%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV033+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:31:22 AM UTC 2025
% Result : Theorem 6.55s 6.72s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV033+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:27:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 6.55/6.72 % SZS status Theorem
% 6.55/6.72 % SZS output start Proof
% 6.55/6.72 tff(leq_type, type, (
% 6.55/6.72 leq: ( $i * $i ) > $o)).
% 6.55/6.72 tff(n3_type, type, (
% 6.55/6.72 n3: $i)).
% 6.55/6.72 tff(n0_type, type, (
% 6.55/6.72 n0: $i)).
% 6.55/6.72 tff(init_type, type, (
% 6.55/6.72 init: $i)).
% 6.55/6.72 tff(a_select3_type, type, (
% 6.55/6.72 a_select3: ( $i * $i * $i ) > $i)).
% 6.55/6.72 tff(tptp_fun_D_13_type, type, (
% 6.55/6.72 tptp_fun_D_13: $i)).
% 6.55/6.72 tff(simplex7_init_type, type, (
% 6.55/6.72 simplex7_init: $i)).
% 6.55/6.72 tff(n2_type, type, (
% 6.55/6.72 n2: $i)).
% 6.55/6.72 tff(tptp_fun_E_14_type, type, (
% 6.55/6.72 tptp_fun_E_14: $i)).
% 6.55/6.72 tff(minus_type, type, (
% 6.55/6.72 minus: ( $i * $i ) > $i)).
% 6.55/6.72 tff(n1_type, type, (
% 6.55/6.72 n1: $i)).
% 6.55/6.72 tff(plus_type, type, (
% 6.55/6.72 plus: ( $i * $i ) > $i)).
% 6.55/6.72 tff(pv1376_type, type, (
% 6.55/6.72 pv1376: $i)).
% 6.55/6.72 tff(tptp_fun_F_15_type, type, (
% 6.55/6.72 tptp_fun_F_15: $i)).
% 6.55/6.72 tff(a_select2_type, type, (
% 6.55/6.72 a_select2: ( $i * $i ) > $i)).
% 6.55/6.72 tff(tptp_update2_type, type, (
% 6.55/6.72 tptp_update2: ( $i * $i * $i ) > $i)).
% 6.55/6.72 tff(s_values7_init_type, type, (
% 6.55/6.72 s_values7_init: $i)).
% 6.55/6.72 tff(pred_type, type, (
% 6.55/6.72 pred: $i > $i)).
% 6.55/6.72 tff(gt_type, type, (
% 6.55/6.72 gt: ( $i * $i ) > $o)).
% 6.55/6.72 tff(succ_type, type, (
% 6.55/6.72 succ: $i > $i)).
% 6.55/6.72 tff(1,plain,
% 6.55/6.72 (^[X: $i] : refl((minus(X, n1) = pred(X)) <=> (minus(X, n1) = pred(X)))),
% 6.55/6.72 inference(bind,[status(th)],[])).
% 6.55/6.72 tff(2,plain,
% 6.55/6.72 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 6.55/6.72 inference(quant_intro,[status(thm)],[1])).
% 6.55/6.72 tff(3,plain,
% 6.55/6.72 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 6.55/6.72 inference(rewrite,[status(thm)],[])).
% 6.55/6.72 tff(4,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 6.55/6.72 tff(5,plain,
% 6.55/6.72 (![X: $i] : (minus(X, n1) = pred(X))),
% 6.55/6.72 inference(modus_ponens,[status(thm)],[4, 3])).
% 6.55/6.72 tff(6,plain,(
% 6.55/6.72 ![X: $i] : (minus(X, n1) = pred(X))),
% 6.55/6.72 inference(skolemize,[status(sab)],[5])).
% 6.55/6.72 tff(7,plain,
% 6.55/6.72 (![X: $i] : (minus(X, n1) = pred(X))),
% 6.55/6.72 inference(modus_ponens,[status(thm)],[6, 2])).
% 6.55/6.72 tff(8,plain,
% 6.55/6.72 ((~![X: $i] : (minus(X, n1) = pred(X))) | (minus(pv1376, n1) = pred(pv1376))),
% 6.55/6.72 inference(quant_inst,[status(thm)],[])).
% 6.55/6.72 tff(9,plain,
% 6.55/6.72 (minus(pv1376, n1) = pred(pv1376)),
% 6.55/6.72 inference(unit_resolution,[status(thm)],[8, 7])).
% 6.55/6.72 tff(10,plain,
% 6.55/6.72 (pred(pv1376) = minus(pv1376, n1)),
% 6.55/6.72 inference(symmetry,[status(thm)],[9])).
% 6.55/6.72 tff(11,plain,
% 6.55/6.72 (leq(F!15, pred(pv1376)) <=> leq(F!15, minus(pv1376, n1))),
% 6.55/6.72 inference(monotonicity,[status(thm)],[10])).
% 6.55/6.72 tff(12,plain,
% 6.55/6.72 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 6.55/6.72 inference(bind,[status(th)],[])).
% 6.55/6.72 tff(13,plain,
% 6.55/6.72 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 6.55/6.72 inference(quant_intro,[status(thm)],[12])).
% 6.55/6.72 tff(14,plain,
% 6.55/6.72 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 6.55/6.72 inference(rewrite,[status(thm)],[])).
% 6.55/6.72 tff(15,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 6.55/6.72 tff(16,plain,
% 6.55/6.72 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 6.55/6.72 inference(modus_ponens,[status(thm)],[15, 14])).
% 6.55/6.72 tff(17,plain,(
% 6.55/6.72 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 6.55/6.72 inference(skolemize,[status(sab)],[16])).
% 6.55/6.72 tff(18,plain,
% 6.55/6.72 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 6.55/6.72 inference(modus_ponens,[status(thm)],[17, 13])).
% 6.55/6.72 tff(19,plain,
% 6.55/6.72 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(F!15, pred(pv1376)) <=> gt(pv1376, F!15))),
% 6.55/6.72 inference(quant_inst,[status(thm)],[])).
% 6.55/6.72 tff(20,plain,
% 6.55/6.72 (leq(F!15, pred(pv1376)) <=> gt(pv1376, F!15)),
% 6.55/6.72 inference(unit_resolution,[status(thm)],[19, 18])).
% 6.55/6.72 tff(21,plain,
% 6.55/6.72 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(pv1376, pred(F!15)) <=> gt(F!15, pv1376))),
% 6.55/6.72 inference(quant_inst,[status(thm)],[])).
% 6.55/6.72 tff(22,plain,
% 6.55/6.72 (leq(pv1376, pred(F!15)) <=> gt(F!15, pv1376)),
% 6.55/6.72 inference(unit_resolution,[status(thm)],[21, 18])).
% 6.55/6.72 tff(23,plain,
% 6.55/6.72 (^[X: $i, Y: $i] : refl((leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> (leq(succ(X), succ(Y)) <=> leq(X, Y)))),
% 6.55/6.72 inference(bind,[status(th)],[])).
% 6.55/6.73 tff(24,plain,
% 6.55/6.73 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 6.55/6.73 inference(quant_intro,[status(thm)],[23])).
% 6.55/6.73 tff(25,plain,
% 6.55/6.73 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(26,axiom,(![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_succ_succ')).
% 6.55/6.73 tff(27,plain,
% 6.55/6.73 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[26, 25])).
% 6.55/6.73 tff(28,plain,(
% 6.55/6.73 ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 6.55/6.73 inference(skolemize,[status(sab)],[27])).
% 6.55/6.73 tff(29,plain,
% 6.55/6.73 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[28, 24])).
% 6.55/6.73 tff(30,plain,
% 6.55/6.73 ((~![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))) | (leq(succ(pv1376), succ(pred(F!15))) <=> leq(pv1376, pred(F!15)))),
% 6.55/6.73 inference(quant_inst,[status(thm)],[])).
% 6.55/6.73 tff(31,plain,
% 6.55/6.73 (leq(succ(pv1376), succ(pred(F!15))) <=> leq(pv1376, pred(F!15))),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[30, 29])).
% 6.55/6.73 tff(32,plain,
% 6.55/6.73 (![X: $i] : (succ(pred(X)) = X) <=> ![X: $i] : (succ(pred(X)) = X)),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(33,plain,
% 6.55/6.73 (![X: $i] : (succ(pred(X)) = X) <=> ![X: $i] : (succ(pred(X)) = X)),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(34,axiom,(![X: $i] : (succ(pred(X)) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','succ_pred')).
% 6.55/6.73 tff(35,plain,
% 6.55/6.73 (![X: $i] : (succ(pred(X)) = X)),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[34, 33])).
% 6.55/6.73 tff(36,plain,(
% 6.55/6.73 ![X: $i] : (succ(pred(X)) = X)),
% 6.55/6.73 inference(skolemize,[status(sab)],[35])).
% 6.55/6.73 tff(37,plain,
% 6.55/6.73 (![X: $i] : (succ(pred(X)) = X)),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[36, 32])).
% 6.55/6.73 tff(38,plain,
% 6.55/6.73 ((~![X: $i] : (succ(pred(X)) = X)) | (succ(pred(F!15)) = F!15)),
% 6.55/6.73 inference(quant_inst,[status(thm)],[])).
% 6.55/6.73 tff(39,plain,
% 6.55/6.73 (succ(pred(F!15)) = F!15),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[38, 37])).
% 6.55/6.73 tff(40,plain,
% 6.55/6.73 (leq(succ(pv1376), succ(pred(F!15))) <=> leq(succ(pv1376), F!15)),
% 6.55/6.73 inference(monotonicity,[status(thm)],[39])).
% 6.55/6.73 tff(41,plain,
% 6.55/6.73 (leq(succ(pv1376), F!15) <=> leq(succ(pv1376), succ(pred(F!15)))),
% 6.55/6.73 inference(symmetry,[status(thm)],[40])).
% 6.55/6.73 tff(42,plain,
% 6.55/6.73 ((~leq(succ(pv1376), F!15)) <=> (~leq(succ(pv1376), succ(pred(F!15))))),
% 6.55/6.73 inference(monotonicity,[status(thm)],[41])).
% 6.55/6.73 tff(43,plain,
% 6.55/6.73 (^[X: $i] : refl((plus(n1, X) = succ(X)) <=> (plus(n1, X) = succ(X)))),
% 6.55/6.73 inference(bind,[status(th)],[])).
% 6.55/6.73 tff(44,plain,
% 6.55/6.73 (![X: $i] : (plus(n1, X) = succ(X)) <=> ![X: $i] : (plus(n1, X) = succ(X))),
% 6.55/6.73 inference(quant_intro,[status(thm)],[43])).
% 6.55/6.73 tff(45,plain,
% 6.55/6.73 (![X: $i] : (plus(n1, X) = succ(X)) <=> ![X: $i] : (plus(n1, X) = succ(X))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(46,axiom,(![X: $i] : (plus(n1, X) = succ(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','succ_plus_1_l')).
% 6.55/6.73 tff(47,plain,
% 6.55/6.73 (![X: $i] : (plus(n1, X) = succ(X))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[46, 45])).
% 6.55/6.73 tff(48,plain,(
% 6.55/6.73 ![X: $i] : (plus(n1, X) = succ(X))),
% 6.55/6.73 inference(skolemize,[status(sab)],[47])).
% 6.55/6.73 tff(49,plain,
% 6.55/6.73 (![X: $i] : (plus(n1, X) = succ(X))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[48, 44])).
% 6.55/6.73 tff(50,plain,
% 6.55/6.73 ((~![X: $i] : (plus(n1, X) = succ(X))) | (plus(n1, pv1376) = succ(pv1376))),
% 6.55/6.73 inference(quant_inst,[status(thm)],[])).
% 6.55/6.73 tff(51,plain,
% 6.55/6.73 (plus(n1, pv1376) = succ(pv1376)),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[50, 49])).
% 6.55/6.73 tff(52,plain,
% 6.55/6.73 (minus(plus(n1, pv1376), n1) = minus(succ(pv1376), n1)),
% 6.55/6.73 inference(monotonicity,[status(thm)],[51])).
% 6.55/6.73 tff(53,plain,
% 6.55/6.73 (minus(succ(pv1376), n1) = minus(plus(n1, pv1376), n1)),
% 6.55/6.73 inference(symmetry,[status(thm)],[52])).
% 6.55/6.73 tff(54,plain,
% 6.55/6.73 ((~![X: $i] : (minus(X, n1) = pred(X))) | (minus(succ(pv1376), n1) = pred(succ(pv1376)))),
% 6.55/6.73 inference(quant_inst,[status(thm)],[])).
% 6.55/6.73 tff(55,plain,
% 6.55/6.73 (minus(succ(pv1376), n1) = pred(succ(pv1376))),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[54, 7])).
% 6.55/6.73 tff(56,plain,
% 6.55/6.73 (pred(succ(pv1376)) = minus(succ(pv1376), n1)),
% 6.55/6.73 inference(symmetry,[status(thm)],[55])).
% 6.55/6.73 tff(57,plain,
% 6.55/6.73 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(58,plain,
% 6.55/6.73 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(59,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 6.55/6.73 tff(60,plain,
% 6.55/6.73 (![X: $i] : (pred(succ(X)) = X)),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[59, 58])).
% 6.55/6.73 tff(61,plain,(
% 6.55/6.73 ![X: $i] : (pred(succ(X)) = X)),
% 6.55/6.73 inference(skolemize,[status(sab)],[60])).
% 6.55/6.73 tff(62,plain,
% 6.55/6.73 (![X: $i] : (pred(succ(X)) = X)),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[61, 57])).
% 6.55/6.73 tff(63,plain,
% 6.55/6.73 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(pv1376)) = pv1376)),
% 6.55/6.73 inference(quant_inst,[status(thm)],[])).
% 6.55/6.73 tff(64,plain,
% 6.55/6.73 (pred(succ(pv1376)) = pv1376),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[63, 62])).
% 6.55/6.73 tff(65,plain,
% 6.55/6.73 (pv1376 = pred(succ(pv1376))),
% 6.55/6.73 inference(symmetry,[status(thm)],[64])).
% 6.55/6.73 tff(66,plain,
% 6.55/6.73 (pv1376 = minus(plus(n1, pv1376), n1)),
% 6.55/6.73 inference(transitivity,[status(thm)],[65, 56, 53])).
% 6.55/6.73 tff(67,plain,
% 6.55/6.73 (leq(F!15, pv1376) <=> leq(F!15, minus(plus(n1, pv1376), n1))),
% 6.55/6.73 inference(monotonicity,[status(thm)],[66])).
% 6.55/6.73 tff(68,plain,
% 6.55/6.73 (leq(F!15, minus(plus(n1, pv1376), n1)) <=> leq(F!15, pv1376)),
% 6.55/6.73 inference(symmetry,[status(thm)],[67])).
% 6.55/6.73 tff(69,assumption,(~((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(plus(n1, pv1376), n1))))), introduced(assumption)).
% 6.55/6.73 tff(70,plain,
% 6.55/6.73 (((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(plus(n1, pv1376), n1)))) | leq(F!15, minus(plus(n1, pv1376), n1))),
% 6.55/6.73 inference(tautology,[status(thm)],[])).
% 6.55/6.73 tff(71,plain,
% 6.55/6.73 (leq(F!15, minus(plus(n1, pv1376), n1))),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[70, 69])).
% 6.55/6.73 tff(72,plain,
% 6.55/6.73 (leq(F!15, pv1376)),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[71, 68])).
% 6.55/6.73 tff(73,plain,
% 6.55/6.73 (^[X: $i, Y: $i] : refl((leq(X, Y) <=> gt(succ(Y), X)) <=> (leq(X, Y) <=> gt(succ(Y), X)))),
% 6.55/6.73 inference(bind,[status(th)],[])).
% 6.55/6.73 tff(74,plain,
% 6.55/6.73 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 6.55/6.73 inference(quant_intro,[status(thm)],[73])).
% 6.55/6.73 tff(75,plain,
% 6.55/6.73 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(76,axiom,(![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_succ_gt_equiv')).
% 6.55/6.73 tff(77,plain,
% 6.55/6.73 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[76, 75])).
% 6.55/6.73 tff(78,plain,(
% 6.55/6.73 ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 6.55/6.73 inference(skolemize,[status(sab)],[77])).
% 6.55/6.73 tff(79,plain,
% 6.55/6.73 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[78, 74])).
% 6.55/6.73 tff(80,plain,
% 6.55/6.73 ((~![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))) | (leq(succ(pv1376), pv1376) <=> gt(succ(pv1376), succ(pv1376)))),
% 6.55/6.73 inference(quant_inst,[status(thm)],[])).
% 6.55/6.73 tff(81,plain,
% 6.55/6.73 (leq(succ(pv1376), pv1376) <=> gt(succ(pv1376), succ(pv1376))),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[80, 79])).
% 6.55/6.73 tff(82,plain,
% 6.55/6.73 (^[X: $i] : refl((~gt(X, X)) <=> (~gt(X, X)))),
% 6.55/6.73 inference(bind,[status(th)],[])).
% 6.55/6.73 tff(83,plain,
% 6.55/6.73 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 6.55/6.73 inference(quant_intro,[status(thm)],[82])).
% 6.55/6.73 tff(84,plain,
% 6.55/6.73 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(85,axiom,(![X: $i] : (~gt(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','irreflexivity_gt')).
% 6.55/6.73 tff(86,plain,
% 6.55/6.73 (![X: $i] : (~gt(X, X))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[85, 84])).
% 6.55/6.73 tff(87,plain,(
% 6.55/6.73 ![X: $i] : (~gt(X, X))),
% 6.55/6.73 inference(skolemize,[status(sab)],[86])).
% 6.55/6.73 tff(88,plain,
% 6.55/6.73 (![X: $i] : (~gt(X, X))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[87, 83])).
% 6.55/6.73 tff(89,plain,
% 6.55/6.73 ((~![X: $i] : (~gt(X, X))) | (~gt(succ(pv1376), succ(pv1376)))),
% 6.55/6.73 inference(quant_inst,[status(thm)],[])).
% 6.55/6.73 tff(90,plain,
% 6.55/6.73 (~gt(succ(pv1376), succ(pv1376))),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[89, 88])).
% 6.55/6.73 tff(91,plain,
% 6.55/6.73 ((~(leq(succ(pv1376), pv1376) <=> gt(succ(pv1376), succ(pv1376)))) | (~leq(succ(pv1376), pv1376)) | gt(succ(pv1376), succ(pv1376))),
% 6.55/6.73 inference(tautology,[status(thm)],[])).
% 6.55/6.73 tff(92,plain,
% 6.55/6.73 (~leq(succ(pv1376), pv1376)),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[91, 90, 81])).
% 6.55/6.73 tff(93,plain,
% 6.55/6.73 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(94,plain,
% 6.55/6.73 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 6.55/6.73 inference(bind,[status(th)],[])).
% 6.55/6.73 tff(95,plain,
% 6.55/6.73 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 6.55/6.73 inference(quant_intro,[status(thm)],[94])).
% 6.55/6.73 tff(96,plain,
% 6.55/6.73 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(97,plain,
% 6.55/6.73 (^[X: $i, Y: $i, Z: $i] : rewrite(((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)))),
% 6.55/6.73 inference(bind,[status(th)],[])).
% 6.55/6.73 tff(98,plain,
% 6.55/6.73 (![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 6.55/6.73 inference(quant_intro,[status(thm)],[97])).
% 6.55/6.73 tff(99,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 6.55/6.73 tff(100,plain,
% 6.55/6.73 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[99, 98])).
% 6.55/6.73 tff(101,plain,
% 6.55/6.73 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[100, 96])).
% 6.55/6.73 tff(102,plain,(
% 6.55/6.73 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 6.55/6.73 inference(skolemize,[status(sab)],[101])).
% 6.55/6.73 tff(103,plain,
% 6.55/6.73 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[102, 95])).
% 6.55/6.73 tff(104,plain,
% 6.55/6.73 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[103, 93])).
% 6.55/6.73 tff(105,plain,
% 6.55/6.73 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(pv1376), pv1376) | (~leq(F!15, pv1376)) | (~leq(succ(pv1376), F!15)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | leq(succ(pv1376), pv1376) | (~leq(F!15, pv1376)) | (~leq(succ(pv1376), F!15)))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(106,plain,
% 6.55/6.73 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(pv1376), pv1376) | (~leq(F!15, pv1376)) | (~leq(succ(pv1376), F!15)))),
% 6.55/6.73 inference(quant_inst,[status(thm)],[])).
% 6.55/6.73 tff(107,plain,
% 6.55/6.73 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | leq(succ(pv1376), pv1376) | (~leq(F!15, pv1376)) | (~leq(succ(pv1376), F!15))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[106, 105])).
% 6.55/6.73 tff(108,plain,
% 6.55/6.73 (~leq(succ(pv1376), F!15)),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[107, 104, 92, 72])).
% 6.55/6.73 tff(109,plain,
% 6.55/6.73 (~leq(succ(pv1376), succ(pred(F!15)))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[108, 42])).
% 6.55/6.73 tff(110,plain,
% 6.55/6.73 ((~(leq(succ(pv1376), succ(pred(F!15))) <=> leq(pv1376, pred(F!15)))) | leq(succ(pv1376), succ(pred(F!15))) | (~leq(pv1376, pred(F!15)))),
% 6.55/6.73 inference(tautology,[status(thm)],[])).
% 6.55/6.73 tff(111,plain,
% 6.55/6.73 (~leq(pv1376, pred(F!15))),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[110, 109, 31])).
% 6.55/6.73 tff(112,plain,
% 6.55/6.73 ((~(leq(pv1376, pred(F!15)) <=> gt(F!15, pv1376))) | leq(pv1376, pred(F!15)) | (~gt(F!15, pv1376))),
% 6.55/6.73 inference(tautology,[status(thm)],[])).
% 6.55/6.73 tff(113,plain,
% 6.55/6.73 (~gt(F!15, pv1376)),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[112, 111, 22])).
% 6.55/6.73 tff(114,plain,
% 6.55/6.73 (((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(plus(n1, pv1376), n1)))) | (~(a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init))),
% 6.55/6.73 inference(tautology,[status(thm)],[])).
% 6.55/6.73 tff(115,plain,
% 6.55/6.73 (~(a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init)),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[114, 69])).
% 6.55/6.73 tff(116,plain,
% 6.55/6.73 (![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL) <=> ![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(117,plain,
% 6.55/6.73 (![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL) <=> ![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(118,axiom,(![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','sel2_update_1')).
% 6.55/6.73 tff(119,plain,
% 6.55/6.73 (![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[118, 117])).
% 6.55/6.73 tff(120,plain,(
% 6.55/6.73 ![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 6.55/6.73 inference(skolemize,[status(sab)],[119])).
% 6.55/6.73 tff(121,plain,
% 6.55/6.73 (![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[120, 116])).
% 6.55/6.73 tff(122,plain,
% 6.55/6.73 ((~![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)) | (a_select2(tptp_update2(s_values7_init, pv1376, init), pv1376) = init)),
% 6.55/6.73 inference(quant_inst,[status(thm)],[])).
% 6.55/6.73 tff(123,plain,
% 6.55/6.73 (a_select2(tptp_update2(s_values7_init, pv1376, init), pv1376) = init),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[122, 121])).
% 6.55/6.73 tff(124,assumption,(pv1376 = F!15), introduced(assumption)).
% 6.55/6.73 tff(125,plain,
% 6.55/6.73 (F!15 = pv1376),
% 6.55/6.73 inference(symmetry,[status(thm)],[124])).
% 6.55/6.73 tff(126,plain,
% 6.55/6.73 (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = a_select2(tptp_update2(s_values7_init, pv1376, init), pv1376)),
% 6.55/6.73 inference(monotonicity,[status(thm)],[125])).
% 6.55/6.73 tff(127,plain,
% 6.55/6.73 (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init),
% 6.55/6.73 inference(transitivity,[status(thm)],[126, 123])).
% 6.55/6.73 tff(128,assumption,(~(a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init)), introduced(assumption)).
% 6.55/6.73 tff(129,plain,
% 6.55/6.73 ($false),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[128, 127])).
% 6.55/6.73 tff(130,plain,((~(pv1376 = F!15)) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init)), inference(lemma,lemma(discharge,[]))).
% 6.55/6.73 tff(131,plain,
% 6.55/6.73 (~(pv1376 = F!15)),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[130, 115])).
% 6.55/6.73 tff(132,plain,
% 6.55/6.73 (^[X: $i, Y: $i] : refl(((X = Y) | gt(Y, X) | gt(X, Y)) <=> ((X = Y) | gt(Y, X) | gt(X, Y)))),
% 6.55/6.73 inference(bind,[status(th)],[])).
% 6.55/6.73 tff(133,plain,
% 6.55/6.73 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | gt(X, Y)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | gt(X, Y))),
% 6.55/6.73 inference(quant_intro,[status(thm)],[132])).
% 6.55/6.73 tff(134,plain,
% 6.55/6.73 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | gt(X, Y)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | gt(X, Y))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(135,plain,
% 6.55/6.73 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((gt(X, Y) | gt(Y, X)) <=> (gt(Y, X) | gt(X, Y))), (((gt(X, Y) | gt(Y, X)) | (X = Y)) <=> ((gt(Y, X) | gt(X, Y)) | (X = Y)))), rewrite(((gt(Y, X) | gt(X, Y)) | (X = Y)) <=> ((X = Y) | gt(Y, X) | gt(X, Y))), (((gt(X, Y) | gt(Y, X)) | (X = Y)) <=> ((X = Y) | gt(Y, X) | gt(X, Y))))),
% 6.55/6.73 inference(bind,[status(th)],[])).
% 6.55/6.73 tff(136,plain,
% 6.55/6.73 (![X: $i, Y: $i] : ((gt(X, Y) | gt(Y, X)) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | gt(X, Y))),
% 6.55/6.73 inference(quant_intro,[status(thm)],[135])).
% 6.55/6.73 tff(137,axiom,(![X: $i, Y: $i] : ((gt(X, Y) | gt(Y, X)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','totality')).
% 6.55/6.73 tff(138,plain,
% 6.55/6.73 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | gt(X, Y))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[137, 136])).
% 6.55/6.73 tff(139,plain,
% 6.55/6.73 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | gt(X, Y))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[138, 134])).
% 6.55/6.73 tff(140,plain,(
% 6.55/6.73 ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | gt(X, Y))),
% 6.55/6.73 inference(skolemize,[status(sab)],[139])).
% 6.55/6.73 tff(141,plain,
% 6.55/6.73 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | gt(X, Y))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[140, 133])).
% 6.55/6.73 tff(142,plain,
% 6.55/6.73 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | gt(X, Y))) | ((pv1376 = F!15) | gt(F!15, pv1376) | gt(pv1376, F!15))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | gt(X, Y))) | (pv1376 = F!15) | gt(F!15, pv1376) | gt(pv1376, F!15))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(143,plain,
% 6.55/6.73 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | gt(X, Y))) | ((pv1376 = F!15) | gt(F!15, pv1376) | gt(pv1376, F!15))),
% 6.55/6.73 inference(quant_inst,[status(thm)],[])).
% 6.55/6.73 tff(144,plain,
% 6.55/6.73 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | gt(X, Y))) | (pv1376 = F!15) | gt(F!15, pv1376) | gt(pv1376, F!15)),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[143, 142])).
% 6.55/6.73 tff(145,plain,
% 6.55/6.73 ((pv1376 = F!15) | gt(F!15, pv1376) | gt(pv1376, F!15)),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[144, 141])).
% 6.55/6.73 tff(146,plain,
% 6.55/6.73 (gt(pv1376, F!15)),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[145, 131, 113])).
% 6.55/6.73 tff(147,plain,
% 6.55/6.73 ((~(leq(F!15, pred(pv1376)) <=> gt(pv1376, F!15))) | leq(F!15, pred(pv1376)) | (~gt(pv1376, F!15))),
% 6.55/6.73 inference(tautology,[status(thm)],[])).
% 6.55/6.73 tff(148,plain,
% 6.55/6.73 (leq(F!15, pred(pv1376))),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[147, 146, 20])).
% 6.55/6.73 tff(149,plain,
% 6.55/6.73 (leq(F!15, minus(pv1376, n1))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[148, 11])).
% 6.55/6.73 tff(150,plain,
% 6.55/6.73 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(151,plain,
% 6.55/6.73 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(152,plain,
% 6.55/6.73 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 6.55/6.73 inference(elim_unused_vars,[status(thm)],[])).
% 6.55/6.73 tff(153,plain,
% 6.55/6.73 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((~((~(I = U)) & (a_select2(X, U) = VAL))) | (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 6.55/6.73 inference(destructive_equality_resolution,[status(thm)],[])).
% 6.55/6.73 tff(154,plain,
% 6.55/6.73 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((~((~(I = U)) & (a_select2(X, U) = VAL))) | (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 6.55/6.73 inference(transitivity,[status(thm)],[153, 152])).
% 6.55/6.73 tff(155,plain,
% 6.55/6.73 (^[I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : rewrite((((~(I = U)) & (a_select2(X, U) = VAL)) => (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ((~((~(I = U)) & (a_select2(X, U) = VAL))) | (a_select2(tptp_update2(X, I, VAL2), U) = VAL)))),
% 6.55/6.73 inference(bind,[status(th)],[])).
% 6.55/6.73 tff(156,plain,
% 6.55/6.73 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : (((~(I = U)) & (a_select2(X, U) = VAL)) => (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((~((~(I = U)) & (a_select2(X, U) = VAL))) | (a_select2(tptp_update2(X, I, VAL2), U) = VAL))),
% 6.55/6.73 inference(quant_intro,[status(thm)],[155])).
% 6.55/6.73 tff(157,plain,
% 6.55/6.73 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : (((~(I = U)) & (a_select2(X, U) = VAL)) => (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 6.55/6.73 inference(transitivity,[status(thm)],[156, 154])).
% 6.55/6.73 tff(158,axiom,(![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : (((~(I = U)) & (a_select2(X, U) = VAL)) => (a_select2(tptp_update2(X, I, VAL2), U) = VAL))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','sel2_update_2')).
% 6.55/6.73 tff(159,plain,
% 6.55/6.73 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[158, 157])).
% 6.55/6.73 tff(160,plain,
% 6.55/6.73 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[159, 151])).
% 6.55/6.73 tff(161,plain,(
% 6.55/6.73 ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 6.55/6.73 inference(skolemize,[status(sab)],[160])).
% 6.55/6.73 tff(162,plain,
% 6.55/6.73 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[161, 150])).
% 6.55/6.73 tff(163,plain,
% 6.55/6.73 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = a_select2(s_values7_init, F!15)) | (pv1376 = F!15))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = a_select2(s_values7_init, F!15)) | (pv1376 = F!15))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(164,plain,
% 6.55/6.73 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = a_select2(s_values7_init, F!15)) | (pv1376 = F!15))),
% 6.55/6.73 inference(quant_inst,[status(thm)],[])).
% 6.55/6.73 tff(165,plain,
% 6.55/6.73 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = a_select2(s_values7_init, F!15)) | (pv1376 = F!15)),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[164, 163])).
% 6.55/6.73 tff(166,plain,
% 6.55/6.73 ((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = a_select2(s_values7_init, F!15)) | (pv1376 = F!15)),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[165, 162])).
% 6.55/6.73 tff(167,plain,
% 6.55/6.73 (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = a_select2(s_values7_init, F!15)),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[166, 131])).
% 6.55/6.73 tff(168,plain,
% 6.55/6.73 ((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init) <=> (a_select2(s_values7_init, F!15) = init)),
% 6.55/6.73 inference(monotonicity,[status(thm)],[167])).
% 6.55/6.73 tff(169,plain,
% 6.55/6.73 ((~(a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init)) <=> (~(a_select2(s_values7_init, F!15) = init))),
% 6.55/6.73 inference(monotonicity,[status(thm)],[168])).
% 6.55/6.73 tff(170,plain,
% 6.55/6.73 (~(a_select2(s_values7_init, F!15) = init)),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[115, 169])).
% 6.55/6.73 tff(171,plain,
% 6.55/6.73 (((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(plus(n1, pv1376), n1)))) | leq(n0, F!15)),
% 6.55/6.73 inference(tautology,[status(thm)],[])).
% 6.55/6.73 tff(172,plain,
% 6.55/6.73 (leq(n0, F!15)),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[171, 69])).
% 6.55/6.73 tff(173,plain,
% 6.55/6.73 (^[C: $i] : refl(((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))) <=> ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))))),
% 6.55/6.73 inference(bind,[status(th)],[])).
% 6.55/6.73 tff(174,plain,
% 6.55/6.73 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))) <=> ![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))),
% 6.55/6.73 inference(quant_intro,[status(thm)],[173])).
% 6.55/6.73 tff(175,plain,
% 6.55/6.73 (^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, C) & leq(C, minus(pv1376, n1))) <=> (~((~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))))), ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) <=> (~(~((~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))))))), rewrite((~(~((~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))))) <=> ((~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))), ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) <=> ((~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))))), (((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)) <=> (((~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)))), rewrite((((~leq(n0, C)) | (~leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)) <=> ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))), (((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)) <=> ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))))),
% 6.55/6.73 inference(bind,[status(th)],[])).
% 6.55/6.73 tff(176,plain,
% 6.55/6.73 (![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)) <=> ![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))),
% 6.55/6.73 inference(quant_intro,[status(thm)],[175])).
% 6.55/6.73 tff(177,plain,
% 6.55/6.73 (![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)) <=> ![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(178,plain,
% 6.55/6.73 ((~((((((init = init) & leq(n0, pv1376)) & leq(pv1376, n3)) & ![A: $i] : ((leq(n0, A) & leq(A, n2)) => ![B: $i] : ((leq(n0, B) & leq(B, n3)) => (a_select3(simplex7_init, B, A) = init)))) & ![C: $i] : ((leq(n0, C) & leq(C, minus(pv1376, n1))) => (a_select2(s_values7_init, C) = init))) => (((init = init) & ![D: $i] : ((leq(n0, D) & leq(D, n2)) => ![E: $i] : ((leq(n0, E) & leq(E, n3)) => (a_select3(simplex7_init, E, D) = init)))) & ![F: $i] : ((leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1))) => (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init))))) <=> (~((~(leq(n0, pv1376) & leq(pv1376, n3) & ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init))) & ![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)))) | (![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init)))))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(179,axiom,(~((((((init = init) & leq(n0, pv1376)) & leq(pv1376, n3)) & ![A: $i] : ((leq(n0, A) & leq(A, n2)) => ![B: $i] : ((leq(n0, B) & leq(B, n3)) => (a_select3(simplex7_init, B, A) = init)))) & ![C: $i] : ((leq(n0, C) & leq(C, minus(pv1376, n1))) => (a_select2(s_values7_init, C) = init))) => (((init = init) & ![D: $i] : ((leq(n0, D) & leq(D, n2)) => ![E: $i] : ((leq(n0, E) & leq(E, n3)) => (a_select3(simplex7_init, E, D) = init)))) & ![F: $i] : ((leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1))) => (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gauss_init_0045')).
% 6.55/6.73 tff(180,plain,
% 6.55/6.73 (~((~(leq(n0, pv1376) & leq(pv1376, n3) & ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init))) & ![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init)))) | (![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init))))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[179, 178])).
% 6.55/6.73 tff(181,plain,
% 6.55/6.73 (leq(n0, pv1376) & leq(pv1376, n3) & ![A: $i] : ((~(leq(n0, A) & leq(A, n2))) | ![B: $i] : ((~(leq(n0, B) & leq(B, n3))) | (a_select3(simplex7_init, B, A) = init))) & ![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init))),
% 6.55/6.73 inference(or_elim,[status(thm)],[180])).
% 6.55/6.73 tff(182,plain,
% 6.55/6.73 (![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init))),
% 6.55/6.73 inference(and_elim,[status(thm)],[181])).
% 6.55/6.73 tff(183,plain,
% 6.55/6.73 (![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[182, 177])).
% 6.55/6.73 tff(184,plain,(
% 6.55/6.73 ![C: $i] : ((~(leq(n0, C) & leq(C, minus(pv1376, n1)))) | (a_select2(s_values7_init, C) = init))),
% 6.55/6.73 inference(skolemize,[status(sab)],[183])).
% 6.55/6.73 tff(185,plain,
% 6.55/6.73 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[184, 176])).
% 6.55/6.73 tff(186,plain,
% 6.55/6.73 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[185, 174])).
% 6.55/6.73 tff(187,plain,
% 6.55/6.73 (((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))) | ((~leq(n0, F!15)) | (a_select2(s_values7_init, F!15) = init) | (~leq(F!15, minus(pv1376, n1))))) <=> ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))) | (~leq(n0, F!15)) | (a_select2(s_values7_init, F!15) = init) | (~leq(F!15, minus(pv1376, n1))))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(188,plain,
% 6.55/6.73 (((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1)))) <=> ((~leq(n0, F!15)) | (a_select2(s_values7_init, F!15) = init) | (~leq(F!15, minus(pv1376, n1))))),
% 6.55/6.73 inference(rewrite,[status(thm)],[])).
% 6.55/6.73 tff(189,plain,
% 6.55/6.73 (((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))) | ((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1))))) <=> ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))) | ((~leq(n0, F!15)) | (a_select2(s_values7_init, F!15) = init) | (~leq(F!15, minus(pv1376, n1)))))),
% 6.55/6.73 inference(monotonicity,[status(thm)],[188])).
% 6.55/6.73 tff(190,plain,
% 6.55/6.73 (((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))) | ((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1))))) <=> ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))) | (~leq(n0, F!15)) | (a_select2(s_values7_init, F!15) = init) | (~leq(F!15, minus(pv1376, n1))))),
% 6.55/6.73 inference(transitivity,[status(thm)],[189, 187])).
% 6.55/6.73 tff(191,plain,
% 6.55/6.73 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))) | ((a_select2(s_values7_init, F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(pv1376, n1))))),
% 6.55/6.73 inference(quant_inst,[status(thm)],[])).
% 6.55/6.73 tff(192,plain,
% 6.55/6.73 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(n0, C)) | (~leq(C, minus(pv1376, n1))))) | (~leq(n0, F!15)) | (a_select2(s_values7_init, F!15) = init) | (~leq(F!15, minus(pv1376, n1)))),
% 6.55/6.73 inference(modus_ponens,[status(thm)],[191, 190])).
% 6.55/6.73 tff(193,plain,
% 6.55/6.73 ((a_select2(s_values7_init, F!15) = init) | (~leq(F!15, minus(pv1376, n1)))),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[192, 186, 172])).
% 6.55/6.73 tff(194,plain,
% 6.55/6.73 ($false),
% 6.55/6.73 inference(unit_resolution,[status(thm)],[193, 170, 149])).
% 6.55/6.74 tff(195,plain,((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(plus(n1, pv1376), n1)))), inference(lemma,lemma(discharge,[]))).
% 6.55/6.74 tff(196,plain,
% 6.55/6.74 (((~((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(plus(n1, pv1376), n1))))) | (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2))))) <=> ((~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2)))) | (~((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(plus(n1, pv1376), n1))))))),
% 6.55/6.74 inference(rewrite,[status(thm)],[])).
% 6.55/6.74 tff(197,plain,
% 6.55/6.74 ((leq(n0, D!13) & leq(D!13, n2) & (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3))))) <=> (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2))))),
% 6.55/6.74 inference(rewrite,[status(thm)],[])).
% 6.55/6.74 tff(198,plain,
% 6.55/6.74 ((~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init))) <=> (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3))))),
% 6.55/6.74 inference(rewrite,[status(thm)],[])).
% 6.55/6.74 tff(199,plain,
% 6.55/6.74 ((leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) <=> (leq(n0, D!13) & leq(D!13, n2) & (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)))))),
% 6.55/6.74 inference(monotonicity,[status(thm)],[198])).
% 6.55/6.74 tff(200,plain,
% 6.55/6.74 ((leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) <=> (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2))))),
% 6.55/6.74 inference(transitivity,[status(thm)],[199, 197])).
% 6.55/6.74 tff(201,plain,
% 6.55/6.74 ((~((~(leq(n0, F!15) & leq(F!15, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init))) <=> (~((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(plus(n1, pv1376), n1)))))),
% 6.55/6.74 inference(rewrite,[status(thm)],[])).
% 6.55/6.74 tff(202,plain,
% 6.55/6.74 (((~((~(leq(n0, F!15) & leq(F!15, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init))) | (leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init))))) <=> ((~((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(plus(n1, pv1376), n1))))) | (~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2)))))),
% 6.55/6.74 inference(monotonicity,[status(thm)],[201, 200])).
% 6.55/6.74 tff(203,plain,
% 6.55/6.74 (((~((~(leq(n0, F!15) & leq(F!15, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init))) | (leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init))))) <=> ((~((a_select3(simplex7_init, E!14, D!13) = init) | (~leq(n0, E!14)) | (~leq(E!14, n3)) | (~leq(n0, D!13)) | (~leq(D!13, n2)))) | (~((a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init) | (~leq(n0, F!15)) | (~leq(F!15, minus(plus(n1, pv1376), n1))))))),
% 6.55/6.74 inference(transitivity,[status(thm)],[202, 196])).
% 6.55/6.74 tff(204,plain,
% 6.55/6.74 (((leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) | (~((~(leq(n0, F!15) & leq(F!15, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init)))) <=> ((~((~(leq(n0, F!15) & leq(F!15, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init))) | (leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))))),
% 6.55/6.74 inference(rewrite,[status(thm)],[])).
% 6.55/6.74 tff(205,plain,
% 6.55/6.74 (((leq(n0, D!13) & leq(D!13, n2)) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) <=> (leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init))))),
% 6.55/6.74 inference(rewrite,[status(thm)],[])).
% 6.55/6.74 tff(206,plain,
% 6.55/6.74 ((((leq(n0, D!13) & leq(D!13, n2)) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) | (~((~(leq(n0, F!15) & leq(F!15, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init)))) <=> ((leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) | (~((~(leq(n0, F!15) & leq(F!15, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init))))),
% 6.55/6.74 inference(monotonicity,[status(thm)],[205])).
% 6.55/6.74 tff(207,plain,
% 6.55/6.74 ((((leq(n0, D!13) & leq(D!13, n2)) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))) | (~((~(leq(n0, F!15) & leq(F!15, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init)))) <=> ((~((~(leq(n0, F!15) & leq(F!15, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F!15) = init))) | (leq(n0, D!13) & leq(D!13, n2) & (~((~(leq(n0, E!14) & leq(E!14, n3))) | (a_select3(simplex7_init, E!14, D!13) = init)))))),
% 6.55/6.74 inference(transitivity,[status(thm)],[206, 204])).
% 6.55/6.74 tff(208,plain,
% 6.55/6.74 ((![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init))) <=> (![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init)))),
% 6.55/6.74 inference(rewrite,[status(thm)],[])).
% 6.55/6.74 tff(209,plain,
% 6.55/6.74 ((~(![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init)))) <=> (~(![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init))))),
% 6.55/6.74 inference(monotonicity,[status(thm)],[208])).
% 6.55/6.74 tff(210,plain,
% 6.55/6.74 ((~(![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init)))) <=> (~(![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init))))),
% 6.55/6.74 inference(rewrite,[status(thm)],[])).
% 6.55/6.74 tff(211,plain,
% 6.55/6.74 (~(![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init)))),
% 6.55/6.74 inference(or_elim,[status(thm)],[180])).
% 6.55/6.74 tff(212,plain,
% 6.55/6.74 (~(![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init)))),
% 6.55/6.74 inference(modus_ponens,[status(thm)],[211, 209])).
% 6.55/6.74 tff(213,plain,
% 6.55/6.74 (~(![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init)))),
% 6.55/6.74 inference(modus_ponens,[status(thm)],[212, 210])).
% 6.55/6.74 tff(214,plain,
% 6.55/6.74 (~(![D: $i] : ((~(leq(n0, D) & leq(D, n2))) | ![E: $i] : ((~(leq(n0, E) & leq(E, n3))) | (a_select3(simplex7_init, E, D) = init))) & ![F: $i] : ((~(leq(n0, F) & leq(F, minus(plus(n1, pv1376), n1)))) | (a_select2(tptp_update2(s_values7_init, pv1376, init), F) = init)))),
% 6.55/6.74 inference(modus_ponens,[status(thm)],[213, 209])).
% 6.55/6.74 unexpected number of arguments: (let ((a!1 (forall ((D $i))
% 6.55/6.74 (let ((a!1 (forall ((E $i))
% 6.55/6.74 (or (not (and (leq n0 E) (leq E n3)))
% 6.55/6.74 (= (a_select3 simplex7_init E D) init)))))
% 6.55/6.74 (or (not (and (leq n0 D) (leq D n2))) a!1))))
% 6.55/6.74 (a!2 (forall ((E $i))
% 6.55/6.74 (or (not (and (leq n0 E) (leq E n3)))
% 6.55/6.74 (= (a_select3 simplex7_init E D!13) init))))
% 6.55/6.74 (a!4 (refl (~ (and (leq n0 D!13) (leq D!13 n2))
% 6.55/6.74 (and (leq n0 D!13) (leq D!13 n2)))))
% 6.55/6.74 (a!5 (or (not (and (leq n0 E!14) (leq E!14 n3)))
% 6.55/6.74 (= (a_select3 simplex7_init E!14 D!13) init)))
% 6.55/6.74 (a!9 (forall ((F $i))
% 6.55/6.74 (let ((a!1 (and (leq n0 F) (leq F (minus (plus n1 pv1376) n1)))))
% 6.55/6.74 (or (not a!1)
% 6.55/6.74 (= (a_select2 (tptp_update2 s_values7_init pv1376 init) F)
% 6.55/6.74 init)))))
% 6.55/6.74 (a!10 (and (leq n0 F!15) (leq F!15 (minus (plus n1 pv1376) n1)))))
% 6.55/6.74 (let ((a!3 (or (not (and (leq n0 D!13) (leq D!13 n2))) a!2))
% 6.55/6.74 (a!6 (and (and (leq n0 D!13) (leq D!13 n2)) (not a!5)))
% 6.55/6.74 (a!11 (or (not a!10)
% 6.55/6.74 (= (a_select2 (tptp_update2 s_values7_init pv1376 init) F!15)
% 6.55/6.74 init))))
% 6.55/6.74 (let ((a!7 (nnf-neg a!4 (sk (~ (not a!2) (not a!5))) (~ (not a!3) a!6))))
% 6.55/6.74 (let ((a!8 (trans (sk (~ (not a!1) (not a!3))) a!7 (~ (not a!1) a!6))))
% 6.55/6.74 (nnf-neg a!8
% 6.55/6.74 (sk (~ (not a!9) (not a!11)))
% 6.55/6.74 (~ (not (and a!1 a!9)) (or a!6 (not a!11))))))))
% 6.55/6.74 Proof display could not be completed: unexpected number of arguments
% 6.55/6.78 % E exiting
%------------------------------------------------------------------------------