%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV053+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n022.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 15:09:46 EDT 2022

% Result   : Theorem 0.20s 0.48s
% Output   : Assurance 0s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWV053+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n022.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Sep  4 01:15:09 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34  Usage: tptp [options] [-file:]file
% 0.19/0.34    -h, -?       prints this message.
% 0.19/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.19/0.34    -m, -model   generate model.
% 0.19/0.34    -p, -proof   generate proof.
% 0.19/0.34    -c, -core    generate unsat core of named formulas.
% 0.19/0.34    -st, -statistics display statistics.
% 0.19/0.34    -t:timeout   set timeout (in second).
% 0.19/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.19/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34    -<param>:<value> configuration parameter and value.
% 0.19/0.34    -o:<output-file> file to place output in.
% 0.20/0.48  % SZS status Theorem
% 0.20/0.48  % SZS output start Proof
% 0.20/0.48  tff(sum_type, type, (
% 0.20/0.48     sum: ( $i * $i * $i ) > $i)).
% 0.20/0.48  tff(sqrt_type, type, (
% 0.20/0.48     sqrt: $i > $i)).
% 0.20/0.48  tff(times_type, type, (
% 0.20/0.48     times: ( $i * $i ) > $i)).
% 0.20/0.48  tff(minus_type, type, (
% 0.20/0.48     minus: ( $i * $i ) > $i)).
% 0.20/0.48  tff(a_select2_type, type, (
% 0.20/0.48     a_select2: ( $i * $i ) > $i)).
% 0.20/0.48  tff(pv10_type, type, (
% 0.20/0.48     pv10: $i)).
% 0.20/0.48  tff(x_type, type, (
% 0.20/0.48     x: $i)).
% 0.20/0.48  tff(a_select3_type, type, (
% 0.20/0.48     a_select3: ( $i * $i * $i ) > $i)).
% 0.20/0.48  tff(succ_type, type, (
% 0.20/0.48     succ: $i > $i)).
% 0.20/0.48  tff(tptp_minus_1_type, type, (
% 0.20/0.48     tptp_minus_1: $i)).
% 0.20/0.48  tff(pv71_type, type, (
% 0.20/0.48     pv71: $i)).
% 0.20/0.48  tff(center_type, type, (
% 0.20/0.48     center: $i)).
% 0.20/0.48  tff(pred_type, type, (
% 0.20/0.48     pred: $i > $i)).
% 0.20/0.48  tff(n1_type, type, (
% 0.20/0.48     n1: $i)).
% 0.20/0.48  tff(n0_type, type, (
% 0.20/0.48     n0: $i)).
% 0.20/0.48  tff(leq_type, type, (
% 0.20/0.48     leq: ( $i * $i ) > $o)).
% 0.20/0.48  tff(tptp_fun_G_16_type, type, (
% 0.20/0.48     tptp_fun_G_16: $i)).
% 0.20/0.48  tff(tptp_fun_H_15_type, type, (
% 0.20/0.48     tptp_fun_H_15: $i)).
% 0.20/0.48  tff(q_type, type, (
% 0.20/0.48     q: $i)).
% 0.20/0.48  tff(n5_type, type, (
% 0.20/0.48     n5: $i)).
% 0.20/0.48  tff(divide_type, type, (
% 0.20/0.48     divide: ( $i * $i ) > $i)).
% 0.20/0.48  tff(pv12_type, type, (
% 0.20/0.48     pv12: $i)).
% 0.20/0.48  tff(n135300_type, type, (
% 0.20/0.48     n135300: $i)).
% 0.20/0.48  tff(tptp_fun_E_14_type, type, (
% 0.20/0.48     tptp_fun_E_14: $i)).
% 0.20/0.48  tff(tptp_fun_F_13_type, type, (
% 0.20/0.48     tptp_fun_F_13: $i)).
% 0.20/0.48  tff(1,plain,
% 0.20/0.48      (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(2,plain,
% 0.20/0.48      (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(3,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 0.20/0.48  tff(4,plain,
% 0.20/0.48      (![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.48  tff(5,plain,(
% 0.20/0.48      ![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.48      inference(skolemize,[status(sab)],[4])).
% 0.20/0.48  tff(6,plain,
% 0.20/0.48      (![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.48  tff(7,plain,
% 0.20/0.48      ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(tptp_minus_1)) = tptp_minus_1)),
% 0.20/0.48      inference(quant_inst,[status(thm)],[])).
% 0.20/0.48  tff(8,plain,
% 0.20/0.48      (pred(succ(tptp_minus_1)) = tptp_minus_1),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[7, 6])).
% 0.20/0.48  tff(9,plain,
% 0.20/0.48      (^[X: $i] : refl((minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.20/0.48      inference(bind,[status(th)],[])).
% 0.20/0.48  tff(10,plain,
% 0.20/0.48      (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.48      inference(quant_intro,[status(thm)],[9])).
% 0.20/0.48  tff(11,plain,
% 0.20/0.48      (^[X: $i] : rewrite((minus(X, n1) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.20/0.48      inference(bind,[status(th)],[])).
% 0.20/0.48  tff(12,plain,
% 0.20/0.48      (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.48      inference(quant_intro,[status(thm)],[11])).
% 0.20/0.48  tff(13,plain,
% 0.20/0.48      (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(14,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 0.20/0.48  tff(15,plain,
% 0.20/0.48      (![X: $i] : (minus(X, n1) = pred(X))),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.48  tff(16,plain,
% 0.20/0.48      (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[15, 12])).
% 0.20/0.48  tff(17,plain,(
% 0.20/0.48      ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.48      inference(skolemize,[status(sab)],[16])).
% 0.20/0.48  tff(18,plain,
% 0.20/0.48      (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[17, 10])).
% 0.20/0.48  tff(19,plain,
% 0.20/0.48      ((~![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))) | (minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))) = pred(succ(tptp_minus_1)))),
% 0.20/0.48      inference(quant_inst,[status(thm)],[])).
% 0.20/0.48  tff(20,plain,
% 0.20/0.48      (minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))) = pred(succ(tptp_minus_1))),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.48  tff(21,plain,
% 0.20/0.48      (minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))) = tptp_minus_1),
% 0.20/0.48      inference(transitivity,[status(thm)],[20, 8])).
% 0.20/0.48  tff(22,plain,
% 0.20/0.48      (sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10))))) = sum(succ(tptp_minus_1), tptp_minus_1, sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)))))),
% 0.20/0.48      inference(monotonicity,[status(thm)],[21])).
% 0.20/0.48  tff(23,plain,
% 0.20/0.48      (sum(succ(tptp_minus_1), tptp_minus_1, sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10))))) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)))))),
% 0.20/0.48      inference(symmetry,[status(thm)],[22])).
% 0.20/0.48  tff(24,plain,
% 0.20/0.48      (^[Body: $i] : refl((sum(succ(tptp_minus_1), tptp_minus_1, Body) = succ(tptp_minus_1)) <=> (sum(succ(tptp_minus_1), tptp_minus_1, Body) = succ(tptp_minus_1)))),
% 0.20/0.48      inference(bind,[status(th)],[])).
% 0.20/0.48  tff(25,plain,
% 0.20/0.48      (![Body: $i] : (sum(succ(tptp_minus_1), tptp_minus_1, Body) = succ(tptp_minus_1)) <=> ![Body: $i] : (sum(succ(tptp_minus_1), tptp_minus_1, Body) = succ(tptp_minus_1))),
% 0.20/0.48      inference(quant_intro,[status(thm)],[24])).
% 0.20/0.48  tff(26,plain,
% 0.20/0.48      (^[Body: $i] : rewrite((sum(n0, tptp_minus_1, Body) = n0) <=> (sum(succ(tptp_minus_1), tptp_minus_1, Body) = succ(tptp_minus_1)))),
% 0.20/0.48      inference(bind,[status(th)],[])).
% 0.20/0.48  tff(27,plain,
% 0.20/0.48      (![Body: $i] : (sum(n0, tptp_minus_1, Body) = n0) <=> ![Body: $i] : (sum(succ(tptp_minus_1), tptp_minus_1, Body) = succ(tptp_minus_1))),
% 0.20/0.48      inference(quant_intro,[status(thm)],[26])).
% 0.20/0.48  tff(28,plain,
% 0.20/0.48      (![Body: $i] : (sum(n0, tptp_minus_1, Body) = n0) <=> ![Body: $i] : (sum(n0, tptp_minus_1, Body) = n0)),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(29,axiom,(![Body: $i] : (sum(n0, tptp_minus_1, Body) = n0)), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','sum_plus_base')).
% 0.20/0.48  tff(30,plain,
% 0.20/0.48      (![Body: $i] : (sum(n0, tptp_minus_1, Body) = n0)),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.48  tff(31,plain,
% 0.20/0.48      (![Body: $i] : (sum(succ(tptp_minus_1), tptp_minus_1, Body) = succ(tptp_minus_1))),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[30, 27])).
% 0.20/0.48  tff(32,plain,(
% 0.20/0.48      ![Body: $i] : (sum(succ(tptp_minus_1), tptp_minus_1, Body) = succ(tptp_minus_1))),
% 0.20/0.48      inference(skolemize,[status(sab)],[31])).
% 0.20/0.48  tff(33,plain,
% 0.20/0.48      (![Body: $i] : (sum(succ(tptp_minus_1), tptp_minus_1, Body) = succ(tptp_minus_1))),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[32, 25])).
% 0.20/0.48  tff(34,plain,
% 0.20/0.48      ((~![Body: $i] : (sum(succ(tptp_minus_1), tptp_minus_1, Body) = succ(tptp_minus_1))) | (sum(succ(tptp_minus_1), tptp_minus_1, sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10))))) = succ(tptp_minus_1))),
% 0.20/0.48      inference(quant_inst,[status(thm)],[])).
% 0.20/0.48  tff(35,plain,
% 0.20/0.48      (sum(succ(tptp_minus_1), tptp_minus_1, sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10))))) = succ(tptp_minus_1)),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[34, 33])).
% 0.20/0.48  tff(36,plain,
% 0.20/0.48      (succ(tptp_minus_1) = sum(succ(tptp_minus_1), tptp_minus_1, sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)))))),
% 0.20/0.48      inference(symmetry,[status(thm)],[35])).
% 0.20/0.48  tff(37,plain,
% 0.20/0.48      (succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)))))),
% 0.20/0.48      inference(transitivity,[status(thm)],[36, 23])).
% 0.20/0.48  tff(38,assumption,(~((sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.20/0.48  tff(39,plain,
% 0.20/0.48      (((sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))) | leq(G!16, minus(pv10, succ(succ(tptp_minus_1))))),
% 0.20/0.48      inference(tautology,[status(thm)],[])).
% 0.20/0.48  tff(40,plain,
% 0.20/0.48      (leq(G!16, minus(pv10, succ(succ(tptp_minus_1))))),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.48  tff(41,plain,
% 0.20/0.48      (((sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), G!16)),
% 0.20/0.48      inference(tautology,[status(thm)],[])).
% 0.20/0.48  tff(42,plain,
% 0.20/0.48      (leq(succ(tptp_minus_1), G!16)),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[41, 38])).
% 0.20/0.48  tff(43,plain,
% 0.20/0.48      (((sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))) | (~(sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))))),
% 0.20/0.48      inference(tautology,[status(thm)],[])).
% 0.20/0.48  tff(44,plain,
% 0.20/0.48      (~(sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1)))),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[43, 38])).
% 0.20/0.48  tff(45,plain,
% 0.20/0.48      (^[C: $i, D: $i] : refl(((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1)))))))),
% 0.20/0.48      inference(bind,[status(th)],[])).
% 0.20/0.48  tff(46,plain,
% 0.20/0.48      (![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1)))))) <=> ![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))),
% 0.20/0.48      inference(quant_intro,[status(thm)],[45])).
% 0.20/0.48  tff(47,plain,
% 0.20/0.48      (^[C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), C) & leq(C, minus(pv10, succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), C)) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), C) & leq(C, minus(pv10, succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), C)) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), C)) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), C) & leq(C, minus(pv10, succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), C) & leq(C, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1)))) <=> (((~leq(succ(tptp_minus_1), C)) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1)))))), rewrite((((~leq(succ(tptp_minus_1), C)) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))), (((~(leq(succ(tptp_minus_1), C) & leq(C, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))))),
% 0.20/0.48      inference(bind,[status(th)],[])).
% 0.20/0.48  tff(48,plain,
% 0.20/0.48      (![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1)))) <=> ![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))),
% 0.20/0.48      inference(quant_intro,[status(thm)],[47])).
% 0.20/0.48  tff(49,plain,
% 0.20/0.48      (^[C: $i, D: $i] : rewrite(((~(leq(n0, C) & leq(C, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, C, D)) = n1)) <=> ((~(leq(succ(tptp_minus_1), C) & leq(C, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1)))))),
% 0.20/0.48      inference(bind,[status(th)],[])).
% 0.20/0.48  tff(50,plain,
% 0.20/0.48      (![C: $i, D: $i] : ((~(leq(n0, C) & leq(C, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, C, D)) = n1)) <=> ![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))))),
% 0.20/0.48      inference(quant_intro,[status(thm)],[49])).
% 0.20/0.48  tff(51,plain,
% 0.20/0.48      (![C: $i, D: $i] : ((~(leq(n0, C) & leq(C, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, C, D)) = n1)) <=> ![C: $i, D: $i] : ((~(leq(n0, C) & leq(C, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, C, D)) = n1))),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(52,plain,
% 0.20/0.48      ((~((((((leq(n0, pv10) & leq(n0, pv12)) & leq(pv10, minus(n135300, n1))) & leq(pv12, minus(n5, n1))) & ![A: $i, B: $i] : ((leq(n0, A) & leq(A, minus(pv12, n1))) => (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, B, n0), a_select2(x, pv10)), minus(a_select3(center, B, n0), a_select2(x, pv10))))))))) & ![C: $i, D: $i] : ((leq(n0, C) & leq(C, minus(pv10, n1))) => (sum(n0, minus(n5, n1), a_select3(q, C, D)) = n1))) => (((((((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & leq(n0, pv10)) & leq(n0, pv12)) & leq(pv10, minus(n135300, n1))) & leq(pv12, minus(n5, n1))) & ![E: $i, F: $i] : ((leq(n0, E) & leq(E, minus(pv12, n1))) => (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10))))))))) & ![G: $i, H: $i] : ((leq(n0, G) & leq(G, minus(pv10, n1))) => (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1))))) <=> (~((~(leq(n0, pv10) & leq(n0, pv12) & leq(pv10, minus(n135300, n1)) & leq(pv12, minus(n5, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(A, minus(pv12, n1)))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, B, n0), a_select2(x, pv10)), minus(a_select3(center, B, n0), a_select2(x, pv10)))))))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(C, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, C, D)) = n1)))) | ((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & leq(n0, pv10) & leq(n0, pv12) & leq(pv10, minus(n135300, n1)) & leq(pv12, minus(n5, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1)))))),
% 0.20/0.49      inference(rewrite,[status(thm)],[])).
% 0.20/0.49  tff(53,axiom,(~((((((leq(n0, pv10) & leq(n0, pv12)) & leq(pv10, minus(n135300, n1))) & leq(pv12, minus(n5, n1))) & ![A: $i, B: $i] : ((leq(n0, A) & leq(A, minus(pv12, n1))) => (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, B, n0), a_select2(x, pv10)), minus(a_select3(center, B, n0), a_select2(x, pv10))))))))) & ![C: $i, D: $i] : ((leq(n0, C) & leq(C, minus(pv10, n1))) => (sum(n0, minus(n5, n1), a_select3(q, C, D)) = n1))) => (((((((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & leq(n0, pv10)) & leq(n0, pv12)) & leq(pv10, minus(n135300, n1))) & leq(pv12, minus(n5, n1))) & ![E: $i, F: $i] : ((leq(n0, E) & leq(E, minus(pv12, n1))) => (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10))))))))) & ![G: $i, H: $i] : ((leq(n0, G) & leq(G, minus(pv10, n1))) => (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cl5_nebula_norm_0031')).
% 0.20/0.49  tff(54,plain,
% 0.20/0.49      (~((~(leq(n0, pv10) & leq(n0, pv12) & leq(pv10, minus(n135300, n1)) & leq(pv12, minus(n5, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(A, minus(pv12, n1)))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, B, n0), a_select2(x, pv10)), minus(a_select3(center, B, n0), a_select2(x, pv10)))))))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(C, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, C, D)) = n1)))) | ((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & leq(n0, pv10) & leq(n0, pv12) & leq(pv10, minus(n135300, n1)) & leq(pv12, minus(n5, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.49  tff(55,plain,
% 0.20/0.49      (leq(n0, pv10) & leq(n0, pv12) & leq(pv10, minus(n135300, n1)) & leq(pv12, minus(n5, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(A, minus(pv12, n1)))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, B, n0), a_select2(x, pv10)), minus(a_select3(center, B, n0), a_select2(x, pv10)))))))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(C, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, C, D)) = n1))),
% 0.20/0.49      inference(or_elim,[status(thm)],[54])).
% 0.20/0.49  tff(56,plain,
% 0.20/0.49      (![C: $i, D: $i] : ((~(leq(n0, C) & leq(C, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, C, D)) = n1))),
% 0.20/0.49      inference(and_elim,[status(thm)],[55])).
% 0.20/0.49  tff(57,plain,
% 0.20/0.49      (![C: $i, D: $i] : ((~(leq(n0, C) & leq(C, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, C, D)) = n1))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[56, 51])).
% 0.20/0.49  tff(58,plain,
% 0.20/0.49      (![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.49  tff(59,plain,(
% 0.20/0.49      ![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(C, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))))),
% 0.20/0.49      inference(skolemize,[status(sab)],[58])).
% 0.20/0.49  tff(60,plain,
% 0.20/0.49      (![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[59, 48])).
% 0.20/0.49  tff(61,plain,
% 0.20/0.49      (![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[60, 46])).
% 0.20/0.49  tff(62,plain,
% 0.20/0.49      (((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))) | ((sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1))))))) <=> ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1))))))),
% 0.20/0.49      inference(rewrite,[status(thm)],[])).
% 0.20/0.49  tff(63,plain,
% 0.20/0.49      (((~leq(succ(tptp_minus_1), G!16)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))) <=> ((sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1))))))),
% 0.20/0.49      inference(rewrite,[status(thm)],[])).
% 0.20/0.49  tff(64,plain,
% 0.20/0.49      (((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))) | ((~leq(succ(tptp_minus_1), G!16)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1))))))) <=> ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))) | ((sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))))),
% 0.20/0.49      inference(monotonicity,[status(thm)],[63])).
% 0.20/0.49  tff(65,plain,
% 0.20/0.49      (((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))) | ((~leq(succ(tptp_minus_1), G!16)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1))))))) <=> ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1))))))),
% 0.20/0.49      inference(transitivity,[status(thm)],[64, 62])).
% 0.20/0.49  tff(66,plain,
% 0.20/0.49      ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))) | ((~leq(succ(tptp_minus_1), G!16)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1))))))),
% 0.20/0.49      inference(quant_inst,[status(thm)],[])).
% 0.20/0.49  tff(67,plain,
% 0.20/0.49      ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, C, D)) = succ(succ(tptp_minus_1))) | (~leq(C, minus(pv10, succ(succ(tptp_minus_1))))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.49  tff(68,plain,
% 0.20/0.49      ($false),
% 0.20/0.49      inference(unit_resolution,[status(thm)],[67, 61, 44, 42, 40])).
% 0.20/0.49  tff(69,plain,((sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49  tff(70,assumption,(~((a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.20/0.50  tff(71,plain,
% 0.20/0.50      (((a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1)))))) | leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(72,plain,
% 0.20/0.50      (leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[71, 70])).
% 0.20/0.50  tff(73,plain,
% 0.20/0.50      (((a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), E!14)),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(74,plain,
% 0.20/0.50      (leq(succ(tptp_minus_1), E!14)),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[73, 70])).
% 0.20/0.50  tff(75,plain,
% 0.20/0.50      (((a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1)))))) | (~(a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(76,plain,
% 0.20/0.50      (~(a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)))))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[75, 70])).
% 0.20/0.50  tff(77,plain,
% 0.20/0.50      (^[A: $i, B: $i] : refl(((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1)))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(78,plain,
% 0.20/0.50      (![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1)))))) <=> ![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[77])).
% 0.20/0.50  tff(79,plain,
% 0.20/0.50      (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), A) & leq(A, minus(pv12, succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), A)) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), A) & leq(A, minus(pv12, succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), A)) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), A)) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), A) & leq(A, minus(pv12, succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), A) & leq(A, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)))))))) <=> (((~leq(succ(tptp_minus_1), A)) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)))))))))), rewrite((((~leq(succ(tptp_minus_1), A)) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)))))))) <=> ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))), (((~(leq(succ(tptp_minus_1), A) & leq(A, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)))))))) <=> ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(80,plain,
% 0.20/0.50      (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)))))))) <=> ![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[79])).
% 0.20/0.50  tff(81,plain,
% 0.20/0.50      (^[A: $i, B: $i] : rewrite(((~(leq(n0, A) & leq(A, minus(pv12, n1)))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, B, n0), a_select2(x, pv10)), minus(a_select3(center, B, n0), a_select2(x, pv10)))))))) <=> ((~(leq(succ(tptp_minus_1), A) & leq(A, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)))))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(82,plain,
% 0.20/0.50      (![A: $i, B: $i] : ((~(leq(n0, A) & leq(A, minus(pv12, n1)))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, B, n0), a_select2(x, pv10)), minus(a_select3(center, B, n0), a_select2(x, pv10)))))))) <=> ![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[81])).
% 0.20/0.50  tff(83,plain,
% 0.20/0.50      (![A: $i, B: $i] : ((~(leq(n0, A) & leq(A, minus(pv12, n1)))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, B, n0), a_select2(x, pv10)), minus(a_select3(center, B, n0), a_select2(x, pv10)))))))) <=> ![A: $i, B: $i] : ((~(leq(n0, A) & leq(A, minus(pv12, n1)))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, B, n0), a_select2(x, pv10)), minus(a_select3(center, B, n0), a_select2(x, pv10))))))))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(84,plain,
% 0.20/0.50      (![A: $i, B: $i] : ((~(leq(n0, A) & leq(A, minus(pv12, n1)))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, B, n0), a_select2(x, pv10)), minus(a_select3(center, B, n0), a_select2(x, pv10))))))))),
% 0.20/0.50      inference(and_elim,[status(thm)],[55])).
% 0.20/0.50  tff(85,plain,
% 0.20/0.50      (![A: $i, B: $i] : ((~(leq(n0, A) & leq(A, minus(pv12, n1)))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, B, n0), a_select2(x, pv10)), minus(a_select3(center, B, n0), a_select2(x, pv10))))))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.50  tff(86,plain,
% 0.20/0.50      (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[85, 82])).
% 0.20/0.50  tff(87,plain,(
% 0.20/0.50      ![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(A, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))))),
% 0.20/0.50      inference(skolemize,[status(sab)],[86])).
% 0.20/0.50  tff(88,plain,
% 0.20/0.50      (![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[87, 80])).
% 0.20/0.50  tff(89,plain,
% 0.20/0.50      (![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[88, 78])).
% 0.20/0.50  tff(90,plain,
% 0.20/0.50      (((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))) | ((a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))))) <=> ((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))) | (a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(91,plain,
% 0.20/0.50      (((~leq(succ(tptp_minus_1), E!14)) | (a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1)))))) <=> ((a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(92,plain,
% 0.20/0.51      (((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))) | ((~leq(succ(tptp_minus_1), E!14)) | (a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))))) <=> ((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))) | ((a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1)))))))),
% 0.20/0.51      inference(monotonicity,[status(thm)],[91])).
% 0.20/0.51  tff(93,plain,
% 0.20/0.51      (((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))) | ((~leq(succ(tptp_minus_1), E!14)) | (a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))))) <=> ((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))) | (a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))))),
% 0.20/0.51      inference(transitivity,[status(thm)],[92, 90])).
% 0.20/0.51  tff(94,plain,
% 0.20/0.51      ((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))) | ((~leq(succ(tptp_minus_1), E!14)) | (a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))))),
% 0.20/0.51      inference(quant_inst,[status(thm)],[])).
% 0.20/0.51  tff(95,plain,
% 0.20/0.51      ((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, A, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, B, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(A, minus(pv12, succ(succ(tptp_minus_1))))))) | (a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1)))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.51  tff(96,plain,
% 0.20/0.51      ($false),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[95, 89, 76, 74, 72])).
% 0.20/0.51  tff(97,plain,((a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51  tff(98,plain,
% 0.20/0.51      (((~(succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~((a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))))) | (~((sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))))) <=> ((~(succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~((a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))))) | (~((sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1))))))))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(99,plain,
% 0.20/0.51      ((~((~(leq(succ(tptp_minus_1), G!16) & leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))))) <=> (~((sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(100,plain,
% 0.20/0.51      ((~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))))) <=> (~((a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1)))))))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(101,plain,
% 0.20/0.51      (((~(succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))))) | (~((~(leq(succ(tptp_minus_1), G!16) & leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1)))))) <=> ((~(succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~((a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))))) | (~((sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1))))))))),
% 0.20/0.51      inference(monotonicity,[status(thm)],[100, 99])).
% 0.20/0.51  tff(102,plain,
% 0.20/0.51      (((~(succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))))) | (~((~(leq(succ(tptp_minus_1), G!16) & leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1)))))) <=> ((~(succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~((a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(E!14, minus(pv12, succ(succ(tptp_minus_1))))))) | (~((sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), G!16)) | (~leq(G!16, minus(pv10, succ(succ(tptp_minus_1))))))))),
% 0.20/0.51      inference(transitivity,[status(thm)],[101, 98])).
% 0.20/0.51  tff(103,plain,
% 0.20/0.51      (((~(succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))))) | (~((~(leq(succ(tptp_minus_1), G!16) & leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1)))))) <=> ((~(succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~((~(leq(succ(tptp_minus_1), E!14) & leq(E!14, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E!14) = divide(sqrt(times(minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E!14, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F!13, succ(tptp_minus_1)), a_select2(x, pv10))))))))) | (~((~(leq(succ(tptp_minus_1), G!16) & leq(G!16, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G!16, H!15)) = succ(succ(tptp_minus_1))))))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(104,plain,
% 0.20/0.52      (((succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G, H)) = succ(succ(tptp_minus_1))))) <=> ((succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G, H)) = succ(succ(tptp_minus_1)))))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(105,plain,
% 0.20/0.52      ((~((succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G, H)) = succ(succ(tptp_minus_1)))))) <=> (~((succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G, H)) = succ(succ(tptp_minus_1))))))),
% 0.20/0.52      inference(monotonicity,[status(thm)],[104])).
% 0.20/0.52  tff(106,plain,
% 0.20/0.52      ((~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1)))) <=> (~((succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G, H)) = succ(succ(tptp_minus_1))))))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(107,plain,
% 0.20/0.52      (((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1))) <=> ((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1)))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(108,plain,
% 0.20/0.52      ((~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1)))) <=> (~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1))))),
% 0.20/0.52      inference(monotonicity,[status(thm)],[107])).
% 0.20/0.52  tff(109,plain,
% 0.20/0.52      ((~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1)))) <=> (~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1))))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(110,plain,
% 0.20/0.52      ((~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & leq(n0, pv10) & leq(n0, pv12) & leq(pv10, minus(n135300, n1)) & leq(pv12, minus(n5, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1)))) <=> (~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1))))),
% 0.20/0.53      inference(rewrite,[status(thm)],[])).
% 0.20/0.53  tff(111,plain,
% 0.20/0.53      (((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & leq(n0, pv10) & leq(n0, pv12) & leq(pv10, minus(n135300, n1)) & leq(pv12, minus(n5, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1))) <=> ((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & leq(n0, pv10) & leq(n0, pv12) & leq(pv10, minus(n135300, n1)) & leq(pv12, minus(n5, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1)))),
% 0.20/0.53      inference(rewrite,[status(thm)],[])).
% 0.20/0.53  tff(112,plain,
% 0.20/0.53      ((~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & leq(n0, pv10) & leq(n0, pv12) & leq(pv10, minus(n135300, n1)) & leq(pv12, minus(n5, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1)))) <=> (~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & leq(n0, pv10) & leq(n0, pv12) & leq(pv10, minus(n135300, n1)) & leq(pv12, minus(n5, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1))))),
% 0.20/0.53      inference(monotonicity,[status(thm)],[111])).
% 0.20/0.53  tff(113,plain,
% 0.20/0.53      (~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & leq(n0, pv10) & leq(n0, pv12) & leq(pv10, minus(n135300, n1)) & leq(pv12, minus(n5, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1)))),
% 0.20/0.53      inference(or_elim,[status(thm)],[54])).
% 0.20/0.53  tff(114,plain,
% 0.20/0.53      (~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & leq(n0, pv10) & leq(n0, pv12) & leq(pv10, minus(n135300, n1)) & leq(pv12, minus(n5, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1)))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.53  tff(115,plain,
% 0.20/0.53      (~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1)))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[114, 110])).
% 0.20/0.53  tff(116,plain,
% 0.20/0.53      (~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1)))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[115, 109])).
% 0.20/0.53  tff(117,plain,
% 0.20/0.53      (~((n0 = sum(n0, minus(n0, n1), sqrt(times(minus(a_select3(center, pv71, n0), a_select2(x, pv10)), minus(a_select3(center, pv71, n0), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(E, minus(pv12, n1)))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, n0), a_select2(x, pv10)), minus(a_select3(center, E, n0), a_select2(x, pv10)))), sum(n0, minus(n5, n1), sqrt(times(minus(a_select3(center, F, n0), a_select2(x, pv10)), minus(a_select3(center, F, n0), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(G, minus(pv10, n1)))) | (sum(n0, minus(n5, n1), a_select3(q, G, H)) = n1)))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[116, 108])).
% 0.20/0.53  tff(118,plain,
% 0.20/0.53      (~((succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G, H)) = succ(succ(tptp_minus_1)))))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[117, 106])).
% 0.20/0.53  tff(119,plain,
% 0.20/0.53      (~((succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G, H)) = succ(succ(tptp_minus_1)))))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[118, 105])).
% 0.20/0.53  tff(120,plain,
% 0.20/0.53      (~((succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G, H)) = succ(succ(tptp_minus_1)))))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[119, 105])).
% 0.20/0.53  tff(121,plain,
% 0.20/0.53      (~((succ(tptp_minus_1) = sum(succ(tptp_minus_1), minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv71, succ(tptp_minus_1)), a_select2(x, pv10)))))) & ![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(E, minus(pv12, succ(succ(tptp_minus_1)))))) | (a_select3(q, pv10, E) = divide(sqrt(times(minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, E, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), sqrt(times(minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, F, succ(tptp_minus_1)), a_select2(x, pv10)))))))) & ![G: $i, H: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(G, minus(pv10, succ(succ(tptp_minus_1)))))) | (sum(succ(tptp_minus_1), minus(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))), succ(succ(tptp_minus_1))), a_select3(q, G, H)) = succ(succ(tptp_minus_1)))))),
% 0.20/0.54      inference(modus_ponens,[status(thm)],[120, 105])).
% 0.20/0.54  unexpected number of arguments: (let ((a!1 (times (minus (a_select3 center pv71 (succ tptp_minus_1))
% 0.20/0.54                           (a_select2 x pv10))
% 0.20/0.54                    (minus (a_select3 center pv71 (succ tptp_minus_1))
% 0.20/0.54                           (a_select2 x pv10))))
% 0.20/0.54        (a!4 (forall ((E $i) (F $i))
% 0.20/0.54               (let ((a!1 (leq E (minus pv12 (succ (succ tptp_minus_1)))))
% 0.20/0.54                     (a!3 (times (minus (a_select3 center E (succ tptp_minus_1))
% 0.20/0.54                                        (a_select2 x pv10))
% 0.20/0.54                                 (minus (a_select3 center E (succ tptp_minus_1))
% 0.20/0.54                                        (a_select2 x pv10))))
% 0.20/0.54                     (a!4 (succ (succ (succ (succ tptp_minus_1)))))
% 0.20/0.54                     (a!5 (times (minus (a_select3 center F (succ tptp_minus_1))
% 0.20/0.54                                        (a_select2 x pv10))
% 0.20/0.54                                 (minus (a_select3 center F (succ tptp_minus_1))
% 0.20/0.54                                        (a_select2 x pv10)))))
% 0.20/0.54               (let ((a!2 (not (and (leq (succ tptp_minus_1) E) a!1)))
% 0.20/0.54                     (a!6 (sum (succ tptp_minus_1)
% 0.20/0.54                               (minus (succ (succ a!4))
% 0.20/0.54                                      (succ (succ tptp_minus_1)))
% 0.20/0.54                               (sqrt a!5))))
% 0.20/0.54                 (or a!2 (= (a_select3 q pv10 E) (divide (sqrt a!3) a!6)))))))
% 0.20/0.54        (a!5 (leq E!14 (minus pv12 (succ (succ tptp_minus_1)))))
% 0.20/0.54        (a!7 (times (minus (a_select3 center E!14 (succ tptp_minus_1))
% 0.20/0.54                           (a_select2 x pv10))
% 0.20/0.54                    (minus (a_select3 center E!14 (succ tptp_minus_1))
% 0.20/0.54                           (a_select2 x pv10))))
% 0.20/0.54        (a!8 (succ (succ (succ (succ tptp_minus_1)))))
% 0.20/0.54        (a!9 (times (minus (a_select3 center F!13 (succ tptp_minus_1))
% 0.20/0.54                           (a_select2 x pv10))
% 0.20/0.54                    (minus (a_select3 center F!13 (succ tptp_minus_1))
% 0.20/0.54                           (a_select2 x pv10))))
% 0.20/0.54        (a!12 (forall ((G $i) (H $i))
% 0.20/0.54                (let ((a!1 (leq G (minus pv10 (succ (succ tptp_minus_1)))))
% 0.20/0.54                      (a!3 (succ (succ (succ (succ tptp_minus_1))))))
% 0.20/0.54                (let ((a!2 (not (and (leq (succ tptp_minus_1) G) a!1)))
% 0.20/0.54                      (a!4 (sum (succ tptp_minus_1)
% 0.20/0.54                                (minus (succ (succ a!3))
% 0.20/0.54                                       (succ (succ tptp_minus_1)))
% 0.20/0.54                                (a_select3 q G H))))
% 0.20/0.54                  (or a!2 (= a!4 (succ (succ tptp_minus_1))))))))
% 0.20/0.54        (a!13 (leq G!16 (minus pv10 (succ (succ tptp_minus_1))))))
% 0.20/0.54  (let ((a!2 (sum (succ tptp_minus_1)
% 0.20/0.54                  (minus (succ tptp_minus_1) (succ (succ tptp_minus_1)))
% 0.20/0.54                  (sqrt a!1)))
% 0.20/0.54        (a!6 (not (and (leq (succ tptp_minus_1) E!14) a!5)))
% 0.20/0.54        (a!10 (sum (succ tptp_minus_1)
% 0.20/0.54                   (minus (succ (succ a!8)) (succ (succ tptp_minus_1)))
% 0.20/0.54                   (sqrt a!9)))
% 0.20/0.54        (a!14 (not (and (leq (succ tptp_minus_1) G!16) a!13)))
% 0.20/0.54        (a!15 (sum (succ tptp_minus_1)
% 0.20/0.54                   (minus (succ (succ a!8)) (succ (succ tptp_minus_1)))
% 0.20/0.54                   (a_select3 q G!16 H!15))))
% 0.20/0.54  (let ((a!3 (~ (not (= (succ tptp_minus_1) a!2))
% 0.20/0.54                (not (= (succ tptp_minus_1) a!2))))
% 0.20/0.54        (a!11 (or a!6 (= (a_select3 q pv10 E!14) (divide (sqrt a!7) a!10))))
% 0.20/0.54        (a!16 (or a!14 (= a!15 (succ (succ tptp_minus_1)))))
% 0.20/0.54        (a!17 (not (and (= (succ tptp_minus_1) a!2) a!4 a!12))))
% 0.20/0.54  (let ((a!18 (or (not (= (succ tptp_minus_1) a!2)) (not a!11) (not a!16))))
% 0.20/0.54    (nnf-neg (refl a!3)
% 0.20/0.54             (sk (~ (not a!4) (not a!11)))
% 0.20/0.54             (sk (~ (not a!12) (not a!16)))
% 0.20/0.54             (~ a!17 a!18))))))
% 0.20/0.54  Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------