv1376, n1) = init)) | (~(a_select3(simplex7_init, pv1376, n2) = init)) | (~(a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) | (~leq(n0, pv19)) | (~leq(n0, pv1376)) | (~leq(pv19, minus(n410, n1))) | (~leq(pv1376, n3)) | (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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F!15) = init)))) <=> ((~(a_select3(simplex7_init, pv1376, n0) = init)) | (~(a_select3(simplex7_init, pv1376, n1) = init)) | (~(a_select3(simplex7_init, pv1376, n2) = init)) | (~(a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) | (~leq(n0, pv19)) | (~leq(n0, pv1376)) | (~leq(pv19, minus(n410, n1))) | (~leq(pv1376, n3)) | (~((~(leq(n0, F!15) & leq(F!15, minus(pv1376, n1)))) | (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)))))),
% 176.24/176.39 inference(rewrite,[status(thm)],[])).
% 176.24/176.39 tff(249,plain,
% 176.24/176.39 (((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))))),
% 176.24/176.40 inference(rewrite,[status(thm)],[])).
% 176.24/176.40 tff(250,plain,
% 176.24/176.40 (((~(a_select3(simplex7_init, pv1376, n0) = init)) | (~(a_select3(simplex7_init, pv1376, n1) = init)) | (~(a_select3(simplex7_init, pv1376, n2) = init)) | (~(a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) | (~leq(n0, pv19)) | (~leq(n0, pv1376)) | (~leq(pv19, minus(n410, n1))) | (~leq(pv1376, n3)) | ((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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F!15) = init)))) <=> ((~(a_select3(simplex7_init, pv1376, n0) = init)) | (~(a_select3(simplex7_init, pv1376, n1) = init)) | (~(a_select3(simplex7_init, pv1376, n2) = init)) | (~(a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) | (~leq(n0, pv19)) | (~leq(n0, pv1376)) | (~leq(pv19, minus(n410, n1))) | (~leq(pv1376, n3)) | (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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F!15) = init))))),
% 176.24/176.40 inference(monotonicity,[status(thm)],[249])).
% 176.24/176.40 tff(251,plain,
% 176.24/176.40 (((~(a_select3(simplex7_init, pv1376, n0) = init)) | (~(a_select3(simplex7_init, pv1376, n1) = init)) | (~(a_select3(simplex7_init, pv1376, n2) = init)) | (~(a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) | (~leq(n0, pv19)) | (~leq(n0, pv1376)) | (~leq(pv19, minus(n410, n1))) | (~leq(pv1376, n3)) | ((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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F!15) = init)))) <=> ((~(a_select3(simplex7_init, pv1376, n0) = init)) | (~(a_select3(simplex7_init, pv1376, n1) = init)) | (~(a_select3(simplex7_init, pv1376, n2) = init)) | (~(a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init)) | (~leq(n0, pv19)) | (~leq(n0, pv1376)) | (~leq(pv19, minus(n410, n1))) | (~leq(pv1376, n3)) | (~((~(leq(n0, F!15) & leq(F!15, minus(pv1376, n1)))) | (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)))))),
% 176.24/176.40 inference(transitivity,[status(thm)],[250, 248])).
% 176.24/176.40 tff(252,plain,
% 176.24/176.40 (((a_select3(simplex7_init, pv1376, n0) = init) & (a_select3(simplex7_init, pv1376, n1) = init) & (a_select3(simplex7_init, pv1376, n2) = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init) & leq(n0, pv19) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F) = init))) <=> ((a_select3(simplex7_init, pv1376, n0) = init) & (a_select3(simplex7_init, pv1376, n1) = init) & (a_select3(simplex7_init, pv1376, n2) = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init) & leq(n0, pv19) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F) = init)))),
% 176.24/176.40 inference(rewrite,[status(thm)],[])).
% 176.24/176.40 tff(253,plain,
% 176.24/176.40 ((~((a_select3(simplex7_init, pv1376, n0) = init) & (a_select3(simplex7_init, pv1376, n1) = init) & (a_select3(simplex7_init, pv1376, n2) = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init) & leq(n0, pv19) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F) = init)))) <=> (~((a_select3(simplex7_init, pv1376, n0) = init) & (a_select3(simplex7_init, pv1376, n1) = init) & (a_select3(simplex7_init, pv1376, n2) = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init) & leq(n0, pv19) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F) = init))))),
% 176.24/176.40 inference(monotonicity,[status(thm)],[252])).
% 176.24/176.40 tff(254,plain,
% 176.24/176.40 ((~((a_select3(simplex7_init, pv1376, n0) = init) & (a_select3(simplex7_init, pv1376, n1) = init) & (a_select3(simplex7_init, pv1376, n2) = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init) & leq(n0, pv19) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F) = init)))) <=> (~((a_select3(simplex7_init, pv1376, n0) = init) & (a_select3(simplex7_init, pv1376, n1) = init) & (a_select3(simplex7_init, pv1376, n2) = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init) & leq(n0, pv19) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F) = init))))),
% 176.24/176.40 inference(rewrite,[status(thm)],[])).
% 176.24/176.40 tff(255,plain,
% 176.24/176.40 (~((a_select3(simplex7_init, pv1376, n0) = init) & (a_select3(simplex7_init, pv1376, n1) = init) & (a_select3(simplex7_init, pv1376, n2) = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init) & leq(n0, pv19) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F) = init)))),
% 176.24/176.40 inference(or_elim,[status(thm)],[16])).
% 176.24/176.40 tff(256,plain,
% 176.24/176.40 (~((a_select3(simplex7_init, pv1376, n0) = init) & (a_select3(simplex7_init, pv1376, n1) = init) & (a_select3(simplex7_init, pv1376, n2) = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init) & leq(n0, pv19) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F) = init)))),
% 176.24/176.40 inference(modus_ponens,[status(thm)],[255, 253])).
% 176.24/176.40 tff(257,plain,
% 176.24/176.40 (~((a_select3(simplex7_init, pv1376, n0) = init) & (a_select3(simplex7_init, pv1376, n1) = init) & (a_select3(simplex7_init, pv1376, n2) = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init) & leq(n0, pv19) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F) = init)))),
% 176.24/176.40 inference(modus_ponens,[status(thm)],[256, 254])).
% 176.24/176.40 tff(258,plain,
% 176.24/176.40 (~((a_select3(simplex7_init, pv1376, n0) = init) & (a_select3(simplex7_init, pv1376, n1) = init) & (a_select3(simplex7_init, pv1376, n2) = init) & (a_select3(tptp_const_array2(dim(n0, minus(n410, n1)), dim(n0, minus(n330, n1)), init), pv19, pv20) = init) & leq(n0, pv19) & leq(n0, pv1376) & leq(pv19, minus(n410, n1)) & leq(pv1376, n3) & ![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, minus(pv1376, n1)))) | (a_select2(s_values7_init, F) = init)))),
% 176.24/176.41 inference(modus_ponens,[status(thm)],[257, 253])).
% 176.24/176.41 unexpected number of arguments: (let ((a!1 (~ (not (= (a_select3 simplex7_init pv1376 n0) init))
% 176.24/176.41 (not (= (a_select3 simplex7_init pv1376 n0) init))))
% 176.24/176.41 (a!2 (~ (not (= (a_select3 simplex7_init pv1376 n1) init))
% 176.24/176.41 (not (= (a_select3 simplex7_init pv1376 n1) init))))
% 176.24/176.41 (a!3 (~ (not (= (a_select3 simplex7_init pv1376 n2) init))
% 176.24/176.41 (not (= (a_select3 simplex7_init pv1376 n2) init))))
% 176.24/176.41 (a!4 (a_select3 (tptp_const_array2
% 176.24/176.41 (dim n0 (minus n410 n1))
% 176.24/176.41 (dim n0 (minus n330 n1))
% 176.24/176.41 init)
% 176.24/176.41 pv19
% 176.24/176.41 pv20))
% 176.24/176.41 (a!6 (refl (~ (not (leq n0 pv19)) (not (leq n0 pv19)))))
% 176.24/176.41 (a!7 (refl (~ (not (leq n0 pv1376)) (not (leq n0 pv1376)))))
% 176.24/176.41 (a!8 (~ (not (leq pv19 (minus n410 n1))) (not (leq pv19 (minus n410 n1)))))
% 176.24/176.41 (a!9 (refl (~ (not (leq pv1376 n3)) (not (leq pv1376 n3)))))
% 176.24/176.41 (a!10 (forall ((D $i))
% 176.24/176.41 (let ((a!1 (forall ((E $i))
% 176.24/176.41 (or (not (and (leq n0 E) (leq E n3)))
% 176.24/176.41 (= (a_select3 simplex7_init E D) init)))))
% 176.24/176.41 (or (not (and (leq n0 D) (leq D n2))) a!1))))
% 176.24/176.41 (a!11 (forall ((E $i))
% 176.24/176.41 (or (not (and (leq n0 E) (leq E n3)))
% 176.24/176.41 (= (a_select3 simplex7_init E D!13) init))))
% 176.24/176.41 (a!13 (refl (~ (and (leq n0 D!13) (leq D!13 n2))
% 176.24/176.41 (and (leq n0 D!13) (leq D!13 n2)))))
% 176.24/176.41 (a!14 (or (not (and (leq n0 E!14) (leq E!14 n3)))
% 176.24/176.41 (= (a_select3 simplex7_init E!14 D!13) init)))
% 176.24/176.41 (a!18 (forall ((F $i))
% 176.24/176.41 (let ((a!1 (not (and (leq n0 F) (leq F (minus pv1376 n1))))))
% 176.24/176.41 (or a!1 (= (a_select2 s_values7_init F) init)))))
% 176.24/176.41 (a!19 (not (and (leq n0 F!15) (leq F!15 (minus pv1376 n1))))))
% 176.24/176.41 (let ((a!5 (refl (~ (not (= a!4 init)) (not (= a!4 init)))))
% 176.24/176.41 (a!12 (or (not (and (leq n0 D!13) (leq D!13 n2))) a!11))
% 176.24/176.41 (a!15 (and (and (leq n0 D!13) (leq D!13 n2)) (not a!14)))
% 176.24/176.41 (a!20 (not (or a!19 (= (a_select2 s_values7_init F!15) init))))
% 176.24/176.41 (a!21 (not (and (= (a_select3 simplex7_init pv1376 n0) init)
% 176.24/176.41 (= (a_select3 simplex7_init pv1376 n1) init)
% 176.24/176.41 (= (a_select3 simplex7_init pv1376 n2) init)
% 176.24/176.41 (= a!4 init)
% 176.24/176.41 (leq n0 pv19)
% 176.24/176.41 (leq n0 pv1376)
% 176.24/176.41 (leq pv19 (minus n410 n1))
% 176.24/176.41 (leq pv1376 n3)
% 176.24/176.41 a!10
% 176.24/176.41 a!18))))
% 176.24/176.41 (let ((a!16 (nnf-neg a!13 (sk (~ (not a!11) (not a!14))) (~ (not a!12) a!15)))
% 176.24/176.41 (a!22 (or (not (= (a_select3 simplex7_init pv1376 n0) init))
% 176.24/176.41 (not (= (a_select3 simplex7_init pv1376 n1) init))
% 176.24/176.41 (not (= (a_select3 simplex7_init pv1376 n2) init))
% 176.24/176.41 (not (= a!4 init))
% 176.24/176.41 (not (leq n0 pv19))
% 176.24/176.41 (not (leq n0 pv1376))
% 176.24/176.41 (not (leq pv19 (minus n410 n1)))
% 176.24/176.41 (not (leq pv1376 n3))
% 176.24/176.41 a!15
% 176.24/176.41 a!20)))
% 176.24/176.41 (let ((a!17 (trans (sk (~ (not a!10) (not a!12))) a!16 (~ (not a!10) a!15))))
% 176.24/176.41 (nnf-neg (refl a!1)
% 176.24/176.41 (refl a!2)
% 176.24/176.41 (refl a!3)
% 176.24/176.41 a!5
% 176.24/176.41 a!6
% 176.24/176.41 a!7
% 176.24/176.41 (refl a!8)
% 176.24/176.41 a!9
% 176.24/176.41 a!17
% 176.24/176.41 (sk (~ (not a!18) a!20))
% 176.24/176.41 (~ a!21 a!22))))))
% 176.24/176.41 Proof display could not be completed: unexpected number of arguments
% 177.07/177.27 % E exiting
%------------------------------------------------------------------------------