TSTP Solution File: SWV042+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV042+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 : Thu Sep 29 15:09:44 EDT 2022
% Result : Theorem 0.16s 0.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWV042+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.09/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n027.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun Sep 4 01:26:06 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.16/0.43 % SZS status Theorem
% 0.16/0.43 % SZS output start Proof
% 0.16/0.43 tff(leq_type, type, (
% 0.16/0.43 leq: ( $i * $i ) > $o)).
% 0.16/0.43 tff(succ_type, type, (
% 0.16/0.43 succ: $i > $i)).
% 0.16/0.43 tff(tptp_minus_1_type, type, (
% 0.16/0.43 tptp_minus_1: $i)).
% 0.16/0.43 tff(init_type, type, (
% 0.16/0.43 init: $i)).
% 0.16/0.43 tff(a_select3_type, type, (
% 0.16/0.43 a_select3: ( $i * $i * $i ) > $i)).
% 0.16/0.43 tff(tptp_fun_E_13_type, type, (
% 0.16/0.43 tptp_fun_E_13: $i)).
% 0.16/0.43 tff(simplex7_init_type, type, (
% 0.16/0.43 simplex7_init: $i)).
% 0.16/0.43 tff(tptp_fun_F_14_type, type, (
% 0.16/0.43 tptp_fun_F_14: $i)).
% 0.16/0.43 tff(tptp_fun_H_16_type, type, (
% 0.16/0.43 tptp_fun_H_16: $i)).
% 0.16/0.43 tff(a_select2_type, type, (
% 0.16/0.43 a_select2: ( $i * $i ) > $i)).
% 0.16/0.43 tff(s_center7_init_type, type, (
% 0.16/0.43 s_center7_init: $i)).
% 0.16/0.43 tff(minus_type, type, (
% 0.16/0.43 minus: ( $i * $i ) > $i)).
% 0.16/0.43 tff(plus_type, type, (
% 0.16/0.43 plus: ( $i * $i ) > $i)).
% 0.16/0.43 tff(pred_type, type, (
% 0.16/0.43 pred: $i > $i)).
% 0.16/0.43 tff(n1_type, type, (
% 0.16/0.43 n1: $i)).
% 0.16/0.43 tff(n2_type, type, (
% 0.16/0.43 n2: $i)).
% 0.16/0.43 tff(n0_type, type, (
% 0.16/0.43 n0: $i)).
% 0.16/0.43 tff(pvar1402_init_type, type, (
% 0.16/0.43 pvar1402_init: $i)).
% 0.16/0.43 tff(pvar1401_init_type, type, (
% 0.16/0.43 pvar1401_init: $i)).
% 0.16/0.43 tff(pvar1400_init_type, type, (
% 0.16/0.43 pvar1400_init: $i)).
% 0.16/0.43 tff(gt_type, type, (
% 0.16/0.43 gt: ( $i * $i ) > $o)).
% 0.16/0.43 tff(loopcounter_type, type, (
% 0.16/0.43 loopcounter: $i)).
% 0.16/0.43 tff(s_values7_init_type, type, (
% 0.16/0.43 s_values7_init: $i)).
% 0.16/0.43 tff(n3_type, type, (
% 0.16/0.43 n3: $i)).
% 0.16/0.43 tff(tptp_fun_G_15_type, type, (
% 0.16/0.43 tptp_fun_G_15: $i)).
% 0.16/0.43 tff(1,plain,
% 0.16/0.43 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(2,plain,
% 0.16/0.43 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(3,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 0.16/0.43 tff(4,plain,
% 0.16/0.43 (![X: $i] : (pred(succ(X)) = X)),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.16/0.43 tff(5,plain,(
% 0.16/0.43 ![X: $i] : (pred(succ(X)) = X)),
% 0.16/0.43 inference(skolemize,[status(sab)],[4])).
% 0.16/0.43 tff(6,plain,
% 0.16/0.43 (![X: $i] : (pred(succ(X)) = X)),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.16/0.43 tff(7,plain,
% 0.16/0.43 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(succ(succ(succ(tptp_minus_1))))) = succ(succ(succ(tptp_minus_1))))),
% 0.16/0.43 inference(quant_inst,[status(thm)],[])).
% 0.16/0.43 tff(8,plain,
% 0.16/0.43 (pred(succ(succ(succ(succ(tptp_minus_1))))) = succ(succ(succ(tptp_minus_1)))),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.16/0.43 tff(9,plain,
% 0.16/0.43 (^[X: $i] : refl((minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.16/0.43 inference(bind,[status(th)],[])).
% 0.16/0.43 tff(10,plain,
% 0.16/0.43 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.16/0.43 inference(quant_intro,[status(thm)],[9])).
% 0.16/0.43 tff(11,plain,
% 0.16/0.43 (^[X: $i] : rewrite((minus(X, n1) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.16/0.43 inference(bind,[status(th)],[])).
% 0.16/0.43 tff(12,plain,
% 0.16/0.43 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.16/0.43 inference(quant_intro,[status(thm)],[11])).
% 0.16/0.43 tff(13,plain,
% 0.16/0.43 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(14,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 0.16/0.43 tff(15,plain,
% 0.16/0.43 (![X: $i] : (minus(X, n1) = pred(X))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.16/0.43 tff(16,plain,
% 0.16/0.43 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.16/0.43 tff(17,plain,(
% 0.16/0.43 ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.16/0.43 inference(skolemize,[status(sab)],[16])).
% 0.16/0.43 tff(18,plain,
% 0.16/0.43 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.16/0.43 tff(19,plain,
% 0.16/0.43 ((~![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))) | (minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))) = pred(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.16/0.43 inference(quant_inst,[status(thm)],[])).
% 0.16/0.43 tff(20,plain,
% 0.16/0.43 (minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))) = pred(succ(succ(succ(succ(tptp_minus_1)))))),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.16/0.43 tff(21,plain,
% 0.16/0.43 (^[X: $i] : refl((plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X))) <=> (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X))))),
% 0.16/0.43 inference(bind,[status(th)],[])).
% 0.16/0.43 tff(22,plain,
% 0.16/0.43 (![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X))) <=> ![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))),
% 0.16/0.43 inference(quant_intro,[status(thm)],[21])).
% 0.16/0.43 tff(23,plain,
% 0.16/0.43 (^[X: $i] : rewrite((plus(X, n2) = succ(succ(X))) <=> (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X))))),
% 0.16/0.43 inference(bind,[status(th)],[])).
% 0.16/0.43 tff(24,plain,
% 0.16/0.43 (![X: $i] : (plus(X, n2) = succ(succ(X))) <=> ![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))),
% 0.16/0.43 inference(quant_intro,[status(thm)],[23])).
% 0.16/0.43 tff(25,plain,
% 0.16/0.43 (![X: $i] : (plus(X, n2) = succ(succ(X))) <=> ![X: $i] : (plus(X, n2) = succ(succ(X)))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(26,axiom,(![X: $i] : (plus(X, n2) = succ(succ(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','succ_plus_2_r')).
% 0.16/0.43 tff(27,plain,
% 0.16/0.43 (![X: $i] : (plus(X, n2) = succ(succ(X)))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.16/0.43 tff(28,plain,
% 0.16/0.43 (![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.16/0.43 tff(29,plain,(
% 0.16/0.43 ![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))),
% 0.16/0.43 inference(skolemize,[status(sab)],[28])).
% 0.16/0.43 tff(30,plain,
% 0.16/0.43 (![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.16/0.43 tff(31,plain,
% 0.16/0.43 ((~![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))) | (plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))) = succ(succ(succ(succ(tptp_minus_1)))))),
% 0.16/0.43 inference(quant_inst,[status(thm)],[])).
% 0.16/0.43 tff(32,plain,
% 0.16/0.43 (plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))) = succ(succ(succ(succ(tptp_minus_1))))),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.16/0.43 tff(33,plain,
% 0.16/0.43 (minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))) = minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))),
% 0.16/0.43 inference(monotonicity,[status(thm)],[32])).
% 0.16/0.43 tff(34,plain,
% 0.16/0.43 (minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))) = succ(succ(succ(tptp_minus_1)))),
% 0.16/0.43 inference(transitivity,[status(thm)],[33, 20, 8])).
% 0.16/0.43 tff(35,plain,
% 0.16/0.43 (leq(H!16, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) <=> leq(H!16, succ(succ(succ(tptp_minus_1))))),
% 0.16/0.43 inference(monotonicity,[status(thm)],[34])).
% 0.16/0.43 tff(36,plain,
% 0.16/0.43 (leq(H!16, succ(succ(succ(tptp_minus_1)))) <=> leq(H!16, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.16/0.43 inference(symmetry,[status(thm)],[35])).
% 0.16/0.43 tff(37,assumption,(~((a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, succ(succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.16/0.43 tff(38,plain,
% 0.16/0.43 (((a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, succ(succ(succ(tptp_minus_1)))))) | leq(H!16, succ(succ(succ(tptp_minus_1))))),
% 0.16/0.43 inference(tautology,[status(thm)],[])).
% 0.16/0.43 tff(39,plain,
% 0.16/0.43 (leq(H!16, succ(succ(succ(tptp_minus_1))))),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.16/0.43 tff(40,plain,
% 0.16/0.43 (leq(H!16, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.16/0.43 tff(41,plain,
% 0.16/0.43 (((a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, succ(succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), H!16)),
% 0.16/0.43 inference(tautology,[status(thm)],[])).
% 0.16/0.43 tff(42,plain,
% 0.16/0.43 (leq(succ(tptp_minus_1), H!16)),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[41, 37])).
% 0.16/0.43 tff(43,plain,
% 0.16/0.43 (((a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, succ(succ(succ(tptp_minus_1)))))) | (~(a_select2(s_center7_init, H!16) = init))),
% 0.16/0.43 inference(tautology,[status(thm)],[])).
% 0.16/0.43 tff(44,plain,
% 0.16/0.43 (~(a_select2(s_center7_init, H!16) = init)),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[43, 37])).
% 0.16/0.43 tff(45,plain,
% 0.16/0.43 (^[D: $i] : refl(((a_select2(s_center7_init, D) = init) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) <=> ((a_select2(s_center7_init, D) = init) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))),
% 0.16/0.43 inference(bind,[status(th)],[])).
% 0.16/0.43 tff(46,plain,
% 0.16/0.43 (![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) <=> ![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.16/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.16/0.43 tff(47,plain,
% 0.16/0.43 (^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), D) & leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), D) & leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), D) & leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), D) & leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, D) = init)) <=> (((~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, D) = init)))), rewrite((((~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, D) = init)) <=> ((a_select2(s_center7_init, D) = init) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))), (((~(leq(succ(tptp_minus_1), D) & leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, D) = init)) <=> ((a_select2(s_center7_init, D) = init) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))))),
% 0.16/0.43 inference(bind,[status(th)],[])).
% 0.16/0.43 tff(48,plain,
% 0.16/0.43 (![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, D) = init)) <=> ![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.16/0.43 inference(quant_intro,[status(thm)],[47])).
% 0.16/0.43 tff(49,plain,
% 0.16/0.43 (^[D: $i] : rewrite(((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init)) <=> ((~(leq(succ(tptp_minus_1), D) & leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, D) = init)))),
% 0.16/0.44 inference(bind,[status(th)],[])).
% 0.16/0.44 tff(50,plain,
% 0.16/0.44 (![D: $i] : ((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init)) <=> ![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, D) = init))),
% 0.16/0.44 inference(quant_intro,[status(thm)],[49])).
% 0.16/0.44 tff(51,plain,
% 0.16/0.44 (![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))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(52,plain,
% 0.16/0.44 ((~((((![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))))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(53,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/sandbox2/benchmark/theBenchmark.p','gauss_init_0081')).
% 0.16/0.44 tff(54,plain,
% 0.16/0.44 (~((~(![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)))))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.16/0.44 tff(55,plain,
% 0.16/0.44 (![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)))),
% 0.16/0.44 inference(or_elim,[status(thm)],[54])).
% 0.16/0.44 tff(56,plain,
% 0.16/0.44 (![D: $i] : ((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init))),
% 0.16/0.44 inference(and_elim,[status(thm)],[55])).
% 0.16/0.44 tff(57,plain,
% 0.16/0.44 (![D: $i] : ((~(leq(n0, D) & leq(D, minus(plus(n1, n2), n1)))) | (a_select2(s_center7_init, D) = init))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[56, 51])).
% 0.16/0.44 tff(58,plain,
% 0.16/0.44 (![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, D) = init))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.16/0.44 tff(59,plain,(
% 0.16/0.44 ![D: $i] : ((~(leq(succ(tptp_minus_1), D) & leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, D) = init))),
% 0.16/0.44 inference(skolemize,[status(sab)],[58])).
% 0.16/0.44 tff(60,plain,
% 0.16/0.44 (![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[59, 48])).
% 0.16/0.44 tff(61,plain,
% 0.16/0.44 (![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[60, 46])).
% 0.16/0.44 tff(62,plain,
% 0.16/0.44 (((~![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | ((a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) <=> ((~![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(63,plain,
% 0.16/0.44 ((~![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | ((a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.16/0.44 inference(quant_inst,[status(thm)],[])).
% 0.16/0.44 tff(64,plain,
% 0.16/0.44 ((~![D: $i] : ((a_select2(s_center7_init, D) = init) | (~leq(succ(tptp_minus_1), D)) | (~leq(D, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.16/0.44 tff(65,plain,
% 0.16/0.44 (~leq(H!16, minus(plus(succ(succ(tptp_minus_1)), succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[64, 61, 44, 42])).
% 0.16/0.45 tff(66,plain,
% 0.16/0.45 ($false),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[65, 40])).
% 0.16/0.45 tff(67,plain,((a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, succ(succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.45 tff(68,assumption,(~((a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1)))))))), introduced(assumption)).
% 0.16/0.45 tff(69,plain,
% 0.16/0.45 (((a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))) | leq(G!15, succ(succ(succ(succ(tptp_minus_1)))))),
% 0.16/0.45 inference(tautology,[status(thm)],[])).
% 0.16/0.45 tff(70,plain,
% 0.16/0.45 (leq(G!15, succ(succ(succ(succ(tptp_minus_1)))))),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.16/0.45 tff(71,plain,
% 0.16/0.45 (((a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))) | leq(succ(tptp_minus_1), G!15)),
% 0.16/0.45 inference(tautology,[status(thm)],[])).
% 0.16/0.45 tff(72,plain,
% 0.16/0.45 (leq(succ(tptp_minus_1), G!15)),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.16/0.45 tff(73,plain,
% 0.16/0.45 (((a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))) | (~(a_select2(s_values7_init, G!15) = init))),
% 0.16/0.45 inference(tautology,[status(thm)],[])).
% 0.16/0.45 tff(74,plain,
% 0.16/0.45 (~(a_select2(s_values7_init, G!15) = init)),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[73, 68])).
% 0.16/0.45 tff(75,plain,
% 0.16/0.45 (^[C: $i] : refl(((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))) <=> ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.16/0.45 inference(bind,[status(th)],[])).
% 0.16/0.45 tff(76,plain,
% 0.16/0.45 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))) <=> ![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.16/0.45 inference(quant_intro,[status(thm)],[75])).
% 0.16/0.45 tff(77,plain,
% 0.16/0.45 (^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1)))))) <=> (~((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))))), ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) <=> (~(~((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))))), (((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init)) <=> (((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init)))), rewrite((((~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init)) <=> ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init)) <=> ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.16/0.45 inference(bind,[status(th)],[])).
% 0.16/0.45 tff(78,plain,
% 0.16/0.45 (![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init)) <=> ![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.16/0.45 inference(quant_intro,[status(thm)],[77])).
% 0.16/0.45 tff(79,plain,
% 0.16/0.45 (^[C: $i] : rewrite(((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init)) <=> ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init)))),
% 0.16/0.45 inference(bind,[status(th)],[])).
% 0.16/0.45 tff(80,plain,
% 0.16/0.45 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init)) <=> ![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init))),
% 0.16/0.45 inference(quant_intro,[status(thm)],[79])).
% 0.16/0.45 tff(81,plain,
% 0.16/0.45 (![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))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(82,plain,
% 0.16/0.45 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 0.16/0.45 inference(and_elim,[status(thm)],[55])).
% 0.16/0.45 tff(83,plain,
% 0.16/0.45 (![C: $i] : ((~(leq(n0, C) & leq(C, n3))) | (a_select2(s_values7_init, C) = init))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.16/0.45 tff(84,plain,
% 0.16/0.45 (![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.16/0.45 tff(85,plain,(
% 0.16/0.45 ![C: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, C) = init))),
% 0.16/0.45 inference(skolemize,[status(sab)],[84])).
% 0.16/0.45 tff(86,plain,
% 0.16/0.45 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.16/0.45 tff(87,plain,
% 0.16/0.45 (![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.16/0.45 tff(88,plain,
% 0.16/0.45 (((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))) | ((a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1)))))))) <=> ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(89,plain,
% 0.16/0.45 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))) | ((a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.16/0.45 inference(quant_inst,[status(thm)],[])).
% 0.16/0.45 tff(90,plain,
% 0.16/0.45 ((~![C: $i] : ((a_select2(s_values7_init, C) = init) | (~leq(succ(tptp_minus_1), C)) | (~leq(C, succ(succ(succ(succ(tptp_minus_1)))))))) | (a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.16/0.45 tff(91,plain,
% 0.16/0.45 ($false),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[90, 87, 74, 72, 70])).
% 0.16/0.45 tff(92,plain,((a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.45 tff(93,plain,
% 0.16/0.45 (((~((a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1)))))))) | (~((a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, succ(succ(succ(tptp_minus_1))))))) | (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(succ(tptp_minus_1), F!14)) | (~leq(F!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(tptp_minus_1)))))))) <=> ((~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(succ(tptp_minus_1), F!14)) | (~leq(F!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(tptp_minus_1))))))) | (~((a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1)))))))) | (~((a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, succ(succ(succ(tptp_minus_1))))))))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(94,plain,
% 0.16/0.45 ((leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))) & (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(succ(tptp_minus_1), F!14)) | (~leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))))) <=> (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(succ(tptp_minus_1), F!14)) | (~leq(F!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(tptp_minus_1)))))))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(95,plain,
% 0.16/0.45 ((~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init))) <=> (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(succ(tptp_minus_1), F!14)) | (~leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(96,plain,
% 0.16/0.45 ((leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init)))) <=> (leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))) & (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(succ(tptp_minus_1), F!14)) | (~leq(F!14, succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.16/0.45 inference(monotonicity,[status(thm)],[95])).
% 0.16/0.45 tff(97,plain,
% 0.16/0.45 ((leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init)))) <=> (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(succ(tptp_minus_1), F!14)) | (~leq(F!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(tptp_minus_1)))))))),
% 0.16/0.45 inference(transitivity,[status(thm)],[96, 94])).
% 0.16/0.45 tff(98,plain,
% 0.16/0.45 ((~((~(leq(succ(tptp_minus_1), H!16) & leq(H!16, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H!16) = init))) <=> (~((a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, succ(succ(succ(tptp_minus_1)))))))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(99,plain,
% 0.16/0.45 ((~((~(leq(succ(tptp_minus_1), G!15) & leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G!15) = init))) <=> (~((a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(100,plain,
% 0.16/0.45 (((~((~(leq(succ(tptp_minus_1), G!15) & leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(succ(tptp_minus_1), H!16) & leq(H!16, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H!16) = init))) | (leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init))))) <=> ((~((a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1)))))))) | (~((a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, succ(succ(succ(tptp_minus_1))))))) | (~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(succ(tptp_minus_1), F!14)) | (~leq(F!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(tptp_minus_1))))))))),
% 0.16/0.45 inference(monotonicity,[status(thm)],[99, 98, 97])).
% 0.16/0.46 tff(101,plain,
% 0.16/0.46 (((~((~(leq(succ(tptp_minus_1), G!15) & leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(succ(tptp_minus_1), H!16) & leq(H!16, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H!16) = init))) | (leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init))))) <=> ((~((a_select3(simplex7_init, F!14, E!13) = init) | (~leq(succ(tptp_minus_1), F!14)) | (~leq(F!14, succ(succ(succ(succ(tptp_minus_1)))))) | (~leq(succ(tptp_minus_1), E!13)) | (~leq(E!13, succ(succ(succ(tptp_minus_1))))))) | (~((a_select2(s_values7_init, G!15) = init) | (~leq(succ(tptp_minus_1), G!15)) | (~leq(G!15, succ(succ(succ(succ(tptp_minus_1)))))))) | (~((a_select2(s_center7_init, H!16) = init) | (~leq(succ(tptp_minus_1), H!16)) | (~leq(H!16, succ(succ(succ(tptp_minus_1))))))))),
% 0.16/0.46 inference(transitivity,[status(thm)],[100, 93])).
% 0.16/0.46 tff(102,plain,
% 0.16/0.46 (((leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init)))) | (~((~(leq(succ(tptp_minus_1), G!15) & leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(succ(tptp_minus_1), H!16) & leq(H!16, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H!16) = init)))) <=> ((~((~(leq(succ(tptp_minus_1), G!15) & leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(succ(tptp_minus_1), H!16) & leq(H!16, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H!16) = init))) | (leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init)))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(103,plain,
% 0.16/0.46 (((leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init)))) <=> (leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(104,plain,
% 0.16/0.46 ((~(~(leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1))))))) <=> (leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(105,plain,
% 0.16/0.46 (((~(~(leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init)))) <=> ((leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init))))),
% 0.16/0.46 inference(monotonicity,[status(thm)],[104])).
% 0.16/0.46 tff(106,plain,
% 0.16/0.46 (((~(~(leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init)))) <=> (leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init))))),
% 0.16/0.46 inference(transitivity,[status(thm)],[105, 103])).
% 0.16/0.46 tff(107,plain,
% 0.16/0.46 ((((~(~(leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init)))) | (~((~(leq(succ(tptp_minus_1), G!15) & leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(succ(tptp_minus_1), H!16) & leq(H!16, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H!16) = init)))) <=> ((leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init)))) | (~((~(leq(succ(tptp_minus_1), G!15) & leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(succ(tptp_minus_1), H!16) & leq(H!16, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H!16) = init))))),
% 0.16/0.46 inference(monotonicity,[status(thm)],[106])).
% 0.16/0.46 tff(108,plain,
% 0.16/0.46 ((((~(~(leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init)))) | (~((~(leq(succ(tptp_minus_1), G!15) & leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(succ(tptp_minus_1), H!16) & leq(H!16, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H!16) = init)))) <=> ((~((~(leq(succ(tptp_minus_1), G!15) & leq(G!15, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G!15) = init))) | (~((~(leq(succ(tptp_minus_1), H!16) & leq(H!16, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H!16) = init))) | (leq(succ(tptp_minus_1), E!13) & leq(E!13, succ(succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), F!14) & leq(F!14, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F!14, E!13) = init)))))),
% 0.16/0.46 inference(transitivity,[status(thm)],[107, 102])).
% 0.16/0.46 tff(109,plain,
% 0.16/0.46 ((![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(succ(tptp_minus_1), H) & leq(H, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H) = init))) <=> (![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(succ(tptp_minus_1), H) & leq(H, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H) = init)))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(110,plain,
% 0.16/0.46 ((~(![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(succ(tptp_minus_1), H) & leq(H, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H) = init)))) <=> (~(![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(succ(tptp_minus_1), H) & leq(H, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H) = init))))),
% 0.16/0.46 inference(monotonicity,[status(thm)],[109])).
% 0.16/0.46 tff(111,plain,
% 0.16/0.46 ((~(![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)))) <=> (~(![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(succ(tptp_minus_1), H) & leq(H, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H) = init))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(112,plain,
% 0.16/0.46 ((![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))) <=> (![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)))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(113,plain,
% 0.16/0.46 ((~(![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)))) <=> (~(![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))))),
% 0.16/0.46 inference(monotonicity,[status(thm)],[112])).
% 0.16/0.46 tff(114,plain,
% 0.16/0.46 ((~(![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)))) <=> (~(![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))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(115,plain,
% 0.16/0.46 ((~(![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))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(116,plain,
% 0.16/0.46 ((![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))))),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(117,plain,
% 0.16/0.47 ((~(![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)))))),
% 0.16/0.47 inference(monotonicity,[status(thm)],[116])).
% 0.16/0.47 tff(118,plain,
% 0.16/0.47 (~(![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))))),
% 0.16/0.47 inference(or_elim,[status(thm)],[54])).
% 0.16/0.47 tff(119,plain,
% 0.16/0.47 (~(![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))))),
% 0.16/0.47 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.16/0.47 tff(120,plain,
% 0.16/0.47 (~(![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)))),
% 0.16/0.47 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.16/0.47 tff(121,plain,
% 0.16/0.47 (~(![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)))),
% 0.16/0.47 inference(modus_ponens,[status(thm)],[120, 114])).
% 0.16/0.47 tff(122,plain,
% 0.16/0.47 (~(![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)))),
% 0.16/0.47 inference(modus_ponens,[status(thm)],[121, 113])).
% 0.16/0.47 tff(123,plain,
% 0.16/0.47 (~(![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(succ(tptp_minus_1), H) & leq(H, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H) = init)))),
% 0.16/0.47 inference(modus_ponens,[status(thm)],[122, 111])).
% 0.16/0.47 tff(124,plain,
% 0.16/0.47 (~(![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(succ(tptp_minus_1), H) & leq(H, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H) = init)))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[123, 110])).
% 0.16/0.48 tff(125,plain,
% 0.16/0.48 (~(![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(succ(tptp_minus_1), H) & leq(H, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H) = init)))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[124, 110])).
% 0.16/0.48 tff(126,plain,
% 0.16/0.48 (~(![E: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, succ(succ(succ(tptp_minus_1)))))) | ![F: $i] : ((~(leq(succ(tptp_minus_1), F) & leq(F, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select3(simplex7_init, F, E) = init))) & ![G: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, succ(succ(succ(succ(tptp_minus_1))))))) | (a_select2(s_values7_init, G) = init)) & ![H: $i] : ((~(leq(succ(tptp_minus_1), H) & leq(H, succ(succ(succ(tptp_minus_1)))))) | (a_select2(s_center7_init, H) = init)))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[125, 110])).
% 0.16/0.48 unexpected number of arguments: (let ((a!1 (forall ((E $i))
% 0.16/0.48 (let ((a!1 (leq E (succ (succ (succ tptp_minus_1)))))
% 0.16/0.48 (a!3 (forall ((F $i))
% 0.16/0.48 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.16/0.48 (let ((a!2 (not (and (leq (succ tptp_minus_1) F)
% 0.16/0.48 (leq F a!1)))))
% 0.16/0.48 (or a!2 (= (a_select3 simplex7_init F E) init)))))))
% 0.16/0.48 (let ((a!2 (not (and (leq (succ tptp_minus_1) E) a!1))))
% 0.16/0.48 (or a!2 a!3)))))
% 0.16/0.48 (a!2 (leq E!13 (succ (succ (succ tptp_minus_1)))))
% 0.16/0.48 (a!4 (forall ((F $i))
% 0.16/0.48 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.16/0.48 (let ((a!2 (not (and (leq (succ tptp_minus_1) F) (leq F a!1)))))
% 0.16/0.48 (or a!2 (= (a_select3 simplex7_init F E!13) init))))))
% 0.16/0.48 (a!6 (succ (succ (succ (succ tptp_minus_1)))))
% 0.16/0.48 (a!11 (forall ((G $i))
% 0.16/0.48 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.16/0.48 (let ((a!2 (not (and (leq (succ tptp_minus_1) G) (leq G a!1)))))
% 0.16/0.48 (or a!2 (= (a_select2 s_values7_init G) init))))))
% 0.16/0.48 (a!14 (forall ((H $i))
% 0.16/0.48 (let ((a!1 (leq H (succ (succ (succ tptp_minus_1))))))
% 0.16/0.48 (let ((a!2 (not (and (leq (succ tptp_minus_1) H) a!1))))
% 0.16/0.48 (or a!2 (= (a_select2 s_center7_init H) init))))))
% 0.16/0.48 (a!15 (leq H!16 (succ (succ (succ tptp_minus_1))))))
% 0.16/0.48 (let ((a!3 (not (and (leq (succ tptp_minus_1) E!13) a!2)))
% 0.16/0.48 (a!7 (not (and (leq (succ tptp_minus_1) F!14) (leq F!14 a!6))))
% 0.16/0.48 (a!12 (not (and (leq (succ tptp_minus_1) G!15) (leq G!15 a!6))))
% 0.16/0.48 (a!16 (not (and (leq (succ tptp_minus_1) H!16) a!15))))
% 0.16/0.48 (let ((a!5 (sk (~ (not a!1) (not (or a!3 a!4)))))
% 0.16/0.48 (a!8 (not (or a!7 (= (a_select3 simplex7_init F!14 E!13) init))))
% 0.16/0.48 (a!13 (not (or a!12 (= (a_select2 s_values7_init G!15) init))))
% 0.16/0.48 (a!17 (not (or a!16 (= (a_select2 s_center7_init H!16) init)))))
% 0.16/0.48 (let ((a!9 (nnf-neg (refl (~ (not a!3) (not a!3)))
% 0.16/0.48 (sk (~ (not a!4) a!8))
% 0.16/0.48 (~ (not (or a!3 a!4)) (and (not a!3) a!8))))
% 0.16/0.48 (a!18 (~ (not (and a!1 a!11 a!14)) (or (and (not a!3) a!8) a!13 a!17))))
% 0.16/0.48 (let ((a!10 (trans a!5 a!9 (~ (not a!1) (and (not a!3) a!8)))))
% 0.16/0.48 (nnf-neg a!10 (sk (~ (not a!11) a!13)) (sk (~ (not a!14) a!17)) a!18))))))
% 0.16/0.48 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------