%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO001-1 : TPTP v9.0.0. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:05:16 AM UTC 2025
% Result : Unsatisfiable 3.55s 3.79s
% Output : Proof 3.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO001-1 : TPTP v9.0.0. Bugfixed v2.5.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 14:01:56 EDT 2025
% 0.11/0.33 % CPUTime :
% 3.55/3.79 % SZS status Unsatisfiable
% 3.55/3.79 % SZS output start Proof
% 3.55/3.79 tff(between_type, type, (
% 3.55/3.79 between: ( $i * $i * $i ) > $o)).
% 3.55/3.79 tff(outer_pasch_type, type, (
% 3.55/3.79 outer_pasch: ( $i * $i * $i * $i * $i ) > $i)).
% 3.55/3.79 tff(b_type, type, (
% 3.55/3.79 b: $i)).
% 3.55/3.79 tff(extension_type, type, (
% 3.55/3.79 extension: ( $i * $i * $i * $i ) > $i)).
% 3.55/3.79 tff(c_type, type, (
% 3.55/3.79 c: $i)).
% 3.55/3.79 tff(a_type, type, (
% 3.55/3.79 a: $i)).
% 3.55/3.79 tff(equidistant_type, type, (
% 3.55/3.79 equidistant: ( $i * $i * $i * $i ) > $o)).
% 3.55/3.79 tff(1,assumption,(between(a, c, c)), introduced(assumption)).
% 3.55/3.79 tff(2,plain,
% 3.55/3.79 (between(a, b, c) <=> between(a, b, c)),
% 3.55/3.79 inference(rewrite,[status(thm)],[])).
% 3.55/3.79 tff(3,axiom,(between(a, b, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_between_a_and_c')).
% 3.55/3.79 tff(4,plain,
% 3.55/3.79 (between(a, b, c)),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[3, 2])).
% 3.55/3.79 tff(5,plain,
% 3.55/3.79 (^[W: $i, V: $i, Z: $i, Y: $i, X: $i] : refl((between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V))) <=> (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V))))),
% 3.55/3.79 inference(bind,[status(th)],[])).
% 3.55/3.79 tff(6,plain,
% 3.55/3.79 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 3.55/3.79 inference(quant_intro,[status(thm)],[5])).
% 3.55/3.79 tff(7,plain,
% 3.55/3.79 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 3.55/3.79 inference(rewrite,[status(thm)],[])).
% 3.55/3.79 tff(8,plain,
% 3.55/3.79 (^[W: $i, V: $i, Z: $i, Y: $i, X: $i] : rewrite((((~between(X, W, V)) | (~between(Y, V, Z))) | between(X, outer_pasch(W, X, Y, Z, V), Y)) <=> (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V))))),
% 3.55/3.79 inference(bind,[status(th)],[])).
% 3.55/3.79 tff(9,plain,
% 3.55/3.79 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (((~between(X, W, V)) | (~between(Y, V, Z))) | between(X, outer_pasch(W, X, Y, Z, V), Y)) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 3.55/3.79 inference(quant_intro,[status(thm)],[8])).
% 3.55/3.79 tff(10,axiom,(![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (((~between(X, W, V)) | (~between(Y, V, Z))) | between(X, outer_pasch(W, X, Y, Z, V), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','outer_pasch1')).
% 3.55/3.79 tff(11,plain,
% 3.55/3.79 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[10, 9])).
% 3.55/3.79 tff(12,plain,
% 3.55/3.79 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[11, 7])).
% 3.55/3.79 tff(13,plain,(
% 3.55/3.79 ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 3.55/3.79 inference(skolemize,[status(sab)],[12])).
% 3.55/3.79 tff(14,plain,
% 3.55/3.79 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[13, 6])).
% 3.55/3.79 tff(15,plain,
% 3.55/3.79 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | ((~between(a, b, c)) | between(a, outer_pasch(b, a, a, c, c), a) | (~between(a, c, c)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (~between(a, b, c)) | between(a, outer_pasch(b, a, a, c, c), a) | (~between(a, c, c)))),
% 3.55/3.79 inference(rewrite,[status(thm)],[])).
% 3.55/3.79 tff(16,plain,
% 3.55/3.79 ((between(a, outer_pasch(b, a, a, c, c), a) | (~between(a, c, c)) | (~between(a, b, c))) <=> ((~between(a, b, c)) | between(a, outer_pasch(b, a, a, c, c), a) | (~between(a, c, c)))),
% 3.55/3.79 inference(rewrite,[status(thm)],[])).
% 3.55/3.79 tff(17,plain,
% 3.55/3.79 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(a, outer_pasch(b, a, a, c, c), a) | (~between(a, c, c)) | (~between(a, b, c)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | ((~between(a, b, c)) | between(a, outer_pasch(b, a, a, c, c), a) | (~between(a, c, c))))),
% 3.55/3.79 inference(monotonicity,[status(thm)],[16])).
% 3.55/3.79 tff(18,plain,
% 3.55/3.79 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(a, outer_pasch(b, a, a, c, c), a) | (~between(a, c, c)) | (~between(a, b, c)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (~between(a, b, c)) | between(a, outer_pasch(b, a, a, c, c), a) | (~between(a, c, c)))),
% 3.55/3.79 inference(transitivity,[status(thm)],[17, 15])).
% 3.55/3.79 tff(19,plain,
% 3.55/3.79 ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(a, outer_pasch(b, a, a, c, c), a) | (~between(a, c, c)) | (~between(a, b, c)))),
% 3.55/3.79 inference(quant_inst,[status(thm)],[])).
% 3.55/3.79 tff(20,plain,
% 3.55/3.79 ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (~between(a, b, c)) | between(a, outer_pasch(b, a, a, c, c), a) | (~between(a, c, c))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[19, 18])).
% 3.55/3.79 tff(21,plain,
% 3.55/3.79 (between(a, outer_pasch(b, a, a, c, c), a) | (~between(a, c, c))),
% 3.55/3.79 inference(unit_resolution,[status(thm)],[20, 14, 4])).
% 3.55/3.79 tff(22,plain,
% 3.55/3.79 (between(a, outer_pasch(b, a, a, c, c), a)),
% 3.55/3.79 inference(unit_resolution,[status(thm)],[21, 1])).
% 3.55/3.79 tff(23,plain,
% 3.55/3.79 (^[Y: $i, X: $i] : refl(((~between(X, Y, X)) | (X = Y)) <=> ((~between(X, Y, X)) | (X = Y)))),
% 3.55/3.79 inference(bind,[status(th)],[])).
% 3.55/3.79 tff(24,plain,
% 3.55/3.79 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y)) <=> ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 3.55/3.79 inference(quant_intro,[status(thm)],[23])).
% 3.55/3.79 tff(25,plain,
% 3.55/3.79 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y)) <=> ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 3.55/3.79 inference(rewrite,[status(thm)],[])).
% 3.55/3.79 tff(26,axiom,(![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','identity_for_betweeness')).
% 3.55/3.79 tff(27,plain,
% 3.55/3.79 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[26, 25])).
% 3.55/3.79 tff(28,plain,(
% 3.55/3.79 ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 3.55/3.79 inference(skolemize,[status(sab)],[27])).
% 3.55/3.79 tff(29,plain,
% 3.55/3.79 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[28, 24])).
% 3.55/3.79 tff(30,plain,
% 3.55/3.79 (((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(a, outer_pasch(b, a, a, c, c), a)) | (a = outer_pasch(b, a, a, c, c)))) <=> ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(a, outer_pasch(b, a, a, c, c), a)) | (a = outer_pasch(b, a, a, c, c)))),
% 3.55/3.79 inference(rewrite,[status(thm)],[])).
% 3.55/3.79 tff(31,plain,
% 3.55/3.79 ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(a, outer_pasch(b, a, a, c, c), a)) | (a = outer_pasch(b, a, a, c, c)))),
% 3.55/3.79 inference(quant_inst,[status(thm)],[])).
% 3.55/3.79 tff(32,plain,
% 3.55/3.79 ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(a, outer_pasch(b, a, a, c, c), a)) | (a = outer_pasch(b, a, a, c, c))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[31, 30])).
% 3.55/3.79 tff(33,plain,
% 3.55/3.79 (a = outer_pasch(b, a, a, c, c)),
% 3.55/3.79 inference(unit_resolution,[status(thm)],[32, 29, 22])).
% 3.55/3.79 tff(34,plain,
% 3.55/3.79 (outer_pasch(b, a, a, c, c) = a),
% 3.55/3.79 inference(symmetry,[status(thm)],[33])).
% 3.55/3.79 tff(35,plain,
% 3.55/3.79 (^[W: $i, V: $i, Y: $i, X: $i] : refl(equidistant(Y, extension(X, Y, W, V), W, V) <=> equidistant(Y, extension(X, Y, W, V), W, V))),
% 3.55/3.79 inference(bind,[status(th)],[])).
% 3.55/3.79 tff(36,plain,
% 3.55/3.79 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V) <=> ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 3.55/3.79 inference(quant_intro,[status(thm)],[35])).
% 3.55/3.79 tff(37,plain,
% 3.55/3.79 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V) <=> ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 3.55/3.79 inference(rewrite,[status(thm)],[])).
% 3.55/3.79 tff(38,axiom,(![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','segment_construction2')).
% 3.55/3.79 tff(39,plain,
% 3.55/3.79 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[38, 37])).
% 3.55/3.79 tff(40,plain,(
% 3.55/3.79 ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 3.55/3.79 inference(skolemize,[status(sab)],[39])).
% 3.55/3.79 tff(41,plain,
% 3.55/3.79 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[40, 36])).
% 3.55/3.79 tff(42,plain,
% 3.55/3.79 ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(c, extension(c, c, c, c), c, c)),
% 3.55/3.79 inference(quant_inst,[status(thm)],[])).
% 3.55/3.79 tff(43,plain,
% 3.55/3.79 (equidistant(c, extension(c, c, c, c), c, c)),
% 3.55/3.79 inference(unit_resolution,[status(thm)],[42, 41])).
% 3.55/3.79 tff(44,plain,
% 3.55/3.79 (^[Z: $i, Y: $i, X: $i] : refl(((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ((~equidistant(X, Y, Z, Z)) | (X = Y)))),
% 3.55/3.79 inference(bind,[status(th)],[])).
% 3.55/3.79 tff(45,plain,
% 3.55/3.79 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 3.55/3.79 inference(quant_intro,[status(thm)],[44])).
% 3.55/3.79 tff(46,plain,
% 3.55/3.79 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 3.55/3.79 inference(rewrite,[status(thm)],[])).
% 3.55/3.79 tff(47,axiom,(![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','identity_for_equidistance')).
% 3.55/3.79 tff(48,plain,
% 3.55/3.79 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[47, 46])).
% 3.55/3.79 tff(49,plain,(
% 3.55/3.79 ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 3.55/3.79 inference(skolemize,[status(sab)],[48])).
% 3.55/3.79 tff(50,plain,
% 3.55/3.79 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[49, 45])).
% 3.55/3.79 tff(51,plain,
% 3.55/3.79 (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(c, extension(c, c, c, c), c, c)) | (c = extension(c, c, c, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(c, extension(c, c, c, c), c, c)) | (c = extension(c, c, c, c)))),
% 3.55/3.79 inference(rewrite,[status(thm)],[])).
% 3.55/3.79 tff(52,plain,
% 3.55/3.79 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(c, extension(c, c, c, c), c, c)) | (c = extension(c, c, c, c)))),
% 3.55/3.79 inference(quant_inst,[status(thm)],[])).
% 3.55/3.79 tff(53,plain,
% 3.55/3.79 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(c, extension(c, c, c, c), c, c)) | (c = extension(c, c, c, c))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[52, 51])).
% 3.55/3.79 tff(54,plain,
% 3.55/3.79 (c = extension(c, c, c, c)),
% 3.55/3.79 inference(unit_resolution,[status(thm)],[53, 50, 43])).
% 3.55/3.79 tff(55,plain,
% 3.55/3.79 (extension(c, c, c, c) = c),
% 3.55/3.79 inference(symmetry,[status(thm)],[54])).
% 3.55/3.79 tff(56,plain,
% 3.55/3.79 (outer_pasch(b, a, a, extension(c, c, c, c), extension(c, c, c, c)) = outer_pasch(b, a, a, c, c)),
% 3.55/3.79 inference(monotonicity,[status(thm)],[55, 55])).
% 3.55/3.79 tff(57,plain,
% 3.55/3.79 (outer_pasch(b, a, a, extension(c, c, c, c), extension(c, c, c, c)) = a),
% 3.55/3.79 inference(transitivity,[status(thm)],[56, 34])).
% 3.55/3.79 tff(58,plain,
% 3.55/3.79 (between(extension(c, c, c, c), b, outer_pasch(b, a, a, extension(c, c, c, c), extension(c, c, c, c))) <=> between(c, b, a)),
% 3.55/3.79 inference(monotonicity,[status(thm)],[55, 57])).
% 3.55/3.79 tff(59,plain,
% 3.55/3.79 (between(c, b, a) <=> between(extension(c, c, c, c), b, outer_pasch(b, a, a, extension(c, c, c, c), extension(c, c, c, c)))),
% 3.55/3.79 inference(symmetry,[status(thm)],[58])).
% 3.55/3.79 tff(60,plain,
% 3.55/3.79 ((~between(c, b, a)) <=> (~between(extension(c, c, c, c), b, outer_pasch(b, a, a, extension(c, c, c, c), extension(c, c, c, c))))),
% 3.55/3.79 inference(monotonicity,[status(thm)],[59])).
% 3.55/3.79 tff(61,plain,
% 3.55/3.79 ((~between(c, b, a)) <=> (~between(c, b, a))),
% 3.55/3.79 inference(rewrite,[status(thm)],[])).
% 3.55/3.79 tff(62,axiom,(~between(c, b, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_b_between_c_and_a')).
% 3.55/3.79 tff(63,plain,
% 3.55/3.79 (~between(c, b, a)),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[62, 61])).
% 3.55/3.79 tff(64,plain,
% 3.55/3.79 (~between(extension(c, c, c, c), b, outer_pasch(b, a, a, extension(c, c, c, c), extension(c, c, c, c)))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[63, 60])).
% 3.55/3.79 tff(65,plain,
% 3.55/3.79 (between(a, extension(c, c, c, c), extension(c, c, c, c)) <=> between(a, c, c)),
% 3.55/3.79 inference(monotonicity,[status(thm)],[55, 55])).
% 3.55/3.79 tff(66,plain,
% 3.55/3.79 (between(a, c, c) <=> between(a, extension(c, c, c, c), extension(c, c, c, c))),
% 3.55/3.79 inference(symmetry,[status(thm)],[65])).
% 3.55/3.79 tff(67,plain,
% 3.55/3.79 (between(a, extension(c, c, c, c), extension(c, c, c, c))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[1, 66])).
% 3.55/3.79 tff(68,plain,
% 3.55/3.79 (between(a, b, extension(c, c, c, c)) <=> between(a, b, c)),
% 3.55/3.79 inference(monotonicity,[status(thm)],[55])).
% 3.55/3.79 tff(69,plain,
% 3.55/3.79 (between(a, b, c) <=> between(a, b, extension(c, c, c, c))),
% 3.55/3.79 inference(symmetry,[status(thm)],[68])).
% 3.55/3.79 tff(70,plain,
% 3.55/3.79 (between(a, b, extension(c, c, c, c))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[4, 69])).
% 3.55/3.79 tff(71,plain,
% 3.55/3.79 (^[W: $i, V: $i, Z: $i, Y: $i, X: $i] : refl(((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V))) <=> ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V))))),
% 3.55/3.79 inference(bind,[status(th)],[])).
% 3.55/3.79 tff(72,plain,
% 3.55/3.79 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 3.55/3.79 inference(quant_intro,[status(thm)],[71])).
% 3.55/3.79 tff(73,plain,
% 3.55/3.79 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 3.55/3.79 inference(rewrite,[status(thm)],[])).
% 3.55/3.79 tff(74,plain,
% 3.55/3.79 (^[W: $i, V: $i, Z: $i, Y: $i, X: $i] : rewrite((((~between(X, W, V)) | (~between(Y, V, Z))) | between(Z, W, outer_pasch(W, X, Y, Z, V))) <=> ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V))))),
% 3.55/3.79 inference(bind,[status(th)],[])).
% 3.55/3.79 tff(75,plain,
% 3.55/3.79 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (((~between(X, W, V)) | (~between(Y, V, Z))) | between(Z, W, outer_pasch(W, X, Y, Z, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 3.55/3.79 inference(quant_intro,[status(thm)],[74])).
% 3.55/3.79 tff(76,axiom,(![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (((~between(X, W, V)) | (~between(Y, V, Z))) | between(Z, W, outer_pasch(W, X, Y, Z, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','outer_pasch2')).
% 3.55/3.79 tff(77,plain,
% 3.55/3.79 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[76, 75])).
% 3.55/3.79 tff(78,plain,
% 3.55/3.79 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[77, 73])).
% 3.55/3.79 tff(79,plain,(
% 3.55/3.79 ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 3.55/3.79 inference(skolemize,[status(sab)],[78])).
% 3.55/3.79 tff(80,plain,
% 3.55/3.79 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[79, 72])).
% 3.55/3.79 tff(81,plain,
% 3.55/3.79 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(a, extension(c, c, c, c), extension(c, c, c, c))) | (~between(a, b, extension(c, c, c, c))) | between(extension(c, c, c, c), b, outer_pasch(b, a, a, extension(c, c, c, c), extension(c, c, c, c))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | (~between(a, extension(c, c, c, c), extension(c, c, c, c))) | (~between(a, b, extension(c, c, c, c))) | between(extension(c, c, c, c), b, outer_pasch(b, a, a, extension(c, c, c, c), extension(c, c, c, c))))),
% 3.55/3.79 inference(rewrite,[status(thm)],[])).
% 3.55/3.79 tff(82,plain,
% 3.55/3.79 ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(a, extension(c, c, c, c), extension(c, c, c, c))) | (~between(a, b, extension(c, c, c, c))) | between(extension(c, c, c, c), b, outer_pasch(b, a, a, extension(c, c, c, c), extension(c, c, c, c))))),
% 3.55/3.79 inference(quant_inst,[status(thm)],[])).
% 3.55/3.79 tff(83,plain,
% 3.55/3.79 ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | (~between(a, extension(c, c, c, c), extension(c, c, c, c))) | (~between(a, b, extension(c, c, c, c))) | between(extension(c, c, c, c), b, outer_pasch(b, a, a, extension(c, c, c, c), extension(c, c, c, c)))),
% 3.55/3.79 inference(modus_ponens,[status(thm)],[82, 81])).
% 3.55/3.79 tff(84,plain,
% 3.55/3.79 ((~between(a, extension(c, c, c, c), extension(c, c, c, c))) | (~between(a, b, extension(c, c, c, c))) | between(extension(c, c, c, c), b, outer_pasch(b, a, a, extension(c, c, c, c), extension(c, c, c, c)))),
% 3.55/3.79 inference(unit_resolution,[status(thm)],[83, 80])).
% 3.55/3.79 tff(85,plain,
% 3.55/3.79 ($false),
% 3.55/3.79 inference(unit_resolution,[status(thm)],[84, 70, 67, 64])).
% 3.55/3.79 tff(86,plain,(~between(a, c, c)), inference(lemma,lemma(discharge,[]))).
% 3.55/3.79 tff(87,plain,
% 3.55/3.79 (^[V: $i, Z: $i, Y: $i, X: $i] : refl(((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z))) <=> ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z))))),
% 3.55/3.79 inference(bind,[status(th)],[])).
% 3.55/3.79 tff(88,plain,
% 3.55/3.79 (![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z))) <=> ![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 3.55/3.79 inference(quant_intro,[status(thm)],[87])).
% 3.55/3.79 tff(89,plain,
% 3.55/3.79 (![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z))) <=> ![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 3.55/3.79 inference(rewrite,[status(thm)],[])).
% 3.55/3.79 tff(90,plain,
% 3.55/3.79 (^[V: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) <=> ((X = Y) | (~between(X, Y, V)) | (~between(X, Y, Z)))), (((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) | between(X, Z, V)) <=> (((X = Y) | (~between(X, Y, V)) | (~between(X, Y, Z))) | between(X, Z, V)))), rewrite((((X = Y) | (~between(X, Y, V)) | (~between(X, Y, Z))) | between(X, Z, V)) <=> ((X = Y) | (~between(X, Y, V)) | between(X, Z, V) | (~between(X, Y, Z)))), (((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) | between(X, Z, V)) <=> ((X = Y) | (~between(X, Y, V)) | between(X, Z, V) | (~between(X, Y, Z))))), ((((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) | between(X, Z, V)) | between(X, V, Z)) <=> (((X = Y) | (~between(X, Y, V)) | between(X, Z, V) | (~between(X, Y, Z))) | between(X, V, Z)))), rewrite((((X = Y) | (~between(X, Y, V)) | between(X, Z, V) | (~between(X, Y, Z))) | between(X, V, Z)) <=> ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))), ((((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) | between(X, Z, V)) | between(X, V, Z)) <=> ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))))),
% 3.55/3.80 inference(bind,[status(th)],[])).
% 3.55/3.80 tff(91,plain,
% 3.55/3.80 (![V: $i, Z: $i, Y: $i, X: $i] : (((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) | between(X, Z, V)) | between(X, V, Z)) <=> ![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 3.55/3.80 inference(quant_intro,[status(thm)],[90])).
% 3.55/3.80 tff(92,axiom,(![V: $i, Z: $i, Y: $i, X: $i] : (((((~between(X, Y, Z)) | (~between(X, Y, V))) | (X = Y)) | between(X, Z, V)) | between(X, V, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','connectivity_for_betweeness')).
% 3.55/3.80 tff(93,plain,
% 3.55/3.80 (![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[92, 91])).
% 3.55/3.80 tff(94,plain,
% 3.55/3.80 (![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[93, 89])).
% 3.55/3.80 tff(95,plain,(
% 3.55/3.80 ![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 3.55/3.80 inference(skolemize,[status(sab)],[94])).
% 3.55/3.80 tff(96,plain,
% 3.55/3.80 (![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[95, 88])).
% 3.55/3.80 tff(97,plain,
% 3.55/3.80 (((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | (between(a, c, c) | (~between(a, b, c)) | (a = b))) <=> ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | between(a, c, c) | (~between(a, b, c)) | (a = b))),
% 3.55/3.80 inference(rewrite,[status(thm)],[])).
% 3.55/3.80 tff(98,plain,
% 3.55/3.80 (((a = b) | (~between(a, b, c)) | between(a, c, c) | between(a, c, c) | (~between(a, b, c))) <=> (between(a, c, c) | (~between(a, b, c)) | (a = b))),
% 3.55/3.80 inference(rewrite,[status(thm)],[])).
% 3.55/3.80 tff(99,plain,
% 3.55/3.80 (((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | ((a = b) | (~between(a, b, c)) | between(a, c, c) | between(a, c, c) | (~between(a, b, c)))) <=> ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | (between(a, c, c) | (~between(a, b, c)) | (a = b)))),
% 3.55/3.80 inference(monotonicity,[status(thm)],[98])).
% 3.55/3.80 tff(100,plain,
% 3.55/3.80 (((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | ((a = b) | (~between(a, b, c)) | between(a, c, c) | between(a, c, c) | (~between(a, b, c)))) <=> ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | between(a, c, c) | (~between(a, b, c)) | (a = b))),
% 3.55/3.80 inference(transitivity,[status(thm)],[99, 97])).
% 3.55/3.80 tff(101,plain,
% 3.55/3.80 ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | ((a = b) | (~between(a, b, c)) | between(a, c, c) | between(a, c, c) | (~between(a, b, c)))),
% 3.55/3.80 inference(quant_inst,[status(thm)],[])).
% 3.55/3.80 tff(102,plain,
% 3.55/3.80 ((~![V: $i, Z: $i, Y: $i, X: $i] : ((X = Y) | (~between(X, Y, V)) | between(X, V, Z) | between(X, Z, V) | (~between(X, Y, Z)))) | between(a, c, c) | (~between(a, b, c)) | (a = b)),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[101, 100])).
% 3.55/3.80 tff(103,plain,
% 3.55/3.80 (between(a, c, c) | (a = b)),
% 3.55/3.80 inference(unit_resolution,[status(thm)],[102, 96, 4])).
% 3.55/3.80 tff(104,plain,
% 3.55/3.80 (a = b),
% 3.55/3.80 inference(unit_resolution,[status(thm)],[103, 86])).
% 3.55/3.80 tff(105,plain,
% 3.55/3.80 (b = a),
% 3.55/3.80 inference(symmetry,[status(thm)],[104])).
% 3.55/3.80 tff(106,plain,
% 3.55/3.80 (between(b, b, b) <=> between(a, a, a)),
% 3.55/3.80 inference(monotonicity,[status(thm)],[105, 105, 105])).
% 3.55/3.80 tff(107,plain,
% 3.55/3.80 (between(a, a, a) <=> between(b, b, b)),
% 3.55/3.80 inference(symmetry,[status(thm)],[106])).
% 3.55/3.80 tff(108,plain,
% 3.55/3.80 (between(a, a, c) <=> between(a, b, c)),
% 3.55/3.80 inference(monotonicity,[status(thm)],[104])).
% 3.55/3.80 tff(109,plain,
% 3.55/3.80 (between(a, b, c) <=> between(a, a, c)),
% 3.55/3.80 inference(symmetry,[status(thm)],[108])).
% 3.55/3.80 tff(110,plain,
% 3.55/3.80 (between(a, a, c)),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[4, 109])).
% 3.55/3.80 tff(111,plain,
% 3.55/3.80 (^[V: $i, Z: $i, Y: $i, X: $i] : refl((between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V))) <=> (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V))))),
% 3.55/3.80 inference(bind,[status(th)],[])).
% 3.55/3.80 tff(112,plain,
% 3.55/3.80 (![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V))) <=> ![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))),
% 3.55/3.80 inference(quant_intro,[status(thm)],[111])).
% 3.55/3.80 tff(113,plain,
% 3.55/3.80 (![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V))) <=> ![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))),
% 3.55/3.80 inference(rewrite,[status(thm)],[])).
% 3.55/3.80 tff(114,plain,
% 3.55/3.80 (^[V: $i, Z: $i, Y: $i, X: $i] : rewrite((((~between(X, Y, V)) | (~between(Y, Z, V))) | between(X, Y, Z)) <=> (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V))))),
% 3.55/3.80 inference(bind,[status(th)],[])).
% 3.55/3.80 tff(115,plain,
% 3.55/3.80 (![V: $i, Z: $i, Y: $i, X: $i] : (((~between(X, Y, V)) | (~between(Y, Z, V))) | between(X, Y, Z)) <=> ![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))),
% 3.55/3.80 inference(quant_intro,[status(thm)],[114])).
% 3.55/3.80 tff(116,axiom,(![V: $i, Z: $i, Y: $i, X: $i] : (((~between(X, Y, V)) | (~between(Y, Z, V))) | between(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax','transitivity_for_betweeness')).
% 3.55/3.80 tff(117,plain,
% 3.55/3.80 (![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[116, 115])).
% 3.55/3.80 tff(118,plain,
% 3.55/3.80 (![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[117, 113])).
% 3.55/3.80 tff(119,plain,(
% 3.55/3.80 ![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))),
% 3.55/3.80 inference(skolemize,[status(sab)],[118])).
% 3.55/3.80 tff(120,plain,
% 3.55/3.80 (![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[119, 112])).
% 3.55/3.80 tff(121,plain,
% 3.55/3.80 (((~![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))) | ((~between(a, a, c)) | between(a, a, a))) <=> ((~![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))) | (~between(a, a, c)) | between(a, a, a))),
% 3.55/3.80 inference(rewrite,[status(thm)],[])).
% 3.55/3.80 tff(122,plain,
% 3.55/3.80 ((between(a, a, a) | (~between(a, a, c)) | (~between(a, a, c))) <=> ((~between(a, a, c)) | between(a, a, a))),
% 3.55/3.80 inference(rewrite,[status(thm)],[])).
% 3.55/3.80 tff(123,plain,
% 3.55/3.80 (((~![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))) | (between(a, a, a) | (~between(a, a, c)) | (~between(a, a, c)))) <=> ((~![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))) | ((~between(a, a, c)) | between(a, a, a)))),
% 3.55/3.80 inference(monotonicity,[status(thm)],[122])).
% 3.55/3.80 tff(124,plain,
% 3.55/3.80 (((~![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))) | (between(a, a, a) | (~between(a, a, c)) | (~between(a, a, c)))) <=> ((~![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))) | (~between(a, a, c)) | between(a, a, a))),
% 3.55/3.80 inference(transitivity,[status(thm)],[123, 121])).
% 3.55/3.80 tff(125,plain,
% 3.55/3.80 ((~![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))) | (between(a, a, a) | (~between(a, a, c)) | (~between(a, a, c)))),
% 3.55/3.80 inference(quant_inst,[status(thm)],[])).
% 3.55/3.80 tff(126,plain,
% 3.55/3.80 ((~![V: $i, Z: $i, Y: $i, X: $i] : (between(X, Y, Z) | (~between(Y, Z, V)) | (~between(X, Y, V)))) | (~between(a, a, c)) | between(a, a, a)),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[125, 124])).
% 3.55/3.80 tff(127,plain,
% 3.55/3.80 ((~between(a, a, c)) | between(a, a, a)),
% 3.55/3.80 inference(unit_resolution,[status(thm)],[126, 120])).
% 3.55/3.80 tff(128,plain,
% 3.55/3.80 (between(a, a, a)),
% 3.55/3.80 inference(unit_resolution,[status(thm)],[127, 110])).
% 3.55/3.80 tff(129,plain,
% 3.55/3.80 (between(b, b, b)),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[128, 107])).
% 3.55/3.80 tff(130,plain,
% 3.55/3.80 (between(b, b, extension(c, c, c, c)) <=> between(a, b, c)),
% 3.55/3.80 inference(monotonicity,[status(thm)],[105, 55])).
% 3.55/3.80 tff(131,plain,
% 3.55/3.80 (between(a, b, c) <=> between(b, b, extension(c, c, c, c))),
% 3.55/3.80 inference(symmetry,[status(thm)],[130])).
% 3.55/3.80 tff(132,plain,
% 3.55/3.80 (between(b, b, extension(c, c, c, c))),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[4, 131])).
% 3.55/3.80 tff(133,plain,
% 3.55/3.80 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | ((~between(b, b, extension(c, c, c, c))) | between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b) | (~between(b, b, b)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (~between(b, b, extension(c, c, c, c))) | between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b) | (~between(b, b, b)))),
% 3.55/3.80 inference(rewrite,[status(thm)],[])).
% 3.55/3.80 tff(134,plain,
% 3.55/3.80 ((between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b) | (~between(b, b, extension(c, c, c, c))) | (~between(b, b, b))) <=> ((~between(b, b, extension(c, c, c, c))) | between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b) | (~between(b, b, b)))),
% 3.55/3.80 inference(rewrite,[status(thm)],[])).
% 3.55/3.80 tff(135,plain,
% 3.55/3.80 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b) | (~between(b, b, extension(c, c, c, c))) | (~between(b, b, b)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | ((~between(b, b, extension(c, c, c, c))) | between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b) | (~between(b, b, b))))),
% 3.55/3.80 inference(monotonicity,[status(thm)],[134])).
% 3.55/3.80 tff(136,plain,
% 3.55/3.80 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b) | (~between(b, b, extension(c, c, c, c))) | (~between(b, b, b)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (~between(b, b, extension(c, c, c, c))) | between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b) | (~between(b, b, b)))),
% 3.55/3.80 inference(transitivity,[status(thm)],[135, 133])).
% 3.55/3.80 tff(137,plain,
% 3.55/3.80 ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b) | (~between(b, b, extension(c, c, c, c))) | (~between(b, b, b)))),
% 3.55/3.80 inference(quant_inst,[status(thm)],[])).
% 3.55/3.80 tff(138,plain,
% 3.55/3.80 ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (between(X, outer_pasch(W, X, Y, Z, V), Y) | (~between(Y, V, Z)) | (~between(X, W, V)))) | (~between(b, b, extension(c, c, c, c))) | between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b) | (~between(b, b, b))),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[137, 136])).
% 3.55/3.80 tff(139,plain,
% 3.55/3.80 (between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b) | (~between(b, b, b))),
% 3.55/3.80 inference(unit_resolution,[status(thm)],[138, 14, 132])).
% 3.55/3.80 tff(140,plain,
% 3.55/3.80 (between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b)),
% 3.55/3.80 inference(unit_resolution,[status(thm)],[139, 129])).
% 3.55/3.80 tff(141,plain,
% 3.55/3.80 (((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b)) | (b = outer_pasch(b, b, b, extension(c, c, c, c), b)))) <=> ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b)) | (b = outer_pasch(b, b, b, extension(c, c, c, c), b)))),
% 3.55/3.80 inference(rewrite,[status(thm)],[])).
% 3.55/3.80 tff(142,plain,
% 3.55/3.80 ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b)) | (b = outer_pasch(b, b, b, extension(c, c, c, c), b)))),
% 3.55/3.80 inference(quant_inst,[status(thm)],[])).
% 3.55/3.80 tff(143,plain,
% 3.55/3.80 ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(b, outer_pasch(b, b, b, extension(c, c, c, c), b), b)) | (b = outer_pasch(b, b, b, extension(c, c, c, c), b))),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[142, 141])).
% 3.55/3.80 tff(144,plain,
% 3.55/3.80 (b = outer_pasch(b, b, b, extension(c, c, c, c), b)),
% 3.55/3.80 inference(unit_resolution,[status(thm)],[143, 29, 140])).
% 3.55/3.80 tff(145,plain,
% 3.55/3.80 (outer_pasch(b, b, b, extension(c, c, c, c), b) = b),
% 3.55/3.80 inference(symmetry,[status(thm)],[144])).
% 3.55/3.80 tff(146,plain,
% 3.55/3.80 (outer_pasch(b, b, b, extension(c, c, c, c), b) = a),
% 3.55/3.80 inference(transitivity,[status(thm)],[145, 105])).
% 3.55/3.80 tff(147,plain,
% 3.55/3.80 (between(extension(c, c, c, c), b, outer_pasch(b, b, b, extension(c, c, c, c), b)) <=> between(c, b, a)),
% 3.55/3.80 inference(monotonicity,[status(thm)],[55, 146])).
% 3.55/3.80 tff(148,plain,
% 3.55/3.80 (between(c, b, a) <=> between(extension(c, c, c, c), b, outer_pasch(b, b, b, extension(c, c, c, c), b))),
% 3.55/3.80 inference(symmetry,[status(thm)],[147])).
% 3.55/3.80 tff(149,plain,
% 3.55/3.80 ((~between(c, b, a)) <=> (~between(extension(c, c, c, c), b, outer_pasch(b, b, b, extension(c, c, c, c), b)))),
% 3.55/3.80 inference(monotonicity,[status(thm)],[148])).
% 3.55/3.80 tff(150,plain,
% 3.55/3.80 (~between(extension(c, c, c, c), b, outer_pasch(b, b, b, extension(c, c, c, c), b))),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[63, 149])).
% 3.55/3.80 tff(151,plain,
% 3.55/3.80 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(b, b, extension(c, c, c, c))) | (~between(b, b, b)) | between(extension(c, c, c, c), b, outer_pasch(b, b, b, extension(c, c, c, c), b)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | (~between(b, b, extension(c, c, c, c))) | (~between(b, b, b)) | between(extension(c, c, c, c), b, outer_pasch(b, b, b, extension(c, c, c, c), b)))),
% 3.55/3.80 inference(rewrite,[status(thm)],[])).
% 3.55/3.80 tff(152,plain,
% 3.55/3.80 ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | ((~between(b, b, extension(c, c, c, c))) | (~between(b, b, b)) | between(extension(c, c, c, c), b, outer_pasch(b, b, b, extension(c, c, c, c), b)))),
% 3.55/3.80 inference(quant_inst,[status(thm)],[])).
% 3.55/3.80 tff(153,plain,
% 3.55/3.80 ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((~between(Y, V, Z)) | (~between(X, W, V)) | between(Z, W, outer_pasch(W, X, Y, Z, V)))) | (~between(b, b, extension(c, c, c, c))) | (~between(b, b, b)) | between(extension(c, c, c, c), b, outer_pasch(b, b, b, extension(c, c, c, c), b))),
% 3.55/3.80 inference(modus_ponens,[status(thm)],[152, 151])).
% 3.55/3.80 tff(154,plain,
% 3.55/3.80 (between(extension(c, c, c, c), b, outer_pasch(b, b, b, extension(c, c, c, c), b))),
% 3.55/3.80 inference(unit_resolution,[status(thm)],[153, 80, 132, 129])).
% 3.55/3.80 tff(155,plain,
% 3.55/3.80 ($false),
% 3.55/3.80 inference(unit_resolution,[status(thm)],[154, 150])).
% 3.55/3.80 % SZS output end Proof
% 3.55/3.81 % E exiting
%------------------------------------------------------------------------------