%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GEO011-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n006.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 20:34:15 EDT 2022

% Result   : Unsatisfiable 0.19s 0.47s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO011-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 31 04:35:54 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.19/0.47  % SZS status Unsatisfiable
% 0.19/0.47  % SZS output start Proof
% 0.19/0.47  tff(between_type, type, (
% 0.19/0.47     between: ( $i * $i * $i ) > $o)).
% 0.19/0.47  tff(outer_pasch_type, type, (
% 0.19/0.47     outer_pasch: ( $i * $i * $i * $i * $i ) > $i)).
% 0.19/0.47  tff(lower_dimension_point_3_type, type, (
% 0.19/0.47     lower_dimension_point_3: $i)).
% 0.19/0.47  tff(lower_dimension_point_2_type, type, (
% 0.19/0.47     lower_dimension_point_2: $i)).
% 0.19/0.47  tff(lower_dimension_point_1_type, type, (
% 0.19/0.47     lower_dimension_point_1: $i)).
% 0.19/0.47  tff(extension_type, type, (
% 0.19/0.47     extension: ( $i * $i * $i * $i ) > $i)).
% 0.19/0.47  tff(equidistant_type, type, (
% 0.19/0.47     equidistant: ( $i * $i * $i * $i ) > $o)).
% 0.19/0.47  tff(colinear_type, type, (
% 0.19/0.47     colinear: ( $i * $i * $i ) > $o)).
% 0.19/0.47  tff(1,plain,
% 0.19/0.47      (^[W: $i, V: $i, Y: $i, X: $i] : refl(equidistant(Y, extension(X, Y, W, V), W, V) <=> equidistant(Y, extension(X, Y, W, V), W, V))),
% 0.19/0.47      inference(bind,[status(th)],[])).
% 0.19/0.47  tff(2,plain,
% 0.19/0.47      (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V) <=> ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.19/0.47      inference(quant_intro,[status(thm)],[1])).
% 0.19/0.47  tff(3,plain,
% 0.19/0.47      (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V) <=> ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(4,axiom,(![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','segment_construction2')).
% 0.19/0.47  tff(5,plain,
% 0.19/0.47      (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.47  tff(6,plain,(
% 0.19/0.47      ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.19/0.47      inference(skolemize,[status(sab)],[5])).
% 0.19/0.47  tff(7,plain,
% 0.19/0.47      (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.47  tff(8,plain,
% 0.19/0.47      ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(lower_dimension_point_2, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)),
% 0.19/0.47      inference(quant_inst,[status(thm)],[])).
% 0.19/0.47  tff(9,plain,
% 0.19/0.47      (equidistant(lower_dimension_point_2, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)),
% 0.19/0.47      inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.47  tff(10,plain,
% 0.19/0.47      (^[Z: $i, Y: $i, X: $i] : refl(((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ((~equidistant(X, Y, Z, Z)) | (X = Y)))),
% 0.19/0.47      inference(bind,[status(th)],[])).
% 0.19/0.47  tff(11,plain,
% 0.19/0.47      (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.19/0.47      inference(quant_intro,[status(thm)],[10])).
% 0.19/0.47  tff(12,plain,
% 0.19/0.47      (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(13,axiom,(![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','identity_for_equidistance')).
% 0.19/0.47  tff(14,plain,
% 0.19/0.47      (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.47  tff(15,plain,(
% 0.19/0.47      ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.19/0.47      inference(skolemize,[status(sab)],[14])).
% 0.19/0.47  tff(16,plain,
% 0.19/0.47      (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.47  tff(17,plain,
% 0.19/0.47      (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(lower_dimension_point_2, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (lower_dimension_point_2 = extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(lower_dimension_point_2, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (lower_dimension_point_2 = extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(18,plain,
% 0.19/0.47      ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(lower_dimension_point_2, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (lower_dimension_point_2 = extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.47      inference(quant_inst,[status(thm)],[])).
% 0.19/0.47  tff(19,plain,
% 0.19/0.47      ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(lower_dimension_point_2, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (lower_dimension_point_2 = extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.47  tff(20,plain,
% 0.19/0.47      (lower_dimension_point_2 = extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)),
% 0.19/0.47      inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.19/0.47  tff(21,plain,
% 0.19/0.47      (extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) = lower_dimension_point_2),
% 0.19/0.47      inference(symmetry,[status(thm)],[20])).
% 0.19/0.47  tff(22,plain,
% 0.19/0.47      (outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3) = outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)),
% 0.19/0.47      inference(monotonicity,[status(thm)],[21, 21])).
% 0.19/0.47  tff(23,plain,
% 0.19/0.47      (outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) = outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)),
% 0.19/0.47      inference(symmetry,[status(thm)],[22])).
% 0.19/0.47  tff(24,plain,
% 0.19/0.47      (between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) <=> between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.47      inference(monotonicity,[status(thm)],[23])).
% 0.19/0.47  tff(25,plain,
% 0.19/0.47      (between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) <=> between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.47      inference(symmetry,[status(thm)],[24])).
% 0.19/0.47  tff(26,plain,
% 0.19/0.47      (between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3) <=> between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)),
% 0.19/0.47      inference(monotonicity,[status(thm)],[21])).
% 0.19/0.47  tff(27,plain,
% 0.19/0.47      (between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) <=> between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)),
% 0.19/0.47      inference(symmetry,[status(thm)],[26])).
% 0.19/0.47  tff(28,plain,
% 0.19/0.47      (between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) <=> between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)),
% 0.19/0.47      inference(monotonicity,[status(thm)],[21])).
% 0.19/0.47  tff(29,plain,
% 0.19/0.47      (between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2) <=> between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.47      inference(symmetry,[status(thm)],[28])).
% 0.19/0.47  tff(30,assumption,(between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)), introduced(assumption)).
% 0.19/0.47  tff(31,plain,
% 0.19/0.47      (between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.47  tff(32,assumption,(lower_dimension_point_1 = lower_dimension_point_3), introduced(assumption)).
% 0.19/0.47  tff(33,plain,
% 0.19/0.47      (lower_dimension_point_3 = lower_dimension_point_1),
% 0.19/0.47      inference(symmetry,[status(thm)],[32])).
% 0.19/0.47  tff(34,plain,
% 0.19/0.47      (between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2) <=> between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)),
% 0.19/0.47      inference(monotonicity,[status(thm)],[33, 32])).
% 0.19/0.47  tff(35,plain,
% 0.19/0.47      (between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2) <=> between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2)),
% 0.19/0.47      inference(symmetry,[status(thm)],[34])).
% 0.19/0.47  tff(36,plain,
% 0.19/0.47      (between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2)),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[30, 35])).
% 0.19/0.47  tff(37,plain,
% 0.19/0.47      ((~between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2)) <=> (~between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(38,axiom,(~between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2)), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','lower_dimension3')).
% 0.19/0.47  tff(39,plain,
% 0.19/0.47      (~between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2)),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.47  tff(40,plain,
% 0.19/0.47      ($false),
% 0.19/0.47      inference(unit_resolution,[status(thm)],[39, 36])).
% 0.19/0.47  tff(41,plain,((~(lower_dimension_point_1 = lower_dimension_point_3)) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47  tff(42,plain,
% 0.19/0.47      (~(lower_dimension_point_1 = lower_dimension_point_3)),
% 0.19/0.47      inference(unit_resolution,[status(thm)],[41, 30])).
% 0.19/0.47  tff(43,assumption,(~(lower_dimension_point_1 = lower_dimension_point_3)), introduced(assumption)).
% 0.19/0.47  tff(44,assumption,(~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))), introduced(assumption)).
% 0.19/0.47  tff(45,assumption,(between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))), introduced(assumption)).
% 0.19/0.47  tff(46,plain,
% 0.19/0.47      (^[V: $i, Z: $i, Y: $i, X: $i] : refl(((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z))) <=> ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z))))),
% 0.19/0.47      inference(bind,[status(th)],[])).
% 0.19/0.47  tff(47,plain,
% 0.19/0.47      (![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z))) <=> ![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 0.19/0.47      inference(quant_intro,[status(thm)],[46])).
% 0.19/0.47  tff(48,plain,
% 0.19/0.47      (![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z))) <=> ![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(49,plain,
% 0.19/0.47      (^[V: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) <=> ((X = Y) | (~between(X, Y, V)) | (~between(X, Y, Z)))), (((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) | between(X, Z, V)) <=> (((X = Y) | (~between(X, Y, V)) | (~between(X, Y, Z))) | between(X, Z, V)))), rewrite((((X = Y) | (~between(X, Y, V)) | (~between(X, Y, Z))) | between(X, Z, V)) <=> ((X = Y) | (~between(X, Y, V)) | between(X, Z, V) | (~between(X, Y, Z)))), (((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) | between(X, Z, V)) <=> ((X = Y) | (~between(X, Y, V)) | between(X, Z, V) | (~between(X, Y, Z))))), ((((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) | between(X, Z, V)) | between(X, V, Z)) <=> (((X = Y) | (~between(X, Y, V)) | between(X, Z, V) | (~between(X, Y, Z))) | between(X, V, Z)))), rewrite((((X = Y) | (~between(X, Y, V)) | between(X, Z, V) | (~between(X, Y, Z))) | between(X, V, Z)) <=> ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))), ((((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) | between(X, Z, V)) | between(X, V, Z)) <=> ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))))),
% 0.19/0.47      inference(bind,[status(th)],[])).
% 0.19/0.47  tff(50,plain,
% 0.19/0.47      (![V: $i, Z: $i, Y: $i, X: $i] : (((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) | between(X, Z, V)) | between(X, V, Z)) <=> ![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 0.19/0.47      inference(quant_intro,[status(thm)],[49])).
% 0.19/0.47  tff(51,axiom,(![V: $i, Z: $i, Y: $i, X: $i] : (((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) | between(X, Z, V)) | between(X, V, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','connectivity_for_betweeness')).
% 0.19/0.47  tff(52,plain,
% 0.19/0.47      (![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.47  tff(53,plain,
% 0.19/0.47      (![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.47  tff(54,plain,(
% 0.19/0.47      ![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 0.19/0.47      inference(skolemize,[status(sab)],[53])).
% 0.19/0.47  tff(55,plain,
% 0.19/0.47      (![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 0.19/0.47      inference(modus_ponens,[status(thm)],[54, 47])).
% 0.19/0.47  tff(56,plain,
% 0.19/0.47      (((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | ((~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (lower_dimension_point_1 = lower_dimension_point_3) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))) <=> ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (lower_dimension_point_1 = lower_dimension_point_3) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(57,plain,
% 0.19/0.47      (((lower_dimension_point_1 = lower_dimension_point_3) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))) <=> ((~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (lower_dimension_point_1 = lower_dimension_point_3) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.47      inference(rewrite,[status(thm)],[])).
% 0.19/0.47  tff(58,plain,
% 0.19/0.47      (((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | ((lower_dimension_point_1 = lower_dimension_point_3) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))) <=> ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | ((~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (lower_dimension_point_1 = lower_dimension_point_3) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.47      inference(monotonicity,[status(thm)],[57])).
% 0.19/0.47  tff(59,plain,
% 0.19/0.47      (((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | ((lower_dimension_point_1 = lower_dimension_point_3) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))) <=> ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (lower_dimension_point_1 = lower_dimension_point_3) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.47      inference(transitivity,[status(thm)],[58, 56])).
% 0.19/0.47  tff(60,plain,
% 0.19/0.47      ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | ((lower_dimension_point_1 = lower_dimension_point_3) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.47      inference(quant_inst,[status(thm)],[])).
% 0.19/0.47  tff(61,plain,
% 0.19/0.47      ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (lower_dimension_point_1 = lower_dimension_point_3) | between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.48  tff(62,plain,
% 0.19/0.48      ($false),
% 0.19/0.48      inference(unit_resolution,[status(thm)],[61, 55, 45, 44, 43])).
% 0.19/0.48  tff(63,plain,(between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (lower_dimension_point_1 = lower_dimension_point_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48  tff(64,plain,
% 0.19/0.48      (between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.48      inference(unit_resolution,[status(thm)],[63, 31, 42])).
% 0.19/0.48  tff(65,plain,
% 0.19/0.48      (^[W: $i, V: $i, Z: $i, Y: $i, X: $i] : refl((between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V))) <=> (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V))))),
% 0.19/0.48      inference(bind,[status(th)],[])).
% 0.19/0.48  tff(66,plain,
% 0.19/0.48      (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 0.19/0.48      inference(quant_intro,[status(thm)],[65])).
% 0.19/0.48  tff(67,plain,
% 0.19/0.48      (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 0.19/0.48      inference(rewrite,[status(thm)],[])).
% 0.19/0.48  tff(68,plain,
% 0.19/0.48      (^[W: $i, V: $i, Z: $i, Y: $i, X: $i] : rewrite((((~between(X, W, V)) | (~between(Y, V, Z))) | between(X, outer_pasch(W, X, Y, Z, V), Y)) <=> (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V))))),
% 0.19/0.48      inference(bind,[status(th)],[])).
% 0.19/0.48  tff(69,plain,
% 0.19/0.48      (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (((~between(X, W, V)) | (~between(Y, V, Z))) | between(X, outer_pasch(W, X, Y, Z, V), Y)) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 0.19/0.48      inference(quant_intro,[status(thm)],[68])).
% 0.19/0.48  tff(70,axiom,(![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (((~between(X, W, V)) | (~between(Y, V, Z))) | between(X, outer_pasch(W, X, Y, Z, V), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','outer_pasch1')).
% 0.19/0.48  tff(71,plain,
% 0.19/0.48      (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.48  tff(72,plain,
% 0.19/0.48      (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.48  tff(73,plain,(
% 0.19/0.48      ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 0.19/0.48      inference(skolemize,[status(sab)],[72])).
% 0.19/0.48  tff(74,plain,
% 0.19/0.48      (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.48  tff(75,plain,
% 0.19/0.48      (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.48      inference(rewrite,[status(thm)],[])).
% 0.19/0.48  tff(76,plain,
% 0.19/0.48      ((between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))) <=> (between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.48      inference(rewrite,[status(thm)],[])).
% 0.19/0.48  tff(77,plain,
% 0.19/0.48      (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))))),
% 0.19/0.48      inference(monotonicity,[status(thm)],[76])).
% 0.19/0.48  tff(78,plain,
% 0.19/0.48      (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.48      inference(transitivity,[status(thm)],[77, 75])).
% 0.19/0.48  tff(79,plain,
% 0.19/0.48      ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.48      inference(quant_inst,[status(thm)],[])).
% 0.19/0.48  tff(80,plain,
% 0.19/0.48      ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.48  tff(81,plain,
% 0.19/0.48      (between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.48      inference(unit_resolution,[status(thm)],[80, 74])).
% 0.19/0.48  tff(82,plain,
% 0.19/0.48      (between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1)),
% 0.19/0.48      inference(unit_resolution,[status(thm)],[81, 64, 31])).
% 0.19/0.48  tff(83,plain,
% 0.19/0.48      (^[Y: $i, X: $i] : refl(((~between(X, Y, X)) | (X = Y)) <=> ((~between(X, Y, X)) | (X = Y)))),
% 0.19/0.48      inference(bind,[status(th)],[])).
% 0.19/0.48  tff(84,plain,
% 0.19/0.48      (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y)) <=> ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.19/0.48      inference(quant_intro,[status(thm)],[83])).
% 0.19/0.48  tff(85,plain,
% 0.19/0.48      (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y)) <=> ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.19/0.48      inference(rewrite,[status(thm)],[])).
% 0.19/0.48  tff(86,axiom,(![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','identity_for_betweeness')).
% 0.19/0.48  tff(87,plain,
% 0.19/0.48      (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.48  tff(88,plain,(
% 0.19/0.48      ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.19/0.48      inference(skolemize,[status(sab)],[87])).
% 0.19/0.48  tff(89,plain,
% 0.19/0.48      (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[88, 84])).
% 0.19/0.48  tff(90,plain,
% 0.19/0.48      (((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1)) | (lower_dimension_point_1 = outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))) <=> ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1)) | (lower_dimension_point_1 = outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.48      inference(rewrite,[status(thm)],[])).
% 0.19/0.48  tff(91,plain,
% 0.19/0.48      ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1)) | (lower_dimension_point_1 = outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.48      inference(quant_inst,[status(thm)],[])).
% 0.19/0.48  tff(92,plain,
% 0.19/0.48      ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), lower_dimension_point_1)) | (lower_dimension_point_1 = outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.48  tff(93,plain,
% 0.19/0.48      (lower_dimension_point_1 = outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.48      inference(unit_resolution,[status(thm)],[92, 89, 82])).
% 0.19/0.48  tff(94,plain,
% 0.19/0.48      (outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) = lower_dimension_point_1),
% 0.19/0.48      inference(symmetry,[status(thm)],[93])).
% 0.19/0.48  tff(95,plain,
% 0.19/0.48      (between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) <=> between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1)),
% 0.19/0.48      inference(monotonicity,[status(thm)],[21, 94])).
% 0.19/0.48  tff(96,plain,
% 0.19/0.48      (between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1) <=> between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.48      inference(symmetry,[status(thm)],[95])).
% 0.19/0.48  tff(97,plain,
% 0.19/0.48      ((~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1)) <=> (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.48      inference(monotonicity,[status(thm)],[96])).
% 0.19/0.48  tff(98,plain,
% 0.19/0.48      ((~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1)) <=> (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1))),
% 0.19/0.48      inference(rewrite,[status(thm)],[])).
% 0.19/0.48  tff(99,axiom,(~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1)), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','lower_dimension2')).
% 0.19/0.48  tff(100,plain,
% 0.19/0.48      (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1)),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.48  tff(101,plain,
% 0.19/0.48      (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[100, 97])).
% 0.19/0.48  tff(102,plain,
% 0.19/0.48      (^[W: $i, V: $i, Z: $i, Y: $i, X: $i] : refl(((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V))) <=> ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V))))),
% 0.19/0.48      inference(bind,[status(th)],[])).
% 0.19/0.48  tff(103,plain,
% 0.19/0.48      (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 0.19/0.48      inference(quant_intro,[status(thm)],[102])).
% 0.19/0.48  tff(104,plain,
% 0.19/0.48      (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 0.19/0.48      inference(rewrite,[status(thm)],[])).
% 0.19/0.48  tff(105,plain,
% 0.19/0.48      (^[W: $i, V: $i, Z: $i, Y: $i, X: $i] : rewrite((((~between(X, W, V)) | (~between(Y, V, Z))) | between(Z, W, outer_pasch(W, X, Y, Z, V))) <=> ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V))))),
% 0.19/0.48      inference(bind,[status(th)],[])).
% 0.19/0.48  tff(106,plain,
% 0.19/0.48      (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (((~between(X, W, V)) | (~between(Y, V, Z))) | between(Z, W, outer_pasch(W, X, Y, Z, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 0.19/0.48      inference(quant_intro,[status(thm)],[105])).
% 0.19/0.48  tff(107,axiom,(![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (((~between(X, W, V)) | (~between(Y, V, Z))) | between(Z, W, outer_pasch(W, X, Y, Z, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','outer_pasch2')).
% 0.19/0.48  tff(108,plain,
% 0.19/0.48      (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.48  tff(109,plain,
% 0.19/0.48      (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[108, 104])).
% 0.19/0.48  tff(110,plain,(
% 0.19/0.48      ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 0.19/0.48      inference(skolemize,[status(sab)],[109])).
% 0.19/0.48  tff(111,plain,
% 0.19/0.48      (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 0.19/0.48      inference(modus_ponens,[status(thm)],[110, 103])).
% 0.19/0.48  tff(112,plain,
% 0.19/0.48      (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.48      inference(rewrite,[status(thm)],[])).
% 0.19/0.48  tff(113,plain,
% 0.19/0.48      (((~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))) <=> ((~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(114,plain,
% 0.19/0.49      (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))))),
% 0.19/0.49      inference(monotonicity,[status(thm)],[113])).
% 0.19/0.49  tff(115,plain,
% 0.19/0.49      (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.49      inference(transitivity,[status(thm)],[114, 112])).
% 0.19/0.49  tff(116,plain,
% 0.19/0.49      ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.49      inference(quant_inst,[status(thm)],[])).
% 0.19/0.49  tff(117,plain,
% 0.19/0.49      ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | (~between(lower_dimension_point_1, lower_dimension_point_3, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (~between(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.49  tff(118,plain,
% 0.19/0.49      (between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[117, 111, 64, 31])).
% 0.19/0.49  tff(119,plain,
% 0.19/0.49      ($false),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[118, 101])).
% 0.19/0.49  tff(120,plain,(~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49  tff(121,plain,
% 0.19/0.49      (colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) <=> colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(122,axiom,(colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_lower_dimension_points_not_colinear')).
% 0.19/0.49  tff(123,plain,
% 0.19/0.49      (colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.49  tff(124,plain,
% 0.19/0.49      (^[Z: $i, Y: $i, X: $i] : refl((between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y)) <=> (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y)))),
% 0.19/0.49      inference(bind,[status(th)],[])).
% 0.19/0.49  tff(125,plain,
% 0.19/0.49      (![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y)) <=> ![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))),
% 0.19/0.49      inference(quant_intro,[status(thm)],[124])).
% 0.19/0.49  tff(126,plain,
% 0.19/0.49      (![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y)) <=> ![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(127,plain,
% 0.19/0.49      (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, X, Z)) <=> (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)))), (((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, X, Z)) | between(X, Z, Y)) <=> ((between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z))) | between(X, Z, Y)))), rewrite(((between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z))) | between(X, Z, Y)) <=> (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))), (((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, X, Z)) | between(X, Z, Y)) <=> (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))))),
% 0.19/0.49      inference(bind,[status(th)],[])).
% 0.19/0.49  tff(128,plain,
% 0.19/0.49      (![Z: $i, Y: $i, X: $i] : ((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, X, Z)) | between(X, Z, Y)) <=> ![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))),
% 0.19/0.49      inference(quant_intro,[status(thm)],[127])).
% 0.19/0.49  tff(129,axiom,(![Z: $i, Y: $i, X: $i] : ((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, X, Z)) | between(X, Z, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-1.ax','colinearity1')).
% 0.19/0.49  tff(130,plain,
% 0.19/0.49      (![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.49  tff(131,plain,
% 0.19/0.49      (![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[130, 126])).
% 0.19/0.49  tff(132,plain,(
% 0.19/0.49      ![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))),
% 0.19/0.49      inference(skolemize,[status(sab)],[131])).
% 0.19/0.49  tff(133,plain,
% 0.19/0.49      (![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[132, 125])).
% 0.19/0.49  tff(134,plain,
% 0.19/0.49      ((~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)) <=> (~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(135,axiom,(~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','lower_dimension1')).
% 0.19/0.49  tff(136,plain,
% 0.19/0.49      (~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.49  tff(137,plain,
% 0.19/0.49      (((~![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))) | (between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) | between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2) | between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3) | (~colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) | between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2) | between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3) | (~colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(138,plain,
% 0.19/0.49      ((between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) | between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3) | (~colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)) | between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)) <=> (between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) | between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2) | between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3) | (~colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(139,plain,
% 0.19/0.49      (((~![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))) | (between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) | between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3) | (~colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)) | between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))) | (between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) | between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2) | between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3) | (~colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3))))),
% 0.19/0.49      inference(monotonicity,[status(thm)],[138])).
% 0.19/0.49  tff(140,plain,
% 0.19/0.49      (((~![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))) | (between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) | between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3) | (~colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)) | between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) | between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2) | between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3) | (~colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)))),
% 0.19/0.49      inference(transitivity,[status(thm)],[139, 137])).
% 0.19/0.49  tff(141,plain,
% 0.19/0.49      ((~![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))) | (between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) | between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3) | (~colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)) | between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2))),
% 0.19/0.49      inference(quant_inst,[status(thm)],[])).
% 0.19/0.49  tff(142,plain,
% 0.19/0.49      ((~![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) | between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2) | between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3) | (~colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3))),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.49  tff(143,plain,
% 0.19/0.49      (between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2) | between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[142, 136, 133, 123])).
% 0.19/0.49  tff(144,plain,
% 0.19/0.49      (between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[143, 120])).
% 0.19/0.49  tff(145,assumption,(~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), introduced(assumption)).
% 0.19/0.49  tff(146,assumption,(between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)), introduced(assumption)).
% 0.19/0.49  tff(147,assumption,(lower_dimension_point_2 = lower_dimension_point_1), introduced(assumption)).
% 0.19/0.49  tff(148,plain,
% 0.19/0.49      (lower_dimension_point_1 = lower_dimension_point_2),
% 0.19/0.49      inference(symmetry,[status(thm)],[147])).
% 0.19/0.49  tff(149,plain,
% 0.19/0.49      (between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3) <=> between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)),
% 0.19/0.49      inference(monotonicity,[status(thm)],[147, 148])).
% 0.19/0.49  tff(150,plain,
% 0.19/0.49      (between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) <=> between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)),
% 0.19/0.49      inference(symmetry,[status(thm)],[149])).
% 0.19/0.49  tff(151,plain,
% 0.19/0.49      ((~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)) <=> (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3))),
% 0.19/0.49      inference(monotonicity,[status(thm)],[150])).
% 0.19/0.49  tff(152,plain,
% 0.19/0.49      (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[136, 151])).
% 0.19/0.49  tff(153,plain,
% 0.19/0.49      ($false),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[146, 152])).
% 0.19/0.49  tff(154,plain,((~(lower_dimension_point_2 = lower_dimension_point_1)) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49  tff(155,plain,
% 0.19/0.49      (~(lower_dimension_point_2 = lower_dimension_point_1)),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[154, 146])).
% 0.19/0.49  tff(156,plain,
% 0.19/0.49      (((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | ((~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | (lower_dimension_point_2 = lower_dimension_point_1))) <=> ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | (lower_dimension_point_2 = lower_dimension_point_1))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(157,plain,
% 0.19/0.49      (((lower_dimension_point_2 = lower_dimension_point_1) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3))) <=> ((~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | (lower_dimension_point_2 = lower_dimension_point_1))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(158,plain,
% 0.19/0.49      (((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | ((lower_dimension_point_2 = lower_dimension_point_1) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)))) <=> ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | ((~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | (lower_dimension_point_2 = lower_dimension_point_1)))),
% 0.19/0.49      inference(monotonicity,[status(thm)],[157])).
% 0.19/0.49  tff(159,plain,
% 0.19/0.49      (((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | ((lower_dimension_point_2 = lower_dimension_point_1) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)))) <=> ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | (lower_dimension_point_2 = lower_dimension_point_1))),
% 0.19/0.49      inference(transitivity,[status(thm)],[158, 156])).
% 0.19/0.49  tff(160,plain,
% 0.19/0.49      ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | ((lower_dimension_point_2 = lower_dimension_point_1) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)))),
% 0.19/0.49      inference(quant_inst,[status(thm)],[])).
% 0.19/0.49  tff(161,plain,
% 0.19/0.49      ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | (lower_dimension_point_2 = lower_dimension_point_1)),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.49  tff(162,plain,
% 0.19/0.49      ($false),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[161, 55, 146, 155, 145])).
% 0.19/0.49  tff(163,plain,(between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49  tff(164,plain,
% 0.19/0.49      (between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[163, 144])).
% 0.19/0.49  tff(165,plain,
% 0.19/0.49      (between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[164, 27])).
% 0.19/0.49  tff(166,plain,
% 0.19/0.49      (between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_3) <=> between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)),
% 0.19/0.49      inference(monotonicity,[status(thm)],[21])).
% 0.19/0.49  tff(167,plain,
% 0.19/0.49      (between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3) <=> between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_3)),
% 0.19/0.49      inference(symmetry,[status(thm)],[166])).
% 0.19/0.49  tff(168,plain,
% 0.19/0.49      (between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_3)),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[144, 167])).
% 0.19/0.49  tff(169,plain,
% 0.19/0.49      (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | ((~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_3)) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_3)) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(170,plain,
% 0.19/0.49      ((between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_3))) <=> ((~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_3)) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(171,plain,
% 0.19/0.49      (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_3)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | ((~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_3)) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.49      inference(monotonicity,[status(thm)],[170])).
% 0.19/0.49  tff(172,plain,
% 0.19/0.49      (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_3)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_3)) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.50      inference(transitivity,[status(thm)],[171, 169])).
% 0.19/0.50  tff(173,plain,
% 0.19/0.50      ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_3)))),
% 0.19/0.50      inference(quant_inst,[status(thm)],[])).
% 0.19/0.50  tff(174,plain,
% 0.19/0.50      ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_3)) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.50      inference(modus_ponens,[status(thm)],[173, 172])).
% 0.19/0.50  tff(175,plain,
% 0.19/0.50      ((~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.50      inference(unit_resolution,[status(thm)],[174, 74, 168])).
% 0.19/0.50  tff(176,plain,
% 0.19/0.50      (between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.50      inference(unit_resolution,[status(thm)],[175, 165])).
% 0.19/0.50  tff(177,plain,
% 0.19/0.50      (between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.50      inference(modus_ponens,[status(thm)],[176, 25])).
% 0.19/0.50  tff(178,plain,
% 0.19/0.50      (((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) = outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))) <=> ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) = outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.50      inference(rewrite,[status(thm)],[])).
% 0.19/0.50  tff(179,plain,
% 0.19/0.50      ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) = outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.50      inference(quant_inst,[status(thm)],[])).
% 0.19/0.50  tff(180,plain,
% 0.19/0.50      ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) = outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.50      inference(modus_ponens,[status(thm)],[179, 178])).
% 0.19/0.50  tff(181,plain,
% 0.19/0.50      ((~between(extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3), extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) | (extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) = outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.50      inference(unit_resolution,[status(thm)],[180, 89])).
% 0.19/0.50  tff(182,plain,
% 0.19/0.50      (extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) = outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)),
% 0.19/0.50      inference(unit_resolution,[status(thm)],[181, 177])).
% 0.19/0.50  tff(183,plain,
% 0.19/0.50      (outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) = extension(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)),
% 0.19/0.50      inference(symmetry,[status(thm)],[182])).
% 0.19/0.50  tff(184,plain,
% 0.19/0.50      (outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) = lower_dimension_point_2),
% 0.19/0.50      inference(transitivity,[status(thm)],[183, 21])).
% 0.19/0.50  tff(185,plain,
% 0.19/0.50      (between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) <=> between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2)),
% 0.19/0.50      inference(monotonicity,[status(thm)],[184])).
% 0.19/0.50  tff(186,plain,
% 0.19/0.50      (between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2) <=> between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.50      inference(symmetry,[status(thm)],[185])).
% 0.19/0.50  tff(187,plain,
% 0.19/0.50      ((~between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2)) <=> (~between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.50      inference(monotonicity,[status(thm)],[186])).
% 0.19/0.50  tff(188,plain,
% 0.19/0.50      (~between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.50      inference(modus_ponens,[status(thm)],[39, 187])).
% 0.19/0.50  tff(189,plain,
% 0.19/0.50      (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.50      inference(rewrite,[status(thm)],[])).
% 0.19/0.50  tff(190,plain,
% 0.19/0.50      (((~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))) <=> ((~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.50      inference(rewrite,[status(thm)],[])).
% 0.19/0.50  tff(191,plain,
% 0.19/0.50      (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.19/0.50      inference(monotonicity,[status(thm)],[190])).
% 0.19/0.50  tff(192,plain,
% 0.19/0.50      (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.50      inference(transitivity,[status(thm)],[191, 189])).
% 0.19/0.50  tff(193,plain,
% 0.19/0.50      ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.19/0.50      inference(quant_inst,[status(thm)],[])).
% 0.19/0.50  tff(194,plain,
% 0.19/0.50      ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.50      inference(modus_ponens,[status(thm)],[193, 192])).
% 0.19/0.50  tff(195,plain,
% 0.19/0.50      ((~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)) | (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.50      inference(unit_resolution,[status(thm)],[194, 111])).
% 0.19/0.50  tff(196,plain,
% 0.19/0.50      (between(lower_dimension_point_3, lower_dimension_point_1, outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.19/0.50      inference(unit_resolution,[status(thm)],[195, 164, 144])).
% 0.19/0.50  tff(197,plain,
% 0.19/0.50      ($false),
% 0.19/0.50      inference(unit_resolution,[status(thm)],[196, 188])).
% 0.19/0.50  % SZS output end Proof
%------------------------------------------------------------------------------