%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO012-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 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 05:05:19 AM UTC 2025
% Result : Unsatisfiable 1.45s 1.67s
% Output : Proof 1.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO012-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:03:17 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.45/1.67 % SZS status Unsatisfiable
% 1.45/1.67 % SZS output start Proof
% 1.45/1.67 tff(between_type, type, (
% 1.45/1.67 between: ( $i * $i * $i ) > $o)).
% 1.45/1.67 tff(a_type, type, (
% 1.45/1.67 a: $i)).
% 1.45/1.67 tff(d_type, type, (
% 1.45/1.67 d: $i)).
% 1.45/1.67 tff(c_type, type, (
% 1.45/1.67 c: $i)).
% 1.45/1.67 tff(insertion_type, type, (
% 1.45/1.67 insertion: ( $i * $i * $i * $i ) > $i)).
% 1.45/1.67 tff(b_type, type, (
% 1.45/1.67 b: $i)).
% 1.45/1.67 tff(extension_type, type, (
% 1.45/1.67 extension: ( $i * $i * $i * $i ) > $i)).
% 1.45/1.67 tff(lower_dimension_point_2_type, type, (
% 1.45/1.67 lower_dimension_point_2: $i)).
% 1.45/1.67 tff(lower_dimension_point_1_type, type, (
% 1.45/1.67 lower_dimension_point_1: $i)).
% 1.45/1.67 tff(colinear_type, type, (
% 1.45/1.67 colinear: ( $i * $i * $i ) > $o)).
% 1.45/1.67 tff(1,plain,
% 1.45/1.67 (^[V: $i, U: $i] : refl(between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2)) <=> between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 1.45/1.67 inference(bind,[status(th)],[])).
% 1.45/1.67 tff(2,plain,
% 1.45/1.67 (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2)) <=> ![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 1.45/1.67 inference(quant_intro,[status(thm)],[1])).
% 1.45/1.67 tff(3,plain,
% 1.45/1.67 (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2)) <=> ![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(4,axiom,(![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e3_3')).
% 1.45/1.67 tff(5,plain,
% 1.45/1.67 (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.45/1.67 tff(6,plain,(
% 1.45/1.67 ![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 1.45/1.67 inference(skolemize,[status(sab)],[5])).
% 1.45/1.67 tff(7,plain,
% 1.45/1.67 (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.45/1.67 tff(8,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))) | between(insertion(d, b, d, b), d, extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(9,plain,
% 1.45/1.67 (between(insertion(d, b, d, b), d, extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.45/1.67 tff(10,plain,
% 1.45/1.67 (^[W: $i, V: $i, U: $i] : refl(((~between(U, V, W)) | (V = insertion(U, W, U, V))) <=> ((~between(U, V, W)) | (V = insertion(U, W, U, V))))),
% 1.45/1.67 inference(bind,[status(th)],[])).
% 1.45/1.67 tff(11,plain,
% 1.45/1.67 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V))) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 1.45/1.67 inference(quant_intro,[status(thm)],[10])).
% 1.45/1.67 tff(12,plain,
% 1.45/1.67 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V))) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(13,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','i3')).
% 1.45/1.67 tff(14,plain,
% 1.45/1.67 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[13, 12])).
% 1.45/1.67 tff(15,plain,(
% 1.45/1.67 ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 1.45/1.67 inference(skolemize,[status(sab)],[14])).
% 1.45/1.67 tff(16,plain,
% 1.45/1.67 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[15, 11])).
% 1.45/1.67 tff(17,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(insertion(d, b, d, b), d, extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2))) | (d = insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(insertion(d, b, d, b), d, extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2))) | (d = insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(18,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(insertion(d, b, d, b), d, extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2))) | (d = insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(19,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(insertion(d, b, d, b), d, extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2))) | (d = insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.45/1.68 tff(20,plain,
% 1.45/1.68 (d = insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 1.45/1.68 tff(21,plain,
% 1.45/1.68 (insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d) = d),
% 1.45/1.68 inference(symmetry,[status(thm)],[20])).
% 1.45/1.68 tff(22,plain,
% 1.45/1.68 (between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a) <=> between(c, d, a)),
% 1.45/1.68 inference(monotonicity,[status(thm)],[21])).
% 1.45/1.68 tff(23,plain,
% 1.45/1.68 ((~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)) <=> (~between(c, d, a))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[22])).
% 1.45/1.68 tff(24,assumption,(~between(d, b, b)), introduced(assumption)).
% 1.45/1.68 tff(25,plain,
% 1.45/1.68 (^[V: $i, U: $i] : refl(between(U, V, V) <=> between(U, V, V))),
% 1.45/1.68 inference(bind,[status(th)],[])).
% 1.45/1.68 tff(26,plain,
% 1.45/1.68 (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 1.45/1.68 inference(quant_intro,[status(thm)],[25])).
% 1.45/1.68 tff(27,plain,
% 1.45/1.68 (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(28,axiom,(![V: $i, U: $i] : between(U, V, V)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3')).
% 1.45/1.68 tff(29,plain,
% 1.45/1.68 (![V: $i, U: $i] : between(U, V, V)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.45/1.68 tff(30,plain,(
% 1.45/1.68 ![V: $i, U: $i] : between(U, V, V)),
% 1.45/1.68 inference(skolemize,[status(sab)],[29])).
% 1.45/1.68 tff(31,plain,
% 1.45/1.68 (![V: $i, U: $i] : between(U, V, V)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.45/1.68 tff(32,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : between(U, V, V)) | between(d, b, b)),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(33,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[32, 31, 24])).
% 1.45/1.68 tff(34,plain,(between(d, b, b)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(35,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(d, b, b)) | (b = insertion(d, b, d, b)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(d, b, b)) | (b = insertion(d, b, d, b)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(36,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(d, b, b)) | (b = insertion(d, b, d, b)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(37,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(d, b, b)) | (b = insertion(d, b, d, b))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.45/1.68 tff(38,plain,
% 1.45/1.68 (b = insertion(d, b, d, b)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[37, 16, 34])).
% 1.45/1.68 tff(39,plain,
% 1.45/1.68 (insertion(d, b, d, b) = b),
% 1.45/1.68 inference(symmetry,[status(thm)],[38])).
% 1.45/1.68 tff(40,plain,
% 1.45/1.68 (between(c, insertion(d, b, d, b), a) <=> between(c, b, a)),
% 1.45/1.68 inference(monotonicity,[status(thm)],[39])).
% 1.45/1.68 tff(41,plain,
% 1.45/1.68 (between(c, b, a) <=> between(c, insertion(d, b, d, b), a)),
% 1.45/1.68 inference(symmetry,[status(thm)],[40])).
% 1.45/1.68 tff(42,plain,
% 1.45/1.68 (between(a, c, insertion(d, b, d, b)) <=> between(a, c, b)),
% 1.45/1.68 inference(monotonicity,[status(thm)],[39])).
% 1.45/1.68 tff(43,plain,
% 1.45/1.68 ((~between(a, c, insertion(d, b, d, b))) <=> (~between(a, c, b))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[42])).
% 1.45/1.68 tff(44,plain,
% 1.45/1.68 (between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a) <=> between(b, d, a)),
% 1.45/1.68 inference(monotonicity,[status(thm)],[39, 21])).
% 1.45/1.68 tff(45,plain,
% 1.45/1.68 (between(b, d, a) <=> between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)),
% 1.45/1.68 inference(symmetry,[status(thm)],[44])).
% 1.45/1.68 tff(46,plain,
% 1.45/1.68 (between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) <=> between(a, b, d)),
% 1.45/1.68 inference(monotonicity,[status(thm)],[39, 21])).
% 1.45/1.68 tff(47,plain,
% 1.45/1.68 ((~between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) <=> (~between(a, b, d))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[46])).
% 1.45/1.68 tff(48,assumption,(between(a, c, insertion(d, b, d, b))), introduced(assumption)).
% 1.45/1.68 tff(49,plain,
% 1.45/1.68 (between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) <=> between(c, b, d)),
% 1.45/1.68 inference(monotonicity,[status(thm)],[39, 21])).
% 1.45/1.68 tff(50,plain,
% 1.45/1.68 (between(c, b, d) <=> between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.45/1.68 inference(symmetry,[status(thm)],[49])).
% 1.45/1.68 tff(51,plain,
% 1.45/1.68 ((~between(c, b, d)) <=> (~between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[50])).
% 1.45/1.68 tff(52,assumption,(~colinear(a, c, d)), introduced(assumption)).
% 1.45/1.68 tff(53,plain,
% 1.45/1.68 (^[Z: $i, Y: $i, X: $i] : refl(((~between(X, Y, Z)) | colinear(X, Y, Z)) <=> ((~between(X, Y, Z)) | colinear(X, Y, Z)))),
% 1.45/1.68 inference(bind,[status(th)],[])).
% 1.45/1.68 tff(54,plain,
% 1.45/1.68 (![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 1.45/1.68 inference(quant_intro,[status(thm)],[53])).
% 1.45/1.68 tff(55,plain,
% 1.45/1.68 (![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(56,axiom,(![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax','colinearity1')).
% 1.45/1.68 tff(57,plain,
% 1.45/1.68 (![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[56, 55])).
% 1.45/1.68 tff(58,plain,(
% 1.45/1.68 ![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 1.45/1.68 inference(skolemize,[status(sab)],[57])).
% 1.45/1.68 tff(59,plain,
% 1.45/1.68 (![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[58, 54])).
% 1.45/1.68 tff(60,plain,
% 1.45/1.68 (((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | ((~between(a, c, d)) | colinear(a, c, d))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | (~between(a, c, d)) | colinear(a, c, d))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(61,plain,
% 1.45/1.68 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | ((~between(a, c, d)) | colinear(a, c, d))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(62,plain,
% 1.45/1.68 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | (~between(a, c, d)) | colinear(a, c, d)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.45/1.68 tff(63,plain,
% 1.45/1.68 (~between(a, c, d)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[62, 59, 52])).
% 1.45/1.68 tff(64,plain,
% 1.45/1.68 (^[W: $i, V: $i, U: $i] : refl(((~between(U, W, V)) | colinear(U, V, W)) <=> ((~between(U, W, V)) | colinear(U, V, W)))),
% 1.45/1.68 inference(bind,[status(th)],[])).
% 1.45/1.68 tff(65,plain,
% 1.45/1.68 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W)) <=> ![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 1.45/1.68 inference(quant_intro,[status(thm)],[64])).
% 1.45/1.68 tff(66,plain,
% 1.45/1.68 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W)) <=> ![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(67,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c2_2')).
% 1.45/1.68 tff(68,plain,
% 1.45/1.68 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.45/1.68 tff(69,plain,(
% 1.45/1.68 ![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 1.45/1.68 inference(skolemize,[status(sab)],[68])).
% 1.45/1.68 tff(70,plain,
% 1.45/1.68 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[69, 65])).
% 1.45/1.68 tff(71,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(a, d, c)) | colinear(a, c, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(a, d, c)) | colinear(a, c, d))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(72,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(a, d, c)) | colinear(a, c, d))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(73,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(a, d, c)) | colinear(a, c, d)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.45/1.68 tff(74,plain,
% 1.45/1.68 (~between(a, d, c)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[73, 70, 52])).
% 1.45/1.68 tff(75,plain,
% 1.45/1.68 (^[W: $i, V: $i, U: $i] : refl(((~between(V, U, W)) | colinear(U, V, W)) <=> ((~between(V, U, W)) | colinear(U, V, W)))),
% 1.45/1.68 inference(bind,[status(th)],[])).
% 1.45/1.68 tff(76,plain,
% 1.45/1.68 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W)) <=> ![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 1.45/1.68 inference(quant_intro,[status(thm)],[75])).
% 1.45/1.68 tff(77,plain,
% 1.45/1.68 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W)) <=> ![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(78,axiom,(![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c2_3')).
% 1.45/1.68 tff(79,plain,
% 1.45/1.68 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.45/1.68 tff(80,plain,(
% 1.45/1.68 ![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 1.45/1.68 inference(skolemize,[status(sab)],[79])).
% 1.45/1.68 tff(81,plain,
% 1.45/1.68 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[80, 76])).
% 1.45/1.68 tff(82,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(c, a, d)) | colinear(a, c, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(c, a, d)) | colinear(a, c, d))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.53/1.68 tff(83,plain,
% 1.53/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(c, a, d)) | colinear(a, c, d))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(84,plain,
% 1.53/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(c, a, d)) | colinear(a, c, d)),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.53/1.68 tff(85,plain,
% 1.53/1.68 (~between(c, a, d)),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[84, 81, 52])).
% 1.53/1.68 tff(86,plain,
% 1.53/1.68 (^[W: $i, V: $i, U: $i] : refl(((~between(W, V, U)) | colinear(U, V, W)) <=> ((~between(W, V, U)) | colinear(U, V, W)))),
% 1.53/1.68 inference(bind,[status(th)],[])).
% 1.53/1.68 tff(87,plain,
% 1.53/1.68 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W)) <=> ![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 1.53/1.68 inference(quant_intro,[status(thm)],[86])).
% 1.53/1.68 tff(88,plain,
% 1.53/1.68 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W)) <=> ![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 1.53/1.68 inference(rewrite,[status(thm)],[])).
% 1.53/1.68 tff(89,axiom,(![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c2_1')).
% 1.53/1.68 tff(90,plain,
% 1.53/1.68 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.53/1.68 tff(91,plain,(
% 1.53/1.68 ![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 1.53/1.68 inference(skolemize,[status(sab)],[90])).
% 1.53/1.68 tff(92,plain,
% 1.53/1.68 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[91, 87])).
% 1.53/1.68 tff(93,plain,
% 1.53/1.68 (((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(d, c, a)) | colinear(a, c, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(d, c, a)) | colinear(a, c, d))),
% 1.53/1.68 inference(rewrite,[status(thm)],[])).
% 1.53/1.68 tff(94,plain,
% 1.53/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(d, c, a)) | colinear(a, c, d))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(95,plain,
% 1.53/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(d, c, a)) | colinear(a, c, d)),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.53/1.68 tff(96,plain,
% 1.53/1.68 (~between(d, c, a)),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[95, 92, 52])).
% 1.53/1.68 tff(97,plain,
% 1.53/1.68 (^[Z: $i, Y: $i, X: $i] : refl(((~between(Y, Z, X)) | colinear(X, Y, Z)) <=> ((~between(Y, Z, X)) | colinear(X, Y, Z)))),
% 1.53/1.68 inference(bind,[status(th)],[])).
% 1.53/1.68 tff(98,plain,
% 1.53/1.68 (![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 1.53/1.68 inference(quant_intro,[status(thm)],[97])).
% 1.53/1.68 tff(99,plain,
% 1.53/1.68 (![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 1.53/1.68 inference(rewrite,[status(thm)],[])).
% 1.53/1.68 tff(100,axiom,(![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax','colinearity2')).
% 1.53/1.68 tff(101,plain,
% 1.53/1.68 (![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[100, 99])).
% 1.53/1.68 tff(102,plain,(
% 1.53/1.68 ![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 1.53/1.68 inference(skolemize,[status(sab)],[101])).
% 1.53/1.68 tff(103,plain,
% 1.53/1.68 (![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[102, 98])).
% 1.53/1.68 tff(104,plain,
% 1.53/1.68 (((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | ((~between(c, d, a)) | colinear(a, c, d))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | (~between(c, d, a)) | colinear(a, c, d))),
% 1.53/1.68 inference(rewrite,[status(thm)],[])).
% 1.53/1.68 tff(105,plain,
% 1.53/1.68 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | ((~between(c, d, a)) | colinear(a, c, d))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(106,plain,
% 1.53/1.68 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | (~between(c, d, a)) | colinear(a, c, d)),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.53/1.68 tff(107,plain,
% 1.53/1.68 (~between(c, d, a)),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[106, 103, 52])).
% 1.53/1.68 tff(108,plain,
% 1.53/1.68 (^[Z: $i, Y: $i, X: $i] : refl(((~between(Z, X, Y)) | colinear(X, Y, Z)) <=> ((~between(Z, X, Y)) | colinear(X, Y, Z)))),
% 1.53/1.68 inference(bind,[status(th)],[])).
% 1.53/1.68 tff(109,plain,
% 1.53/1.68 (![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 1.53/1.68 inference(quant_intro,[status(thm)],[108])).
% 1.53/1.68 tff(110,plain,
% 1.53/1.68 (![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 1.53/1.68 inference(rewrite,[status(thm)],[])).
% 1.53/1.68 tff(111,axiom,(![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax','colinearity3')).
% 1.53/1.68 tff(112,plain,
% 1.53/1.68 (![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[111, 110])).
% 1.53/1.68 tff(113,plain,(
% 1.53/1.68 ![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 1.53/1.68 inference(skolemize,[status(sab)],[112])).
% 1.53/1.68 tff(114,plain,
% 1.53/1.68 (![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[113, 109])).
% 1.53/1.68 tff(115,plain,
% 1.53/1.68 (((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | ((~between(d, a, c)) | colinear(a, c, d))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | (~between(d, a, c)) | colinear(a, c, d))),
% 1.53/1.68 inference(rewrite,[status(thm)],[])).
% 1.53/1.68 tff(116,plain,
% 1.53/1.68 ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | ((~between(d, a, c)) | colinear(a, c, d))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(117,plain,
% 1.53/1.68 ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | (~between(d, a, c)) | colinear(a, c, d)),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[116, 115])).
% 1.53/1.68 tff(118,plain,
% 1.53/1.68 (~between(d, a, c)),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[117, 114, 52])).
% 1.53/1.68 tff(119,assumption,(~between(a, d, b)), introduced(assumption)).
% 1.53/1.68 tff(120,assumption,(~between(a, c, d)), introduced(assumption)).
% 1.53/1.68 tff(121,assumption,(~between(c, a, d)), introduced(assumption)).
% 1.53/1.68 tff(122,assumption,(~between(d, c, a)), introduced(assumption)).
% 1.53/1.68 tff(123,assumption,(~between(c, d, a)), introduced(assumption)).
% 1.53/1.68 tff(124,assumption,(~between(a, d, c)), introduced(assumption)).
% 1.53/1.68 tff(125,assumption,(between(c, b, a)), introduced(assumption)).
% 1.53/1.68 tff(126,plain,
% 1.53/1.68 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(c, b, a)) | (b = insertion(c, a, c, b)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(c, b, a)) | (b = insertion(c, a, c, b)))),
% 1.53/1.68 inference(rewrite,[status(thm)],[])).
% 1.53/1.68 tff(127,plain,
% 1.53/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(c, b, a)) | (b = insertion(c, a, c, b)))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(128,plain,
% 1.53/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(c, b, a)) | (b = insertion(c, a, c, b))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.53/1.68 tff(129,plain,
% 1.53/1.68 (b = insertion(c, a, c, b)),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[128, 16, 125])).
% 1.53/1.68 tff(130,plain,
% 1.53/1.68 (insertion(c, a, c, b) = b),
% 1.53/1.68 inference(symmetry,[status(thm)],[129])).
% 1.53/1.68 tff(131,plain,
% 1.53/1.68 (between(a, insertion(c, a, c, b), c) <=> between(a, b, c)),
% 1.53/1.68 inference(monotonicity,[status(thm)],[130])).
% 1.53/1.68 tff(132,plain,
% 1.53/1.68 (between(a, b, c) <=> between(a, insertion(c, a, c, b), c)),
% 1.53/1.68 inference(symmetry,[status(thm)],[131])).
% 1.53/1.68 tff(133,plain,
% 1.53/1.68 (^[W: $i, V: $i, U: $i] : refl(((~between(U, V, W)) | between(W, V, U)) <=> ((~between(U, V, W)) | between(W, V, U)))),
% 1.53/1.68 inference(bind,[status(th)],[])).
% 1.53/1.68 tff(134,plain,
% 1.53/1.68 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U)) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 1.53/1.68 inference(quant_intro,[status(thm)],[133])).
% 1.53/1.68 tff(135,plain,
% 1.53/1.68 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U)) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 1.53/1.68 inference(rewrite,[status(thm)],[])).
% 1.53/1.68 tff(136,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1')).
% 1.53/1.68 tff(137,plain,
% 1.53/1.68 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.53/1.68 tff(138,plain,(
% 1.53/1.68 ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 1.53/1.68 inference(skolemize,[status(sab)],[137])).
% 1.53/1.68 tff(139,plain,
% 1.53/1.68 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[138, 134])).
% 1.53/1.68 tff(140,plain,
% 1.53/1.68 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(c, b, a)) | between(a, b, c))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(c, b, a)) | between(a, b, c))),
% 1.53/1.68 inference(rewrite,[status(thm)],[])).
% 1.53/1.68 tff(141,plain,
% 1.53/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(c, b, a)) | between(a, b, c))),
% 1.53/1.68 inference(quant_inst,[status(thm)],[])).
% 1.53/1.68 tff(142,plain,
% 1.53/1.68 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(c, b, a)) | between(a, b, c)),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[141, 140])).
% 1.53/1.68 tff(143,plain,
% 1.53/1.68 (between(a, b, c)),
% 1.53/1.68 inference(unit_resolution,[status(thm)],[142, 139, 125])).
% 1.53/1.68 tff(144,plain,
% 1.53/1.68 (between(a, insertion(c, a, c, b), c)),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[143, 132])).
% 1.53/1.68 tff(145,plain,
% 1.53/1.68 ((a = insertion(c, a, c, b)) <=> (a = b)),
% 1.53/1.68 inference(monotonicity,[status(thm)],[130])).
% 1.53/1.68 tff(146,plain,
% 1.53/1.68 ((a = b) <=> (a = insertion(c, a, c, b))),
% 1.53/1.68 inference(symmetry,[status(thm)],[145])).
% 1.53/1.68 tff(147,plain,
% 1.53/1.68 ((~(a = b)) <=> (~(a = insertion(c, a, c, b)))),
% 1.53/1.68 inference(monotonicity,[status(thm)],[146])).
% 1.53/1.68 tff(148,plain,
% 1.53/1.68 ((~(a = b)) <=> (~(a = b))),
% 1.53/1.68 inference(rewrite,[status(thm)],[])).
% 1.53/1.68 tff(149,axiom,(~(a = b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_not_b')).
% 1.53/1.68 tff(150,plain,
% 1.53/1.68 (~(a = b)),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.53/1.68 tff(151,plain,
% 1.53/1.68 (~(a = insertion(c, a, c, b))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[150, 147])).
% 1.53/1.68 tff(152,plain,
% 1.53/1.68 (^[W: $i, V: $i, U: $i] : refl(((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))) <=> ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))))),
% 1.53/1.68 inference(bind,[status(th)],[])).
% 1.53/1.68 tff(153,plain,
% 1.53/1.68 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 1.53/1.68 inference(quant_intro,[status(thm)],[152])).
% 1.53/1.68 tff(154,plain,
% 1.53/1.68 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 1.53/1.68 inference(rewrite,[status(thm)],[])).
% 1.53/1.68 tff(155,plain,
% 1.53/1.68 (^[W: $i, V: $i, U: $i] : rewrite((((~between(U, V, W)) | (U = V)) | (W = extension(U, V, V, W))) <=> ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))))),
% 1.53/1.68 inference(bind,[status(th)],[])).
% 1.53/1.68 tff(156,plain,
% 1.53/1.68 (![W: $i, V: $i, U: $i] : (((~between(U, V, W)) | (U = V)) | (W = extension(U, V, V, W))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 1.53/1.68 inference(quant_intro,[status(thm)],[155])).
% 1.53/1.68 tff(157,axiom,(![W: $i, V: $i, U: $i] : (((~between(U, V, W)) | (U = V)) | (W = extension(U, V, V, W)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_1')).
% 1.53/1.68 tff(158,plain,
% 1.53/1.68 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 1.53/1.68 inference(modus_ponens,[status(thm)],[157, 156])).
% 1.53/1.68 tff(159,plain,
% 1.53/1.68 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[158, 154])).
% 1.53/1.69 tff(160,plain,(
% 1.53/1.69 ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 1.53/1.69 inference(skolemize,[status(sab)],[159])).
% 1.53/1.69 tff(161,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[160, 153])).
% 1.53/1.69 tff(162,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(163,plain,
% 1.53/1.69 (((a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), c)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))) <=> ((~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(164,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), c)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[163])).
% 1.53/1.69 tff(165,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), c)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))),
% 1.53/1.69 inference(transitivity,[status(thm)],[164, 162])).
% 1.53/1.69 tff(166,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), c)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(167,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.53/1.69 tff(168,plain,
% 1.53/1.69 ((~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[167, 161])).
% 1.53/1.69 tff(169,plain,
% 1.53/1.69 (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[168, 151, 144])).
% 1.53/1.69 tff(170,plain,
% 1.53/1.69 (extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c) = c),
% 1.53/1.69 inference(symmetry,[status(thm)],[169])).
% 1.53/1.69 tff(171,plain,
% 1.53/1.69 (between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) <=> between(a, b, c)),
% 1.53/1.69 inference(monotonicity,[status(thm)],[130, 170])).
% 1.53/1.69 tff(172,plain,
% 1.53/1.69 (between(a, b, c) <=> between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))),
% 1.53/1.69 inference(symmetry,[status(thm)],[171])).
% 1.53/1.69 tff(173,plain,
% 1.53/1.69 (between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[143, 172])).
% 1.53/1.69 tff(174,plain,
% 1.53/1.69 (between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) <=> between(a, d, c)),
% 1.53/1.69 inference(monotonicity,[status(thm)],[170])).
% 1.53/1.69 tff(175,plain,
% 1.53/1.69 (between(a, d, c) <=> between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))),
% 1.53/1.69 inference(symmetry,[status(thm)],[174])).
% 1.53/1.69 tff(176,plain,
% 1.53/1.69 ((~between(a, d, c)) <=> (~between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[175])).
% 1.53/1.69 tff(177,plain,
% 1.53/1.69 (~between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[124, 176])).
% 1.53/1.69 tff(178,plain,
% 1.53/1.69 (between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) <=> between(a, c, d)),
% 1.53/1.69 inference(monotonicity,[status(thm)],[170])).
% 1.53/1.69 tff(179,plain,
% 1.53/1.69 (between(a, c, d) <=> between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d)),
% 1.53/1.69 inference(symmetry,[status(thm)],[178])).
% 1.53/1.69 tff(180,plain,
% 1.53/1.69 ((~between(a, c, d)) <=> (~between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[179])).
% 1.53/1.69 tff(181,plain,
% 1.53/1.69 (~between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[120, 180])).
% 1.53/1.69 tff(182,plain,
% 1.53/1.69 (between(d, insertion(c, a, c, b), a) <=> between(d, b, a)),
% 1.53/1.69 inference(monotonicity,[status(thm)],[130])).
% 1.53/1.69 tff(183,plain,
% 1.53/1.69 (between(d, b, a) <=> between(d, insertion(c, a, c, b), a)),
% 1.53/1.69 inference(symmetry,[status(thm)],[182])).
% 1.53/1.69 tff(184,plain,
% 1.53/1.69 ((b = a) <=> (a = b)),
% 1.53/1.69 inference(commutativity,[status(thm)],[])).
% 1.53/1.69 tff(185,plain,
% 1.53/1.69 ((a = b) <=> (b = a)),
% 1.53/1.69 inference(symmetry,[status(thm)],[184])).
% 1.53/1.69 tff(186,plain,
% 1.53/1.69 ((~(a = b)) <=> (~(b = a))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[185])).
% 1.53/1.69 tff(187,plain,
% 1.53/1.69 (~(b = a)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[150, 186])).
% 1.53/1.69 tff(188,plain,
% 1.53/1.69 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W)) <=> ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W)))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(189,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[188])).
% 1.53/1.69 tff(190,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(191,plain,
% 1.53/1.69 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~between(U, V, W)) | (~between(V, W, X))) | between(U, W, X)) <=> ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)))), (((((~between(U, V, W)) | (~between(V, W, X))) | between(U, W, X)) | (V = W)) <=> (((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X))) | (V = W)))), rewrite((((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X))) | (V = W)) <=> ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))), (((((~between(U, V, W)) | (~between(V, W, X))) | between(U, W, X)) | (V = W)) <=> ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(192,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, W)) | (~between(V, W, X))) | between(U, W, X)) | (V = W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[191])).
% 1.53/1.69 tff(193,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, W)) | (~between(V, W, X))) | between(U, W, X)) | (V = W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b6')).
% 1.53/1.69 tff(194,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.53/1.69 tff(195,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[194, 190])).
% 1.53/1.69 tff(196,plain,(
% 1.53/1.69 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 1.53/1.69 inference(skolemize,[status(sab)],[195])).
% 1.53/1.69 tff(197,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[196, 189])).
% 1.53/1.69 tff(198,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | (between(c, a, d) | (~between(c, b, a)) | (b = a) | (~between(b, a, d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | between(c, a, d) | (~between(c, b, a)) | (b = a) | (~between(b, a, d)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(199,plain,
% 1.53/1.69 (((~between(c, b, a)) | between(c, a, d) | (~between(b, a, d)) | (b = a)) <=> (between(c, a, d) | (~between(c, b, a)) | (b = a) | (~between(b, a, d)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(200,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(c, b, a)) | between(c, a, d) | (~between(b, a, d)) | (b = a))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | (between(c, a, d) | (~between(c, b, a)) | (b = a) | (~between(b, a, d))))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[199])).
% 1.53/1.69 tff(201,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(c, b, a)) | between(c, a, d) | (~between(b, a, d)) | (b = a))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | between(c, a, d) | (~between(c, b, a)) | (b = a) | (~between(b, a, d)))),
% 1.53/1.69 inference(transitivity,[status(thm)],[200, 198])).
% 1.53/1.69 tff(202,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(c, b, a)) | between(c, a, d) | (~between(b, a, d)) | (b = a))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(203,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | between(c, a, d) | (~between(c, b, a)) | (b = a) | (~between(b, a, d))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[202, 201])).
% 1.53/1.69 tff(204,plain,
% 1.53/1.69 ((b = a) | (~between(b, a, d))),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[203, 197, 125, 121])).
% 1.53/1.69 tff(205,plain,
% 1.53/1.69 (~between(b, a, d)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[204, 187])).
% 1.53/1.69 tff(206,plain,
% 1.53/1.69 (colinear(a, b, d) <=> colinear(a, b, d)),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(207,axiom,(colinear(a, b, d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abd_colinear')).
% 1.53/1.69 tff(208,plain,
% 1.53/1.69 (colinear(a, b, d)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.53/1.69 tff(209,plain,
% 1.53/1.69 (^[W: $i, V: $i, U: $i] : refl(((~colinear(U, V, W)) | colinear(V, U, W)) <=> ((~colinear(U, V, W)) | colinear(V, U, W)))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(210,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W)) <=> ![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[209])).
% 1.53/1.69 tff(211,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W)) <=> ![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(212,axiom,(![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t10_5')).
% 1.53/1.69 tff(213,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[212, 211])).
% 1.53/1.69 tff(214,plain,(
% 1.53/1.69 ![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))),
% 1.53/1.69 inference(skolemize,[status(sab)],[213])).
% 1.53/1.69 tff(215,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[214, 210])).
% 1.53/1.69 tff(216,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | ((~colinear(a, b, d)) | colinear(b, a, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | (~colinear(a, b, d)) | colinear(b, a, d))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(217,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | ((~colinear(a, b, d)) | colinear(b, a, d))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(218,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | (~colinear(a, b, d)) | colinear(b, a, d)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[217, 216])).
% 1.53/1.69 tff(219,plain,
% 1.53/1.69 (colinear(b, a, d)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[218, 215, 208])).
% 1.53/1.69 tff(220,plain,
% 1.53/1.69 (^[Z: $i, Y: $i, X: $i] : refl((between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) <=> (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(221,plain,
% 1.53/1.69 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[220])).
% 1.53/1.69 tff(222,plain,
% 1.53/1.69 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(223,plain,
% 1.53/1.69 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) <=> (between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))), (((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) <=> ((between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) | between(Z, X, Y)))), rewrite(((between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) | between(Z, X, Y)) <=> (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))), (((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) <=> (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(224,plain,
% 1.53/1.69 (![Z: $i, Y: $i, X: $i] : ((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) <=> ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[223])).
% 1.53/1.69 tff(225,axiom,(![Z: $i, Y: $i, X: $i] : ((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax','colinearity4')).
% 1.53/1.69 tff(226,plain,
% 1.53/1.69 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[225, 224])).
% 1.53/1.69 tff(227,plain,
% 1.53/1.69 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[226, 222])).
% 1.53/1.69 tff(228,plain,(
% 1.53/1.69 ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 1.53/1.69 inference(skolemize,[status(sab)],[227])).
% 1.53/1.69 tff(229,plain,
% 1.53/1.69 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[228, 221])).
% 1.53/1.69 tff(230,plain,
% 1.53/1.69 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, b, a) | between(a, d, b) | between(b, a, d) | (~colinear(b, a, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | between(d, b, a) | between(a, d, b) | between(b, a, d) | (~colinear(b, a, d)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(231,plain,
% 1.53/1.69 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, b, a) | between(a, d, b) | between(b, a, d) | (~colinear(b, a, d)))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(232,plain,
% 1.53/1.69 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | between(d, b, a) | between(a, d, b) | between(b, a, d) | (~colinear(b, a, d))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[231, 230])).
% 1.53/1.69 tff(233,plain,
% 1.53/1.69 (between(d, b, a) | between(a, d, b) | between(b, a, d)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[232, 229, 219])).
% 1.53/1.69 tff(234,plain,
% 1.53/1.69 (between(d, b, a)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[233, 205, 119])).
% 1.53/1.69 tff(235,plain,
% 1.53/1.69 (between(d, insertion(c, a, c, b), a)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[234, 183])).
% 1.53/1.69 tff(236,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, insertion(c, a, c, b), a)) | between(a, insertion(c, a, c, b), d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, insertion(c, a, c, b), a)) | between(a, insertion(c, a, c, b), d))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(237,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, insertion(c, a, c, b), a)) | between(a, insertion(c, a, c, b), d))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(238,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, insertion(c, a, c, b), a)) | between(a, insertion(c, a, c, b), d)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[237, 236])).
% 1.53/1.69 tff(239,plain,
% 1.53/1.69 ((~between(d, insertion(c, a, c, b), a)) | between(a, insertion(c, a, c, b), d)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[238, 139])).
% 1.53/1.69 tff(240,plain,
% 1.53/1.69 (between(a, insertion(c, a, c, b), d)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[239, 235])).
% 1.53/1.69 tff(241,plain,
% 1.53/1.69 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W)))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(242,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[241])).
% 1.53/1.69 tff(243,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(244,plain,
% 1.53/1.69 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~between(U, V, W)) | (~between(U, V, X))) <=> ((~between(U, V, X)) | (~between(U, V, W)))), ((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) <=> (((~between(U, V, X)) | (~between(U, V, W))) | (U = V)))), rewrite((((~between(U, V, X)) | (~between(U, V, W))) | (U = V)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)))), ((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W))))), (((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(U, W, X)) <=> (((~between(U, V, X)) | (U = V) | (~between(U, V, W))) | between(U, W, X)))), rewrite((((~between(U, V, X)) | (U = V) | (~between(U, V, W))) | between(U, W, X)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X))), (((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(U, W, X)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X)))), ((((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(U, W, X)) | between(U, X, W)) <=> (((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X)) | between(U, X, W)))), rewrite((((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X)) | between(U, X, W)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))), ((((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(U, W, X)) | between(U, X, W)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(245,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i, X: $i] : (((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(U, W, X)) | between(U, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[244])).
% 1.53/1.69 tff(246,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(U, W, X)) | between(U, X, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b12')).
% 1.53/1.69 tff(247,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[246, 245])).
% 1.53/1.69 tff(248,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[247, 243])).
% 1.53/1.69 tff(249,plain,(
% 1.53/1.69 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 1.53/1.69 inference(skolemize,[status(sab)],[248])).
% 1.53/1.69 tff(250,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[249, 242])).
% 1.53/1.69 tff(251,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((a = insertion(c, a, c, b)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | (~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | (a = insertion(c, a, c, b)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | (~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(252,plain,
% 1.53/1.69 (((~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))) | (a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d)) <=> ((a = insertion(c, a, c, b)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | (~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(253,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))) | (a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((a = insertion(c, a, c, b)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | (~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[252])).
% 1.53/1.70 tff(254,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))) | (a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | (a = insertion(c, a, c, b)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | (~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[253, 251])).
% 1.53/1.70 tff(255,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))) | (a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(256,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | (a = insertion(c, a, c, b)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | (~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[255, 254])).
% 1.53/1.70 tff(257,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[256, 250, 151, 240, 181, 177, 173])).
% 1.53/1.70 tff(258,plain,((~between(c, b, a)) | between(a, d, c) | between(a, c, d) | between(a, d, b) | between(c, a, d)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(259,plain,
% 1.53/1.70 (~between(c, b, a)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[258, 119, 120, 124, 121])).
% 1.53/1.70 tff(260,assumption,(~between(c, b, a)), introduced(assumption)).
% 1.53/1.70 tff(261,assumption,(between(b, a, d)), introduced(assumption)).
% 1.53/1.70 tff(262,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(b, a, d)) | (a = insertion(b, d, b, a)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(b, a, d)) | (a = insertion(b, d, b, a)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(263,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(b, a, d)) | (a = insertion(b, d, b, a)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(264,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(b, a, d)) | (a = insertion(b, d, b, a))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[263, 262])).
% 1.53/1.70 tff(265,plain,
% 1.53/1.70 (a = insertion(b, d, b, a)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[264, 16, 261])).
% 1.53/1.70 tff(266,plain,
% 1.53/1.70 (insertion(b, d, b, a) = a),
% 1.53/1.70 inference(symmetry,[status(thm)],[265])).
% 1.53/1.70 tff(267,plain,
% 1.53/1.70 (between(insertion(b, d, b, a), c, b) <=> between(a, c, b)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[266])).
% 1.53/1.70 tff(268,plain,
% 1.53/1.70 ((~between(insertion(b, d, b, a), c, b)) <=> (~between(a, c, b))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[267])).
% 1.53/1.70 tff(269,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((b = a) | (~between(b, a, d)) | (d = extension(b, a, a, d)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (b = a) | (~between(b, a, d)) | (d = extension(b, a, a, d)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(270,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((b = a) | (~between(b, a, d)) | (d = extension(b, a, a, d)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(271,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (b = a) | (~between(b, a, d)) | (d = extension(b, a, a, d))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[270, 269])).
% 1.53/1.70 tff(272,plain,
% 1.53/1.70 ((b = a) | (d = extension(b, a, a, d))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[271, 161, 261])).
% 1.53/1.70 tff(273,plain,
% 1.53/1.70 (d = extension(b, a, a, d)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[272, 187])).
% 1.53/1.70 tff(274,plain,
% 1.53/1.70 (extension(b, a, a, d) = d),
% 1.53/1.70 inference(symmetry,[status(thm)],[273])).
% 1.53/1.70 tff(275,plain,
% 1.53/1.70 (between(extension(b, a, a, d), insertion(b, d, b, a), b) <=> between(d, a, b)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[274, 266])).
% 1.53/1.70 tff(276,plain,
% 1.53/1.70 (between(d, a, b) <=> between(extension(b, a, a, d), insertion(b, d, b, a), b)),
% 1.53/1.70 inference(symmetry,[status(thm)],[275])).
% 1.53/1.70 tff(277,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(b, a, d)) | between(d, a, b))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(b, a, d)) | between(d, a, b))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(278,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(b, a, d)) | between(d, a, b))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(279,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(b, a, d)) | between(d, a, b)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[278, 277])).
% 1.53/1.70 tff(280,plain,
% 1.53/1.70 (between(d, a, b)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[279, 139, 261])).
% 1.53/1.70 tff(281,plain,
% 1.53/1.70 (between(extension(b, a, a, d), insertion(b, d, b, a), b)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[280, 276])).
% 1.53/1.70 tff(282,plain,
% 1.53/1.70 (between(extension(b, a, a, d), c, b) <=> between(d, c, b)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[274])).
% 1.53/1.70 tff(283,plain,
% 1.53/1.70 (between(d, c, b) <=> between(extension(b, a, a, d), c, b)),
% 1.53/1.70 inference(symmetry,[status(thm)],[282])).
% 1.53/1.70 tff(284,plain,
% 1.53/1.70 ((~between(d, c, b)) <=> (~between(extension(b, a, a, d), c, b))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[283])).
% 1.53/1.70 tff(285,plain,
% 1.53/1.70 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X)) <=> ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X)))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(286,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[285])).
% 1.53/1.70 tff(287,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(288,plain,
% 1.53/1.70 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~between(U, V, X)) | (~between(U, W, X))) | between(V, W, X)) <=> ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)))), (((((~between(U, V, X)) | (~between(U, W, X))) | between(V, W, X)) | between(W, V, X)) <=> (((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X))) | between(W, V, X)))), rewrite((((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X))) | between(W, V, X)) <=> ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))), (((((~between(U, V, X)) | (~between(U, W, X))) | between(V, W, X)) | between(W, V, X)) <=> ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(289,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, X)) | (~between(U, W, X))) | between(V, W, X)) | between(W, V, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[288])).
% 1.53/1.70 tff(290,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, X)) | (~between(U, W, X))) | between(V, W, X)) | between(W, V, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b14')).
% 1.53/1.70 tff(291,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[290, 289])).
% 1.53/1.70 tff(292,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[291, 287])).
% 1.53/1.70 tff(293,plain,(
% 1.53/1.70 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 1.53/1.70 inference(skolemize,[status(sab)],[292])).
% 1.53/1.70 tff(294,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[293, 286])).
% 1.53/1.70 tff(295,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, c, d)) | between(c, a, d) | between(a, c, d) | (~between(b, a, d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | (~between(b, c, d)) | between(c, a, d) | between(a, c, d) | (~between(b, a, d)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(296,plain,
% 1.53/1.70 (((~between(b, a, d)) | between(a, c, d) | (~between(b, c, d)) | between(c, a, d)) <=> ((~between(b, c, d)) | between(c, a, d) | between(a, c, d) | (~between(b, a, d)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(297,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, a, d)) | between(a, c, d) | (~between(b, c, d)) | between(c, a, d))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, c, d)) | between(c, a, d) | between(a, c, d) | (~between(b, a, d))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[296])).
% 1.53/1.70 tff(298,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, a, d)) | between(a, c, d) | (~between(b, c, d)) | between(c, a, d))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | (~between(b, c, d)) | between(c, a, d) | between(a, c, d) | (~between(b, a, d)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[297, 295])).
% 1.53/1.70 tff(299,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, a, d)) | between(a, c, d) | (~between(b, c, d)) | between(c, a, d))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(300,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | (~between(b, c, d)) | between(c, a, d) | between(a, c, d) | (~between(b, a, d))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[299, 298])).
% 1.53/1.70 tff(301,plain,
% 1.53/1.70 (~between(b, c, d)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[300, 294, 261, 121, 120])).
% 1.53/1.70 tff(302,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, c, b)) | between(b, c, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, c, b)) | between(b, c, d))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(303,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, c, b)) | between(b, c, d))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(304,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, c, b)) | between(b, c, d)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[303, 302])).
% 1.53/1.70 tff(305,plain,
% 1.53/1.70 (~between(d, c, b)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[304, 139, 301])).
% 1.53/1.70 tff(306,plain,
% 1.53/1.70 (~between(extension(b, a, a, d), c, b)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[305, 284])).
% 1.53/1.70 tff(307,plain,
% 1.53/1.70 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))) <=> ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(308,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[307])).
% 1.53/1.70 tff(309,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(310,plain,
% 1.53/1.70 (^[W: $i, V: $i, U: $i, X: $i] : rewrite((((~between(U, V, X)) | (~between(V, W, X))) | between(U, W, X)) <=> ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(311,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, X)) | (~between(V, W, X))) | between(U, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[310])).
% 1.53/1.70 tff(312,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, X)) | (~between(V, W, X))) | between(U, W, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b8')).
% 1.53/1.70 tff(313,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[312, 311])).
% 1.53/1.70 tff(314,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[313, 309])).
% 1.53/1.70 tff(315,plain,(
% 1.53/1.70 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 1.53/1.70 inference(skolemize,[status(sab)],[314])).
% 1.53/1.70 tff(316,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[315, 308])).
% 1.53/1.70 tff(317,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(extension(b, a, a, d), insertion(b, d, b, a), b)) | between(extension(b, a, a, d), c, b) | (~between(insertion(b, d, b, a), c, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(extension(b, a, a, d), insertion(b, d, b, a), b)) | between(extension(b, a, a, d), c, b) | (~between(insertion(b, d, b, a), c, b)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(318,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(extension(b, a, a, d), insertion(b, d, b, a), b)) | between(extension(b, a, a, d), c, b) | (~between(insertion(b, d, b, a), c, b)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(319,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(extension(b, a, a, d), insertion(b, d, b, a), b)) | between(extension(b, a, a, d), c, b) | (~between(insertion(b, d, b, a), c, b))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[318, 317])).
% 1.53/1.70 tff(320,plain,
% 1.53/1.70 ((~between(extension(b, a, a, d), insertion(b, d, b, a), b)) | between(extension(b, a, a, d), c, b) | (~between(insertion(b, d, b, a), c, b))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[319, 316])).
% 1.53/1.70 tff(321,plain,
% 1.53/1.70 (~between(insertion(b, d, b, a), c, b)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[320, 306, 281])).
% 1.53/1.70 tff(322,plain,
% 1.53/1.70 (~between(a, c, b)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[321, 268])).
% 1.53/1.70 tff(323,plain,
% 1.53/1.70 (between(b, insertion(b, d, b, a), c) <=> between(b, a, c)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[266])).
% 1.53/1.70 tff(324,plain,
% 1.53/1.70 ((~between(b, insertion(b, d, b, a), c)) <=> (~between(b, a, c))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[323])).
% 1.53/1.70 tff(325,plain,
% 1.53/1.70 (between(d, insertion(b, d, b, a), b) <=> between(d, a, b)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[266])).
% 1.53/1.70 tff(326,plain,
% 1.53/1.70 (between(d, a, b) <=> between(d, insertion(b, d, b, a), b)),
% 1.53/1.70 inference(symmetry,[status(thm)],[325])).
% 1.53/1.70 tff(327,plain,
% 1.53/1.70 (between(d, insertion(b, d, b, a), b)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[280, 326])).
% 1.53/1.70 tff(328,plain,
% 1.53/1.70 (between(c, d, insertion(b, d, b, a)) <=> between(c, d, a)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[266])).
% 1.53/1.70 tff(329,plain,
% 1.53/1.70 (between(c, d, a) <=> between(c, d, insertion(b, d, b, a))),
% 1.53/1.70 inference(symmetry,[status(thm)],[328])).
% 1.53/1.70 tff(330,plain,
% 1.53/1.70 ((~between(c, d, a)) <=> (~between(c, d, insertion(b, d, b, a)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[329])).
% 1.53/1.70 tff(331,plain,
% 1.53/1.70 (~between(c, d, insertion(b, d, b, a))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[123, 330])).
% 1.53/1.70 tff(332,plain,
% 1.53/1.70 (between(d, c, insertion(b, d, b, a)) <=> between(d, c, a)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[266])).
% 1.53/1.70 tff(333,plain,
% 1.53/1.70 (between(d, c, a) <=> between(d, c, insertion(b, d, b, a))),
% 1.53/1.70 inference(symmetry,[status(thm)],[332])).
% 1.53/1.70 tff(334,plain,
% 1.53/1.70 ((~between(d, c, a)) <=> (~between(d, c, insertion(b, d, b, a)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[333])).
% 1.53/1.70 tff(335,plain,
% 1.53/1.70 (~between(d, c, insertion(b, d, b, a))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[122, 334])).
% 1.53/1.70 tff(336,plain,
% 1.53/1.70 ((insertion(b, d, b, a) = b) <=> (a = b)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[266])).
% 1.53/1.70 tff(337,plain,
% 1.53/1.70 ((a = b) <=> (insertion(b, d, b, a) = b)),
% 1.53/1.70 inference(symmetry,[status(thm)],[336])).
% 1.53/1.70 tff(338,plain,
% 1.53/1.70 ((~(a = b)) <=> (~(insertion(b, d, b, a) = b))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[337])).
% 1.53/1.70 tff(339,plain,
% 1.53/1.70 (~(insertion(b, d, b, a) = b)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[150, 338])).
% 1.53/1.70 tff(340,plain,
% 1.53/1.70 (^[W: $i, V: $i, U: $i, X: $i] : refl(((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W)) <=> ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W)))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(341,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[340])).
% 1.53/1.70 tff(342,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(343,plain,
% 1.53/1.70 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) <=> ((W = X) | (~between(U, W, X)) | (~between(V, W, X)))), (((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) | between(U, V, W)) <=> (((W = X) | (~between(U, W, X)) | (~between(V, W, X))) | between(U, V, W)))), rewrite((((W = X) | (~between(U, W, X)) | (~between(V, W, X))) | between(U, V, W)) <=> ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)))), (((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) | between(U, V, W)) <=> ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X))))), ((((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) | between(U, V, W)) | between(V, U, W)) <=> (((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X))) | between(V, U, W)))), rewrite((((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X))) | between(V, U, W)) <=> ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))), ((((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) | between(U, V, W)) | between(V, U, W)) <=> ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(344,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : (((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) | between(U, V, W)) | between(V, U, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[343])).
% 1.53/1.71 tff(345,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) | between(U, V, W)) | between(V, U, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7')).
% 1.53/1.71 tff(346,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[345, 344])).
% 1.53/1.71 tff(347,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[346, 342])).
% 1.53/1.71 tff(348,plain,(
% 1.53/1.71 ![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 1.53/1.71 inference(skolemize,[status(sab)],[347])).
% 1.53/1.71 tff(349,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[348, 341])).
% 1.53/1.71 tff(350,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | ((~between(d, insertion(b, d, b, a), b)) | (insertion(b, d, b, a) = b) | between(d, c, insertion(b, d, b, a)) | between(c, d, insertion(b, d, b, a)) | (~between(c, insertion(b, d, b, a), b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | (~between(d, insertion(b, d, b, a), b)) | (insertion(b, d, b, a) = b) | between(d, c, insertion(b, d, b, a)) | between(c, d, insertion(b, d, b, a)) | (~between(c, insertion(b, d, b, a), b)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(351,plain,
% 1.53/1.71 (((insertion(b, d, b, a) = b) | between(d, c, insertion(b, d, b, a)) | (~between(d, insertion(b, d, b, a), b)) | (~between(c, insertion(b, d, b, a), b)) | between(c, d, insertion(b, d, b, a))) <=> ((~between(d, insertion(b, d, b, a), b)) | (insertion(b, d, b, a) = b) | between(d, c, insertion(b, d, b, a)) | between(c, d, insertion(b, d, b, a)) | (~between(c, insertion(b, d, b, a), b)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(352,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | ((insertion(b, d, b, a) = b) | between(d, c, insertion(b, d, b, a)) | (~between(d, insertion(b, d, b, a), b)) | (~between(c, insertion(b, d, b, a), b)) | between(c, d, insertion(b, d, b, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | ((~between(d, insertion(b, d, b, a), b)) | (insertion(b, d, b, a) = b) | between(d, c, insertion(b, d, b, a)) | between(c, d, insertion(b, d, b, a)) | (~between(c, insertion(b, d, b, a), b))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[351])).
% 1.53/1.71 tff(353,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | ((insertion(b, d, b, a) = b) | between(d, c, insertion(b, d, b, a)) | (~between(d, insertion(b, d, b, a), b)) | (~between(c, insertion(b, d, b, a), b)) | between(c, d, insertion(b, d, b, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | (~between(d, insertion(b, d, b, a), b)) | (insertion(b, d, b, a) = b) | between(d, c, insertion(b, d, b, a)) | between(c, d, insertion(b, d, b, a)) | (~between(c, insertion(b, d, b, a), b)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[352, 350])).
% 1.53/1.71 tff(354,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | ((insertion(b, d, b, a) = b) | between(d, c, insertion(b, d, b, a)) | (~between(d, insertion(b, d, b, a), b)) | (~between(c, insertion(b, d, b, a), b)) | between(c, d, insertion(b, d, b, a)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(355,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | (~between(d, insertion(b, d, b, a), b)) | (insertion(b, d, b, a) = b) | between(d, c, insertion(b, d, b, a)) | between(c, d, insertion(b, d, b, a)) | (~between(c, insertion(b, d, b, a), b))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[354, 353])).
% 1.53/1.71 tff(356,plain,
% 1.53/1.71 ((~between(d, insertion(b, d, b, a), b)) | (insertion(b, d, b, a) = b) | between(d, c, insertion(b, d, b, a)) | between(c, d, insertion(b, d, b, a)) | (~between(c, insertion(b, d, b, a), b))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[355, 349])).
% 1.53/1.71 tff(357,plain,
% 1.53/1.71 (~between(c, insertion(b, d, b, a), b)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[356, 339, 335, 331, 327])).
% 1.53/1.71 tff(358,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(b, insertion(b, d, b, a), c)) | between(c, insertion(b, d, b, a), b))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(b, insertion(b, d, b, a), c)) | between(c, insertion(b, d, b, a), b))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(359,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(b, insertion(b, d, b, a), c)) | between(c, insertion(b, d, b, a), b))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(360,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(b, insertion(b, d, b, a), c)) | between(c, insertion(b, d, b, a), b)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.53/1.71 tff(361,plain,
% 1.53/1.71 (~between(b, insertion(b, d, b, a), c)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[360, 139, 357])).
% 1.53/1.71 tff(362,plain,
% 1.53/1.71 (~between(b, a, c)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[361, 324])).
% 1.53/1.71 tff(363,plain,
% 1.53/1.71 (colinear(a, b, c) <=> colinear(a, b, c)),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(364,axiom,(colinear(a, b, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abc_colinear')).
% 1.53/1.71 tff(365,plain,
% 1.53/1.71 (colinear(a, b, c)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[364, 363])).
% 1.53/1.71 tff(366,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | ((~colinear(a, b, c)) | colinear(b, a, c))) <=> ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | (~colinear(a, b, c)) | colinear(b, a, c))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(367,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | ((~colinear(a, b, c)) | colinear(b, a, c))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(368,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | (~colinear(a, b, c)) | colinear(b, a, c)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[367, 366])).
% 1.53/1.71 tff(369,plain,
% 1.53/1.71 (colinear(b, a, c)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[368, 215, 365])).
% 1.53/1.71 tff(370,plain,
% 1.53/1.71 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(c, b, a) | between(a, c, b) | between(b, a, c) | (~colinear(b, a, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | between(c, b, a) | between(a, c, b) | between(b, a, c) | (~colinear(b, a, c)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(371,plain,
% 1.53/1.71 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(c, b, a) | between(a, c, b) | between(b, a, c) | (~colinear(b, a, c)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(372,plain,
% 1.53/1.71 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | between(c, b, a) | between(a, c, b) | between(b, a, c) | (~colinear(b, a, c))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[371, 370])).
% 1.53/1.71 tff(373,plain,
% 1.53/1.71 (between(c, b, a) | between(a, c, b) | between(b, a, c)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[372, 229, 369])).
% 1.53/1.71 tff(374,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[373, 362, 322, 260])).
% 1.53/1.71 tff(375,plain,((~between(b, a, d)) | between(c, b, a) | between(c, d, a) | between(d, c, a) | between(c, a, d) | between(a, c, d)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(376,plain,
% 1.53/1.71 (~between(b, a, d)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[375, 259, 123, 122, 121, 120])).
% 1.53/1.71 tff(377,plain,
% 1.53/1.71 (between(d, b, a)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[233, 376, 119])).
% 1.53/1.71 tff(378,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(d, b, a)) | (b = insertion(d, a, d, b)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(d, b, a)) | (b = insertion(d, a, d, b)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(379,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(d, b, a)) | (b = insertion(d, a, d, b)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(380,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(d, b, a)) | (b = insertion(d, a, d, b))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[379, 378])).
% 1.53/1.71 tff(381,plain,
% 1.53/1.71 (b = insertion(d, a, d, b)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[380, 16, 377])).
% 1.53/1.71 tff(382,plain,
% 1.53/1.71 (insertion(d, a, d, b) = b),
% 1.53/1.71 inference(symmetry,[status(thm)],[381])).
% 1.53/1.71 tff(383,plain,
% 1.53/1.71 (between(a, insertion(d, a, d, b), d) <=> between(a, b, d)),
% 1.53/1.71 inference(monotonicity,[status(thm)],[382])).
% 1.53/1.71 tff(384,plain,
% 1.53/1.71 (between(a, b, d) <=> between(a, insertion(d, a, d, b), d)),
% 1.53/1.71 inference(symmetry,[status(thm)],[383])).
% 1.53/1.71 tff(385,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, b, a)) | between(a, b, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, b, a)) | between(a, b, d))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(386,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, b, a)) | between(a, b, d))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(387,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, b, a)) | between(a, b, d)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[386, 385])).
% 1.53/1.71 tff(388,plain,
% 1.53/1.71 (between(a, b, d)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[387, 139, 377])).
% 1.53/1.71 tff(389,plain,
% 1.53/1.71 (between(a, insertion(d, a, d, b), d)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[388, 384])).
% 1.53/1.71 tff(390,plain,
% 1.53/1.71 (between(a, c, insertion(d, a, d, b)) <=> between(a, c, b)),
% 1.53/1.71 inference(monotonicity,[status(thm)],[382])).
% 1.53/1.71 tff(391,plain,
% 1.53/1.71 (between(a, c, b) <=> between(a, c, insertion(d, a, d, b))),
% 1.53/1.71 inference(symmetry,[status(thm)],[390])).
% 1.53/1.71 tff(392,assumption,(~between(d, a, c)), introduced(assumption)).
% 1.53/1.71 tff(393,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | (between(d, a, c) | (b = a) | (~between(b, a, c)) | (~between(d, b, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | between(d, a, c) | (b = a) | (~between(b, a, c)) | (~between(d, b, a)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(394,plain,
% 1.53/1.71 (((~between(d, b, a)) | between(d, a, c) | (~between(b, a, c)) | (b = a)) <=> (between(d, a, c) | (b = a) | (~between(b, a, c)) | (~between(d, b, a)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(395,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(d, b, a)) | between(d, a, c) | (~between(b, a, c)) | (b = a))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | (between(d, a, c) | (b = a) | (~between(b, a, c)) | (~between(d, b, a))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[394])).
% 1.53/1.71 tff(396,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(d, b, a)) | between(d, a, c) | (~between(b, a, c)) | (b = a))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | between(d, a, c) | (b = a) | (~between(b, a, c)) | (~between(d, b, a)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[395, 393])).
% 1.53/1.71 tff(397,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(d, b, a)) | between(d, a, c) | (~between(b, a, c)) | (b = a))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(398,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | between(d, a, c) | (b = a) | (~between(b, a, c)) | (~between(d, b, a))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[397, 396])).
% 1.53/1.71 tff(399,plain,
% 1.53/1.71 ((b = a) | (~between(b, a, c))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[398, 197, 377, 392])).
% 1.53/1.71 tff(400,plain,
% 1.53/1.71 (~between(b, a, c)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[399, 187])).
% 1.53/1.71 tff(401,plain,
% 1.53/1.71 (between(a, c, b)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[373, 400, 259])).
% 1.53/1.71 tff(402,plain,
% 1.53/1.71 (between(a, c, insertion(d, a, d, b))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[401, 391])).
% 1.53/1.71 tff(403,plain,
% 1.53/1.71 (^[W: $i, V: $i, U: $i, X: $i] : refl((between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X))) <=> (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(404,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[403])).
% 1.53/1.71 tff(405,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(406,plain,
% 1.53/1.71 (^[W: $i, V: $i, U: $i, X: $i] : rewrite((((~between(U, V, W)) | (~between(U, W, X))) | between(U, V, X)) <=> (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(407,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(U, W, X))) | between(U, V, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[406])).
% 1.53/1.71 tff(408,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(U, W, X))) | between(U, V, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b9')).
% 1.53/1.71 tff(409,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[408, 407])).
% 1.53/1.71 tff(410,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[409, 405])).
% 1.53/1.71 tff(411,plain,(
% 1.53/1.71 ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 1.53/1.71 inference(skolemize,[status(sab)],[410])).
% 1.53/1.71 tff(412,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[411, 404])).
% 1.53/1.71 tff(413,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(a, c, d) | (~between(a, c, insertion(d, a, d, b))) | (~between(a, insertion(d, a, d, b), d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | between(a, c, d) | (~between(a, c, insertion(d, a, d, b))) | (~between(a, insertion(d, a, d, b), d)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(414,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(a, c, d) | (~between(a, c, insertion(d, a, d, b))) | (~between(a, insertion(d, a, d, b), d)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(415,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | between(a, c, d) | (~between(a, c, insertion(d, a, d, b))) | (~between(a, insertion(d, a, d, b), d))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[414, 413])).
% 1.53/1.71 tff(416,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[415, 412, 120, 402, 389])).
% 1.53/1.71 tff(417,plain,(between(a, d, b) | between(a, c, d) | between(d, a, c) | between(c, d, a) | between(d, c, a) | between(c, a, d) | between(a, d, c)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(418,plain,
% 1.53/1.71 (between(a, d, b)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[417, 63, 118, 107, 96, 85, 74])).
% 1.53/1.71 tff(419,plain,
% 1.53/1.71 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X))) <=> ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(420,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[419])).
% 1.53/1.71 tff(421,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(422,plain,
% 1.53/1.71 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~between(U, V, X)) | (~between(U, W, X))) | between(U, V, W)) <=> ((~between(U, V, X)) | between(U, V, W) | (~between(U, W, X)))), (((((~between(U, V, X)) | (~between(U, W, X))) | between(U, V, W)) | between(U, W, V)) <=> (((~between(U, V, X)) | between(U, V, W) | (~between(U, W, X))) | between(U, W, V)))), rewrite((((~between(U, V, X)) | between(U, V, W) | (~between(U, W, X))) | between(U, W, V)) <=> ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))), (((((~between(U, V, X)) | (~between(U, W, X))) | between(U, V, W)) | between(U, W, V)) <=> ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(423,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, X)) | (~between(U, W, X))) | between(U, V, W)) | between(U, W, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[422])).
% 1.53/1.71 tff(424,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, X)) | (~between(U, W, X))) | between(U, V, W)) | between(U, W, V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t9')).
% 1.53/1.71 tff(425,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[424, 423])).
% 1.53/1.71 tff(426,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[425, 421])).
% 1.53/1.71 tff(427,plain,(
% 1.53/1.71 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 1.53/1.71 inference(skolemize,[status(sab)],[426])).
% 1.53/1.71 tff(428,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[427, 420])).
% 1.53/1.71 tff(429,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | (between(a, d, c) | between(a, c, d) | (~between(a, d, b)) | (~between(a, c, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | between(a, d, c) | between(a, c, d) | (~between(a, d, b)) | (~between(a, c, b)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(430,plain,
% 1.53/1.71 (((~between(a, d, b)) | between(a, c, d) | between(a, d, c) | (~between(a, c, b))) <=> (between(a, d, c) | between(a, c, d) | (~between(a, d, b)) | (~between(a, c, b)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(431,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(a, d, b)) | between(a, c, d) | between(a, d, c) | (~between(a, c, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | (between(a, d, c) | between(a, c, d) | (~between(a, d, b)) | (~between(a, c, b))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[430])).
% 1.53/1.71 tff(432,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(a, d, b)) | between(a, c, d) | between(a, d, c) | (~between(a, c, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | between(a, d, c) | between(a, c, d) | (~between(a, d, b)) | (~between(a, c, b)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[431, 429])).
% 1.53/1.71 tff(433,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(a, d, b)) | between(a, c, d) | between(a, d, c) | (~between(a, c, b)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(434,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | between(a, d, c) | between(a, c, d) | (~between(a, d, b)) | (~between(a, c, b))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[433, 432])).
% 1.53/1.71 tff(435,plain,
% 1.53/1.71 (~between(a, c, b)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[434, 428, 418, 74, 63])).
% 1.53/1.71 tff(436,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(a, d, c) | (~between(a, b, c)) | (~between(a, d, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | between(a, d, c) | (~between(a, b, c)) | (~between(a, d, b)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(437,plain,
% 1.53/1.71 ((between(a, d, c) | (~between(a, d, b)) | (~between(a, b, c))) <=> (between(a, d, c) | (~between(a, b, c)) | (~between(a, d, b)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(438,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(a, d, c) | (~between(a, d, b)) | (~between(a, b, c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(a, d, c) | (~between(a, b, c)) | (~between(a, d, b))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[437])).
% 1.53/1.71 tff(439,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(a, d, c) | (~between(a, d, b)) | (~between(a, b, c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | between(a, d, c) | (~between(a, b, c)) | (~between(a, d, b)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[438, 436])).
% 1.53/1.72 tff(440,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(a, d, c) | (~between(a, d, b)) | (~between(a, b, c)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(441,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | between(a, d, c) | (~between(a, b, c)) | (~between(a, d, b))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[440, 439])).
% 1.53/1.72 tff(442,plain,
% 1.53/1.72 (~between(a, b, c)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[441, 412, 418, 74])).
% 1.53/1.72 tff(443,plain,
% 1.53/1.72 (~between(c, b, a)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[142, 139, 442])).
% 1.53/1.72 tff(444,plain,
% 1.53/1.72 (between(b, a, c)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[373, 443, 435])).
% 1.53/1.72 tff(445,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(a, d, b)) | (d = insertion(a, b, a, d)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(a, d, b)) | (d = insertion(a, b, a, d)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(446,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(a, d, b)) | (d = insertion(a, b, a, d)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(447,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(a, d, b)) | (d = insertion(a, b, a, d))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[446, 445])).
% 1.53/1.72 tff(448,plain,
% 1.53/1.72 (d = insertion(a, b, a, d)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[447, 16, 418])).
% 1.53/1.72 tff(449,plain,
% 1.53/1.72 (insertion(a, b, a, d) = d),
% 1.53/1.72 inference(symmetry,[status(thm)],[448])).
% 1.53/1.72 tff(450,plain,
% 1.53/1.72 (between(b, insertion(a, b, a, d), a) <=> between(b, d, a)),
% 1.53/1.72 inference(monotonicity,[status(thm)],[449])).
% 1.53/1.72 tff(451,plain,
% 1.53/1.72 (between(b, d, a) <=> between(b, insertion(a, b, a, d), a)),
% 1.53/1.72 inference(symmetry,[status(thm)],[450])).
% 1.53/1.72 tff(452,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(a, d, b)) | between(b, d, a))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(a, d, b)) | between(b, d, a))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(453,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(a, d, b)) | between(b, d, a))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(454,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(a, d, b)) | between(b, d, a)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[453, 452])).
% 1.53/1.72 tff(455,plain,
% 1.53/1.72 (between(b, d, a)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[454, 139, 418])).
% 1.53/1.72 tff(456,plain,
% 1.53/1.72 (between(b, insertion(a, b, a, d), a)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[455, 451])).
% 1.53/1.72 tff(457,plain,
% 1.53/1.72 (between(insertion(a, b, a, d), a, c) <=> between(d, a, c)),
% 1.53/1.72 inference(monotonicity,[status(thm)],[449])).
% 1.53/1.72 tff(458,plain,
% 1.53/1.72 (between(d, a, c) <=> between(insertion(a, b, a, d), a, c)),
% 1.53/1.72 inference(symmetry,[status(thm)],[457])).
% 1.53/1.72 tff(459,plain,
% 1.53/1.72 ((~between(d, a, c)) <=> (~between(insertion(a, b, a, d), a, c))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[458])).
% 1.53/1.72 tff(460,plain,
% 1.53/1.72 (~between(insertion(a, b, a, d), a, c)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[118, 459])).
% 1.53/1.72 tff(461,plain,
% 1.53/1.72 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))) <=> ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))))),
% 1.53/1.72 inference(bind,[status(th)],[])).
% 1.53/1.72 tff(462,plain,
% 1.53/1.72 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 1.53/1.72 inference(quant_intro,[status(thm)],[461])).
% 1.53/1.72 tff(463,plain,
% 1.53/1.72 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(464,plain,
% 1.53/1.72 (^[W: $i, V: $i, U: $i, X: $i] : rewrite((((~between(U, V, W)) | (~between(U, W, X))) | between(V, W, X)) <=> ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))))),
% 1.53/1.72 inference(bind,[status(th)],[])).
% 1.53/1.72 tff(465,plain,
% 1.53/1.72 (![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(U, W, X))) | between(V, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 1.53/1.72 inference(quant_intro,[status(thm)],[464])).
% 1.53/1.72 tff(466,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(U, W, X))) | between(V, W, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b5')).
% 1.53/1.72 tff(467,plain,
% 1.53/1.72 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[466, 465])).
% 1.53/1.72 tff(468,plain,
% 1.53/1.72 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[467, 463])).
% 1.53/1.72 tff(469,plain,(
% 1.53/1.72 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 1.53/1.72 inference(skolemize,[status(sab)],[468])).
% 1.53/1.72 tff(470,plain,
% 1.53/1.72 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[469, 462])).
% 1.53/1.72 tff(471,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(b, a, c)) | (~between(b, insertion(a, b, a, d), a)) | between(insertion(a, b, a, d), a, c))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(b, a, c)) | (~between(b, insertion(a, b, a, d), a)) | between(insertion(a, b, a, d), a, c))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(472,plain,
% 1.53/1.72 (((~between(b, insertion(a, b, a, d), a)) | between(insertion(a, b, a, d), a, c) | (~between(b, a, c))) <=> ((~between(b, a, c)) | (~between(b, insertion(a, b, a, d), a)) | between(insertion(a, b, a, d), a, c))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(473,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(b, insertion(a, b, a, d), a)) | between(insertion(a, b, a, d), a, c) | (~between(b, a, c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(b, a, c)) | (~between(b, insertion(a, b, a, d), a)) | between(insertion(a, b, a, d), a, c)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[472])).
% 1.53/1.72 tff(474,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(b, insertion(a, b, a, d), a)) | between(insertion(a, b, a, d), a, c) | (~between(b, a, c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(b, a, c)) | (~between(b, insertion(a, b, a, d), a)) | between(insertion(a, b, a, d), a, c))),
% 1.53/1.72 inference(transitivity,[status(thm)],[473, 471])).
% 1.53/1.72 tff(475,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(b, insertion(a, b, a, d), a)) | between(insertion(a, b, a, d), a, c) | (~between(b, a, c)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(476,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(b, a, c)) | (~between(b, insertion(a, b, a, d), a)) | between(insertion(a, b, a, d), a, c)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[475, 474])).
% 1.53/1.72 tff(477,plain,
% 1.53/1.72 ((~between(b, a, c)) | (~between(b, insertion(a, b, a, d), a)) | between(insertion(a, b, a, d), a, c)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[476, 470])).
% 1.53/1.72 tff(478,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[477, 460, 456, 444])).
% 1.53/1.72 tff(479,plain,(colinear(a, c, d)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(480,plain,
% 1.53/1.72 (((~colinear(a, c, d)) | (~colinear(b, c, d))) <=> ((~colinear(a, c, d)) | (~colinear(b, c, d)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(481,axiom,((~colinear(a, c, d)) | (~colinear(b, c, d))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_colinearity')).
% 1.53/1.72 tff(482,plain,
% 1.53/1.72 ((~colinear(a, c, d)) | (~colinear(b, c, d))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[481, 480])).
% 1.53/1.72 tff(483,plain,
% 1.53/1.72 (~colinear(b, c, d)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[482, 479])).
% 1.53/1.72 tff(484,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(c, b, d)) | colinear(b, c, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(c, b, d)) | colinear(b, c, d))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(485,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(c, b, d)) | colinear(b, c, d))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(486,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(c, b, d)) | colinear(b, c, d)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.53/1.72 tff(487,plain,
% 1.53/1.72 (~between(c, b, d)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[486, 81, 483])).
% 1.53/1.72 tff(488,plain,
% 1.53/1.72 (~between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[487, 51])).
% 1.53/1.72 tff(489,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(490,plain,
% 1.53/1.72 (((~between(a, c, insertion(d, b, d, b))) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))) <=> (between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(491,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(a, c, insertion(d, b, d, b))) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[490])).
% 1.53/1.72 tff(492,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(a, c, insertion(d, b, d, b))) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[491, 489])).
% 1.53/1.72 tff(493,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(a, c, insertion(d, b, d, b))) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(494,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[493, 492])).
% 1.53/1.72 tff(495,plain,
% 1.53/1.72 ((~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[494, 470, 488])).
% 1.53/1.72 tff(496,plain,
% 1.53/1.72 (~between(a, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[495, 48])).
% 1.53/1.72 tff(497,plain,
% 1.53/1.72 (~between(a, b, d)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[496, 47])).
% 1.53/1.72 tff(498,plain,
% 1.53/1.72 (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b)) <=> between(d, a, b)),
% 1.53/1.72 inference(monotonicity,[status(thm)],[21, 39])).
% 1.53/1.72 tff(499,plain,
% 1.53/1.72 ((~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b))) <=> (~between(d, a, b))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[498])).
% 1.53/1.72 tff(500,plain,
% 1.53/1.72 (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(d, b, d, b)) <=> between(d, b, b)),
% 1.53/1.72 inference(monotonicity,[status(thm)],[21, 39, 39])).
% 1.53/1.72 tff(501,plain,
% 1.53/1.72 (between(d, b, b) <=> between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(d, b, d, b))),
% 1.53/1.72 inference(symmetry,[status(thm)],[500])).
% 1.53/1.72 tff(502,plain,
% 1.53/1.72 (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(d, b, d, b))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[34, 501])).
% 1.53/1.72 tff(503,plain,
% 1.53/1.72 (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) <=> between(d, c, b)),
% 1.53/1.72 inference(monotonicity,[status(thm)],[21, 39])).
% 1.53/1.72 tff(504,plain,
% 1.53/1.72 (between(d, c, b) <=> between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b))),
% 1.53/1.72 inference(symmetry,[status(thm)],[503])).
% 1.53/1.72 tff(505,plain,
% 1.53/1.72 ((~between(d, c, b)) <=> (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[504])).
% 1.53/1.72 tff(506,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(d, c, b)) | colinear(b, c, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(d, c, b)) | colinear(b, c, d))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(507,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(d, c, b)) | colinear(b, c, d))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(508,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(d, c, b)) | colinear(b, c, d)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[507, 506])).
% 1.53/1.72 tff(509,plain,
% 1.53/1.72 (~between(d, c, b)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[508, 92, 483])).
% 1.53/1.72 tff(510,plain,
% 1.53/1.72 (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[509, 505])).
% 1.53/1.72 tff(511,plain,
% 1.53/1.72 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y))) <=> (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y))))),
% 1.53/1.72 inference(bind,[status(th)],[])).
% 1.53/1.72 tff(512,plain,
% 1.53/1.72 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))),
% 1.53/1.72 inference(quant_intro,[status(thm)],[511])).
% 1.53/1.72 tff(513,plain,
% 1.53/1.72 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(514,plain,
% 1.53/1.72 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~between(U, V, Y)) | (~between(V, W, X))) | (~between(U, X, Y))) <=> ((~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))), (((((~between(U, V, Y)) | (~between(V, W, X))) | (~between(U, X, Y))) | between(U, W, Y)) <=> (((~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y))) | between(U, W, Y)))), rewrite((((~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y))) | between(U, W, Y)) <=> (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))), (((((~between(U, V, Y)) | (~between(V, W, X))) | (~between(U, X, Y))) | between(U, W, Y)) <=> (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(515,plain,
% 1.53/1.73 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((~between(U, V, Y)) | (~between(V, W, X))) | (~between(U, X, Y))) | between(U, W, Y)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[514])).
% 1.53/1.73 tff(516,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((~between(U, V, Y)) | (~between(V, W, X))) | (~between(U, X, Y))) | between(U, W, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8')).
% 1.53/1.73 tff(517,plain,
% 1.53/1.73 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[516, 515])).
% 1.53/1.73 tff(518,plain,
% 1.53/1.73 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[517, 513])).
% 1.53/1.73 tff(519,plain,(
% 1.53/1.73 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))),
% 1.53/1.73 inference(skolemize,[status(sab)],[518])).
% 1.53/1.73 tff(520,plain,
% 1.53/1.73 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[519, 512])).
% 1.53/1.73 tff(521,plain,
% 1.53/1.73 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))) | (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(d, b, d, b))) | (~between(a, c, insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))) | between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(d, b, d, b))) | (~between(a, c, insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(522,plain,
% 1.53/1.73 ((between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | (~between(a, c, insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b)))) <=> (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(d, b, d, b))) | (~between(a, c, insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(523,plain,
% 1.53/1.73 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))) | (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | (~between(a, c, insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))) | (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(d, b, d, b))) | (~between(a, c, insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b)))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[522])).
% 1.53/1.73 tff(524,plain,
% 1.53/1.73 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))) | (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | (~between(a, c, insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))) | between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(d, b, d, b))) | (~between(a, c, insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[523, 521])).
% 1.53/1.73 tff(525,plain,
% 1.53/1.73 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))) | (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | (~between(a, c, insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(526,plain,
% 1.53/1.73 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (between(U, W, Y) | (~between(V, W, X)) | (~between(U, X, Y)) | (~between(U, V, Y)))) | between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(d, b, d, b))) | (~between(a, c, insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[525, 524])).
% 1.53/1.73 tff(527,plain,
% 1.53/1.73 ((~between(a, c, insertion(d, b, d, b))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[526, 520, 510, 502])).
% 1.53/1.73 tff(528,plain,
% 1.53/1.73 (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, insertion(d, b, d, b))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[527, 48])).
% 1.53/1.73 tff(529,plain,
% 1.53/1.73 (~between(d, a, b)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[528, 499])).
% 1.53/1.73 tff(530,plain,
% 1.53/1.73 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | ((~colinear(a, b, d)) | between(d, a, b) | between(b, d, a) | between(a, b, d))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(a, b, d)) | between(d, a, b) | between(b, d, a) | between(a, b, d))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(531,plain,
% 1.53/1.73 ((between(d, a, b) | between(b, d, a) | between(a, b, d) | (~colinear(a, b, d))) <=> ((~colinear(a, b, d)) | between(d, a, b) | between(b, d, a) | between(a, b, d))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(532,plain,
% 1.53/1.73 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, a, b) | between(b, d, a) | between(a, b, d) | (~colinear(a, b, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | ((~colinear(a, b, d)) | between(d, a, b) | between(b, d, a) | between(a, b, d)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[531])).
% 1.53/1.73 tff(533,plain,
% 1.53/1.73 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, a, b) | between(b, d, a) | between(a, b, d) | (~colinear(a, b, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(a, b, d)) | between(d, a, b) | between(b, d, a) | between(a, b, d))),
% 1.53/1.73 inference(transitivity,[status(thm)],[532, 530])).
% 1.53/1.73 tff(534,plain,
% 1.53/1.73 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, a, b) | between(b, d, a) | between(a, b, d) | (~colinear(a, b, d)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(535,plain,
% 1.53/1.73 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(a, b, d)) | between(d, a, b) | between(b, d, a) | between(a, b, d)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[534, 533])).
% 1.53/1.73 tff(536,plain,
% 1.53/1.73 (between(d, a, b) | between(b, d, a) | between(a, b, d)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[535, 229, 208])).
% 1.53/1.73 tff(537,plain,
% 1.53/1.73 (between(b, d, a)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[536, 529, 497])).
% 1.53/1.73 tff(538,plain,
% 1.53/1.73 (between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[537, 45])).
% 1.53/1.73 tff(539,plain,
% 1.53/1.73 (between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) <=> between(c, d, b)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[21, 39])).
% 1.53/1.73 tff(540,plain,
% 1.53/1.73 (between(c, d, b) <=> between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))),
% 1.53/1.73 inference(symmetry,[status(thm)],[539])).
% 1.53/1.73 tff(541,plain,
% 1.53/1.73 ((~between(c, d, b)) <=> (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[540])).
% 1.53/1.73 tff(542,plain,
% 1.53/1.73 (((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | ((~between(c, d, b)) | colinear(b, c, d))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | (~between(c, d, b)) | colinear(b, c, d))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(543,plain,
% 1.53/1.73 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | ((~between(c, d, b)) | colinear(b, c, d))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(544,plain,
% 1.53/1.73 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | (~between(c, d, b)) | colinear(b, c, d)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[543, 542])).
% 1.53/1.73 tff(545,plain,
% 1.53/1.73 (~between(c, d, b)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[544, 103, 483])).
% 1.53/1.73 tff(546,plain,
% 1.53/1.73 (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[545, 541])).
% 1.53/1.73 tff(547,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(548,plain,
% 1.53/1.73 (((~between(a, c, insertion(d, b, d, b))) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))) | between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b))) <=> (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(549,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(a, c, insertion(d, b, d, b))) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))) | between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[548])).
% 1.53/1.74 tff(550,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(a, c, insertion(d, b, d, b))) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))) | between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[549, 547])).
% 1.53/1.74 tff(551,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(a, c, insertion(d, b, d, b))) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))) | between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(552,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c, insertion(d, b, d, b)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[551, 550])).
% 1.53/1.74 tff(553,plain,
% 1.53/1.74 ((~between(a, c, insertion(d, b, d, b))) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[552, 294, 510, 546])).
% 1.53/1.74 tff(554,plain,
% 1.53/1.74 (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[553, 48])).
% 1.53/1.74 tff(555,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)) | between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)) | between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(556,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)) | between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(557,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)) | between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[556, 555])).
% 1.53/1.74 tff(558,plain,
% 1.53/1.74 (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[557, 139, 554])).
% 1.53/1.74 tff(559,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[558, 538])).
% 1.53/1.74 tff(560,plain,(~between(a, c, insertion(d, b, d, b))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(561,plain,
% 1.53/1.74 (~between(a, c, b)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[560, 43])).
% 1.53/1.74 tff(562,plain,
% 1.53/1.74 (between(insertion(d, b, d, b), a, c) <=> between(b, a, c)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[39])).
% 1.53/1.74 tff(563,plain,
% 1.53/1.74 (between(b, a, c) <=> between(insertion(d, b, d, b), a, c)),
% 1.53/1.74 inference(symmetry,[status(thm)],[562])).
% 1.53/1.74 tff(564,assumption,(between(b, a, c)), introduced(assumption)).
% 1.53/1.74 tff(565,plain,
% 1.53/1.74 (between(insertion(d, b, d, b), a, c)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[564, 563])).
% 1.53/1.74 tff(566,plain,
% 1.53/1.74 ((insertion(d, b, d, b) = a) <=> (b = a)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[39])).
% 1.53/1.74 tff(567,plain,
% 1.53/1.74 ((insertion(d, b, d, b) = a) <=> (a = b)),
% 1.53/1.74 inference(transitivity,[status(thm)],[566, 184])).
% 1.53/1.74 tff(568,plain,
% 1.53/1.74 ((a = b) <=> (insertion(d, b, d, b) = a)),
% 1.53/1.74 inference(symmetry,[status(thm)],[567])).
% 1.53/1.74 tff(569,plain,
% 1.53/1.74 ((~(a = b)) <=> (~(insertion(d, b, d, b) = a))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[568])).
% 1.53/1.74 tff(570,plain,
% 1.53/1.74 (~(insertion(d, b, d, b) = a)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[150, 569])).
% 1.53/1.74 tff(571,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(insertion(d, b, d, b), a, c)) | (c = extension(insertion(d, b, d, b), a, a, c)) | (insertion(d, b, d, b) = a))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(insertion(d, b, d, b), a, c)) | (c = extension(insertion(d, b, d, b), a, a, c)) | (insertion(d, b, d, b) = a))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(572,plain,
% 1.53/1.74 (((insertion(d, b, d, b) = a) | (~between(insertion(d, b, d, b), a, c)) | (c = extension(insertion(d, b, d, b), a, a, c))) <=> ((~between(insertion(d, b, d, b), a, c)) | (c = extension(insertion(d, b, d, b), a, a, c)) | (insertion(d, b, d, b) = a))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(573,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((insertion(d, b, d, b) = a) | (~between(insertion(d, b, d, b), a, c)) | (c = extension(insertion(d, b, d, b), a, a, c)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(insertion(d, b, d, b), a, c)) | (c = extension(insertion(d, b, d, b), a, a, c)) | (insertion(d, b, d, b) = a)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[572])).
% 1.53/1.74 tff(574,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((insertion(d, b, d, b) = a) | (~between(insertion(d, b, d, b), a, c)) | (c = extension(insertion(d, b, d, b), a, a, c)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(insertion(d, b, d, b), a, c)) | (c = extension(insertion(d, b, d, b), a, a, c)) | (insertion(d, b, d, b) = a))),
% 1.53/1.74 inference(transitivity,[status(thm)],[573, 571])).
% 1.53/1.74 tff(575,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((insertion(d, b, d, b) = a) | (~between(insertion(d, b, d, b), a, c)) | (c = extension(insertion(d, b, d, b), a, a, c)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(576,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(insertion(d, b, d, b), a, c)) | (c = extension(insertion(d, b, d, b), a, a, c)) | (insertion(d, b, d, b) = a)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[575, 574])).
% 1.53/1.74 tff(577,plain,
% 1.53/1.74 ((~between(insertion(d, b, d, b), a, c)) | (c = extension(insertion(d, b, d, b), a, a, c)) | (insertion(d, b, d, b) = a)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[576, 161])).
% 1.53/1.74 tff(578,plain,
% 1.53/1.74 (c = extension(insertion(d, b, d, b), a, a, c)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[577, 570, 565])).
% 1.53/1.74 tff(579,plain,
% 1.53/1.74 (extension(insertion(d, b, d, b), a, a, c) = c),
% 1.53/1.74 inference(symmetry,[status(thm)],[578])).
% 1.53/1.74 tff(580,plain,
% 1.53/1.74 (between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) <=> between(b, c, d)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[39, 579, 21])).
% 1.53/1.74 tff(581,plain,
% 1.53/1.74 (between(b, c, d) <=> between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.53/1.74 inference(symmetry,[status(thm)],[580])).
% 1.53/1.74 tff(582,plain,
% 1.53/1.74 ((~between(b, c, d)) <=> (~between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[581])).
% 1.53/1.74 tff(583,plain,
% 1.53/1.74 (((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | ((~between(b, c, d)) | colinear(b, c, d))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | (~between(b, c, d)) | colinear(b, c, d))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(584,plain,
% 1.53/1.74 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | ((~between(b, c, d)) | colinear(b, c, d))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(585,plain,
% 1.53/1.74 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | (~between(b, c, d)) | colinear(b, c, d)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[584, 583])).
% 1.53/1.74 tff(586,plain,
% 1.53/1.74 (~between(b, c, d)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[585, 59, 483])).
% 1.53/1.74 tff(587,plain,
% 1.53/1.74 (~between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[586, 582])).
% 1.53/1.74 tff(588,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(insertion(d, b, d, b), a, c)) | (a = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(insertion(d, b, d, b), a, c)) | (a = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(589,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(insertion(d, b, d, b), a, c)) | (a = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(590,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(insertion(d, b, d, b), a, c)) | (a = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.53/1.74 tff(591,plain,
% 1.53/1.74 ((~between(insertion(d, b, d, b), a, c)) | (a = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[590, 16])).
% 1.53/1.74 tff(592,plain,
% 1.53/1.74 (a = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[591, 565])).
% 1.53/1.74 tff(593,plain,
% 1.53/1.74 (insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = a),
% 1.53/1.74 inference(symmetry,[status(thm)],[592])).
% 1.53/1.74 tff(594,plain,
% 1.53/1.74 (between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) <=> between(b, a, d)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[39, 593, 21])).
% 1.53/1.74 tff(595,plain,
% 1.53/1.74 (between(b, a, d) <=> between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.53/1.75 inference(symmetry,[status(thm)],[594])).
% 1.53/1.75 tff(596,plain,
% 1.53/1.75 (between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) <=> between(a, d, b)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[593, 21, 39])).
% 1.53/1.75 tff(597,plain,
% 1.53/1.75 ((~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))) <=> (~between(a, d, b))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[596])).
% 1.53/1.75 tff(598,plain,
% 1.53/1.75 (between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b)) <=> between(c, a, b)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[579, 593, 39])).
% 1.53/1.75 tff(599,plain,
% 1.53/1.75 (between(c, a, b) <=> between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))),
% 1.53/1.75 inference(symmetry,[status(thm)],[598])).
% 1.53/1.75 tff(600,plain,
% 1.53/1.75 (between(c, a, insertion(d, b, d, b)) <=> between(c, a, b)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[39])).
% 1.53/1.75 tff(601,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(insertion(d, b, d, b), a, c)) | between(c, a, insertion(d, b, d, b)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(insertion(d, b, d, b), a, c)) | between(c, a, insertion(d, b, d, b)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(602,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(insertion(d, b, d, b), a, c)) | between(c, a, insertion(d, b, d, b)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(603,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(insertion(d, b, d, b), a, c)) | between(c, a, insertion(d, b, d, b))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[602, 601])).
% 1.53/1.75 tff(604,plain,
% 1.53/1.75 ((~between(insertion(d, b, d, b), a, c)) | between(c, a, insertion(d, b, d, b))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[603, 139])).
% 1.53/1.75 tff(605,plain,
% 1.53/1.75 (between(c, a, insertion(d, b, d, b))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[604, 565])).
% 1.53/1.75 tff(606,plain,
% 1.53/1.75 (between(c, a, b)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[605, 600])).
% 1.53/1.75 tff(607,plain,
% 1.53/1.75 (between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[606, 599])).
% 1.53/1.75 tff(608,plain,
% 1.53/1.75 (between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) <=> between(c, d, b)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[579, 21, 39])).
% 1.53/1.75 tff(609,plain,
% 1.53/1.75 (between(c, d, b) <=> between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))),
% 1.53/1.75 inference(symmetry,[status(thm)],[608])).
% 1.53/1.75 tff(610,plain,
% 1.53/1.75 ((~between(c, d, b)) <=> (~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[609])).
% 1.53/1.75 tff(611,plain,
% 1.53/1.75 (~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[545, 610])).
% 1.53/1.75 tff(612,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(613,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(614,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[613, 612])).
% 1.53/1.75 tff(615,plain,
% 1.53/1.75 ((~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[614, 316])).
% 1.53/1.75 tff(616,plain,
% 1.53/1.75 (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[615, 611, 607])).
% 1.53/1.75 tff(617,plain,
% 1.53/1.75 (~between(a, d, b)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[616, 597])).
% 1.53/1.75 tff(618,plain,
% 1.53/1.75 (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)) <=> between(d, b, a)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[21, 39, 593])).
% 1.53/1.75 tff(619,plain,
% 1.53/1.75 ((~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a))) <=> (~between(d, b, a))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[618])).
% 1.53/1.75 tff(620,plain,
% 1.53/1.75 (between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) <=> between(c, b, d)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[579, 39, 21])).
% 1.53/1.75 tff(621,plain,
% 1.53/1.75 (between(c, b, d) <=> between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.53/1.75 inference(symmetry,[status(thm)],[620])).
% 1.53/1.75 tff(622,plain,
% 1.53/1.75 ((~between(c, b, d)) <=> (~between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[621])).
% 1.53/1.75 tff(623,plain,
% 1.53/1.75 (~between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[487, 622])).
% 1.53/1.75 tff(624,plain,
% 1.53/1.75 ((insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b)) <=> (a = b)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[593, 39])).
% 1.53/1.75 tff(625,plain,
% 1.53/1.75 ((a = b) <=> (insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b))),
% 1.53/1.75 inference(symmetry,[status(thm)],[624])).
% 1.53/1.75 tff(626,plain,
% 1.53/1.75 ((~(a = b)) <=> (~(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[625])).
% 1.53/1.75 tff(627,plain,
% 1.53/1.75 (~(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[150, 626])).
% 1.53/1.75 tff(628,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | (insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b)) | between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | (~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | (insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b)) | between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(629,plain,
% 1.53/1.76 (((~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b))) <=> ((~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | (insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b)) | between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(630,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | (insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b)) | between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[629])).
% 1.53/1.76 tff(631,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | (~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | (insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b)) | between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[630, 628])).
% 1.53/1.76 tff(632,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(633,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | (~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | (insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b)) | between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[632, 631])).
% 1.53/1.76 tff(634,plain,
% 1.53/1.76 ((~between(extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b))) | (insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a) = insertion(d, b, d, b)) | between(extension(insertion(d, b, d, b), a, a, c), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[633, 197])).
% 1.53/1.76 tff(635,plain,
% 1.53/1.76 (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[634, 627, 623, 607])).
% 1.53/1.76 tff(636,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a))) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a))) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(637,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a))) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(638,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a))) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[637, 636])).
% 1.53/1.76 tff(639,plain,
% 1.53/1.76 (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[638, 139, 635])).
% 1.53/1.76 tff(640,plain,
% 1.53/1.76 (~between(d, b, a)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[639, 619])).
% 1.53/1.76 tff(641,plain,
% 1.53/1.76 (between(b, a, d)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[233, 640, 617])).
% 1.53/1.76 tff(642,plain,
% 1.53/1.76 (between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[641, 595])).
% 1.53/1.76 tff(643,plain,
% 1.53/1.76 (between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c)) <=> between(b, a, c)),
% 1.53/1.76 inference(monotonicity,[status(thm)],[39, 593, 579])).
% 1.53/1.76 tff(644,plain,
% 1.53/1.76 (between(b, a, c) <=> between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c))),
% 1.53/1.76 inference(symmetry,[status(thm)],[643])).
% 1.53/1.76 tff(645,plain,
% 1.53/1.76 (between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[564, 644])).
% 1.53/1.76 tff(646,plain,
% 1.53/1.76 (between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c)) <=> between(a, d, c)),
% 1.53/1.76 inference(monotonicity,[status(thm)],[593, 21, 579])).
% 1.53/1.76 tff(647,plain,
% 1.53/1.76 (between(a, d, c) <=> between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c))),
% 1.53/1.76 inference(symmetry,[status(thm)],[646])).
% 1.53/1.76 tff(648,plain,
% 1.53/1.76 ((~between(a, d, c)) <=> (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[647])).
% 1.53/1.76 tff(649,plain,
% 1.53/1.76 (between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c) <=> between(a, d, c)),
% 1.53/1.76 inference(monotonicity,[status(thm)],[21])).
% 1.53/1.76 tff(650,plain,
% 1.53/1.76 ((~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c)) <=> (~between(a, d, c))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[649])).
% 1.53/1.76 tff(651,plain,
% 1.53/1.76 (between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c) <=> between(b, d, c)),
% 1.53/1.76 inference(monotonicity,[status(thm)],[39, 21])).
% 1.53/1.76 tff(652,plain,
% 1.53/1.76 (between(b, d, c) <=> between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c)),
% 1.53/1.76 inference(symmetry,[status(thm)],[651])).
% 1.53/1.76 tff(653,plain,
% 1.53/1.76 ((~between(b, d, c)) <=> (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[652])).
% 1.53/1.76 tff(654,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(b, d, c)) | colinear(b, c, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(b, d, c)) | colinear(b, c, d))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(655,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(b, d, c)) | colinear(b, c, d))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(656,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(b, d, c)) | colinear(b, c, d)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[655, 654])).
% 1.53/1.76 tff(657,plain,
% 1.53/1.76 (~between(b, d, c)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[656, 70, 483])).
% 1.53/1.76 tff(658,plain,
% 1.53/1.76 (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[657, 653])).
% 1.53/1.76 tff(659,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c) | (~between(insertion(d, b, d, b), a, c)) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c) | (~between(insertion(d, b, d, b), a, c)) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(660,plain,
% 1.53/1.77 (((~between(insertion(d, b, d, b), a, c)) | between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c))) <=> (between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c) | (~between(insertion(d, b, d, b), a, c)) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(661,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(insertion(d, b, d, b), a, c)) | between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c) | (~between(insertion(d, b, d, b), a, c)) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[660])).
% 1.53/1.77 tff(662,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(insertion(d, b, d, b), a, c)) | between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c) | (~between(insertion(d, b, d, b), a, c)) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[661, 659])).
% 1.53/1.77 tff(663,plain,
% 1.53/1.77 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(insertion(d, b, d, b), a, c)) | between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(664,plain,
% 1.53/1.77 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c) | (~between(insertion(d, b, d, b), a, c)) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[663, 662])).
% 1.53/1.77 tff(665,plain,
% 1.53/1.77 ((~between(insertion(d, b, d, b), a, c)) | (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[664, 316, 658])).
% 1.53/1.77 tff(666,plain,
% 1.53/1.77 (~between(a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), c)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[665, 565])).
% 1.53/1.77 tff(667,plain,
% 1.53/1.77 (~between(a, d, c)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[666, 650])).
% 1.53/1.77 tff(668,plain,
% 1.53/1.77 (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[667, 648])).
% 1.53/1.77 tff(669,plain,
% 1.53/1.77 ((insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)) <=> (b = a)),
% 1.53/1.77 inference(monotonicity,[status(thm)],[39, 593])).
% 1.53/1.77 tff(670,plain,
% 1.53/1.77 ((insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)) <=> (a = b)),
% 1.53/1.77 inference(transitivity,[status(thm)],[669, 184])).
% 1.53/1.77 tff(671,plain,
% 1.53/1.77 ((a = b) <=> (insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a))),
% 1.53/1.77 inference(symmetry,[status(thm)],[670])).
% 1.53/1.77 tff(672,plain,
% 1.53/1.77 ((~(a = b)) <=> (~(insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[671])).
% 1.53/1.77 tff(673,plain,
% 1.53/1.77 (~(insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[150, 672])).
% 1.53/1.77 tff(674,plain,
% 1.53/1.77 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W)))),
% 1.53/1.77 inference(bind,[status(th)],[])).
% 1.53/1.77 tff(675,plain,
% 1.53/1.77 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))),
% 1.53/1.77 inference(quant_intro,[status(thm)],[674])).
% 1.53/1.77 tff(676,plain,
% 1.53/1.77 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(677,plain,
% 1.53/1.77 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~between(U, V, W)) | (~between(U, V, X))) <=> ((~between(U, V, X)) | (~between(U, V, W)))), ((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) <=> (((~between(U, V, X)) | (~between(U, V, W))) | (U = V)))), rewrite((((~between(U, V, X)) | (~between(U, V, W))) | (U = V)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)))), ((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W))))), (((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(V, W, X)) <=> (((~between(U, V, X)) | (U = V) | (~between(U, V, W))) | between(V, W, X)))), rewrite((((~between(U, V, X)) | (U = V) | (~between(U, V, W))) | between(V, W, X)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X))), (((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(V, W, X)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X)))), ((((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(V, W, X)) | between(V, X, W)) <=> (((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X)) | between(V, X, W)))), rewrite((((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X)) | between(V, X, W)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))), ((((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(V, W, X)) | between(V, X, W)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))))),
% 1.53/1.77 inference(bind,[status(th)],[])).
% 1.53/1.77 tff(678,plain,
% 1.53/1.77 (![W: $i, V: $i, U: $i, X: $i] : (((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(V, W, X)) | between(V, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))),
% 1.53/1.77 inference(quant_intro,[status(thm)],[677])).
% 1.53/1.77 tff(679,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(V, W, X)) | between(V, X, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b13')).
% 1.53/1.77 tff(680,plain,
% 1.53/1.77 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[679, 678])).
% 1.53/1.77 tff(681,plain,
% 1.53/1.77 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[680, 676])).
% 1.53/1.77 tff(682,plain,(
% 1.53/1.77 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))),
% 1.53/1.77 inference(skolemize,[status(sab)],[681])).
% 1.53/1.77 tff(683,plain,
% 1.53/1.77 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[682, 675])).
% 1.53/1.77 tff(684,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))) | ((insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))) | (insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(685,plain,
% 1.53/1.77 (((~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c))) | (insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) <=> ((insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(686,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))) | ((~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c))) | (insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))) | ((insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[685])).
% 1.53/1.78 tff(687,plain,
% 1.53/1.78 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))) | ((~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c))) | (insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))) | (insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[686, 684])).
% 1.53/1.78 tff(688,plain,
% 1.53/1.78 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))) | ((~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c))) | (insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(689,plain,
% 1.53/1.78 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(V, W, X) | between(V, X, W))) | (insertion(d, b, d, b) = insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), extension(insertion(d, b, d, b), a, a, c)) | between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[688, 687])).
% 1.63/1.78 tff(690,plain,
% 1.63/1.78 (between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[689, 683, 673, 668, 645, 642])).
% 1.63/1.78 tff(691,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(692,plain,
% 1.63/1.78 (((~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))) <=> ((~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(693,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[692])).
% 1.63/1.78 tff(694,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[693, 691])).
% 1.63/1.79 tff(695,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(696,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (~between(insertion(d, b, d, b), insertion(insertion(d, b, d, b), c, insertion(d, b, d, b), a), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | between(insertion(d, b, d, b), extension(insertion(d, b, d, b), a, a, c), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[695, 694])).
% 1.63/1.79 tff(697,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[696, 316, 690, 642, 587])).
% 1.63/1.79 tff(698,plain,(~between(b, a, c)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(699,plain,
% 1.63/1.79 (between(c, b, a)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[373, 698, 561])).
% 1.63/1.79 tff(700,plain,
% 1.63/1.79 (between(c, insertion(d, b, d, b), a)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[699, 41])).
% 1.63/1.79 tff(701,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | (between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(c, insertion(d, b, d, b), a)) | (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(c, insertion(d, b, d, b), a)) | (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(702,plain,
% 1.63/1.79 (((~between(c, insertion(d, b, d, b), a)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a))) <=> (between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(c, insertion(d, b, d, b), a)) | (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(703,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(c, insertion(d, b, d, b), a)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | (between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(c, insertion(d, b, d, b), a)) | (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[702])).
% 1.63/1.79 tff(704,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(c, insertion(d, b, d, b), a)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(c, insertion(d, b, d, b), a)) | (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[703, 701])).
% 1.63/1.79 tff(705,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(c, insertion(d, b, d, b), a)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(706,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), insertion(d, b, d, b)) | (~between(c, insertion(d, b, d, b), a)) | (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[705, 704])).
% 1.63/1.79 tff(707,plain,
% 1.63/1.79 ((~between(c, insertion(d, b, d, b), a)) | (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a))),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[706, 428, 488, 546])).
% 1.63/1.79 tff(708,plain,
% 1.63/1.79 (~between(c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[707, 700])).
% 1.63/1.79 tff(709,plain,
% 1.63/1.79 (~between(c, d, a)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[708, 23])).
% 1.63/1.79 tff(710,plain,
% 1.63/1.79 (between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, c) <=> between(d, a, c)),
% 1.63/1.79 inference(monotonicity,[status(thm)],[21])).
% 1.63/1.79 tff(711,plain,
% 1.63/1.79 ((~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, c)) <=> (~between(d, a, c))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[710])).
% 1.63/1.79 tff(712,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(c, insertion(d, b, d, b), a)) | (~between(c, a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(c, insertion(d, b, d, b), a)) | (~between(c, a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(713,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(c, insertion(d, b, d, b), a)) | (~between(c, a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(714,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | between(c, insertion(d, b, d, b), insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(c, insertion(d, b, d, b), a)) | (~between(c, a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[713, 712])).
% 1.63/1.79 tff(715,plain,
% 1.63/1.79 ((~between(c, insertion(d, b, d, b), a)) | (~between(c, a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[714, 412, 488])).
% 1.63/1.79 tff(716,plain,
% 1.63/1.79 (~between(c, a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[715, 700])).
% 1.63/1.79 tff(717,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, c)) | between(c, a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, c)) | between(c, a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(718,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, c)) | between(c, a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(719,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, c)) | between(c, a, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[718, 717])).
% 1.63/1.79 tff(720,plain,
% 1.63/1.79 (~between(insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d), a, c)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[719, 139, 716])).
% 1.63/1.79 tff(721,plain,
% 1.63/1.79 (~between(d, a, c)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[720, 711])).
% 1.63/1.79 tff(722,plain,
% 1.63/1.79 (between(a, c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) <=> between(a, c, d)),
% 1.63/1.79 inference(monotonicity,[status(thm)],[21])).
% 1.63/1.79 tff(723,plain,
% 1.63/1.79 ((~between(a, c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) <=> (~between(a, c, d))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[722])).
% 1.63/1.79 tff(724,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(c, insertion(d, b, d, b), a)) | between(a, insertion(d, b, d, b), c))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(c, insertion(d, b, d, b), a)) | between(a, insertion(d, b, d, b), c))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(725,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(c, insertion(d, b, d, b), a)) | between(a, insertion(d, b, d, b), c))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(726,plain,
% 1.64/1.80 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(c, insertion(d, b, d, b), a)) | between(a, insertion(d, b, d, b), c)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[725, 724])).
% 1.64/1.80 tff(727,plain,
% 1.64/1.80 ((~between(c, insertion(d, b, d, b), a)) | between(a, insertion(d, b, d, b), c)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[726, 139])).
% 1.64/1.80 tff(728,plain,
% 1.64/1.80 (between(a, insertion(d, b, d, b), c)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[727, 700])).
% 1.64/1.80 tff(729,plain,
% 1.64/1.80 (between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) <=> between(b, c, d)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[39, 21])).
% 1.64/1.80 tff(730,plain,
% 1.64/1.80 (between(b, c, d) <=> between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.64/1.80 inference(symmetry,[status(thm)],[729])).
% 1.64/1.80 tff(731,plain,
% 1.64/1.80 ((~between(b, c, d)) <=> (~between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[730])).
% 1.64/1.80 tff(732,plain,
% 1.64/1.80 (~between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[586, 731])).
% 1.64/1.80 tff(733,plain,
% 1.64/1.80 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (~between(a, insertion(d, b, d, b), c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (~between(a, insertion(d, b, d, b), c)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(734,plain,
% 1.64/1.80 (((~between(a, insertion(d, b, d, b), c)) | between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)))) <=> (between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (~between(a, insertion(d, b, d, b), c)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(735,plain,
% 1.64/1.80 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(a, insertion(d, b, d, b), c)) | between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (~between(a, insertion(d, b, d, b), c))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[734])).
% 1.64/1.80 tff(736,plain,
% 1.64/1.80 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(a, insertion(d, b, d, b), c)) | between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (~between(a, insertion(d, b, d, b), c)))),
% 1.64/1.80 inference(transitivity,[status(thm)],[735, 733])).
% 1.64/1.80 tff(737,plain,
% 1.64/1.80 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(a, insertion(d, b, d, b), c)) | between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(738,plain,
% 1.64/1.80 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | between(insertion(d, b, d, b), c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d)) | (~between(a, c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))) | (~between(a, insertion(d, b, d, b), c))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[737, 736])).
% 1.64/1.80 tff(739,plain,
% 1.64/1.80 (~between(a, c, insertion(insertion(d, b, d, b), extension(insertion(d, b, d, b), d, lower_dimension_point_1, lower_dimension_point_2), insertion(d, b, d, b), d))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[738, 470, 732, 728])).
% 1.64/1.80 tff(740,plain,
% 1.64/1.80 (~between(a, c, d)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[739, 723])).
% 1.64/1.80 tff(741,plain,
% 1.64/1.80 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | ((~colinear(a, c, d)) | between(d, a, c) | between(a, c, d) | between(c, d, a))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(a, c, d)) | between(d, a, c) | between(a, c, d) | between(c, d, a))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(742,plain,
% 1.64/1.80 ((between(d, a, c) | between(c, d, a) | between(a, c, d) | (~colinear(a, c, d))) <=> ((~colinear(a, c, d)) | between(d, a, c) | between(a, c, d) | between(c, d, a))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(743,plain,
% 1.64/1.80 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, a, c) | between(c, d, a) | between(a, c, d) | (~colinear(a, c, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | ((~colinear(a, c, d)) | between(d, a, c) | between(a, c, d) | between(c, d, a)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[742])).
% 1.64/1.80 tff(744,plain,
% 1.64/1.80 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, a, c) | between(c, d, a) | between(a, c, d) | (~colinear(a, c, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(a, c, d)) | between(d, a, c) | between(a, c, d) | between(c, d, a))),
% 1.64/1.80 inference(transitivity,[status(thm)],[743, 741])).
% 1.64/1.80 tff(745,plain,
% 1.64/1.80 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, a, c) | between(c, d, a) | between(a, c, d) | (~colinear(a, c, d)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(746,plain,
% 1.64/1.80 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(a, c, d)) | between(d, a, c) | between(a, c, d) | between(c, d, a)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[745, 744])).
% 1.64/1.80 tff(747,plain,
% 1.64/1.80 (between(d, a, c) | between(a, c, d) | between(c, d, a)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[746, 229, 479])).
% 1.64/1.80 tff(748,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[747, 740, 721, 709])).
% 1.64/1.80 % SZS output end Proof
% 1.64/1.81 % E exiting
%------------------------------------------------------------------------------