%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GEO331+1 : TPTP v8.1.0. Released v4.1.0.
% 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 : Fri Sep 16 20:36:22 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Proof 0.48s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GEO331+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33  % Computer : n022.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 300
% 0.14/0.33  % DateTime : Wed Aug 31 08:11:10 EDT 2022
% 0.14/0.33  % CPUTime  : 
% 0.14/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34  Usage: tptp [options] [-file:]file
% 0.14/0.34    -h, -?       prints this message.
% 0.14/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.34    -m, -model   generate model.
% 0.14/0.34    -p, -proof   generate proof.
% 0.14/0.34    -c, -core    generate unsat core of named formulas.
% 0.14/0.34    -st, -statistics display statistics.
% 0.14/0.34    -t:timeout   set timeout (in second).
% 0.14/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34    -<param>:<value> configuration parameter and value.
% 0.14/0.34    -o:<output-file> file to place output in.
% 0.20/0.52  % SZS status Theorem
% 0.20/0.52  % SZS output start Proof
% 0.20/0.52  tff(tptp_fun_Vd1358_1_type, type, (
% 0.20/0.52     tptp_fun_Vd1358_1: $i)).
% 0.20/0.52  tff(rpoint_type, type, (
% 0.20/0.52     rpoint: $i > $o)).
% 0.20/0.52  tff(tptp_fun_Vd1357_2_type, type, (
% 0.20/0.52     tptp_fun_Vd1357_2: $i)).
% 0.20/0.52  tff(vd1352_type, type, (
% 0.20/0.52     vd1352: $i)).
% 0.20/0.52  tff(rless_type, type, (
% 0.20/0.52     rless: ( $i * $i ) > $o)).
% 0.20/0.52  tff(vf_type, type, (
% 0.20/0.52     vf: ( $i * $i ) > $i)).
% 0.20/0.52  tff(tptp_fun_Vd1359_0_type, type, (
% 0.20/0.52     tptp_fun_Vd1359_0: $i)).
% 0.20/0.52  tff(vd1354_type, type, (
% 0.20/0.52     vd1354: $i)).
% 0.20/0.52  tff(vd1353_type, type, (
% 0.20/0.52     vd1353: $i)).
% 0.20/0.52  tff(vangle_type, type, (
% 0.20/0.52     vangle: ( $i * $i * $i ) > $i)).
% 0.20/0.52  tff(1,assumption,(~![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))), introduced(assumption)).
% 0.20/0.52  tff(2,assumption,(![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))), introduced(assumption)).
% 0.20/0.52  tff(3,plain,
% 0.20/0.52      (?[Vd1357: $i] : ((vd1352 = Vd1357) & rpoint(Vd1357)) <=> ?[Vd1357: $i] : ((vd1352 = Vd1357) & rpoint(Vd1357))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(4,axiom,(?[Vd1357: $i] : ((vd1352 = Vd1357) & rpoint(Vd1357))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''qe(s1(plural(383)))'')).
% 0.20/0.52  tff(5,plain,
% 0.20/0.52      (?[Vd1357: $i] : ((vd1352 = Vd1357) & rpoint(Vd1357))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.52  tff(6,plain,(
% 0.20/0.52      (vd1352 = Vd1357!2) & rpoint(Vd1357!2)),
% 0.20/0.52      inference(skolemize,[status(sab)],[5])).
% 0.20/0.52  tff(7,plain,
% 0.20/0.52      (rpoint(Vd1357!2)),
% 0.20/0.52      inference(and_elim,[status(thm)],[6])).
% 0.20/0.52  tff(8,plain,
% 0.20/0.52      (((~![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) | (~rpoint(Vd1357!2))) <=> ((~![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) | (~rpoint(Vd1357!2)))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(9,plain,
% 0.20/0.52      (((~rpoint(Vd1357!2)) | $false) <=> (~rpoint(Vd1357!2))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(10,plain,
% 0.20/0.52      ((~$true) <=> $false),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(11,plain,
% 0.20/0.52      ((Vd1357!2 = Vd1357!2) <=> $true),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(12,plain,
% 0.20/0.52      ((~(Vd1357!2 = Vd1357!2)) <=> (~$true)),
% 0.20/0.52      inference(monotonicity,[status(thm)],[11])).
% 0.20/0.52  tff(13,plain,
% 0.20/0.52      ((~(Vd1357!2 = Vd1357!2)) <=> $false),
% 0.20/0.52      inference(transitivity,[status(thm)],[12, 10])).
% 0.20/0.52  tff(14,plain,
% 0.20/0.52      (((~rpoint(Vd1357!2)) | (~(Vd1357!2 = Vd1357!2))) <=> ((~rpoint(Vd1357!2)) | $false)),
% 0.20/0.52      inference(monotonicity,[status(thm)],[13])).
% 0.20/0.52  tff(15,plain,
% 0.20/0.52      (((~rpoint(Vd1357!2)) | (~(Vd1357!2 = Vd1357!2))) <=> (~rpoint(Vd1357!2))),
% 0.20/0.52      inference(transitivity,[status(thm)],[14, 9])).
% 0.20/0.52  tff(16,plain,
% 0.20/0.52      (((~![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) | ((~rpoint(Vd1357!2)) | (~(Vd1357!2 = Vd1357!2)))) <=> ((~![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) | (~rpoint(Vd1357!2)))),
% 0.20/0.52      inference(monotonicity,[status(thm)],[15])).
% 0.20/0.52  tff(17,plain,
% 0.20/0.52      (((~![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) | ((~rpoint(Vd1357!2)) | (~(Vd1357!2 = Vd1357!2)))) <=> ((~![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) | (~rpoint(Vd1357!2)))),
% 0.20/0.52      inference(transitivity,[status(thm)],[16, 8])).
% 0.20/0.52  tff(18,plain,
% 0.20/0.52      ((~![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) | ((~rpoint(Vd1357!2)) | (~(Vd1357!2 = Vd1357!2)))),
% 0.20/0.52      inference(quant_inst,[status(thm)],[])).
% 0.20/0.52  tff(19,plain,
% 0.20/0.52      ((~![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) | (~rpoint(Vd1357!2))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.52  tff(20,plain,
% 0.20/0.52      ($false),
% 0.20/0.52      inference(unit_resolution,[status(thm)],[19, 7, 2])).
% 0.20/0.52  tff(21,plain,(~![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52  tff(22,assumption,(![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368)))), introduced(assumption)).
% 0.20/0.52  tff(23,plain,
% 0.20/0.52      (?[Vd1359: $i] : ((vd1354 = Vd1359) & rpoint(Vd1359)) <=> ?[Vd1359: $i] : ((vd1354 = Vd1359) & rpoint(Vd1359))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(24,axiom,(?[Vd1359: $i] : ((vd1354 = Vd1359) & rpoint(Vd1359))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''qe(s3(plural(383)))'')).
% 0.20/0.52  tff(25,plain,
% 0.20/0.52      (?[Vd1359: $i] : ((vd1354 = Vd1359) & rpoint(Vd1359))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.52  tff(26,plain,(
% 0.20/0.52      (vd1354 = Vd1359!0) & rpoint(Vd1359!0)),
% 0.20/0.52      inference(skolemize,[status(sab)],[25])).
% 0.20/0.52  tff(27,plain,
% 0.20/0.52      (rpoint(Vd1359!0)),
% 0.20/0.52      inference(and_elim,[status(thm)],[26])).
% 0.20/0.52  tff(28,plain,
% 0.20/0.52      (((~![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368)))) | (~rpoint(Vd1359!0))) <=> ((~![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368)))) | (~rpoint(Vd1359!0)))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(29,plain,
% 0.20/0.52      (((~rpoint(Vd1359!0)) | $false) <=> (~rpoint(Vd1359!0))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(30,plain,
% 0.20/0.52      ((Vd1359!0 = Vd1359!0) <=> $true),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(31,plain,
% 0.20/0.52      ((~(Vd1359!0 = Vd1359!0)) <=> (~$true)),
% 0.20/0.52      inference(monotonicity,[status(thm)],[30])).
% 0.20/0.52  tff(32,plain,
% 0.20/0.52      ((~(Vd1359!0 = Vd1359!0)) <=> $false),
% 0.20/0.52      inference(transitivity,[status(thm)],[31, 10])).
% 0.20/0.52  tff(33,plain,
% 0.20/0.52      (((~rpoint(Vd1359!0)) | (~(Vd1359!0 = Vd1359!0))) <=> ((~rpoint(Vd1359!0)) | $false)),
% 0.20/0.52      inference(monotonicity,[status(thm)],[32])).
% 0.20/0.52  tff(34,plain,
% 0.20/0.52      (((~rpoint(Vd1359!0)) | (~(Vd1359!0 = Vd1359!0))) <=> (~rpoint(Vd1359!0))),
% 0.20/0.52      inference(transitivity,[status(thm)],[33, 29])).
% 0.20/0.52  tff(35,plain,
% 0.20/0.52      (((~![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368)))) | ((~rpoint(Vd1359!0)) | (~(Vd1359!0 = Vd1359!0)))) <=> ((~![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368)))) | (~rpoint(Vd1359!0)))),
% 0.20/0.52      inference(monotonicity,[status(thm)],[34])).
% 0.20/0.52  tff(36,plain,
% 0.20/0.52      (((~![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368)))) | ((~rpoint(Vd1359!0)) | (~(Vd1359!0 = Vd1359!0)))) <=> ((~![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368)))) | (~rpoint(Vd1359!0)))),
% 0.20/0.52      inference(transitivity,[status(thm)],[35, 28])).
% 0.20/0.52  tff(37,plain,
% 0.20/0.52      ((~![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368)))) | ((~rpoint(Vd1359!0)) | (~(Vd1359!0 = Vd1359!0)))),
% 0.20/0.52      inference(quant_inst,[status(thm)],[])).
% 0.20/0.52  tff(38,plain,
% 0.20/0.52      ((~![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368)))) | (~rpoint(Vd1359!0))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.52  tff(39,plain,
% 0.20/0.52      ($false),
% 0.20/0.52      inference(unit_resolution,[status(thm)],[38, 27, 22])).
% 0.20/0.52  tff(40,plain,(~![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52  tff(41,plain,
% 0.20/0.52      (?[Vd1358: $i] : ((vd1353 = Vd1358) & rpoint(Vd1358)) <=> ?[Vd1358: $i] : ((vd1353 = Vd1358) & rpoint(Vd1358))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(42,axiom,(?[Vd1358: $i] : ((vd1353 = Vd1358) & rpoint(Vd1358))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''qe(s2(plural(383)))'')).
% 0.20/0.52  tff(43,plain,
% 0.20/0.52      (?[Vd1358: $i] : ((vd1353 = Vd1358) & rpoint(Vd1358))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.52  tff(44,plain,(
% 0.20/0.52      (vd1353 = Vd1358!1) & rpoint(Vd1358!1)),
% 0.20/0.52      inference(skolemize,[status(sab)],[43])).
% 0.20/0.52  tff(45,plain,
% 0.20/0.52      (vd1353 = Vd1358!1),
% 0.20/0.52      inference(and_elim,[status(thm)],[44])).
% 0.20/0.52  tff(46,plain,
% 0.20/0.52      (Vd1358!1 = vd1353),
% 0.20/0.52      inference(symmetry,[status(thm)],[45])).
% 0.20/0.52  tff(47,plain,
% 0.20/0.52      (vd1352 = Vd1357!2),
% 0.20/0.52      inference(and_elim,[status(thm)],[6])).
% 0.20/0.52  tff(48,plain,
% 0.20/0.52      (Vd1357!2 = vd1352),
% 0.20/0.52      inference(symmetry,[status(thm)],[47])).
% 0.20/0.52  tff(49,plain,
% 0.20/0.52      ((Vd1357!2 = Vd1358!1) <=> (vd1352 = vd1353)),
% 0.20/0.52      inference(monotonicity,[status(thm)],[48, 46])).
% 0.20/0.52  tff(50,plain,
% 0.20/0.52      ((vd1352 = vd1353) <=> (Vd1357!2 = Vd1358!1)),
% 0.20/0.52      inference(symmetry,[status(thm)],[49])).
% 0.20/0.52  tff(51,plain,
% 0.20/0.52      ((~(vd1352 = vd1353)) <=> (~(Vd1357!2 = Vd1358!1))),
% 0.20/0.52      inference(monotonicity,[status(thm)],[50])).
% 0.20/0.52  tff(52,plain,
% 0.20/0.52      ((~(vd1352 = vd1353)) <=> (~(vd1352 = vd1353))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(53,axiom,(~(vd1352 = vd1353)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''pred(383, 7)'')).
% 0.20/0.52  tff(54,plain,
% 0.20/0.52      (~(vd1352 = vd1353)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.52  tff(55,plain,
% 0.20/0.52      (~(Vd1357!2 = Vd1358!1)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[54, 51])).
% 0.20/0.52  tff(56,plain,
% 0.20/0.52      ((vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) <=> (vf(Vd1357!2, Vd1359!0) = vf(Vd1357!2, Vd1358!1))),
% 0.20/0.52      inference(commutativity,[status(thm)],[])).
% 0.20/0.52  tff(57,plain,
% 0.20/0.52      ((vf(Vd1357!2, Vd1359!0) = vf(Vd1357!2, Vd1358!1)) <=> (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0))),
% 0.20/0.52      inference(symmetry,[status(thm)],[56])).
% 0.20/0.52  tff(58,plain,
% 0.20/0.52      (vd1354 = Vd1359!0),
% 0.20/0.52      inference(and_elim,[status(thm)],[26])).
% 0.20/0.52  tff(59,plain,
% 0.20/0.52      (Vd1359!0 = vd1354),
% 0.20/0.52      inference(symmetry,[status(thm)],[58])).
% 0.20/0.52  tff(60,plain,
% 0.20/0.52      (vf(Vd1357!2, Vd1359!0) = vf(vd1352, vd1354)),
% 0.20/0.52      inference(monotonicity,[status(thm)],[48, 59])).
% 0.20/0.52  tff(61,plain,
% 0.20/0.52      (vf(vd1352, vd1354) = vf(Vd1357!2, Vd1359!0)),
% 0.20/0.52      inference(symmetry,[status(thm)],[60])).
% 0.20/0.52  tff(62,plain,
% 0.20/0.52      (vf(Vd1357!2, Vd1358!1) = vf(vd1352, vd1353)),
% 0.20/0.52      inference(monotonicity,[status(thm)],[48, 46])).
% 0.20/0.52  tff(63,plain,
% 0.20/0.52      (vf(vd1352, vd1353) = vf(Vd1357!2, Vd1358!1)),
% 0.20/0.52      inference(symmetry,[status(thm)],[62])).
% 0.20/0.52  tff(64,plain,
% 0.20/0.52      ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) <=> (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0))),
% 0.20/0.52      inference(monotonicity,[status(thm)],[63, 61])).
% 0.20/0.52  tff(65,plain,
% 0.20/0.52      ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) <=> (vf(Vd1357!2, Vd1359!0) = vf(Vd1357!2, Vd1358!1))),
% 0.20/0.52      inference(transitivity,[status(thm)],[64, 56])).
% 0.20/0.52  tff(66,plain,
% 0.20/0.52      ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) <=> (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0))),
% 0.20/0.52      inference(transitivity,[status(thm)],[65, 57])).
% 0.20/0.52  tff(67,plain,
% 0.20/0.52      ((~(vf(vd1352, vd1353) = vf(vd1352, vd1354))) <=> (~(vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)))),
% 0.20/0.52      inference(monotonicity,[status(thm)],[66])).
% 0.20/0.52  tff(68,plain,
% 0.20/0.52      ((~(vf(vd1352, vd1353) = vf(vd1352, vd1354))) <=> (~(vf(vd1352, vd1353) = vf(vd1352, vd1354)))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(69,axiom,(~(vf(vd1352, vd1353) = vf(vd1352, vd1354))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(384, 1360, 0)'')).
% 0.20/0.52  tff(70,plain,
% 0.20/0.52      (~(vf(vd1352, vd1353) = vf(vd1352, vd1354))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.52  tff(71,plain,
% 0.20/0.52      (~(vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[70, 67])).
% 0.20/0.52  tff(72,plain,
% 0.20/0.52      ((Vd1357!2 = Vd1359!0) <=> (vd1352 = vd1354)),
% 0.20/0.52      inference(monotonicity,[status(thm)],[48, 59])).
% 0.20/0.52  tff(73,plain,
% 0.20/0.52      ((vd1352 = vd1354) <=> (Vd1357!2 = Vd1359!0)),
% 0.20/0.52      inference(symmetry,[status(thm)],[72])).
% 0.20/0.52  tff(74,plain,
% 0.20/0.52      ((~(vd1352 = vd1354)) <=> (~(Vd1357!2 = Vd1359!0))),
% 0.20/0.52      inference(monotonicity,[status(thm)],[73])).
% 0.20/0.52  tff(75,plain,
% 0.20/0.52      ((~(vd1352 = vd1354)) <=> (~(vd1352 = vd1354))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(76,axiom,(~(vd1352 = vd1354)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''pred(383, 8)'')).
% 0.20/0.52  tff(77,plain,
% 0.20/0.52      (~(vd1352 = vd1354)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.52  tff(78,plain,
% 0.20/0.52      (~(Vd1357!2 = Vd1359!0)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[77, 74])).
% 0.20/0.52  tff(79,plain,
% 0.20/0.52      (vangle(Vd1357!2, Vd1359!0, Vd1358!1) = vangle(vd1352, vd1354, vd1353)),
% 0.20/0.52      inference(monotonicity,[status(thm)],[48, 59, 46])).
% 0.20/0.52  tff(80,plain,
% 0.20/0.52      (vangle(vd1352, vd1354, vd1353) = vangle(Vd1357!2, Vd1359!0, Vd1358!1)),
% 0.20/0.52      inference(symmetry,[status(thm)],[79])).
% 0.20/0.52  tff(81,plain,
% 0.20/0.52      ((vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353)) <=> (vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(82,axiom,(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(383, 1356, 0)'')).
% 0.20/0.52  tff(83,plain,
% 0.20/0.52      (vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.52  tff(84,plain,
% 0.20/0.52      (vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(vd1352, vd1353, vd1354)),
% 0.20/0.52      inference(monotonicity,[status(thm)],[48, 46, 59])).
% 0.20/0.52  tff(85,plain,
% 0.20/0.52      (vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1)),
% 0.20/0.52      inference(transitivity,[status(thm)],[84, 83, 80])).
% 0.20/0.52  tff(86,plain,
% 0.20/0.52      ((Vd1358!1 = Vd1359!0) <=> (vd1353 = vd1354)),
% 0.20/0.52      inference(monotonicity,[status(thm)],[46, 59])).
% 0.20/0.52  tff(87,plain,
% 0.20/0.52      ((vd1353 = vd1354) <=> (Vd1358!1 = Vd1359!0)),
% 0.20/0.52      inference(symmetry,[status(thm)],[86])).
% 0.20/0.52  tff(88,plain,
% 0.20/0.52      ((~(vd1353 = vd1354)) <=> (~(Vd1358!1 = Vd1359!0))),
% 0.20/0.52      inference(monotonicity,[status(thm)],[87])).
% 0.20/0.52  tff(89,plain,
% 0.20/0.52      ((~(vd1353 = vd1354)) <=> (~(vd1353 = vd1354))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(90,axiom,(~(vd1353 = vd1354)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''pred(383, 9)'')).
% 0.20/0.52  tff(91,plain,
% 0.20/0.52      (~(vd1353 = vd1354)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.52  tff(92,plain,
% 0.20/0.52      (~(Vd1358!1 = Vd1359!0)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[91, 88])).
% 0.20/0.52  tff(93,plain,
% 0.20/0.52      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : refl(((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))))),
% 0.20/0.52      inference(bind,[status(th)],[])).
% 0.20/0.52  tff(94,plain,
% 0.20/0.52      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.52      inference(quant_intro,[status(thm)],[93])).
% 0.20/0.52  tff(95,plain,
% 0.20/0.52      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : rewrite(((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))))),
% 0.20/0.52      inference(bind,[status(th)],[])).
% 0.20/0.52  tff(96,plain,
% 0.20/0.52      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.52      inference(quant_intro,[status(thm)],[95])).
% 0.20/0.52  tff(97,plain,
% 0.20/0.52      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.52      inference(transitivity,[status(thm)],[96, 94])).
% 0.20/0.52  tff(98,plain,
% 0.20/0.52      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(quant_intro(proof_bind(^[Vd1368: $i] : trans(monotonicity(rewrite(((Vd1363 = Vd1368) & rpoint(Vd1368)) <=> (~((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))))), ((~((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> (~(~((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))))))), rewrite((~(~((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))))) <=> ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368)))), ((~((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368)))))), (![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))))), quant_intro(proof_bind(^[Vd1367: $i] : trans(monotonicity(rewrite(((Vd1362 = Vd1367) & rpoint(Vd1367)) <=> (~((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))))), ((~((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> (~(~((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))))))), rewrite((~(~((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))))) <=> ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367)))), ((~((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367)))))), (![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))))), quant_intro(proof_bind(^[Vd1366: $i] : trans(monotonicity(rewrite(((Vd1361 = Vd1366) & rpoint(Vd1366)) <=> (~((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))), ((~((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> (~(~((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))))), rewrite((~(~((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) <=> ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))), ((~((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))))), (![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))), (((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))))), rewrite(((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))), (((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))))),
% 0.20/0.53      inference(bind,[status(th)],[])).
% 0.20/0.53  tff(99,plain,
% 0.20/0.53      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.53      inference(quant_intro,[status(thm)],[98])).
% 0.20/0.53  tff(100,plain,
% 0.20/0.53      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(trans(monotonicity(rewrite((~(~(Vd1362 = Vd1363))) <=> (Vd1362 = Vd1363)), rewrite((~(~(Vd1361 = Vd1363))) <=> (Vd1361 = Vd1363)), rewrite((~(~(Vd1361 = Vd1362))) <=> (Vd1361 = Vd1362)), (((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (Vd1362 = Vd1363) | (Vd1361 = Vd1363) | (Vd1361 = Vd1362) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))))), rewrite(((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (Vd1362 = Vd1363) | (Vd1361 = Vd1363) | (Vd1361 = Vd1362) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))), (((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))))), (((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))))), rewrite(((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))), (((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))))),
% 0.20/0.53      inference(bind,[status(th)],[])).
% 0.20/0.53  tff(101,plain,
% 0.20/0.53      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))),
% 0.20/0.53      inference(quant_intro,[status(thm)],[100])).
% 0.20/0.53  tff(102,plain,
% 0.20/0.53      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.20/0.53      inference(rewrite,[status(thm)],[])).
% 0.20/0.53  tff(103,plain,
% 0.20/0.53      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)))), (((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)))), (((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))))), ((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)))), ((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))))), (((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)))), (((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))))), ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))), ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))))), rewrite(((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))), (((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))), (((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))))),
% 0.20/0.53      inference(bind,[status(th)],[])).
% 0.20/0.53  tff(104,plain,
% 0.20/0.53      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.20/0.53      inference(quant_intro,[status(thm)],[103])).
% 0.20/0.53  tff(105,axiom,(![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(proof(385), 0), 2)'')).
% 0.20/0.53  tff(106,plain,
% 0.20/0.53      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.53  tff(107,plain,
% 0.20/0.53      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.53  tff(108,plain,(
% 0.20/0.53      ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.20/0.53      inference(skolemize,[status(sab)],[107])).
% 0.20/0.53  tff(109,plain,
% 0.20/0.53      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[108, 101])).
% 0.20/0.53  tff(110,plain,
% 0.20/0.53      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[109, 99])).
% 0.20/0.53  tff(111,plain,
% 0.20/0.53      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[110, 97])).
% 0.20/0.53  tff(112,plain,
% 0.20/0.53      (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | (Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))),
% 0.20/0.53      inference(rewrite,[status(thm)],[])).
% 0.20/0.53  tff(113,plain,
% 0.20/0.53      (((vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) <=> ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))),
% 0.20/0.53      inference(rewrite,[status(thm)],[])).
% 0.20/0.53  tff(114,plain,
% 0.20/0.53      (^[Vd1367: $i] : rewrite(((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) <=> ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))),
% 0.20/0.53      inference(bind,[status(th)],[])).
% 0.20/0.53  tff(115,plain,
% 0.20/0.53      (![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) <=> ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))),
% 0.20/0.53      inference(quant_intro,[status(thm)],[114])).
% 0.20/0.53  tff(116,plain,
% 0.20/0.53      (^[Vd1368: $i] : rewrite(((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) <=> ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))))),
% 0.20/0.53      inference(bind,[status(th)],[])).
% 0.20/0.53  tff(117,plain,
% 0.20/0.53      (![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) <=> ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368)))),
% 0.20/0.53      inference(quant_intro,[status(thm)],[116])).
% 0.20/0.53  tff(118,plain,
% 0.20/0.53      (((vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) <=> ((vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))))),
% 0.20/0.53      inference(monotonicity,[status(thm)],[117, 115])).
% 0.20/0.53  tff(119,plain,
% 0.20/0.53      (((vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) <=> ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))),
% 0.20/0.53      inference(transitivity,[status(thm)],[118, 113])).
% 0.20/0.53  tff(120,plain,
% 0.20/0.53      (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | ((vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))))),
% 0.20/0.53      inference(monotonicity,[status(thm)],[119])).
% 0.20/0.53  tff(121,plain,
% 0.20/0.53      (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | ((vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | (Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))),
% 0.20/0.53      inference(transitivity,[status(thm)],[120, 112])).
% 0.20/0.53  tff(122,plain,
% 0.20/0.53      ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | ((vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))))),
% 0.20/0.53      inference(quant_inst,[status(thm)],[])).
% 0.20/0.53  tff(123,plain,
% 0.20/0.53      ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | (Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.53  tff(124,plain,
% 0.20/0.53      ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))),
% 0.20/0.53      inference(unit_resolution,[status(thm)],[123, 111])).
% 0.20/0.53  tff(125,plain,
% 0.20/0.53      (![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))),
% 0.20/0.53      inference(unit_resolution,[status(thm)],[124, 92, 85, 78, 71, 55])).
% 0.20/0.53  tff(126,plain,
% 0.20/0.53      (![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))),
% 0.20/0.53      inference(unit_resolution,[status(thm)],[125, 40])).
% 0.20/0.53  tff(127,plain,
% 0.20/0.53      (~rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1))),
% 0.20/0.53      inference(unit_resolution,[status(thm)],[126, 1, 21])).
% 0.20/0.53  tff(128,plain,
% 0.20/0.53      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : refl(((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))))),
% 0.20/0.53      inference(bind,[status(th)],[])).
% 0.20/0.53  tff(129,plain,
% 0.20/0.53      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.53      inference(quant_intro,[status(thm)],[128])).
% 0.20/0.53  tff(130,plain,
% 0.20/0.53      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : rewrite(((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))))),
% 0.20/0.54      inference(bind,[status(th)],[])).
% 0.20/0.54  tff(131,plain,
% 0.20/0.54      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.54      inference(quant_intro,[status(thm)],[130])).
% 0.20/0.54  tff(132,plain,
% 0.20/0.54      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.54      inference(transitivity,[status(thm)],[131, 129])).
% 0.20/0.54  tff(133,plain,
% 0.20/0.54      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(quant_intro(proof_bind(^[Vd1368: $i] : trans(monotonicity(rewrite(((Vd1363 = Vd1368) & rpoint(Vd1368)) <=> (~((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))))), ((~((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> (~(~((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))))))), rewrite((~(~((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))))) <=> ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368)))), ((~((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368)))))), (![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))))), quant_intro(proof_bind(^[Vd1367: $i] : trans(monotonicity(rewrite(((Vd1362 = Vd1367) & rpoint(Vd1367)) <=> (~((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))))), ((~((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> (~(~((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))))))), rewrite((~(~((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))))) <=> ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367)))), ((~((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367)))))), (![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))))), quant_intro(proof_bind(^[Vd1366: $i] : trans(monotonicity(rewrite(((Vd1361 = Vd1366) & rpoint(Vd1366)) <=> (~((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))), ((~((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> (~(~((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))))), rewrite((~(~((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) <=> ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))), ((~((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))))), (![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))), (((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))))), rewrite(((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))), (((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))))),
% 0.20/0.54      inference(bind,[status(th)],[])).
% 0.20/0.54  tff(134,plain,
% 0.20/0.54      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.54      inference(quant_intro,[status(thm)],[133])).
% 0.20/0.54  tff(135,plain,
% 0.20/0.54      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(trans(monotonicity(rewrite((~(~(Vd1362 = Vd1363))) <=> (Vd1362 = Vd1363)), rewrite((~(~(Vd1361 = Vd1363))) <=> (Vd1361 = Vd1363)), rewrite((~(~(Vd1361 = Vd1362))) <=> (Vd1361 = Vd1362)), (((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (Vd1362 = Vd1363) | (Vd1361 = Vd1363) | (Vd1361 = Vd1362) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))))), rewrite(((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (Vd1362 = Vd1363) | (Vd1361 = Vd1363) | (Vd1361 = Vd1362) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))), (((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))))), (((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))))), rewrite(((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))), (((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))))),
% 0.20/0.54      inference(bind,[status(th)],[])).
% 0.20/0.54  tff(136,plain,
% 0.20/0.54      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))),
% 0.20/0.54      inference(quant_intro,[status(thm)],[135])).
% 0.20/0.54  tff(137,plain,
% 0.20/0.54      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.20/0.54      inference(rewrite,[status(thm)],[])).
% 0.20/0.54  tff(138,plain,
% 0.20/0.54      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)))), (((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)))), (((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))))), ((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)))), ((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))))), (((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)))), (((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))))), ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))), ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))))), rewrite(((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)))), (((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))), (((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))))),
% 0.20/0.54      inference(bind,[status(th)],[])).
% 0.20/0.54  tff(139,plain,
% 0.20/0.54      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.20/0.54      inference(quant_intro,[status(thm)],[138])).
% 0.20/0.54  tff(140,axiom,(![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(proof(385), 0), 1)'')).
% 0.20/0.54  tff(141,plain,
% 0.20/0.54      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.20/0.54      inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.54  tff(142,plain,
% 0.20/0.54      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.20/0.54      inference(modus_ponens,[status(thm)],[141, 137])).
% 0.20/0.54  tff(143,plain,(
% 0.20/0.54      ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.20/0.54      inference(skolemize,[status(sab)],[142])).
% 0.20/0.54  tff(144,plain,
% 0.20/0.54      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))),
% 0.20/0.54      inference(modus_ponens,[status(thm)],[143, 136])).
% 0.20/0.54  tff(145,plain,
% 0.20/0.54      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.54      inference(modus_ponens,[status(thm)],[144, 134])).
% 0.20/0.54  tff(146,plain,
% 0.20/0.54      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.54      inference(modus_ponens,[status(thm)],[145, 132])).
% 0.20/0.54  tff(147,plain,
% 0.20/0.54      (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | (~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | (Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | (~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))),
% 0.20/0.54      inference(rewrite,[status(thm)],[])).
% 0.20/0.54  tff(148,plain,
% 0.20/0.54      (((~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) <=> ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | (~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))),
% 0.20/0.54      inference(rewrite,[status(thm)],[])).
% 0.20/0.54  tff(149,plain,
% 0.20/0.54      (((~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) <=> ((~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))))),
% 0.20/0.54      inference(monotonicity,[status(thm)],[117, 115])).
% 0.20/0.54  tff(150,plain,
% 0.20/0.54      (((~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) <=> ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | (~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))),
% 0.20/0.54      inference(transitivity,[status(thm)],[149, 148])).
% 0.20/0.54  tff(151,plain,
% 0.20/0.54      (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | ((~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | (~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))))),
% 0.20/0.54      inference(monotonicity,[status(thm)],[150])).
% 0.20/0.54  tff(152,plain,
% 0.20/0.54      (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | ((~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | (Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | (~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))),
% 0.20/0.54      inference(transitivity,[status(thm)],[151, 147])).
% 0.20/0.54  tff(153,plain,
% 0.20/0.54      ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | ((~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))))),
% 0.20/0.54      inference(quant_inst,[status(thm)],[])).
% 0.20/0.54  tff(154,plain,
% 0.20/0.54      ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | (Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | (~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))),
% 0.20/0.54      inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.54  tff(155,plain,
% 0.20/0.54      ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | (~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))),
% 0.20/0.54      inference(unit_resolution,[status(thm)],[154, 146])).
% 0.20/0.54  tff(156,plain,
% 0.20/0.54      ((~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))),
% 0.20/0.54      inference(unit_resolution,[status(thm)],[155, 92, 85, 78, 55, 71])).
% 0.20/0.54  tff(157,plain,
% 0.20/0.54      ((~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))),
% 0.20/0.54      inference(unit_resolution,[status(thm)],[156, 40])).
% 0.20/0.54  tff(158,plain,
% 0.20/0.54      (~rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0))),
% 0.20/0.54      inference(unit_resolution,[status(thm)],[157, 1, 21])).
% 0.20/0.54  tff(159,plain,
% 0.20/0.54      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : refl((rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))))),
% 0.20/0.54      inference(bind,[status(th)],[])).
% 0.20/0.54  tff(160,plain,
% 0.20/0.54      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.55      inference(quant_intro,[status(thm)],[159])).
% 0.20/0.55  tff(161,plain,
% 0.20/0.55      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : rewrite((rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))))),
% 0.20/0.55      inference(bind,[status(th)],[])).
% 0.20/0.55  tff(162,plain,
% 0.20/0.55      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.55      inference(quant_intro,[status(thm)],[161])).
% 0.20/0.55  tff(163,plain,
% 0.20/0.55      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.20/0.55      inference(transitivity,[status(thm)],[162, 160])).
% 0.20/0.55  tff(164,plain,
% 0.46/0.55      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(quant_intro(proof_bind(^[Vd1368: $i] : trans(monotonicity(rewrite(((Vd1363 = Vd1368) & rpoint(Vd1368)) <=> (~((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))))), ((~((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> (~(~((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))))))), rewrite((~(~((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))))) <=> ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368)))), ((~((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368)))))), (![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))))), quant_intro(proof_bind(^[Vd1367: $i] : trans(monotonicity(rewrite(((Vd1362 = Vd1367) & rpoint(Vd1367)) <=> (~((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))))), ((~((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> (~(~((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))))))), rewrite((~(~((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))))) <=> ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367)))), ((~((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367)))))), (![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))))), quant_intro(proof_bind(^[Vd1366: $i] : trans(monotonicity(rewrite(((Vd1361 = Vd1366) & rpoint(Vd1366)) <=> (~((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))), ((~((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> (~(~((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))))), rewrite((~(~((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) <=> ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))), ((~((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))))), (![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))), ((rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))))), rewrite((rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))), ((rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))))),
% 0.46/0.55      inference(bind,[status(th)],[])).
% 0.46/0.55  tff(165,plain,
% 0.46/0.55      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.46/0.55      inference(quant_intro,[status(thm)],[164])).
% 0.46/0.55  tff(166,plain,
% 0.46/0.55      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(trans(monotonicity(rewrite((~(~(Vd1362 = Vd1363))) <=> (Vd1362 = Vd1363)), rewrite((~(~(Vd1361 = Vd1363))) <=> (Vd1361 = Vd1363)), rewrite((~(~(Vd1361 = Vd1362))) <=> (Vd1361 = Vd1362)), (((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (Vd1362 = Vd1363) | (Vd1361 = Vd1363) | (Vd1361 = Vd1362) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))))), rewrite(((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (Vd1362 = Vd1363) | (Vd1361 = Vd1363) | (Vd1361 = Vd1362) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))), (((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))) <=> ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))))), ((rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))))), rewrite((rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))), ((rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))))),
% 0.46/0.55      inference(bind,[status(th)],[])).
% 0.46/0.55  tff(167,plain,
% 0.46/0.55      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))),
% 0.46/0.55      inference(quant_intro,[status(thm)],[166])).
% 0.46/0.55  tff(168,plain,
% 0.46/0.55      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.46/0.55      inference(rewrite,[status(thm)],[])).
% 0.46/0.55  tff(169,plain,
% 0.46/0.55      (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)))), (((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)))), (((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))))), ((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)))), ((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))))), (((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)))), (((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))))), ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))), ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))))), trans(monotonicity(rewrite((rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)))), (((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)))) <=> ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)))))), rewrite(((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)))), (((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))))), (((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))), (((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))))),
% 0.46/0.55      inference(bind,[status(th)],[])).
% 0.46/0.55  tff(170,plain,
% 0.46/0.55      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.46/0.55      inference(quant_intro,[status(thm)],[169])).
% 0.46/0.55  tff(171,axiom,(![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(proof(385), 0), 0)'')).
% 0.46/0.55  tff(172,plain,
% 0.46/0.55      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.46/0.55      inference(modus_ponens,[status(thm)],[171, 170])).
% 0.46/0.55  tff(173,plain,
% 0.46/0.55      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.46/0.55      inference(modus_ponens,[status(thm)],[172, 168])).
% 0.46/0.55  tff(174,plain,(
% 0.46/0.55      ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | (~(~(Vd1362 = Vd1363))) | (~(~(Vd1361 = Vd1363))) | (~(~(Vd1361 = Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366)))))),
% 0.46/0.55      inference(skolemize,[status(sab)],[173])).
% 0.46/0.55  tff(175,plain,
% 0.46/0.55      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : (~((Vd1363 = Vd1368) & rpoint(Vd1368))) | ![Vd1367: $i] : (~((Vd1362 = Vd1367) & rpoint(Vd1367))) | ![Vd1366: $i] : (~((Vd1361 = Vd1366) & rpoint(Vd1366))))),
% 0.46/0.55      inference(modus_ponens,[status(thm)],[174, 167])).
% 0.46/0.55  tff(176,plain,
% 0.46/0.55      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.46/0.55      inference(modus_ponens,[status(thm)],[175, 165])).
% 0.46/0.55  tff(177,plain,
% 0.46/0.55      (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))),
% 0.46/0.55      inference(modus_ponens,[status(thm)],[176, 163])).
% 0.46/0.55  tff(178,plain,
% 0.46/0.55      (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | (Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))),
% 0.46/0.55      inference(rewrite,[status(thm)],[])).
% 0.46/0.55  tff(179,plain,
% 0.46/0.55      ((rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) <=> ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))),
% 0.46/0.55      inference(rewrite,[status(thm)],[])).
% 0.46/0.55  tff(180,plain,
% 0.46/0.55      ((rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) <=> (rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))))),
% 0.46/0.55      inference(monotonicity,[status(thm)],[117, 115])).
% 0.46/0.55  tff(181,plain,
% 0.46/0.55      ((rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366)))) <=> ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))),
% 0.46/0.55      inference(transitivity,[status(thm)],[180, 179])).
% 0.46/0.55  tff(182,plain,
% 0.46/0.55      (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | (rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))))),
% 0.46/0.55      inference(monotonicity,[status(thm)],[181])).
% 0.46/0.55  tff(183,plain,
% 0.46/0.55      (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | (rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | (Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367))))),
% 0.46/0.56      inference(transitivity,[status(thm)],[182, 178])).
% 0.46/0.56  tff(184,plain,
% 0.46/0.56      ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | (rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | (Vd1357!2 = Vd1359!0) | (Vd1358!1 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | ![Vd1368: $i] : ((~(Vd1359!0 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1358!1 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))))),
% 0.46/0.56      inference(quant_inst,[status(thm)],[])).
% 0.46/0.56  tff(185,plain,
% 0.46/0.56      ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))) | ![Vd1368: $i] : ((~(Vd1363 = Vd1368)) | (~rpoint(Vd1368))) | ![Vd1367: $i] : ((~(Vd1362 = Vd1367)) | (~rpoint(Vd1367))) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1361 = Vd1366))))) | (Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))),
% 0.46/0.56      inference(modus_ponens,[status(thm)],[184, 183])).
% 0.46/0.56  tff(186,plain,
% 0.46/0.56      ((Vd1357!2 = Vd1359!0) | (Vd1357!2 = Vd1358!1) | (Vd1358!1 = Vd1359!0) | (~(vangle(Vd1357!2, Vd1358!1, Vd1359!0) = vangle(Vd1357!2, Vd1359!0, Vd1358!1))) | rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | (vf(Vd1357!2, Vd1358!1) = vf(Vd1357!2, Vd1359!0)) | rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))),
% 0.46/0.56      inference(unit_resolution,[status(thm)],[185, 177])).
% 0.46/0.56  tff(187,plain,
% 0.46/0.56      (rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | ![Vd1368: $i] : ((~rpoint(Vd1368)) | (~(Vd1359!0 = Vd1368))) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))),
% 0.46/0.56      inference(unit_resolution,[status(thm)],[186, 92, 85, 78, 55, 71])).
% 0.46/0.56  tff(188,plain,
% 0.46/0.56      (rless(vf(Vd1357!2, Vd1358!1), vf(Vd1357!2, Vd1359!0)) | ![Vd1366: $i] : ((~rpoint(Vd1366)) | (~(Vd1357!2 = Vd1366))) | rless(vf(Vd1357!2, Vd1359!0), vf(Vd1357!2, Vd1358!1)) | ![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))),
% 0.46/0.56      inference(unit_resolution,[status(thm)],[187, 40])).
% 0.46/0.56  tff(189,plain,
% 0.46/0.56      ($false),
% 0.46/0.56      inference(unit_resolution,[status(thm)],[188, 158, 127, 21, 1])).
% 0.46/0.56  tff(190,plain,(![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.56  tff(191,plain,
% 0.46/0.56      (rpoint(Vd1358!1)),
% 0.46/0.56      inference(and_elim,[status(thm)],[44])).
% 0.46/0.56  tff(192,plain,
% 0.46/0.56      (((~![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))) | (~rpoint(Vd1358!1))) <=> ((~![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))) | (~rpoint(Vd1358!1)))),
% 0.48/0.57      inference(rewrite,[status(thm)],[])).
% 0.48/0.57  tff(193,plain,
% 0.48/0.57      (((~rpoint(Vd1358!1)) | $false) <=> (~rpoint(Vd1358!1))),
% 0.48/0.57      inference(rewrite,[status(thm)],[])).
% 0.48/0.57  tff(194,plain,
% 0.48/0.57      ((Vd1358!1 = Vd1358!1) <=> $true),
% 0.48/0.57      inference(rewrite,[status(thm)],[])).
% 0.48/0.57  tff(195,plain,
% 0.48/0.57      ((~(Vd1358!1 = Vd1358!1)) <=> (~$true)),
% 0.48/0.57      inference(monotonicity,[status(thm)],[194])).
% 0.48/0.57  tff(196,plain,
% 0.48/0.57      ((~(Vd1358!1 = Vd1358!1)) <=> $false),
% 0.48/0.57      inference(transitivity,[status(thm)],[195, 10])).
% 0.48/0.57  tff(197,plain,
% 0.48/0.57      (((~rpoint(Vd1358!1)) | (~(Vd1358!1 = Vd1358!1))) <=> ((~rpoint(Vd1358!1)) | $false)),
% 0.48/0.57      inference(monotonicity,[status(thm)],[196])).
% 0.48/0.57  tff(198,plain,
% 0.48/0.57      (((~rpoint(Vd1358!1)) | (~(Vd1358!1 = Vd1358!1))) <=> (~rpoint(Vd1358!1))),
% 0.48/0.57      inference(transitivity,[status(thm)],[197, 193])).
% 0.48/0.57  tff(199,plain,
% 0.48/0.57      (((~![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))) | ((~rpoint(Vd1358!1)) | (~(Vd1358!1 = Vd1358!1)))) <=> ((~![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))) | (~rpoint(Vd1358!1)))),
% 0.48/0.57      inference(monotonicity,[status(thm)],[198])).
% 0.48/0.57  tff(200,plain,
% 0.48/0.57      (((~![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))) | ((~rpoint(Vd1358!1)) | (~(Vd1358!1 = Vd1358!1)))) <=> ((~![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))) | (~rpoint(Vd1358!1)))),
% 0.48/0.57      inference(transitivity,[status(thm)],[199, 192])).
% 0.48/0.57  tff(201,plain,
% 0.48/0.57      ((~![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))) | ((~rpoint(Vd1358!1)) | (~(Vd1358!1 = Vd1358!1)))),
% 0.48/0.57      inference(quant_inst,[status(thm)],[])).
% 0.48/0.57  tff(202,plain,
% 0.48/0.57      ((~![Vd1367: $i] : ((~rpoint(Vd1367)) | (~(Vd1358!1 = Vd1367)))) | (~rpoint(Vd1358!1))),
% 0.48/0.57      inference(modus_ponens,[status(thm)],[201, 200])).
% 0.48/0.57  tff(203,plain,
% 0.48/0.57      ($false),
% 0.48/0.57      inference(unit_resolution,[status(thm)],[202, 191, 190])).
% 0.48/0.57  % SZS output end Proof
%------------------------------------------------------------------------------