%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV038+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:31:23 AM UTC 2025
% Result : Theorem 257.44s 257.77s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV038+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:23:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 257.44/257.77 % SZS status Theorem
% 257.44/257.77 % SZS output start Proof
% 257.44/257.77 tff(gt_type, type, (
% 257.44/257.77 gt: ( $i * $i ) > $o)).
% 257.44/257.77 tff(n1_type, type, (
% 257.44/257.77 n1: $i)).
% 257.44/257.77 tff(loopcounter_type, type, (
% 257.44/257.77 loopcounter: $i)).
% 257.44/257.77 tff(init_type, type, (
% 257.44/257.77 init: $i)).
% 257.44/257.77 tff(pvar1402_init_type, type, (
% 257.44/257.77 pvar1402_init: $i)).
% 257.44/257.77 tff(pvar1401_init_type, type, (
% 257.44/257.77 pvar1401_init: $i)).
% 257.44/257.77 tff(pvar1400_init_type, type, (
% 257.44/257.77 pvar1400_init: $i)).
% 257.44/257.77 tff(leq_type, type, (
% 257.44/257.77 leq: ( $i * $i ) > $o)).
% 257.44/257.77 tff(n2_type, type, (
% 257.44/257.77 n2: $i)).
% 257.44/257.77 tff(tptp_fun_F_13_type, type, (
% 257.44/257.77 tptp_fun_F_13: $i)).
% 257.44/257.77 tff(n0_type, type, (
% 257.44/257.77 n0: $i)).
% 257.44/257.77 tff(n3_type, type, (
% 257.44/257.77 n3: $i)).
% 257.44/257.77 tff(tptp_fun_G_14_type, type, (
% 257.44/257.77 tptp_fun_G_14: $i)).
% 257.44/257.77 tff(a_select3_type, type, (
% 257.44/257.77 a_select3: ( $i * $i * $i ) > $i)).
% 257.44/257.77 tff(simplex7_init_type, type, (
% 257.44/257.77 simplex7_init: $i)).
% 257.44/257.77 tff(a_select2_type, type, (
% 257.44/257.77 a_select2: ( $i * $i ) > $i)).
% 257.44/257.77 tff(s_try7_init_type, type, (
% 257.44/257.77 s_try7_init: $i)).
% 257.44/257.77 tff(minus_type, type, (
% 257.44/257.77 minus: ( $i * $i ) > $i)).
% 257.44/257.77 tff(s_center7_init_type, type, (
% 257.44/257.77 s_center7_init: $i)).
% 257.44/257.77 tff(s_values7_init_type, type, (
% 257.44/257.77 s_values7_init: $i)).
% 257.44/257.77 tff(s_worst7_type, type, (
% 257.44/257.77 s_worst7: $i)).
% 257.44/257.77 tff(s_sworst7_type, type, (
% 257.44/257.77 s_sworst7: $i)).
% 257.44/257.77 tff(s_best7_type, type, (
% 257.44/257.77 s_best7: $i)).
% 257.44/257.77 tff(s_worst7_init_type, type, (
% 257.44/257.77 s_worst7_init: $i)).
% 257.44/257.77 tff(s_sworst7_init_type, type, (
% 257.44/257.77 s_sworst7_init: $i)).
% 257.44/257.77 tff(s_best7_init_type, type, (
% 257.44/257.77 s_best7_init: $i)).
% 257.44/257.77 tff(pv1413_type, type, (
% 257.44/257.77 pv1413: $i)).
% 257.44/257.77 tff(true_type, type, (
% 257.44/257.77 true: $o)).
% 257.44/257.77 tff(tptp_fun_J_17_type, type, (
% 257.44/257.77 tptp_fun_J_17: $i)).
% 257.44/257.77 tff(tptp_fun_I_16_type, type, (
% 257.44/257.77 tptp_fun_I_16: $i)).
% 257.44/257.77 tff(tptp_fun_H_15_type, type, (
% 257.44/257.77 tptp_fun_H_15: $i)).
% 257.44/257.77 tff(1,assumption,(~((a_select3(simplex7_init, G!14, F!13) = init) | (~leq(n0, G!14)) | (~leq(G!14, n3)) | (~leq(n0, F!13)) | (~leq(F!13, n2)))), introduced(assumption)).
% 257.44/257.77 tff(2,plain,
% 257.44/257.77 (((a_select3(simplex7_init, G!14, F!13) = init) | (~leq(n0, G!14)) | (~leq(G!14, n3)) | (~leq(n0, F!13)) | (~leq(F!13, n2))) | leq(F!13, n2)),
% 257.44/257.77 inference(tautology,[status(thm)],[])).
% 257.44/257.77 tff(3,plain,
% 257.44/257.77 (leq(F!13, n2)),
% 257.44/257.77 inference(unit_resolution,[status(thm)],[2, 1])).
% 257.44/257.77 tff(4,plain,
% 257.44/257.77 (((a_select3(simplex7_init, G!14, F!13) = init) | (~leq(n0, G!14)) | (~leq(G!14, n3)) | (~leq(n0, F!13)) | (~leq(F!13, n2))) | leq(n0, F!13)),
% 257.44/257.77 inference(tautology,[status(thm)],[])).
% 257.44/257.77 tff(5,plain,
% 257.44/257.77 (leq(n0, F!13)),
% 257.44/257.77 inference(unit_resolution,[status(thm)],[4, 1])).
% 257.44/257.77 tff(6,plain,
% 257.44/257.77 (^[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)))))),
% 257.44/257.77 inference(bind,[status(th)],[])).
% 257.44/257.77 tff(7,plain,
% 257.44/257.77 (![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))))),
% 257.44/257.77 inference(quant_intro,[status(thm)],[6])).
% 257.44/257.77 tff(8,plain,
% 257.44/257.77 (^[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)))))),
% 257.44/257.77 inference(bind,[status(th)],[])).
% 257.44/257.77 tff(9,plain,
% 257.44/257.77 (![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))))),
% 257.44/257.77 inference(quant_intro,[status(thm)],[8])).
% 257.44/257.77 tff(10,plain,
% 257.44/257.77 (![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))))),
% 257.44/257.77 inference(transitivity,[status(thm)],[9, 7])).
% 257.44/257.77 tff(11,plain,
% 257.44/257.77 (^[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))))))),
% 257.53/257.78 inference(bind,[status(th)],[])).
% 257.53/257.78 tff(12,plain,
% 257.53/257.78 (![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))))),
% 257.53/257.78 inference(quant_intro,[status(thm)],[11])).
% 257.53/257.78 tff(13,plain,
% 257.53/257.78 (![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)))),
% 257.53/257.78 inference(rewrite,[status(thm)],[])).
% 257.53/257.78 tff(14,plain,
% 257.53/257.78 ((~(((((((((((((((s_best7_init = init) & (s_sworst7_init = init)) & (s_worst7_init = init)) & leq(n0, s_best7)) & leq(n0, s_sworst7)) & leq(n0, s_worst7)) & leq(s_best7, n3)) & leq(s_sworst7, n3)) & leq(s_worst7, 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, n3)) => (a_select2(s_values7_init, C) = init))) & ![D: $i] : ((leq(n0, D) & leq(D, n2)) => (a_select2(s_center7_init, D) = init))) & ![E: $i] : ((leq(n0, E) & leq(E, minus(n3, n1))) => (a_select2(s_try7_init, E) = init))) & (gt(loopcounter, n1) => (((pvar1400_init = init) & (pvar1401_init = init)) & (pvar1402_init = init)))) => (((init = init) & ((~(n0 = pv1413)) => (((((((((((((((init = init) & (s_best7_init = init)) & (s_sworst7_init = init)) & (s_worst7_init = init)) & leq(n0, s_best7)) & leq(n0, s_sworst7)) & leq(n0, s_worst7)) & leq(s_best7, n3)) & leq(s_sworst7, n3)) & leq(s_worst7, n3)) & ![F: $i] : ((leq(n0, F) & leq(F, n2)) => ![G: $i] : ((leq(n0, G) & leq(G, n3)) => (a_select3(simplex7_init, G, F) = init)))) & ![H: $i] : ((leq(n0, H) & leq(H, n3)) => (a_select2(s_values7_init, H) = init))) & ![I: $i] : ((leq(n0, I) & leq(I, n2)) => (a_select2(s_center7_init, I) = init))) & ![J: $i] : ((leq(n0, J) & leq(J, minus(n3, n1))) => (a_select2(s_try7_init, J) = init))) & (gt(loopcounter, n1) => (((pvar1400_init = init) & (pvar1401_init = init)) & (pvar1402_init = init)))))) & ((n0 = pv1413) => true)))) <=> (~((~((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, 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, n3))) | (a_select2(s_values7_init, C) = init)) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | (a_select2(s_center7_init, D) = init)) & ![E: $i] : ((~(leq(n0, E) & leq(E, minus(n3, n1)))) | (a_select2(s_try7_init, E) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) | (((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) & (true | (~(n0 = pv1413))))))),
% 257.53/257.78 inference(rewrite,[status(thm)],[])).
% 257.53/257.78 tff(15,axiom,(~(((((((((((((((s_best7_init = init) & (s_sworst7_init = init)) & (s_worst7_init = init)) & leq(n0, s_best7)) & leq(n0, s_sworst7)) & leq(n0, s_worst7)) & leq(s_best7, n3)) & leq(s_sworst7, n3)) & leq(s_worst7, 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, n3)) => (a_select2(s_values7_init, C) = init))) & ![D: $i] : ((leq(n0, D) & leq(D, n2)) => (a_select2(s_center7_init, D) = init))) & ![E: $i] : ((leq(n0, E) & leq(E, minus(n3, n1))) => (a_select2(s_try7_init, E) = init))) & (gt(loopcounter, n1) => (((pvar1400_init = init) & (pvar1401_init = init)) & (pvar1402_init = init)))) => (((init = init) & ((~(n0 = pv1413)) => (((((((((((((((init = init) & (s_best7_init = init)) & (s_sworst7_init = init)) & (s_worst7_init = init)) & leq(n0, s_best7)) & leq(n0, s_sworst7)) & leq(n0, s_worst7)) & leq(s_best7, n3)) & leq(s_sworst7, n3)) & leq(s_worst7, n3)) & ![F: $i] : ((leq(n0, F) & leq(F, n2)) => ![G: $i] : ((leq(n0, G) & leq(G, n3)) => (a_select3(simplex7_init, G, F) = init)))) & ![H: $i] : ((leq(n0, H) & leq(H, n3)) => (a_select2(s_values7_init, H) = init))) & ![I: $i] : ((leq(n0, I) & leq(I, n2)) => (a_select2(s_center7_init, I) = init))) & ![J: $i] : ((leq(n0, J) & leq(J, minus(n3, n1))) => (a_select2(s_try7_init, J) = init))) & (gt(loopcounter, n1) => (((pvar1400_init = init) & (pvar1401_init = init)) & (pvar1402_init = init)))))) & ((n0 = pv1413) => true)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gauss_init_0065')).
% 257.53/257.78 tff(16,plain,
% 257.53/257.78 (~((~((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, 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, n3))) | (a_select2(s_values7_init, C) = init)) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | (a_select2(s_center7_init, D) = init)) & ![E: $i] : ((~(leq(n0, E) & leq(E, minus(n3, n1)))) | (a_select2(s_try7_init, E) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) | (((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) & (true | (~(n0 = pv1413)))))),
% 257.53/257.78 inference(modus_ponens,[status(thm)],[15, 14])).
% 257.53/257.78 tff(17,plain,
% 257.53/257.78 ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, 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, n3))) | (a_select2(s_values7_init, C) = init)) & ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | (a_select2(s_center7_init, D) = init)) & ![E: $i] : ((~(leq(n0, E) & leq(E, minus(n3, n1)))) | (a_select2(s_try7_init, E) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))),
% 257.53/257.78 inference(or_elim,[status(thm)],[16])).
% 257.53/257.78 tff(18,plain,
% 257.53/257.78 (![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)))),
% 257.53/257.78 inference(and_elim,[status(thm)],[17])).
% 257.53/257.78 tff(19,plain,
% 257.53/257.78 (![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)))),
% 257.53/257.78 inference(modus_ponens,[status(thm)],[18, 13])).
% 257.53/257.78 tff(20,plain,(
% 257.53/257.78 ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init)))),
% 257.53/257.78 inference(skolemize,[status(sab)],[19])).
% 257.53/257.78 tff(21,plain,
% 257.53/257.78 (![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 257.53/257.78 inference(modus_ponens,[status(thm)],[20, 12])).
% 257.53/257.78 tff(22,plain,
% 257.53/257.78 (![A: $i] : ((~leq(n0, A)) | (~leq(A, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, A) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 257.53/257.78 inference(modus_ponens,[status(thm)],[21, 10])).
% 257.53/257.78 tff(23,plain,
% 257.53/257.78 (((~![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, F!13)) | (~leq(F!13, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, F!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, F!13)) | (~leq(F!13, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, F!13) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 257.53/257.78 inference(rewrite,[status(thm)],[])).
% 257.53/257.78 tff(24,plain,
% 257.53/257.78 ((~![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, F!13)) | (~leq(F!13, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, F!13) = init) | (~leq(n0, B)) | (~leq(B, n3))))),
% 257.53/257.78 inference(quant_inst,[status(thm)],[])).
% 257.53/257.78 tff(25,plain,
% 257.53/257.78 ((~![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, F!13)) | (~leq(F!13, n2)) | ![B: $i] : ((a_select3(simplex7_init, B, F!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))),
% 257.53/257.78 inference(modus_ponens,[status(thm)],[24, 23])).
% 257.53/257.78 tff(26,plain,
% 257.53/257.78 (![B: $i] : ((a_select3(simplex7_init, B, F!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))),
% 257.53/257.78 inference(unit_resolution,[status(thm)],[25, 22, 5, 3])).
% 257.53/257.78 tff(27,plain,
% 257.53/257.78 (((a_select3(simplex7_init, G!14, F!13) = init) | (~leq(n0, G!14)) | (~leq(G!14, n3)) | (~leq(n0, F!13)) | (~leq(F!13, n2))) | leq(G!14, n3)),
% 257.53/257.78 inference(tautology,[status(thm)],[])).
% 257.53/257.78 tff(28,plain,
% 257.53/257.78 (leq(G!14, n3)),
% 257.53/257.78 inference(unit_resolution,[status(thm)],[27, 1])).
% 257.53/257.78 tff(29,plain,
% 257.53/257.78 (((a_select3(simplex7_init, G!14, F!13) = init) | (~leq(n0, G!14)) | (~leq(G!14, n3)) | (~leq(n0, F!13)) | (~leq(F!13, n2))) | leq(n0, G!14)),
% 257.53/257.78 inference(tautology,[status(thm)],[])).
% 257.53/257.78 tff(30,plain,
% 257.53/257.78 (leq(n0, G!14)),
% 257.53/257.78 inference(unit_resolution,[status(thm)],[29, 1])).
% 257.53/257.78 tff(31,plain,
% 257.53/257.78 (((a_select3(simplex7_init, G!14, F!13) = init) | (~leq(n0, G!14)) | (~leq(G!14, n3)) | (~leq(n0, F!13)) | (~leq(F!13, n2))) | (~(a_select3(simplex7_init, G!14, F!13) = init))),
% 257.53/257.78 inference(tautology,[status(thm)],[])).
% 257.53/257.78 tff(32,plain,
% 257.53/257.78 (~(a_select3(simplex7_init, G!14, F!13) = init)),
% 257.53/257.78 inference(unit_resolution,[status(thm)],[31, 1])).
% 257.53/257.78 tff(33,plain,
% 257.53/257.78 (((~![B: $i] : ((a_select3(simplex7_init, B, F!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))) | ((a_select3(simplex7_init, G!14, F!13) = init) | (~leq(n0, G!14)) | (~leq(G!14, n3)))) <=> ((~![B: $i] : ((a_select3(simplex7_init, B, F!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))) | (a_select3(simplex7_init, G!14, F!13) = init) | (~leq(n0, G!14)) | (~leq(G!14, n3)))),
% 257.53/257.78 inference(rewrite,[status(thm)],[])).
% 257.53/257.78 tff(34,plain,
% 257.53/257.78 ((~![B: $i] : ((a_select3(simplex7_init, B, F!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))) | ((a_select3(simplex7_init, G!14, F!13) = init) | (~leq(n0, G!14)) | (~leq(G!14, n3)))),
% 257.53/257.78 inference(quant_inst,[status(thm)],[])).
% 257.53/257.78 tff(35,plain,
% 257.53/257.78 ((~![B: $i] : ((a_select3(simplex7_init, B, F!13) = init) | (~leq(n0, B)) | (~leq(B, n3)))) | (a_select3(simplex7_init, G!14, F!13) = init) | (~leq(n0, G!14)) | (~leq(G!14, n3))),
% 257.53/257.78 inference(modus_ponens,[status(thm)],[34, 33])).
% 257.53/257.78 tff(36,plain,
% 257.53/257.78 ($false),
% 257.53/257.78 inference(unit_resolution,[status(thm)],[35, 32, 30, 28, 26])).
% 257.53/257.78 tff(37,plain,((a_select3(simplex7_init, G!14, F!13) = init) | (~leq(n0, G!14)) | (~leq(G!14, n3)) | (~leq(n0, F!13)) | (~leq(F!13, n2))), inference(lemma,lemma(discharge,[]))).
% 257.53/257.78 tff(38,assumption,(~((a_select2(s_try7_init, J!17) = init) | (~leq(n0, J!17)) | (~leq(J!17, minus(n3, n1))))), introduced(assumption)).
% 257.53/257.78 tff(39,plain,
% 257.53/257.78 (((a_select2(s_try7_init, J!17) = init) | (~leq(n0, J!17)) | (~leq(J!17, minus(n3, n1)))) | leq(J!17, minus(n3, n1))),
% 257.53/257.78 inference(tautology,[status(thm)],[])).
% 257.53/257.78 tff(40,plain,
% 257.53/257.78 (leq(J!17, minus(n3, n1))),
% 257.53/257.78 inference(unit_resolution,[status(thm)],[39, 38])).
% 257.53/257.78 tff(41,plain,
% 257.53/257.78 (((a_select2(s_try7_init, J!17) = init) | (~leq(n0, J!17)) | (~leq(J!17, minus(n3, n1)))) | leq(n0, J!17)),
% 257.53/257.78 inference(tautology,[status(thm)],[])).
% 257.53/257.78 tff(42,plain,
% 257.53/257.78 (leq(n0, J!17)),
% 257.53/257.78 inference(unit_resolution,[status(thm)],[41, 38])).
% 257.53/257.78 tff(43,plain,
% 257.53/257.78 (((a_select2(s_try7_init, J!17) = init) | (~leq(n0, J!17)) | (~leq(J!17, minus(n3, n1)))) | (~(a_select2(s_try7_init, J!17) = init))),
% 257.53/257.78 inference(tautology,[status(thm)],[])).
% 257.53/257.78 tff(44,plain,
% 257.53/257.78 (~(a_select2(s_try7_init, J!17) = init)),
% 257.53/257.78 inference(unit_resolution,[status(thm)],[43, 38])).
% 257.53/257.78 tff(45,plain,
% 257.53/257.78 (^[E: $i] : refl(((a_select2(s_try7_init, E) = init) | (~leq(n0, E)) | (~leq(E, minus(n3, n1)))) <=> ((a_select2(s_try7_init, E) = init) | (~leq(n0, E)) | (~leq(E, minus(n3, n1)))))),
% 257.53/257.78 inference(bind,[status(th)],[])).
% 257.53/257.78 tff(46,plain,
% 257.53/257.78 (![E: $i] : ((a_select2(s_try7_init, E) = init) | (~leq(n0, E)) | (~leq(E, minus(n3, n1)))) <=> ![E: $i] : ((a_select2(s_try7_init, E) = init) | (~leq(n0, E)) | (~leq(E, minus(n3, n1))))),
% 257.53/257.78 inference(quant_intro,[status(thm)],[45])).
% 257.53/257.78 tff(47,plain,
% 257.53/257.78 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, E) & leq(E, minus(n3, n1))) <=> (~((~leq(n0, E)) | (~leq(E, minus(n3, n1)))))), ((~(leq(n0, E) & leq(E, minus(n3, n1)))) <=> (~(~((~leq(n0, E)) | (~leq(E, minus(n3, n1)))))))), rewrite((~(~((~leq(n0, E)) | (~leq(E, minus(n3, n1)))))) <=> ((~leq(n0, E)) | (~leq(E, minus(n3, n1))))), ((~(leq(n0, E) & leq(E, minus(n3, n1)))) <=> ((~leq(n0, E)) | (~leq(E, minus(n3, n1)))))), (((~(leq(n0, E) & leq(E, minus(n3, n1)))) | (a_select2(s_try7_init, E) = init)) <=> (((~leq(n0, E)) | (~leq(E, minus(n3, n1)))) | (a_select2(s_try7_init, E) = init)))), rewrite((((~leq(n0, E)) | (~leq(E, minus(n3, n1)))) | (a_select2(s_try7_init, E) = init)) <=> ((a_select2(s_try7_init, E) = init) | (~leq(n0, E)) | (~leq(E, minus(n3, n1))))), (((~(leq(n0, E) & leq(E, minus(n3, n1)))) | (a_select2(s_try7_init, E) = init)) <=> ((a_select2(s_try7_init, E) = init) | (~leq(n0, E)) | (~leq(E, minus(n3, n1))))))),
% 257.53/257.79 inference(bind,[status(th)],[])).
% 257.53/257.79 tff(48,plain,
% 257.53/257.79 (![E: $i] : ((~(leq(n0, E) & leq(E, minus(n3, n1)))) | (a_select2(s_try7_init, E) = init)) <=> ![E: $i] : ((a_select2(s_try7_init, E) = init) | (~leq(n0, E)) | (~leq(E, minus(n3, n1))))),
% 257.53/257.79 inference(quant_intro,[status(thm)],[47])).
% 257.53/257.79 tff(49,plain,
% 257.53/257.79 (![E: $i] : ((~(leq(n0, E) & leq(E, minus(n3, n1)))) | (a_select2(s_try7_init, E) = init)) <=> ![E: $i] : ((~(leq(n0, E) & leq(E, minus(n3, n1)))) | (a_select2(s_try7_init, E) = init))),
% 257.53/257.79 inference(rewrite,[status(thm)],[])).
% 257.53/257.79 tff(50,plain,
% 257.53/257.79 (![E: $i] : ((~(leq(n0, E) & leq(E, minus(n3, n1)))) | (a_select2(s_try7_init, E) = init))),
% 257.53/257.79 inference(and_elim,[status(thm)],[17])).
% 257.53/257.79 tff(51,plain,
% 257.53/257.79 (![E: $i] : ((~(leq(n0, E) & leq(E, minus(n3, n1)))) | (a_select2(s_try7_init, E) = init))),
% 257.53/257.79 inference(modus_ponens,[status(thm)],[50, 49])).
% 257.53/257.79 tff(52,plain,(
% 257.53/257.79 ![E: $i] : ((~(leq(n0, E) & leq(E, minus(n3, n1)))) | (a_select2(s_try7_init, E) = init))),
% 257.53/257.79 inference(skolemize,[status(sab)],[51])).
% 257.53/257.79 tff(53,plain,
% 257.53/257.79 (![E: $i] : ((a_select2(s_try7_init, E) = init) | (~leq(n0, E)) | (~leq(E, minus(n3, n1))))),
% 257.53/257.79 inference(modus_ponens,[status(thm)],[52, 48])).
% 257.53/257.79 tff(54,plain,
% 257.53/257.79 (![E: $i] : ((a_select2(s_try7_init, E) = init) | (~leq(n0, E)) | (~leq(E, minus(n3, n1))))),
% 257.53/257.79 inference(modus_ponens,[status(thm)],[53, 46])).
% 257.53/257.79 tff(55,plain,
% 257.53/257.79 (((~![E: $i] : ((a_select2(s_try7_init, E) = init) | (~leq(n0, E)) | (~leq(E, minus(n3, n1))))) | ((a_select2(s_try7_init, J!17) = init) | (~leq(n0, J!17)) | (~leq(J!17, minus(n3, n1))))) <=> ((~![E: $i] : ((a_select2(s_try7_init, E) = init) | (~leq(n0, E)) | (~leq(E, minus(n3, n1))))) | (a_select2(s_try7_init, J!17) = init) | (~leq(n0, J!17)) | (~leq(J!17, minus(n3, n1))))),
% 257.53/257.79 inference(rewrite,[status(thm)],[])).
% 257.53/257.79 tff(56,plain,
% 257.53/257.79 ((~![E: $i] : ((a_select2(s_try7_init, E) = init) | (~leq(n0, E)) | (~leq(E, minus(n3, n1))))) | ((a_select2(s_try7_init, J!17) = init) | (~leq(n0, J!17)) | (~leq(J!17, minus(n3, n1))))),
% 257.53/257.79 inference(quant_inst,[status(thm)],[])).
% 257.53/257.79 tff(57,plain,
% 257.53/257.79 ((~![E: $i] : ((a_select2(s_try7_init, E) = init) | (~leq(n0, E)) | (~leq(E, minus(n3, n1))))) | (a_select2(s_try7_init, J!17) = init) | (~leq(n0, J!17)) | (~leq(J!17, minus(n3, n1)))),
% 257.53/257.79 inference(modus_ponens,[status(thm)],[56, 55])).
% 257.53/257.79 tff(58,plain,
% 257.53/257.79 ($false),
% 257.53/257.79 inference(unit_resolution,[status(thm)],[57, 54, 44, 42, 40])).
% 257.53/257.79 tff(59,plain,((a_select2(s_try7_init, J!17) = init) | (~leq(n0, J!17)) | (~leq(J!17, minus(n3, n1)))), inference(lemma,lemma(discharge,[]))).
% 257.53/257.79 tff(60,assumption,(~((a_select2(s_center7_init, I!16) = init) | (~leq(n0, I!16)) | (~leq(I!16, n2)))), introduced(assumption)).
% 257.53/257.79 tff(61,plain,
% 257.53/257.79 (((a_select2(s_center7_init, I!16) = init) | (~leq(n0, I!16)) | (~leq(I!16, n2))) | leq(I!16, n2)),
% 257.53/257.79 inference(tautology,[status(thm)],[])).
% 257.53/257.79 tff(62,plain,
% 257.53/257.79 (leq(I!16, n2)),
% 257.53/257.79 inference(unit_resolution,[status(thm)],[61, 60])).
% 257.53/257.79 tff(63,plain,
% 257.53/257.79 (((a_select2(s_center7_init, I!16) = init) | (~leq(n0, I!16)) | (~leq(I!16, n2))) | leq(n0, I!16)),
% 257.53/257.79 inference(tautology,[status(thm)],[])).
% 257.53/257.79 tff(64,plain,
% 257.53/257.79 (leq(n0, I!16)),
% 257.53/257.79 inference(unit_resolution,[status(thm)],[63, 60])).
% 257.53/257.79 tff(65,plain,
% 257.53/257.79 (((a_select2(s_center7_init, I!16) = init) | (~leq(n0, I!16)) | (~leq(I!16, n2))) | (~(a_select2(s_center7_init, I!16) = init))),
% 257.53/257.79 inference(tautology,[status(thm)],[])).
% 257.53/257.79 tff(66,plain,
% 257.53/257.79 (~(a_select2(s_center7_init, I!16) = init)),
% 257.53/257.79 inference(unit_resolution,[status(thm)],[65, 60])).
% 257.53/257.79 tff(67,plain,
% 257.53/257.79 (^[D: $i] : refl(((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, n2))) <=> ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, n2))))),
% 257.53/257.79 inference(bind,[status(th)],[])).
% 257.53/257.79 tff(68,plain,
% 257.53/257.79 (![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, n2))) <=> ![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, n2)))),
% 257.53/257.79 inference(quant_intro,[status(thm)],[67])).
% 257.53/257.79 tff(69,plain,
% 257.53/257.79 (^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, D) & leq(D, n2)) <=> (~((~leq(n0, D)) | (~leq(D, n2))))), ((~(leq(n0, D) & leq(D, n2))) <=> (~(~((~leq(n0, D)) | (~leq(D, n2))))))), rewrite((~(~((~leq(n0, D)) | (~leq(D, n2))))) <=> ((~leq(n0, D)) | (~leq(D, n2)))), ((~(leq(n0, D) & leq(D, n2))) <=> ((~leq(n0, D)) | (~leq(D, n2))))), (((~(leq(n0, D) & leq(D, n2))) | (a_select2(s_center7_init, D) = init)) <=> (((~leq(n0, D)) | (~leq(D, n2))) | (a_select2(s_center7_init, D) = init)))), rewrite((((~leq(n0, D)) | (~leq(D, n2))) | (a_select2(s_center7_init, D) = init)) <=> ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, n2)))), (((~(leq(n0, D) & leq(D, n2))) | (a_select2(s_center7_init, D) = init)) <=> ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, n2)))))),
% 257.53/257.79 inference(bind,[status(th)],[])).
% 257.53/257.79 tff(70,plain,
% 257.53/257.79 (![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | (a_select2(s_center7_init, D) = init)) <=> ![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, n2)))),
% 257.53/257.79 inference(quant_intro,[status(thm)],[69])).
% 257.53/257.79 tff(71,plain,
% 257.53/257.79 (![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | (a_select2(s_center7_init, D) = init)) <=> ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | (a_select2(s_center7_init, D) = init))),
% 257.53/257.79 inference(rewrite,[status(thm)],[])).
% 257.53/257.79 tff(72,plain,
% 257.53/257.79 (![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | (a_select2(s_center7_init, D) = init))),
% 257.53/257.79 inference(and_elim,[status(thm)],[17])).
% 257.53/257.79 tff(73,plain,
% 257.53/257.79 (![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | (a_select2(s_center7_init, D) = init))),
% 257.53/257.79 inference(modus_ponens,[status(thm)],[72, 71])).
% 257.53/257.79 tff(74,plain,(
% 257.53/257.79 ![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | (a_select2(s_center7_init, D) = init))),
% 257.53/257.79 inference(skolemize,[status(sab)],[73])).
% 257.53/257.79 tff(75,plain,
% 257.53/257.79 (![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, n2)))),
% 257.53/257.79 inference(modus_ponens,[status(thm)],[74, 70])).
% 257.53/257.79 tff(76,plain,
% 257.53/257.79 (![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, n2)))),
% 257.53/257.79 inference(modus_ponens,[status(thm)],[75, 68])).
% 257.53/257.79 tff(77,plain,
% 257.53/257.79 (((~![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, n2)))) | ((a_select2(s_center7_init, I!16) = init) | (~leq(n0, I!16)) | (~leq(I!16, n2)))) <=> ((~![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, n2)))) | (a_select2(s_center7_init, I!16) = init) | (~leq(n0, I!16)) | (~leq(I!16, n2)))),
% 257.53/257.79 inference(rewrite,[status(thm)],[])).
% 257.53/257.79 tff(78,plain,
% 257.53/257.79 ((~![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, n2)))) | ((a_select2(s_center7_init, I!16) = init) | (~leq(n0, I!16)) | (~leq(I!16, n2)))),
% 257.53/257.79 inference(quant_inst,[status(thm)],[])).
% 257.53/257.79 tff(79,plain,
% 257.53/257.79 ((~![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, n2)))) | (a_select2(s_center7_init, I!16) = init) | (~leq(n0, I!16)) | (~leq(I!16, n2))),
% 257.53/257.79 inference(modus_ponens,[status(thm)],[78, 77])).
% 257.53/257.79 tff(80,plain,
% 257.53/257.79 ($false),
% 257.53/257.79 inference(unit_resolution,[status(thm)],[79, 76, 66, 64, 62])).
% 257.53/257.79 tff(81,plain,((a_select2(s_center7_init, I!16) = init) | (~leq(n0, I!16)) | (~leq(I!16, n2))), inference(lemma,lemma(discharge,[]))).
% 257.53/257.79 tff(82,assumption,(~((a_select2(s_values7_init, H!15) = init) | (~leq(n0, H!15)) | (~leq(H!15, n3)))), introduced(assumption)).
% 257.53/257.79 tff(83,plain,
% 257.53/257.79 (((a_select2(s_values7_init, H!15) = init) | (~leq(n0, H!15)) | (~leq(H!15, n3))) | leq(H!15, n3)),
% 257.53/257.79 inference(tautology,[status(thm)],[])).
% 257.53/257.79 tff(84,plain,
% 257.53/257.79 (leq(H!15, n3)),
% 257.53/257.79 inference(unit_resolution,[status(thm)],[83, 82])).
% 257.53/257.79 tff(85,plain,
% 257.53/257.79 (((a_select2(s_values7_init, H!15) = init) | (~leq(n0, H!15)) | (~leq(H!15, n3))) | leq(n0, H!15)),
% 257.53/257.79 inference(tautology,[status(thm)],[])).
% 257.53/257.79 tff(86,plain,
% 257.53/257.79 (leq(n0, H!15)),
% 257.53/257.79 inference(unit_resolution,[status(thm)],[85, 82])).
% 257.53/257.79 tff(87,plain,
% 257.53/257.79 (((a_select2(s_values7_init, H!15) = init) | (~leq(n0, H!15)) | (~leq(H!15, n3))) | (~(a_select2(s_values7_init, H!15) = init))),
% 257.53/257.79 inference(tautology,[status(thm)],[])).
% 257.53/257.79 tff(88,plain,
% 257.53/257.79 (~(a_select2(s_values7_init, H!15) = init)),
% 257.53/257.79 inference(unit_resolution,[status(thm)],[87, 82])).
% 257.53/257.79 tff(89,plain,
% 257.53/257.79 (^[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))))),
% 257.53/257.79 inference(bind,[status(th)],[])).
% 257.53/257.79 tff(90,plain,
% 257.53/257.79 (![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)))),
% 257.53/257.79 inference(quant_intro,[status(thm)],[89])).
% 257.53/257.79 tff(91,plain,
% 257.53/257.79 (^[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)))))),
% 257.53/257.79 inference(bind,[status(th)],[])).
% 257.53/257.79 tff(92,plain,
% 257.53/257.79 (![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)))),
% 257.53/257.79 inference(quant_intro,[status(thm)],[91])).
% 257.53/257.79 tff(93,plain,
% 257.53/257.79 (![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))),
% 257.53/257.79 inference(rewrite,[status(thm)],[])).
% 257.53/257.79 tff(94,plain,
% 257.53/257.79 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 257.53/257.79 inference(and_elim,[status(thm)],[17])).
% 257.53/257.79 tff(95,plain,
% 257.53/257.79 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 257.53/257.79 inference(modus_ponens,[status(thm)],[94, 93])).
% 257.53/257.79 tff(96,plain,(
% 257.53/257.79 ![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 257.53/257.79 inference(skolemize,[status(sab)],[95])).
% 257.53/257.79 tff(97,plain,
% 257.53/257.79 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))),
% 257.53/257.79 inference(modus_ponens,[status(thm)],[96, 92])).
% 257.53/257.79 tff(98,plain,
% 257.53/257.79 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))),
% 257.53/257.79 inference(modus_ponens,[status(thm)],[97, 90])).
% 257.53/257.79 tff(99,plain,
% 257.53/257.79 (((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))) | ((a_select2(s_values7_init, H!15) = init) | (~leq(n0, H!15)) | (~leq(H!15, n3)))) <=> ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))) | (a_select2(s_values7_init, H!15) = init) | (~leq(n0, H!15)) | (~leq(H!15, n3)))),
% 257.53/257.79 inference(rewrite,[status(thm)],[])).
% 257.53/257.79 tff(100,plain,
% 257.53/257.79 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))) | ((a_select2(s_values7_init, H!15) = init) | (~leq(n0, H!15)) | (~leq(H!15, n3)))),
% 257.53/257.79 inference(quant_inst,[status(thm)],[])).
% 257.53/257.79 tff(101,plain,
% 257.53/257.79 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))) | (a_select2(s_values7_init, H!15) = init) | (~leq(n0, H!15)) | (~leq(H!15, n3))),
% 257.53/257.79 inference(modus_ponens,[status(thm)],[100, 99])).
% 257.53/257.79 tff(102,plain,
% 257.53/257.79 ($false),
% 257.53/257.79 inference(unit_resolution,[status(thm)],[101, 98, 88, 86, 84])).
% 257.53/257.79 tff(103,plain,((a_select2(s_values7_init, H!15) = init) | (~leq(n0, H!15)) | (~leq(H!15, n3))), inference(lemma,lemma(discharge,[]))).
% 257.53/257.79 tff(104,plain,
% 257.53/257.79 (true <=> true),
% 257.53/257.79 inference(rewrite,[status(thm)],[])).
% 257.53/257.79 tff(105,axiom,(true), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','ttrue')).
% 257.53/257.79 tff(106,plain,
% 257.53/257.79 (true),
% 257.53/257.79 inference(modus_ponens,[status(thm)],[105, 104])).
% 257.55/257.79 tff(107,plain,
% 257.55/257.79 ((true | (~(n0 = pv1413))) | (~true)),
% 257.55/257.79 inference(tautology,[status(thm)],[])).
% 257.55/257.79 tff(108,plain,
% 257.55/257.79 (true | (~(n0 = pv1413))),
% 257.55/257.79 inference(unit_resolution,[status(thm)],[107, 106])).
% 257.55/257.79 tff(109,plain,
% 257.55/257.79 (((~(true | (~(n0 = pv1413)))) | ((~(n0 = pv1413)) & ((~(s_best7_init = init)) | (~(s_sworst7_init = init)) | (~(s_worst7_init = init)) | (~leq(n0, s_best7)) | (~leq(n0, s_sworst7)) | (~leq(n0, s_worst7)) | (~leq(s_best7, n3)) | (~leq(s_sworst7, n3)) | (~leq(s_worst7, n3)) | (~((~(leq(n0, H!15) & leq(H!15, n3))) | (a_select2(s_values7_init, H!15) = init))) | (~((~(leq(n0, I!16) & leq(I!16, n2))) | (a_select2(s_center7_init, I!16) = init))) | (~((~(leq(n0, J!17) & leq(J!17, minus(n3, n1)))) | (a_select2(s_try7_init, J!17) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))) | (leq(n0, F!13) & leq(F!13, n2) & (~((~(leq(n0, G!14) & leq(G!14, n3))) | (a_select3(simplex7_init, G!14, F!13) = init))))))) <=> ((~(true | (~(n0 = pv1413)))) | (~((n0 = pv1413) | (~((~(s_best7_init = init)) | (~(s_sworst7_init = init)) | (~(s_worst7_init = init)) | (~leq(n0, s_best7)) | (~leq(n0, s_sworst7)) | (~leq(n0, s_worst7)) | (~leq(s_best7, n3)) | (~leq(s_sworst7, n3)) | (~leq(s_worst7, n3)) | (~((~gt(loopcounter, n1)) | (~((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init)))))) | (~((a_select3(simplex7_init, G!14, F!13) = init) | (~leq(n0, G!14)) | (~leq(G!14, n3)) | (~leq(n0, F!13)) | (~leq(F!13, n2)))) | (~((a_select2(s_values7_init, H!15) = init) | (~leq(n0, H!15)) | (~leq(H!15, n3)))) | (~((a_select2(s_center7_init, I!16) = init) | (~leq(n0, I!16)) | (~leq(I!16, n2)))) | (~((a_select2(s_try7_init, J!17) = init) | (~leq(n0, J!17)) | (~leq(J!17, minus(n3, n1))))))))))),
% 257.55/257.79 inference(rewrite,[status(thm)],[])).
% 257.55/257.79 tff(110,plain,
% 257.55/257.79 ((((~(n0 = pv1413)) & ((~(s_best7_init = init)) | (~(s_sworst7_init = init)) | (~(s_worst7_init = init)) | (~leq(n0, s_best7)) | (~leq(n0, s_sworst7)) | (~leq(n0, s_worst7)) | (~leq(s_best7, n3)) | (~leq(s_sworst7, n3)) | (~leq(s_worst7, n3)) | (~((~(leq(n0, H!15) & leq(H!15, n3))) | (a_select2(s_values7_init, H!15) = init))) | (~((~(leq(n0, I!16) & leq(I!16, n2))) | (a_select2(s_center7_init, I!16) = init))) | (~((~(leq(n0, J!17) & leq(J!17, minus(n3, n1)))) | (a_select2(s_try7_init, J!17) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))) | (leq(n0, F!13) & leq(F!13, n2) & (~((~(leq(n0, G!14) & leq(G!14, n3))) | (a_select3(simplex7_init, G!14, F!13) = init)))))) | (~(true | (~(n0 = pv1413))))) <=> ((~(true | (~(n0 = pv1413)))) | ((~(n0 = pv1413)) & ((~(s_best7_init = init)) | (~(s_sworst7_init = init)) | (~(s_worst7_init = init)) | (~leq(n0, s_best7)) | (~leq(n0, s_sworst7)) | (~leq(n0, s_worst7)) | (~leq(s_best7, n3)) | (~leq(s_sworst7, n3)) | (~leq(s_worst7, n3)) | (~((~(leq(n0, H!15) & leq(H!15, n3))) | (a_select2(s_values7_init, H!15) = init))) | (~((~(leq(n0, I!16) & leq(I!16, n2))) | (a_select2(s_center7_init, I!16) = init))) | (~((~(leq(n0, J!17) & leq(J!17, minus(n3, n1)))) | (a_select2(s_try7_init, J!17) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))) | (leq(n0, F!13) & leq(F!13, n2) & (~((~(leq(n0, G!14) & leq(G!14, n3))) | (a_select3(simplex7_init, G!14, F!13) = init)))))))),
% 257.55/257.79 inference(rewrite,[status(thm)],[])).
% 257.55/257.79 tff(111,plain,
% 257.55/257.79 (((~(n0 = pv1413)) & ((~(s_best7_init = init)) | (~(s_sworst7_init = init)) | (~(s_worst7_init = init)) | (~leq(n0, s_best7)) | (~leq(n0, s_sworst7)) | (~leq(n0, s_worst7)) | (~leq(s_best7, n3)) | (~leq(s_sworst7, n3)) | (~leq(s_worst7, n3)) | ((leq(n0, F!13) & leq(F!13, n2)) & (~((~(leq(n0, G!14) & leq(G!14, n3))) | (a_select3(simplex7_init, G!14, F!13) = init)))) | (~((~(leq(n0, H!15) & leq(H!15, n3))) | (a_select2(s_values7_init, H!15) = init))) | (~((~(leq(n0, I!16) & leq(I!16, n2))) | (a_select2(s_center7_init, I!16) = init))) | (~((~(leq(n0, J!17) & leq(J!17, minus(n3, n1)))) | (a_select2(s_try7_init, J!17) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))))) <=> ((~(n0 = pv1413)) & ((~(s_best7_init = init)) | (~(s_sworst7_init = init)) | (~(s_worst7_init = init)) | (~leq(n0, s_best7)) | (~leq(n0, s_sworst7)) | (~leq(n0, s_worst7)) | (~leq(s_best7, n3)) | (~leq(s_sworst7, n3)) | (~leq(s_worst7, n3)) | (~((~(leq(n0, H!15) & leq(H!15, n3))) | (a_select2(s_values7_init, H!15) = init))) | (~((~(leq(n0, I!16) & leq(I!16, n2))) | (a_select2(s_center7_init, I!16) = init))) | (~((~(leq(n0, J!17) & leq(J!17, minus(n3, n1)))) | (a_select2(s_try7_init, J!17) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))) | (leq(n0, F!13) & leq(F!13, n2) & (~((~(leq(n0, G!14) & leq(G!14, n3))) | (a_select3(simplex7_init, G!14, F!13) = init))))))),
% 257.55/257.80 inference(rewrite,[status(thm)],[])).
% 257.55/257.80 tff(112,plain,
% 257.55/257.80 ((((~(n0 = pv1413)) & ((~(s_best7_init = init)) | (~(s_sworst7_init = init)) | (~(s_worst7_init = init)) | (~leq(n0, s_best7)) | (~leq(n0, s_sworst7)) | (~leq(n0, s_worst7)) | (~leq(s_best7, n3)) | (~leq(s_sworst7, n3)) | (~leq(s_worst7, n3)) | ((leq(n0, F!13) & leq(F!13, n2)) & (~((~(leq(n0, G!14) & leq(G!14, n3))) | (a_select3(simplex7_init, G!14, F!13) = init)))) | (~((~(leq(n0, H!15) & leq(H!15, n3))) | (a_select2(s_values7_init, H!15) = init))) | (~((~(leq(n0, I!16) & leq(I!16, n2))) | (a_select2(s_center7_init, I!16) = init))) | (~((~(leq(n0, J!17) & leq(J!17, minus(n3, n1)))) | (a_select2(s_try7_init, J!17) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))))) | (~(true | (~(n0 = pv1413))))) <=> (((~(n0 = pv1413)) & ((~(s_best7_init = init)) | (~(s_sworst7_init = init)) | (~(s_worst7_init = init)) | (~leq(n0, s_best7)) | (~leq(n0, s_sworst7)) | (~leq(n0, s_worst7)) | (~leq(s_best7, n3)) | (~leq(s_sworst7, n3)) | (~leq(s_worst7, n3)) | (~((~(leq(n0, H!15) & leq(H!15, n3))) | (a_select2(s_values7_init, H!15) = init))) | (~((~(leq(n0, I!16) & leq(I!16, n2))) | (a_select2(s_center7_init, I!16) = init))) | (~((~(leq(n0, J!17) & leq(J!17, minus(n3, n1)))) | (a_select2(s_try7_init, J!17) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))) | (leq(n0, F!13) & leq(F!13, n2) & (~((~(leq(n0, G!14) & leq(G!14, n3))) | (a_select3(simplex7_init, G!14, F!13) = init)))))) | (~(true | (~(n0 = pv1413)))))),
% 257.55/257.80 inference(monotonicity,[status(thm)],[111])).
% 257.55/257.80 tff(113,plain,
% 257.55/257.80 ((((~(n0 = pv1413)) & ((~(s_best7_init = init)) | (~(s_sworst7_init = init)) | (~(s_worst7_init = init)) | (~leq(n0, s_best7)) | (~leq(n0, s_sworst7)) | (~leq(n0, s_worst7)) | (~leq(s_best7, n3)) | (~leq(s_sworst7, n3)) | (~leq(s_worst7, n3)) | ((leq(n0, F!13) & leq(F!13, n2)) & (~((~(leq(n0, G!14) & leq(G!14, n3))) | (a_select3(simplex7_init, G!14, F!13) = init)))) | (~((~(leq(n0, H!15) & leq(H!15, n3))) | (a_select2(s_values7_init, H!15) = init))) | (~((~(leq(n0, I!16) & leq(I!16, n2))) | (a_select2(s_center7_init, I!16) = init))) | (~((~(leq(n0, J!17) & leq(J!17, minus(n3, n1)))) | (a_select2(s_try7_init, J!17) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))))) | (~(true | (~(n0 = pv1413))))) <=> ((~(true | (~(n0 = pv1413)))) | ((~(n0 = pv1413)) & ((~(s_best7_init = init)) | (~(s_sworst7_init = init)) | (~(s_worst7_init = init)) | (~leq(n0, s_best7)) | (~leq(n0, s_sworst7)) | (~leq(n0, s_worst7)) | (~leq(s_best7, n3)) | (~leq(s_sworst7, n3)) | (~leq(s_worst7, n3)) | (~((~(leq(n0, H!15) & leq(H!15, n3))) | (a_select2(s_values7_init, H!15) = init))) | (~((~(leq(n0, I!16) & leq(I!16, n2))) | (a_select2(s_center7_init, I!16) = init))) | (~((~(leq(n0, J!17) & leq(J!17, minus(n3, n1)))) | (a_select2(s_try7_init, J!17) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))) | (leq(n0, F!13) & leq(F!13, n2) & (~((~(leq(n0, G!14) & leq(G!14, n3))) | (a_select3(simplex7_init, G!14, F!13) = init)))))))),
% 257.55/257.80 inference(transitivity,[status(thm)],[112, 110])).
% 257.55/257.80 tff(114,plain,
% 257.55/257.80 (((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))) <=> ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))),
% 257.55/257.80 inference(rewrite,[status(thm)],[])).
% 257.55/257.80 tff(115,plain,
% 257.55/257.80 (((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) <=> ((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))))),
% 257.55/257.80 inference(monotonicity,[status(thm)],[114])).
% 257.55/257.80 tff(116,plain,
% 257.55/257.80 ((((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) & (true | (~(n0 = pv1413)))) <=> (((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) & (true | (~(n0 = pv1413))))),
% 257.55/257.80 inference(monotonicity,[status(thm)],[115])).
% 257.55/257.80 tff(117,plain,
% 257.55/257.80 ((~(((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) & (true | (~(n0 = pv1413))))) <=> (~(((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) & (true | (~(n0 = pv1413)))))),
% 257.55/257.80 inference(monotonicity,[status(thm)],[116])).
% 257.55/257.80 tff(118,plain,
% 257.55/257.80 ((~(((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) & (true | (~(n0 = pv1413))))) <=> (~(((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) & (true | (~(n0 = pv1413)))))),
% 257.55/257.80 inference(rewrite,[status(thm)],[])).
% 257.55/257.80 tff(119,plain,
% 257.55/257.80 (~(((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) & (true | (~(n0 = pv1413))))),
% 257.55/257.81 inference(or_elim,[status(thm)],[16])).
% 257.55/257.81 tff(120,plain,
% 257.55/257.81 (~(((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) & (true | (~(n0 = pv1413))))),
% 257.55/257.81 inference(modus_ponens,[status(thm)],[119, 117])).
% 257.55/257.81 tff(121,plain,
% 257.55/257.81 (~(((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) & (true | (~(n0 = pv1413))))),
% 257.55/257.81 inference(modus_ponens,[status(thm)],[120, 118])).
% 257.55/257.81 tff(122,plain,
% 257.55/257.81 (~(((n0 = pv1413) | ((s_best7_init = init) & (s_sworst7_init = init) & (s_worst7_init = init) & leq(n0, s_best7) & leq(n0, s_sworst7) & leq(n0, s_worst7) & leq(s_best7, n3) & leq(s_sworst7, n3) & leq(s_worst7, n3) & ![F: $i] : ((~(leq(n0, F) & leq(F, n2))) | ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select3(simplex7_init, G, F) = init))) & ![H: $i] : ((~(leq(n0, H) & leq(H, n3))) | (a_select2(s_values7_init, H) = init)) & ![I: $i] : ((~(leq(n0, I) & leq(I, n2))) | (a_select2(s_center7_init, I) = init)) & ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n3, n1)))) | (a_select2(s_try7_init, J) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) & (true | (~(n0 = pv1413))))),
% 257.55/257.81 inference(modus_ponens,[status(thm)],[121, 117])).
% 257.55/257.81 unexpected number of arguments: (let ((a!1 (refl (~ (not (= n0 pv1413)) (not (= n0 pv1413)))))
% 257.55/257.81 (a!2 (refl (~ (not (= s_best7_init init)) (not (= s_best7_init init)))))
% 257.55/257.81 (a!3 (refl (~ (not (= s_sworst7_init init)) (not (= s_sworst7_init init)))))
% 257.55/257.81 (a!4 (refl (~ (not (= s_worst7_init init)) (not (= s_worst7_init init)))))
% 257.55/257.81 (a!5 (refl (~ (not (leq n0 s_best7)) (not (leq n0 s_best7)))))
% 257.55/257.81 (a!6 (refl (~ (not (leq n0 s_sworst7)) (not (leq n0 s_sworst7)))))
% 257.55/257.81 (a!7 (refl (~ (not (leq n0 s_worst7)) (not (leq n0 s_worst7)))))
% 257.55/257.81 (a!8 (refl (~ (not (leq s_best7 n3)) (not (leq s_best7 n3)))))
% 257.55/257.81 (a!9 (refl (~ (not (leq s_sworst7 n3)) (not (leq s_sworst7 n3)))))
% 257.55/257.81 (a!10 (refl (~ (not (leq s_worst7 n3)) (not (leq s_worst7 n3)))))
% 257.55/257.81 (a!11 (forall ((F $i))
% 257.55/257.81 (let ((a!1 (forall ((G $i))
% 257.55/257.81 (or (not (and (leq n0 G) (leq G n3)))
% 257.55/257.81 (= (a_select3 simplex7_init G F) init)))))
% 257.55/257.81 (or (not (and (leq n0 F) (leq F n2))) a!1))))
% 257.55/257.81 (a!12 (forall ((G $i))
% 257.55/257.81 (or (not (and (leq n0 G) (leq G n3)))
% 257.55/257.81 (= (a_select3 simplex7_init G F!13) init))))
% 257.55/257.81 (a!14 (refl (~ (and (leq n0 F!13) (leq F!13 n2))
% 257.55/257.81 (and (leq n0 F!13) (leq F!13 n2)))))
% 257.55/257.81 (a!15 (or (not (and (leq n0 G!14) (leq G!14 n3)))
% 257.55/257.81 (= (a_select3 simplex7_init G!14 F!13) init)))
% 257.55/257.81 (a!19 (forall ((H $i))
% 257.55/257.81 (or (not (and (leq n0 H) (leq H n3)))
% 257.55/257.81 (= (a_select2 s_values7_init H) init))))
% 257.55/257.81 (a!20 (or (not (and (leq n0 H!15) (leq H!15 n3)))
% 257.55/257.81 (= (a_select2 s_values7_init H!15) init)))
% 257.55/257.81 (a!21 (forall ((I $i))
% 257.55/257.81 (or (not (and (leq n0 I) (leq I n2)))
% 257.55/257.81 (= (a_select2 s_center7_init I) init))))
% 257.55/257.81 (a!22 (or (not (and (leq n0 I!16) (leq I!16 n2)))
% 257.55/257.81 (= (a_select2 s_center7_init I!16) init)))
% 257.55/257.81 (a!23 (forall ((J $i))
% 257.55/257.81 (let ((a!1 (not (and (leq n0 J) (leq J (minus n3 n1))))))
% 257.55/257.81 (or a!1 (= (a_select2 s_try7_init J) init)))))
% 257.55/257.81 (a!24 (not (and (leq n0 J!17) (leq J!17 (minus n3 n1)))))
% 257.55/257.81 (a!26 (or (not (gt loopcounter n1))
% 257.55/257.81 (and (= pvar1400_init init)
% 257.55/257.81 (= pvar1401_init init)
% 257.55/257.81 (= pvar1402_init init))))
% 257.55/257.81 (a!31 (not (or true (not (= n0 pv1413))))))
% 257.55/257.81 (let ((a!13 (or (not (and (leq n0 F!13) (leq F!13 n2))) a!12))
% 257.55/257.81 (a!16 (and (and (leq n0 F!13) (leq F!13 n2)) (not a!15)))
% 257.55/257.81 (a!25 (not (or a!24 (= (a_select2 s_try7_init J!17) init))))
% 257.55/257.81 (a!27 (and (= s_best7_init init)
% 257.55/257.81 (= s_sworst7_init init)
% 257.55/257.81 (= s_worst7_init init)
% 257.55/257.81 (leq n0 s_best7)
% 257.55/257.81 (leq n0 s_sworst7)
% 257.55/257.81 (leq n0 s_worst7)
% 257.55/257.81 (leq s_best7 n3)
% 257.55/257.81 (leq s_sworst7 n3)
% 257.55/257.81 (leq s_worst7 n3)
% 257.55/257.81 a!11
% 257.55/257.81 a!19
% 257.55/257.81 a!21
% 257.55/257.81 a!23
% 257.55/257.81 a!26)))
% 257.55/257.81 (let ((a!17 (nnf-neg a!14 (sk (~ (not a!12) (not a!15))) (~ (not a!13) a!16)))
% 257.55/257.81 (a!28 (or (not (= s_best7_init init))
% 257.55/257.81 (not (= s_sworst7_init init))
% 257.55/257.81 (not (= s_worst7_init init))
% 257.55/257.81 (not (leq n0 s_best7))
% 257.55/257.81 (not (leq n0 s_sworst7))
% 257.55/257.81 (not (leq n0 s_worst7))
% 257.55/257.81 (not (leq s_best7 n3))
% 257.55/257.81 (not (leq s_sworst7 n3))
% 257.55/257.81 (not (leq s_worst7 n3))
% 257.55/257.81 a!16
% 257.55/257.81 (not a!20)
% 257.55/257.81 (not a!22)
% 257.55/257.81 a!25
% 257.55/257.81 (not a!26)))
% 257.55/257.81 (a!32 (and (or (= n0 pv1413) a!27) (or true (not (= n0 pv1413))))))
% 257.55/257.81 (let ((a!18 (trans (sk (~ (not a!11) (not a!13))) a!17 (~ (not a!11) a!16)))
% 257.55/257.81 (a!30 (~ (not (or (= n0 pv1413) a!27)) (and (not (= n0 pv1413)) a!28)))
% 257.55/257.81 (a!33 (or (and (not (= n0 pv1413)) a!28) a!31)))
% 257.55/257.81 (let ((a!29 (nnf-neg a!2
% 257.55/257.81 a!3
% 257.55/257.81 a!4
% 257.55/257.81 a!5
% 257.55/257.81 a!6
% 257.55/257.81 a!7
% 257.55/257.81 a!8
% 257.55/257.81 a!9
% 257.55/257.81 a!10
% 257.55/257.81 a!18
% 257.55/257.81 (sk (~ (not a!19) (not a!20)))
% 257.55/257.81 (sk (~ (not a!21) (not a!22)))
% 257.55/257.81 (sk (~ (not a!23) a!25))
% 257.55/257.81 (refl (~ (not a!26) (not a!26)))
% 257.55/257.81 (~ (not a!27) a!28))))
% 257.55/257.81 (nnf-neg (nnf-neg a!1 a!29 a!30) (refl (~ a!31 a!31)) (~ (not a!32) a!33)))))))
% 257.55/257.81 Proof display could not be completed: unexpected number of arguments
% 258.05/258.37 % E exiting
%------------------------------------------------------------------------------