%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO011-1 : TPTP v9.0.0. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:18 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO011-1 : TPTP v9.0.0. Bugfixed v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:03:02 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(between_type, type, (
% 0.20/0.45 between: ( $i * $i * $i ) > $o)).
% 0.20/0.45 tff(lower_dimension_point_1_type, type, (
% 0.20/0.45 lower_dimension_point_1: $i)).
% 0.20/0.45 tff(lower_dimension_point_3_type, type, (
% 0.20/0.45 lower_dimension_point_3: $i)).
% 0.20/0.45 tff(lower_dimension_point_2_type, type, (
% 0.20/0.45 lower_dimension_point_2: $i)).
% 0.20/0.45 tff(outer_pasch_type, type, (
% 0.20/0.45 outer_pasch: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.45 tff(extension_type, type, (
% 0.20/0.45 extension: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.45 tff(equidistant_type, type, (
% 0.20/0.45 equidistant: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.45 tff(colinear_type, type, (
% 0.20/0.45 colinear: ( $i * $i * $i ) > $o)).
% 0.20/0.45 tff(1,plain,
% 0.20/0.45 (^[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))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 (![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)),
% 0.20/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (![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)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 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')).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.45 tff(6,plain,(
% 0.20/0.45 ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.20/0.45 inference(skolemize,[status(sab)],[5])).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(lower_dimension_point_3, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (equidistant(lower_dimension_point_3, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 (^[Z: $i, Y: $i, X: $i] : refl(((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ((~equidistant(X, Y, Z, Z)) | (X = Y)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(11,plain,
% 0.20/0.45 (![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))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 (![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))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 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')).
% 0.20/0.45 tff(14,plain,
% 0.20/0.45 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.45 tff(15,plain,(
% 0.20/0.45 ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.20/0.45 inference(skolemize,[status(sab)],[14])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(lower_dimension_point_3, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (lower_dimension_point_3 = extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, 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_3, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (lower_dimension_point_3 = extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(lower_dimension_point_3, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (lower_dimension_point_3 = extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(lower_dimension_point_3, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_3, lower_dimension_point_3)) | (lower_dimension_point_3 = extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 (lower_dimension_point_3 = extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 (extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3) = lower_dimension_point_3),
% 0.20/0.45 inference(symmetry,[status(thm)],[20])).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 (outer_pasch(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) = outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.45 tff(23,plain,
% 0.20/0.45 (outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) = outer_pasch(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)),
% 0.20/0.45 inference(symmetry,[status(thm)],[22])).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1) <=> between(lower_dimension_point_1, outer_pasch(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (between(lower_dimension_point_1, outer_pasch(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1) <=> between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1)),
% 0.20/0.45 inference(symmetry,[status(thm)],[24])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2) <=> between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2) <=> between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2)),
% 0.20/0.45 inference(symmetry,[status(thm)],[26])).
% 0.20/0.45 tff(28,assumption,(between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)), introduced(assumption)).
% 0.20/0.45 tff(29,assumption,(~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)), introduced(assumption)).
% 0.20/0.45 tff(30,assumption,(lower_dimension_point_2 = lower_dimension_point_1), introduced(assumption)).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (lower_dimension_point_1 = lower_dimension_point_2),
% 0.20/0.45 inference(symmetry,[status(thm)],[30])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 (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)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[30, 31])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 (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)),
% 0.20/0.45 inference(symmetry,[status(thm)],[32])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 ((~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))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 ((~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))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(36,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')).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 (~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[28, 38])).
% 0.20/0.45 tff(40,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,[]))).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (~(lower_dimension_point_2 = lower_dimension_point_1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[40, 28])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.45 tff(47,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')).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.45 tff(50,plain,(
% 0.20/0.45 ![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)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[49])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (((~![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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 (((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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 (((~![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)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 (((~![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))),
% 0.20/0.46 inference(transitivity,[status(thm)],[54, 52])).
% 0.20/0.46 tff(56,plain,
% 0.20/0.46 ((~![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)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3) | (lower_dimension_point_2 = lower_dimension_point_1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[57, 51, 28, 41, 29])).
% 0.20/0.46 tff(59,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,[]))).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 (between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[59, 28])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(62,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.46 tff(63,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.46 tff(66,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')).
% 0.20/0.46 tff(67,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.46 tff(68,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.20/0.46 tff(69,plain,(
% 0.20/0.46 ![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)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[68])).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.20/0.46 tff(71,plain,
% 0.20/0.46 (((~![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_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, 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) | (~between(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_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, 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) | (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 ((between(lower_dimension_point_2, 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) | (~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, 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) | (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(73,plain,
% 0.20/0.46 (((~![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_2, 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) | (~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)))) <=> ((~![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_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, 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) | (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 (((~![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_2, 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) | (~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)))) <=> ((~![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_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, 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) | (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[73, 71])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 ((~![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_2, 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) | (~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)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 ((~![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_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, 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) | (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 ((~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)) | between(lower_dimension_point_2, 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) | (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[76, 70])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 (between(lower_dimension_point_2, 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)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[77, 60, 28])).
% 0.20/0.46 tff(79,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : refl(((~between(X, Y, X)) | (X = Y)) <=> ((~between(X, Y, X)) | (X = Y)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y)) <=> ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y)) <=> ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(82,axiom,(![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','identity_for_betweeness')).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.46 tff(84,plain,(
% 0.20/0.46 ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.20/0.46 inference(skolemize,[status(sab)],[83])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(lower_dimension_point_2, 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)) | (lower_dimension_point_2 = 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(lower_dimension_point_2, 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)) | (lower_dimension_point_2 = outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(lower_dimension_point_2, 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)) | (lower_dimension_point_2 = outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(lower_dimension_point_2, 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)) | (lower_dimension_point_2 = outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (lower_dimension_point_2 = outer_pasch(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[88, 85, 78])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (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))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.47 tff(91,plain,
% 0.20/0.47 (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)),
% 0.20/0.47 inference(symmetry,[status(thm)],[90])).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.47 tff(97,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')).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.20/0.47 tff(100,plain,(
% 0.20/0.47 ![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)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[99])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 (((~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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (((~![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))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[104, 102])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 ((~![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)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 ((~![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))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 ((~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))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[107, 101])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (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))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[108, 60, 28])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[109, 91])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 ((~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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(112,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')).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (~between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[113, 110])).
% 0.20/0.47 tff(115,plain,(~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 (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)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(117,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')).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (colinear(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 (^[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)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.47 tff(124,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')).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.20/0.47 tff(127,plain,(
% 0.20/0.47 ![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))),
% 0.20/0.47 inference(skolemize,[status(sab)],[126])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (![Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | between(Y, X, Z) | (~colinear(X, Y, Z)) | between(X, Z, Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 ((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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 (((~![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))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[130])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[131, 129])).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 ((~![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))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 ((~![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))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 (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)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[134, 37, 128, 118])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 (between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[135, 115])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 (between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[136, 27])).
% 0.20/0.47 tff(138,assumption,(between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)), introduced(assumption)).
% 0.20/0.47 tff(139,assumption,(lower_dimension_point_1 = lower_dimension_point_3), introduced(assumption)).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 (lower_dimension_point_3 = lower_dimension_point_1),
% 0.20/0.47 inference(symmetry,[status(thm)],[139])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 (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)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[139, 140])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (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)),
% 0.20/0.47 inference(symmetry,[status(thm)],[141])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 ((~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))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[113, 143])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[138, 144])).
% 0.20/0.47 tff(146,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,[]))).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (~(lower_dimension_point_1 = lower_dimension_point_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[146, 138])).
% 0.20/0.47 tff(148,assumption,(~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)), introduced(assumption)).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 (((~![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, lower_dimension_point_2)) | between(lower_dimension_point_1, lower_dimension_point_2, 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_1, lower_dimension_point_3, lower_dimension_point_2)) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) | (lower_dimension_point_1 = lower_dimension_point_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 (((lower_dimension_point_1 = 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_2) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2))) <=> ((~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_2) | (lower_dimension_point_1 = lower_dimension_point_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (((~![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, lower_dimension_point_2)) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)))) <=> ((~![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, lower_dimension_point_2)) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) | (lower_dimension_point_1 = lower_dimension_point_3)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 (((~![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, lower_dimension_point_2)) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)))) <=> ((~![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, lower_dimension_point_2)) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) | (lower_dimension_point_1 = lower_dimension_point_3))),
% 0.20/0.47 inference(transitivity,[status(thm)],[151, 149])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 ((~![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, lower_dimension_point_2)) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)) | between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) | (lower_dimension_point_1 = lower_dimension_point_3)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[154, 51, 138, 148, 147])).
% 0.20/0.48 tff(156,plain,(between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[156, 136])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 (((~![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, lower_dimension_point_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2)) | between(lower_dimension_point_1, outer_pasch(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1))) <=> ((~![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, lower_dimension_point_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2)) | between(lower_dimension_point_1, outer_pasch(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 ((between(lower_dimension_point_1, outer_pasch(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1) | (~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2))) <=> ((~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2)) | between(lower_dimension_point_1, outer_pasch(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 (((~![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(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1) | (~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2)))) <=> ((~![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, lower_dimension_point_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2)) | between(lower_dimension_point_1, outer_pasch(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[159])).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 (((~![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(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1) | (~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2)))) <=> ((~![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, lower_dimension_point_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2)) | between(lower_dimension_point_1, outer_pasch(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1))),
% 0.20/0.48 inference(transitivity,[status(thm)],[160, 158])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 ((~![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(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1) | (~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 ((~![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, lower_dimension_point_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2)) | between(lower_dimension_point_1, outer_pasch(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 ((~between(lower_dimension_point_1, extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_2)) | between(lower_dimension_point_1, outer_pasch(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[163, 70, 157])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 (between(lower_dimension_point_1, outer_pasch(extension(extension(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2), lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3), lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[164, 137])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 (between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[165, 25])).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 (((~![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, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1)) | (lower_dimension_point_1 = outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)))) <=> ((~![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, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1)) | (lower_dimension_point_1 = outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(168,plain,
% 0.20/0.48 ((~![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, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1)) | (lower_dimension_point_1 = outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 ((~![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, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1)) | (lower_dimension_point_1 = outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.48 tff(170,plain,
% 0.20/0.48 ((~between(lower_dimension_point_1, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2), lower_dimension_point_1)) | (lower_dimension_point_1 = outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[169, 85])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 (lower_dimension_point_1 = outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[170, 166])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 (between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1) <=> between(lower_dimension_point_2, lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[171])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (between(lower_dimension_point_2, lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)) <=> between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1)),
% 0.20/0.48 inference(symmetry,[status(thm)],[172])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 (((~![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_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)) | between(lower_dimension_point_2, lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)))) <=> ((~![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_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)) | between(lower_dimension_point_2, lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 ((~![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_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)) | between(lower_dimension_point_2, lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 ((~![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_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)) | between(lower_dimension_point_2, lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 ((~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2)) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_2)) | between(lower_dimension_point_2, lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[176, 101])).
% 0.20/0.48 tff(178,plain,
% 0.20/0.48 (between(lower_dimension_point_2, lower_dimension_point_3, outer_pasch(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[177, 157, 136])).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 (between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[178, 173])).
% 0.20/0.48 tff(180,plain,
% 0.20/0.48 ((~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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(181,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')).
% 0.20/0.48 tff(182,plain,
% 0.20/0.48 (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[182, 179])).
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------