%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV042+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 14.65s 14.82s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV042+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.06/0.11 % 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 09:23:20 EDT 2025
% 0.11/0.32 % CPUTime :
% 14.65/14.82 % SZS status Theorem
% 14.65/14.82 % SZS output start Proof
% 14.65/14.82 tff(leq_type, type, (
% 14.65/14.82 leq: ( $i * $i ) > $o)).
% 14.65/14.82 tff(n3_type, type, (
% 14.65/14.82 n3: $i)).
% 14.65/14.82 tff(n0_type, type, (
% 14.65/14.82 n0: $i)).
% 14.65/14.82 tff(init_type, type, (
% 14.65/14.82 init: $i)).
% 14.65/14.82 tff(a_select3_type, type, (
% 14.65/14.82 a_select3: ( $i * $i * $i ) > $i)).
% 14.65/14.82 tff(tptp_fun_E_13_type, type, (
% 14.65/14.82 tptp_fun_E_13: $i)).
% 14.65/14.82 tff(simplex7_init_type, type, (
% 14.65/14.82 simplex7_init: $i)).
% 14.65/14.82 tff(n2_type, type, (
% 14.65/14.82 n2: $i)).
% 14.65/14.82 tff(tptp_fun_F_14_type, type, (
% 14.65/14.82 tptp_fun_F_14: $i)).
% 14.65/14.82 tff(pvar1402_init_type, type, (
% 14.65/14.82 pvar1402_init: $i)).
% 14.65/14.82 tff(pvar1401_init_type, type, (
% 14.65/14.82 pvar1401_init: $i)).
% 14.65/14.82 tff(pvar1400_init_type, type, (
% 14.65/14.82 pvar1400_init: $i)).
% 14.65/14.82 tff(gt_type, type, (
% 14.65/14.82 gt: ( $i * $i ) > $o)).
% 14.65/14.82 tff(n1_type, type, (
% 14.65/14.82 n1: $i)).
% 14.65/14.82 tff(loopcounter_type, type, (
% 14.65/14.82 loopcounter: $i)).
% 14.65/14.82 tff(a_select2_type, type, (
% 14.65/14.82 a_select2: ( $i * $i ) > $i)).
% 14.65/14.82 tff(s_center7_init_type, type, (
% 14.65/14.82 s_center7_init: $i)).
% 14.65/14.82 tff(minus_type, type, (
% 14.65/14.82 minus: ( $i * $i ) > $i)).
% 14.65/14.82 tff(plus_type, type, (
% 14.65/14.82 plus: ( $i * $i ) > $i)).
% 14.65/14.82 tff(s_values7_init_type, type, (
% 14.65/14.82 s_values7_init: $i)).
% 14.65/14.82 tff(tptp_fun_H_16_type, type, (
% 14.65/14.82 tptp_fun_H_16: $i)).
% 14.65/14.82 tff(pred_type, type, (
% 14.65/14.82 pred: $i > $i)).
% 14.65/14.82 tff(succ_type, type, (
% 14.65/14.82 succ: $i > $i)).
% 14.65/14.82 tff(tptp_fun_G_15_type, type, (
% 14.65/14.82 tptp_fun_G_15: $i)).
% 14.65/14.82 tff(1,assumption,(~((~gt(loopcounter, n1)) | (~((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init)))))), introduced(assumption)).
% 14.65/14.82 tff(2,plain,
% 14.65/14.82 (((~gt(loopcounter, n1)) | (~((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init))))) | gt(loopcounter, n1)),
% 14.65/14.82 inference(tautology,[status(thm)],[])).
% 14.65/14.82 tff(3,plain,
% 14.65/14.82 (gt(loopcounter, n1)),
% 14.65/14.82 inference(unit_resolution,[status(thm)],[2, 1])).
% 14.65/14.82 tff(4,plain,
% 14.65/14.82 (((~gt(loopcounter, n1)) | (~((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init))))) | ((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init)))),
% 14.65/14.82 inference(tautology,[status(thm)],[])).
% 14.65/14.82 tff(5,plain,
% 14.65/14.82 ((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init))),
% 14.65/14.82 inference(unit_resolution,[status(thm)],[4, 1])).
% 14.65/14.82 tff(6,plain,
% 14.65/14.82 (((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))) <=> ((~gt(loopcounter, n1)) | (~((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init)))))),
% 14.65/14.82 inference(rewrite,[status(thm)],[])).
% 14.65/14.82 tff(7,plain,
% 14.65/14.82 (((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))) <=> ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))),
% 14.65/14.82 inference(rewrite,[status(thm)],[])).
% 14.65/14.82 tff(8,plain,
% 14.65/14.82 ((~((((![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, minus(plus(n1, n2), n1))) => (a_select2(s_center7_init, D) = init))) & (gt(loopcounter, n1) => (((pvar1400_init = init) & (pvar1401_init = init)) & (pvar1402_init = init)))) => (((![E: $i] : ((leq(n0, E) & leq(E, n2)) => ![F: $i] : ((leq(n0, F) & leq(F, n3)) => (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((leq(n0, G) & leq(G, n3)) => (a_select2(s_values7_init, G) = init))) & ![H: $i] : ((leq(n0, H) & leq(H, n2)) => (a_select2(s_center7_init, H) = init))) & (gt(loopcounter, n1) => (((pvar1400_init = init) & (pvar1401_init = init)) & (pvar1402_init = init)))))) <=> (~((~(![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, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) | (![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(n0, H) & leq(H, n2))) | (a_select2(s_center7_init, H) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))))),
% 14.65/14.82 inference(rewrite,[status(thm)],[])).
% 14.65/14.82 tff(9,axiom,(~((((![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, minus(plus(n1, n2), n1))) => (a_select2(s_center7_init, D) = init))) & (gt(loopcounter, n1) => (((pvar1400_init = init) & (pvar1401_init = init)) & (pvar1402_init = init)))) => (((![E: $i] : ((leq(n0, E) & leq(E, n2)) => ![F: $i] : ((leq(n0, F) & leq(F, n3)) => (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((leq(n0, G) & leq(G, n3)) => (a_select2(s_values7_init, G) = init))) & ![H: $i] : ((leq(n0, H) & leq(H, n2)) => (a_select2(s_center7_init, H) = init))) & (gt(loopcounter, n1) => (((pvar1400_init = init) & (pvar1401_init = init)) & (pvar1402_init = init)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gauss_init_0081')).
% 14.65/14.82 tff(10,plain,
% 14.65/14.82 (~((~(![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, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) | (![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(n0, H) & leq(H, n2))) | (a_select2(s_center7_init, H) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))))),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[9, 8])).
% 14.65/14.82 tff(11,plain,
% 14.65/14.82 (![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: $i] : ((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))),
% 14.65/14.82 inference(or_elim,[status(thm)],[10])).
% 14.65/14.82 tff(12,plain,
% 14.65/14.82 ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))),
% 14.65/14.82 inference(and_elim,[status(thm)],[11])).
% 14.65/14.82 tff(13,plain,
% 14.65/14.82 ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[12, 7])).
% 14.65/14.82 tff(14,plain,
% 14.65/14.82 ((~gt(loopcounter, n1)) | (~((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init))))),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[13, 6])).
% 14.65/14.82 tff(15,plain,
% 14.65/14.82 ($false),
% 14.65/14.82 inference(unit_resolution,[status(thm)],[14, 5, 3])).
% 14.65/14.82 tff(16,plain,((~gt(loopcounter, n1)) | (~((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init))))), inference(lemma,lemma(discharge,[]))).
% 14.65/14.82 tff(17,plain,
% 14.65/14.82 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 14.65/14.82 inference(rewrite,[status(thm)],[])).
% 14.65/14.82 tff(18,plain,
% 14.65/14.82 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 14.65/14.82 inference(rewrite,[status(thm)],[])).
% 14.65/14.82 tff(19,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 14.65/14.82 tff(20,plain,
% 14.65/14.82 (![X: $i] : (pred(succ(X)) = X)),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[19, 18])).
% 14.65/14.82 tff(21,plain,(
% 14.65/14.82 ![X: $i] : (pred(succ(X)) = X)),
% 14.65/14.82 inference(skolemize,[status(sab)],[20])).
% 14.65/14.82 tff(22,plain,
% 14.65/14.82 (![X: $i] : (pred(succ(X)) = X)),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[21, 17])).
% 14.65/14.82 tff(23,plain,
% 14.65/14.82 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(n2)) = n2)),
% 14.65/14.82 inference(quant_inst,[status(thm)],[])).
% 14.65/14.82 tff(24,plain,
% 14.65/14.82 (pred(succ(n2)) = n2),
% 14.65/14.82 inference(unit_resolution,[status(thm)],[23, 22])).
% 14.65/14.82 tff(25,plain,
% 14.65/14.82 ((succ(succ(n0)) = n2) <=> (succ(succ(n0)) = n2)),
% 14.65/14.82 inference(rewrite,[status(thm)],[])).
% 14.65/14.82 tff(26,axiom,(succ(succ(n0)) = n2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','successor_2')).
% 14.65/14.82 tff(27,plain,
% 14.65/14.82 (succ(succ(n0)) = n2),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[26, 25])).
% 14.65/14.82 tff(28,plain,
% 14.65/14.82 (n2 = succ(succ(n0))),
% 14.65/14.82 inference(symmetry,[status(thm)],[27])).
% 14.65/14.82 tff(29,plain,
% 14.65/14.82 (succ(n2) = succ(succ(succ(n0)))),
% 14.65/14.82 inference(monotonicity,[status(thm)],[28])).
% 14.65/14.82 tff(30,plain,
% 14.65/14.82 (succ(succ(succ(n0))) = succ(n2)),
% 14.65/14.82 inference(symmetry,[status(thm)],[29])).
% 14.65/14.82 tff(31,plain,
% 14.65/14.82 ((succ(succ(succ(n0))) = n3) <=> (succ(succ(succ(n0))) = n3)),
% 14.65/14.82 inference(rewrite,[status(thm)],[])).
% 14.65/14.82 tff(32,axiom,(succ(succ(succ(n0))) = n3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','successor_3')).
% 14.65/14.82 tff(33,plain,
% 14.65/14.82 (succ(succ(succ(n0))) = n3),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[32, 31])).
% 14.65/14.82 tff(34,plain,
% 14.65/14.82 (n3 = succ(succ(succ(n0)))),
% 14.65/14.82 inference(symmetry,[status(thm)],[33])).
% 14.65/14.82 tff(35,plain,
% 14.65/14.82 (n3 = succ(n2)),
% 14.65/14.82 inference(transitivity,[status(thm)],[34, 30])).
% 14.65/14.82 tff(36,plain,
% 14.65/14.82 (pred(n3) = pred(succ(n2))),
% 14.65/14.82 inference(monotonicity,[status(thm)],[35])).
% 14.65/14.82 tff(37,plain,
% 14.65/14.82 (^[X: $i] : refl((minus(X, n1) = pred(X)) <=> (minus(X, n1) = pred(X)))),
% 14.65/14.82 inference(bind,[status(th)],[])).
% 14.65/14.82 tff(38,plain,
% 14.65/14.82 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 14.65/14.82 inference(quant_intro,[status(thm)],[37])).
% 14.65/14.82 tff(39,plain,
% 14.65/14.82 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 14.65/14.82 inference(rewrite,[status(thm)],[])).
% 14.65/14.82 tff(40,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 14.65/14.82 tff(41,plain,
% 14.65/14.82 (![X: $i] : (minus(X, n1) = pred(X))),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[40, 39])).
% 14.65/14.82 tff(42,plain,(
% 14.65/14.82 ![X: $i] : (minus(X, n1) = pred(X))),
% 14.65/14.82 inference(skolemize,[status(sab)],[41])).
% 14.65/14.82 tff(43,plain,
% 14.65/14.82 (![X: $i] : (minus(X, n1) = pred(X))),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[42, 38])).
% 14.65/14.82 tff(44,plain,
% 14.65/14.82 ((~![X: $i] : (minus(X, n1) = pred(X))) | (minus(n3, n1) = pred(n3))),
% 14.65/14.82 inference(quant_inst,[status(thm)],[])).
% 14.65/14.82 tff(45,plain,
% 14.65/14.82 (minus(n3, n1) = pred(n3)),
% 14.65/14.82 inference(unit_resolution,[status(thm)],[44, 43])).
% 14.65/14.82 tff(46,plain,
% 14.65/14.82 (^[X: $i] : refl((plus(n1, X) = succ(X)) <=> (plus(n1, X) = succ(X)))),
% 14.65/14.82 inference(bind,[status(th)],[])).
% 14.65/14.82 tff(47,plain,
% 14.65/14.82 (![X: $i] : (plus(n1, X) = succ(X)) <=> ![X: $i] : (plus(n1, X) = succ(X))),
% 14.65/14.82 inference(quant_intro,[status(thm)],[46])).
% 14.65/14.82 tff(48,plain,
% 14.65/14.82 (![X: $i] : (plus(n1, X) = succ(X)) <=> ![X: $i] : (plus(n1, X) = succ(X))),
% 14.65/14.82 inference(rewrite,[status(thm)],[])).
% 14.65/14.82 tff(49,axiom,(![X: $i] : (plus(n1, X) = succ(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','succ_plus_1_l')).
% 14.65/14.82 tff(50,plain,
% 14.65/14.82 (![X: $i] : (plus(n1, X) = succ(X))),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[49, 48])).
% 14.65/14.82 tff(51,plain,(
% 14.65/14.82 ![X: $i] : (plus(n1, X) = succ(X))),
% 14.65/14.82 inference(skolemize,[status(sab)],[50])).
% 14.65/14.82 tff(52,plain,
% 14.65/14.82 (![X: $i] : (plus(n1, X) = succ(X))),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[51, 47])).
% 14.65/14.82 tff(53,plain,
% 14.65/14.82 ((~![X: $i] : (plus(n1, X) = succ(X))) | (plus(n1, n2) = succ(n2))),
% 14.65/14.82 inference(quant_inst,[status(thm)],[])).
% 14.65/14.82 tff(54,plain,
% 14.65/14.82 (plus(n1, n2) = succ(n2)),
% 14.65/14.82 inference(unit_resolution,[status(thm)],[53, 52])).
% 14.65/14.82 tff(55,plain,
% 14.65/14.82 (plus(n1, n2) = n3),
% 14.65/14.82 inference(transitivity,[status(thm)],[54, 29, 33])).
% 14.65/14.82 tff(56,plain,
% 14.65/14.82 (minus(plus(n1, n2), n1) = minus(n3, n1)),
% 14.65/14.82 inference(monotonicity,[status(thm)],[55])).
% 14.65/14.82 tff(57,plain,
% 14.65/14.82 (minus(plus(n1, n2), n1) = n2),
% 14.65/14.82 inference(transitivity,[status(thm)],[56, 45, 36, 24])).
% 14.65/14.82 tff(58,plain,
% 14.65/14.82 (leq(H!16, minus(plus(n1, n2), n1)) <=> leq(H!16, n2)),
% 14.65/14.82 inference(monotonicity,[status(thm)],[57])).
% 14.65/14.82 tff(59,plain,
% 14.65/14.82 (leq(H!16, n2) <=> leq(H!16, minus(plus(n1, n2), n1))),
% 14.65/14.82 inference(symmetry,[status(thm)],[58])).
% 14.65/14.82 tff(60,assumption,(~((a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, n2)))), introduced(assumption)).
% 14.65/14.82 tff(61,plain,
% 14.65/14.82 (((a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, n2))) | leq(H!16, n2)),
% 14.65/14.82 inference(tautology,[status(thm)],[])).
% 14.65/14.82 tff(62,plain,
% 14.65/14.82 (leq(H!16, n2)),
% 14.65/14.82 inference(unit_resolution,[status(thm)],[61, 60])).
% 14.65/14.82 tff(63,plain,
% 14.65/14.82 (leq(H!16, minus(plus(n1, n2), n1))),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[62, 59])).
% 14.65/14.82 tff(64,plain,
% 14.65/14.82 (((a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, n2))) | leq(n0, H!16)),
% 14.65/14.82 inference(tautology,[status(thm)],[])).
% 14.65/14.82 tff(65,plain,
% 14.65/14.82 (leq(n0, H!16)),
% 14.65/14.82 inference(unit_resolution,[status(thm)],[64, 60])).
% 14.65/14.82 tff(66,plain,
% 14.65/14.82 (((a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, n2))) | (~(a_select2(s_center7_init, H!16) = init))),
% 14.65/14.82 inference(tautology,[status(thm)],[])).
% 14.65/14.82 tff(67,plain,
% 14.65/14.82 (~(a_select2(s_center7_init, H!16) = init)),
% 14.65/14.82 inference(unit_resolution,[status(thm)],[66, 60])).
% 14.65/14.82 tff(68,plain,
% 14.65/14.82 (^[D: $i] : refl(((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1)))) <=> ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1)))))),
% 14.65/14.82 inference(bind,[status(th)],[])).
% 14.65/14.82 tff(69,plain,
% 14.65/14.82 (![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1)))) <=> ![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1))))),
% 14.65/14.82 inference(quant_intro,[status(thm)],[68])).
% 14.65/14.82 tff(70,plain,
% 14.65/14.82 (^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, D) & leq(D, minus(plus(n1, n2), n1))) <=> (~((~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1)))))), ((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) <=> (~(~((~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1)))))))), rewrite((~(~((~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1)))))) <=> ((~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1))))), ((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) <=> ((~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1)))))), (((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init)) <=> (((~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init)))), rewrite((((~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init)) <=> ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1))))), (((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init)) <=> ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1))))))),
% 14.65/14.82 inference(bind,[status(th)],[])).
% 14.65/14.82 tff(71,plain,
% 14.65/14.82 (![D: $i] : ((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init)) <=> ![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1))))),
% 14.65/14.82 inference(quant_intro,[status(thm)],[70])).
% 14.65/14.82 tff(72,plain,
% 14.65/14.82 (![D: $i] : ((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init)) <=> ![D: $i] : ((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init))),
% 14.65/14.82 inference(rewrite,[status(thm)],[])).
% 14.65/14.82 tff(73,plain,
% 14.65/14.82 (![D: $i] : ((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init))),
% 14.65/14.82 inference(and_elim,[status(thm)],[11])).
% 14.65/14.82 tff(74,plain,
% 14.65/14.82 (![D: $i] : ((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init))),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[73, 72])).
% 14.65/14.82 tff(75,plain,(
% 14.65/14.82 ![D: $i] : ((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init))),
% 14.65/14.82 inference(skolemize,[status(sab)],[74])).
% 14.65/14.82 tff(76,plain,
% 14.65/14.82 (![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1))))),
% 14.65/14.82 inference(modus_ponens,[status(thm)],[75, 71])).
% 14.65/14.83 tff(77,plain,
% 14.65/14.83 (![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1))))),
% 14.65/14.83 inference(modus_ponens,[status(thm)],[76, 69])).
% 14.65/14.83 tff(78,plain,
% 14.65/14.83 (((~![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1))))) | ((a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, minus(plus(n1, n2), n1))))) <=> ((~![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1))))) | (a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, minus(plus(n1, n2), n1))))),
% 14.65/14.83 inference(rewrite,[status(thm)],[])).
% 14.65/14.83 tff(79,plain,
% 14.65/14.83 ((~![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1))))) | ((a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, minus(plus(n1, n2), n1))))),
% 14.65/14.83 inference(quant_inst,[status(thm)],[])).
% 14.65/14.83 tff(80,plain,
% 14.65/14.83 ((~![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(n0, D)) | (~leq(D, minus(plus(n1, n2), n1))))) | (a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, minus(plus(n1, n2), n1)))),
% 14.65/14.83 inference(modus_ponens,[status(thm)],[79, 78])).
% 14.65/14.83 tff(81,plain,
% 14.65/14.83 (~leq(H!16, minus(plus(n1, n2), n1))),
% 14.65/14.83 inference(unit_resolution,[status(thm)],[80, 77, 67, 65])).
% 14.65/14.83 tff(82,plain,
% 14.65/14.83 ($false),
% 14.65/14.83 inference(unit_resolution,[status(thm)],[81, 63])).
% 14.65/14.83 tff(83,plain,((a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, n2))), inference(lemma,lemma(discharge,[]))).
% 14.65/14.83 tff(84,assumption,(~((a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3)))), introduced(assumption)).
% 14.65/14.83 tff(85,plain,
% 14.65/14.83 (((a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3))) | leq(G!15, n3)),
% 14.65/14.83 inference(tautology,[status(thm)],[])).
% 14.65/14.83 tff(86,plain,
% 14.65/14.83 (leq(G!15, n3)),
% 14.65/14.83 inference(unit_resolution,[status(thm)],[85, 84])).
% 14.65/14.83 tff(87,plain,
% 14.65/14.83 (((a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3))) | leq(n0, G!15)),
% 14.65/14.83 inference(tautology,[status(thm)],[])).
% 14.65/14.83 tff(88,plain,
% 14.65/14.83 (leq(n0, G!15)),
% 14.65/14.83 inference(unit_resolution,[status(thm)],[87, 84])).
% 14.65/14.83 tff(89,plain,
% 14.65/14.83 (((a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3))) | (~(a_select2(s_values7_init, G!15) = init))),
% 14.65/14.83 inference(tautology,[status(thm)],[])).
% 14.65/14.83 tff(90,plain,
% 14.65/14.83 (~(a_select2(s_values7_init, G!15) = init)),
% 14.65/14.83 inference(unit_resolution,[status(thm)],[89, 84])).
% 14.65/14.83 tff(91,plain,
% 14.65/14.83 (^[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))))),
% 14.65/14.83 inference(bind,[status(th)],[])).
% 14.65/14.83 tff(92,plain,
% 14.65/14.83 (![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)))),
% 14.65/14.83 inference(quant_intro,[status(thm)],[91])).
% 14.65/14.83 tff(93,plain,
% 14.65/14.83 (^[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)))))),
% 14.65/14.83 inference(bind,[status(th)],[])).
% 14.65/14.83 tff(94,plain,
% 14.65/14.83 (![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)))),
% 14.65/14.83 inference(quant_intro,[status(thm)],[93])).
% 14.65/14.83 tff(95,plain,
% 14.65/14.83 (![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))),
% 14.65/14.83 inference(rewrite,[status(thm)],[])).
% 14.65/14.83 tff(96,plain,
% 14.65/14.83 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 14.65/14.83 inference(and_elim,[status(thm)],[11])).
% 14.65/14.83 tff(97,plain,
% 14.65/14.83 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 14.65/14.83 inference(modus_ponens,[status(thm)],[96, 95])).
% 14.65/14.83 tff(98,plain,(
% 14.65/14.83 ![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 14.65/14.83 inference(skolemize,[status(sab)],[97])).
% 14.65/14.83 tff(99,plain,
% 14.65/14.83 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))),
% 14.65/14.83 inference(modus_ponens,[status(thm)],[98, 94])).
% 14.65/14.83 tff(100,plain,
% 14.65/14.83 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))),
% 14.65/14.83 inference(modus_ponens,[status(thm)],[99, 92])).
% 14.65/14.83 tff(101,plain,
% 14.65/14.83 (((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))) | ((a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3)))) <=> ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))) | (a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3)))),
% 14.65/14.83 inference(rewrite,[status(thm)],[])).
% 14.65/14.83 tff(102,plain,
% 14.65/14.83 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))) | ((a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3)))),
% 14.65/14.83 inference(quant_inst,[status(thm)],[])).
% 14.65/14.83 tff(103,plain,
% 14.65/14.83 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, n3)))) | (a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3))),
% 14.65/14.83 inference(modus_ponens,[status(thm)],[102, 101])).
% 14.65/14.83 tff(104,plain,
% 14.65/14.83 ($false),
% 14.65/14.83 inference(unit_resolution,[status(thm)],[103, 100, 90, 88, 86])).
% 14.65/14.83 tff(105,plain,((a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3))), inference(lemma,lemma(discharge,[]))).
% 14.65/14.83 tff(106,plain,
% 14.65/14.83 (((~((a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3)))) | (~((a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, n2)))) | (~((~gt(loopcounter, n1)) | (~((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init)))))) | (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(n0, F!14)) | (~leq(F!14, n3)) | (~leq(n0, E!13)) | (~leq(E!13, n2))))) <=> ((~((~gt(loopcounter, n1)) | (~((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init)))))) | (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(n0, F!14)) | (~leq(F!14, n3)) | (~leq(n0, E!13)) | (~leq(E!13, n2)))) | (~((a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3)))) | (~((a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, n2)))))),
% 14.65/14.83 inference(rewrite,[status(thm)],[])).
% 14.65/14.83 tff(107,plain,
% 14.65/14.83 ((leq(n0, E!13) & leq(E!13, n2) & (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(n0, F!14)) | (~leq(F!14, n3))))) <=> (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(n0, F!14)) | (~leq(F!14, n3)) | (~leq(n0, E!13)) | (~leq(E!13, n2))))),
% 14.65/14.83 inference(rewrite,[status(thm)],[])).
% 14.65/14.83 tff(108,plain,
% 14.65/14.83 ((~((~(leq(n0, F!14) & leq(F!14, n3))) | (a_select3(simplex7_init, F!14, E!13) = init))) <=> (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(n0, F!14)) | (~leq(F!14, n3))))),
% 14.65/14.83 inference(rewrite,[status(thm)],[])).
% 14.65/14.83 tff(109,plain,
% 14.65/14.83 ((leq(n0, E!13) & leq(E!13, n2) & (~((~(leq(n0, F!14) & leq(F!14, n3))) | (a_select3(simplex7_init, F!14, E!13) = init)))) <=> (leq(n0, E!13) & leq(E!13, n2) & (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(n0, F!14)) | (~leq(F!14, n3)))))),
% 14.65/14.83 inference(monotonicity,[status(thm)],[108])).
% 14.65/14.83 tff(110,plain,
% 14.65/14.83 ((leq(n0, E!13) & leq(E!13, n2) & (~((~(leq(n0, F!14) & leq(F!14, n3))) | (a_select3(simplex7_init, F!14, E!13) = init)))) <=> (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(n0, F!14)) | (~leq(F!14, n3)) | (~leq(n0, E!13)) | (~leq(E!13, n2))))),
% 14.65/14.83 inference(transitivity,[status(thm)],[109, 107])).
% 14.65/14.83 tff(111,plain,
% 14.65/14.83 ((~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))) <=> (~((~gt(loopcounter, n1)) | (~((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init))))))),
% 14.65/14.83 inference(rewrite,[status(thm)],[])).
% 14.65/14.83 tff(112,plain,
% 14.65/14.83 ((~((~(leq(n0, H!16) & leq(H!16, n2))) | (a_select2(s_center7_init, H!16) = init))) <=> (~((a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, n2))))),
% 14.65/14.83 inference(rewrite,[status(thm)],[])).
% 14.65/14.83 tff(113,plain,
% 14.65/14.83 ((~((~(leq(n0, G!15) & leq(G!15, n3))) | (a_select2(s_values7_init, G!15) = init))) <=> (~((a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3))))),
% 14.65/14.83 inference(rewrite,[status(thm)],[])).
% 14.65/14.83 tff(114,plain,
% 14.65/14.83 (((~((~(leq(n0, G!15) & leq(G!15, n3))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(n0, H!16) & leq(H!16, n2))) | (a_select2(s_center7_init, H!16) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))) | (leq(n0, E!13) & leq(E!13, n2) & (~((~(leq(n0, F!14) & leq(F!14, n3))) | (a_select3(simplex7_init, F!14, E!13) = init))))) <=> ((~((a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3)))) | (~((a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, n2)))) | (~((~gt(loopcounter, n1)) | (~((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init)))))) | (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(n0, F!14)) | (~leq(F!14, n3)) | (~leq(n0, E!13)) | (~leq(E!13, n2)))))),
% 14.65/14.83 inference(monotonicity,[status(thm)],[113, 112, 111, 110])).
% 14.65/14.83 tff(115,plain,
% 14.65/14.83 (((~((~(leq(n0, G!15) & leq(G!15, n3))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(n0, H!16) & leq(H!16, n2))) | (a_select2(s_center7_init, H!16) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))) | (leq(n0, E!13) & leq(E!13, n2) & (~((~(leq(n0, F!14) & leq(F!14, n3))) | (a_select3(simplex7_init, F!14, E!13) = init))))) <=> ((~((~gt(loopcounter, n1)) | (~((~(pvar1400_init = init)) | (~(pvar1401_init = init)) | (~(pvar1402_init = init)))))) | (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(n0, F!14)) | (~leq(F!14, n3)) | (~leq(n0, E!13)) | (~leq(E!13, n2)))) | (~((a_select2(s_values7_init, G!15) = init) | (~leq(n0, G!15)) | (~leq(G!15, n3)))) | (~((a_select2(s_center7_init, H!16) = init) | (~leq(n0, H!16)) | (~leq(H!16, n2)))))),
% 14.65/14.83 inference(transitivity,[status(thm)],[114, 106])).
% 14.65/14.83 tff(116,plain,
% 14.65/14.83 (((leq(n0, E!13) & leq(E!13, n2) & (~((~(leq(n0, F!14) & leq(F!14, n3))) | (a_select3(simplex7_init, F!14, E!13) = init)))) | (~((~(leq(n0, G!15) & leq(G!15, n3))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(n0, H!16) & leq(H!16, n2))) | (a_select2(s_center7_init, H!16) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) <=> ((~((~(leq(n0, G!15) & leq(G!15, n3))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(n0, H!16) & leq(H!16, n2))) | (a_select2(s_center7_init, H!16) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))) | (leq(n0, E!13) & leq(E!13, n2) & (~((~(leq(n0, F!14) & leq(F!14, n3))) | (a_select3(simplex7_init, F!14, E!13) = init)))))),
% 14.65/14.83 inference(rewrite,[status(thm)],[])).
% 14.65/14.83 tff(117,plain,
% 14.65/14.83 (((leq(n0, E!13) & leq(E!13, n2)) & (~((~(leq(n0, F!14) & leq(F!14, n3))) | (a_select3(simplex7_init, F!14, E!13) = init)))) <=> (leq(n0, E!13) & leq(E!13, n2) & (~((~(leq(n0, F!14) & leq(F!14, n3))) | (a_select3(simplex7_init, F!14, E!13) = init))))),
% 14.65/14.83 inference(rewrite,[status(thm)],[])).
% 14.65/14.83 tff(118,plain,
% 14.65/14.83 ((((leq(n0, E!13) & leq(E!13, n2)) & (~((~(leq(n0, F!14) & leq(F!14, n3))) | (a_select3(simplex7_init, F!14, E!13) = init)))) | (~((~(leq(n0, G!15) & leq(G!15, n3))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(n0, H!16) & leq(H!16, n2))) | (a_select2(s_center7_init, H!16) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) <=> ((leq(n0, E!13) & leq(E!13, n2) & (~((~(leq(n0, F!14) & leq(F!14, n3))) | (a_select3(simplex7_init, F!14, E!13) = init)))) | (~((~(leq(n0, G!15) & leq(G!15, n3))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(n0, H!16) & leq(H!16, n2))) | (a_select2(s_center7_init, H!16) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))))),
% 14.68/14.83 inference(monotonicity,[status(thm)],[117])).
% 14.68/14.83 tff(119,plain,
% 14.68/14.83 ((((leq(n0, E!13) & leq(E!13, n2)) & (~((~(leq(n0, F!14) & leq(F!14, n3))) | (a_select3(simplex7_init, F!14, E!13) = init)))) | (~((~(leq(n0, G!15) & leq(G!15, n3))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(n0, H!16) & leq(H!16, n2))) | (a_select2(s_center7_init, H!16) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) <=> ((~((~(leq(n0, G!15) & leq(G!15, n3))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(n0, H!16) & leq(H!16, n2))) | (a_select2(s_center7_init, H!16) = init))) | (~((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))) | (leq(n0, E!13) & leq(E!13, n2) & (~((~(leq(n0, F!14) & leq(F!14, n3))) | (a_select3(simplex7_init, F!14, E!13) = init)))))),
% 14.68/14.83 inference(transitivity,[status(thm)],[118, 116])).
% 14.68/14.83 tff(120,plain,
% 14.68/14.83 ((![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(n0, H) & leq(H, n2))) | (a_select2(s_center7_init, H) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))) <=> (![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(n0, H) & leq(H, n2))) | (a_select2(s_center7_init, H) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))),
% 14.68/14.83 inference(rewrite,[status(thm)],[])).
% 14.68/14.83 tff(121,plain,
% 14.68/14.83 ((~(![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(n0, H) & leq(H, n2))) | (a_select2(s_center7_init, H) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) <=> (~(![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(n0, H) & leq(H, n2))) | (a_select2(s_center7_init, H) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))))),
% 14.68/14.83 inference(monotonicity,[status(thm)],[120])).
% 14.68/14.83 tff(122,plain,
% 14.68/14.83 ((~(![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(n0, H) & leq(H, n2))) | (a_select2(s_center7_init, H) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))) <=> (~(![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(n0, H) & leq(H, n2))) | (a_select2(s_center7_init, H) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init)))))),
% 14.68/14.84 inference(rewrite,[status(thm)],[])).
% 14.68/14.84 tff(123,plain,
% 14.68/14.84 (~(![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(n0, H) & leq(H, n2))) | (a_select2(s_center7_init, H) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))),
% 14.68/14.84 inference(or_elim,[status(thm)],[10])).
% 14.68/14.84 tff(124,plain,
% 14.68/14.84 (~(![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(n0, H) & leq(H, n2))) | (a_select2(s_center7_init, H) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))),
% 14.68/14.84 inference(modus_ponens,[status(thm)],[123, 121])).
% 14.68/14.84 tff(125,plain,
% 14.68/14.84 (~(![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(n0, H) & leq(H, n2))) | (a_select2(s_center7_init, H) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))),
% 14.68/14.84 inference(modus_ponens,[status(thm)],[124, 122])).
% 14.68/14.84 tff(126,plain,
% 14.68/14.84 (~(![E: $i] : ((~(leq(n0, E) & leq(E, n2))) | ![F: $i] : ((~(leq(n0, F) & leq(F, n3))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(n0, G) & leq(G, n3))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(n0, H) & leq(H, n2))) | (a_select2(s_center7_init, H) = init)) & ((~gt(loopcounter, n1)) | ((pvar1400_init = init) & (pvar1401_init = init) & (pvar1402_init = init))))),
% 14.68/14.84 inference(modus_ponens,[status(thm)],[125, 121])).
% 14.68/14.84 unexpected number of arguments: (let ((a!1 (forall ((E $i))
% 14.68/14.84 (let ((a!1 (forall ((F $i))
% 14.68/14.84 (or (not (and (leq n0 F) (leq F n3)))
% 14.68/14.84 (= (a_select3 simplex7_init F E) init)))))
% 14.68/14.84 (or (not (and (leq n0 E) (leq E n2))) a!1))))
% 14.68/14.84 (a!2 (forall ((F $i))
% 14.68/14.84 (or (not (and (leq n0 F) (leq F n3)))
% 14.68/14.84 (= (a_select3 simplex7_init F E!13) init))))
% 14.68/14.84 (a!4 (refl (~ (and (leq n0 E!13) (leq E!13 n2))
% 14.68/14.84 (and (leq n0 E!13) (leq E!13 n2)))))
% 14.68/14.84 (a!5 (or (not (and (leq n0 F!14) (leq F!14 n3)))
% 14.68/14.84 (= (a_select3 simplex7_init F!14 E!13) init)))
% 14.68/14.84 (a!9 (forall ((G $i))
% 14.68/14.84 (or (not (and (leq n0 G) (leq G n3)))
% 14.68/14.84 (= (a_select2 s_values7_init G) init))))
% 14.68/14.84 (a!10 (or (not (and (leq n0 G!15) (leq G!15 n3)))
% 14.68/14.84 (= (a_select2 s_values7_init G!15) init)))
% 14.68/14.84 (a!11 (forall ((H $i))
% 14.68/14.84 (or (not (and (leq n0 H) (leq H n2)))
% 14.68/14.84 (= (a_select2 s_center7_init H) init))))
% 14.68/14.84 (a!12 (or (not (and (leq n0 H!16) (leq H!16 n2)))
% 14.68/14.84 (= (a_select2 s_center7_init H!16) init)))
% 14.68/14.84 (a!13 (or (not (gt loopcounter n1))
% 14.68/14.84 (and (= pvar1400_init init)
% 14.68/14.84 (= pvar1401_init init)
% 14.68/14.84 (= pvar1402_init init)))))
% 14.68/14.84 (let ((a!3 (or (not (and (leq n0 E!13) (leq E!13 n2))) a!2))
% 14.68/14.84 (a!6 (and (and (leq n0 E!13) (leq E!13 n2)) (not a!5))))
% 14.68/14.84 (let ((a!7 (nnf-neg a!4 (sk (~ (not a!2) (not a!5))) (~ (not a!3) a!6))))
% 14.68/14.84 (let ((a!8 (trans (sk (~ (not a!1) (not a!3))) a!7 (~ (not a!1) a!6))))
% 14.68/14.84 (nnf-neg a!8
% 14.68/14.84 (sk (~ (not a!9) (not a!10)))
% 14.68/14.84 (sk (~ (not a!11) (not a!12)))
% 14.68/14.84 (refl (~ (not a!13) (not a!13)))
% 14.68/14.84 (~ (not (and a!1 a!9 a!11 a!13))
% 14.68/14.84 (or a!6 (not a!10) (not a!12) (not a!13))))))))
% 14.68/14.84 Proof display could not be completed: unexpected number of arguments
% 14.68/14.90 % E exiting
%------------------------------------------------------------------------------