%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO010-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:18 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO010-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.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 14:02:09 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(colinear_type, type, (
% 0.20/0.40 colinear: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(a_type, type, (
% 0.20/0.40 a: $i)).
% 0.20/0.40 tff(b_type, type, (
% 0.20/0.40 b: $i)).
% 0.20/0.40 tff(c_type, type, (
% 0.20/0.40 c: $i)).
% 0.20/0.40 tff(between_type, type, (
% 0.20/0.40 between: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(1,assumption,(~colinear(c, b, a)), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (^[W: $i, V: $i, U: $i] : refl(((~between(W, V, U)) | colinear(U, V, W)) <=> ((~between(W, V, U)) | colinear(U, V, W)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![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))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![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))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(5,axiom,(![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c2_1')).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.40 tff(7,plain,(
% 0.20/0.40 ![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.20/0.40 inference(skolemize,[status(sab)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(a, b, c)) | colinear(c, b, a))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(a, b, c)) | colinear(c, b, a))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(a, b, c)) | colinear(c, b, a))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(a, b, c)) | colinear(c, b, a)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (~between(a, b, c)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (^[W: $i, V: $i, U: $i] : refl(((~between(V, U, W)) | colinear(U, V, W)) <=> ((~between(V, U, W)) | colinear(U, V, W)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![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))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![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))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(16,axiom,(![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c2_3')).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.41 tff(18,plain,(
% 0.20/0.41 ![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.20/0.41 inference(skolemize,[status(sab)],[17])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(b, c, a)) | colinear(c, b, a))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(b, c, a)) | colinear(c, b, a))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(b, c, a)) | colinear(c, b, a))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(b, c, a)) | colinear(c, b, a)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (~between(b, c, a)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[22, 19, 1])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (^[W: $i, V: $i, U: $i] : refl(((~between(U, W, V)) | colinear(U, V, W)) <=> ((~between(U, W, V)) | colinear(U, V, W)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c2_2')).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.41 tff(29,plain,(
% 0.20/0.41 ![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.20/0.41 inference(skolemize,[status(sab)],[28])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(c, a, b)) | colinear(c, b, a))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(c, a, b)) | colinear(c, b, a))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(c, a, b)) | colinear(c, b, a))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(c, a, b)) | colinear(c, b, a)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (~between(c, a, b)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[33, 30, 1])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (colinear(a, b, c) <=> colinear(a, b, c)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(36,axiom,(colinear(a, b, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abc_colinear')).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (colinear(a, b, c)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.41 tff(43,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/sandbox/benchmark/Axioms/GEO002-1.ax','colinearity4')).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.41 tff(46,plain,(
% 0.20/0.41 ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[45])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(c, a, b) | between(b, c, a) | between(a, b, c) | (~colinear(a, b, 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, a, b) | between(b, c, a) | between(a, b, c) | (~colinear(a, b, c)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(c, a, b) | between(b, c, a) | between(a, b, c) | (~colinear(a, b, c)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | between(c, a, b) | between(b, c, a) | between(a, b, c) | (~colinear(a, b, c))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (between(c, a, b) | between(b, c, a) | between(a, b, c)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[50, 47, 37])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[51, 34, 23, 12])).
% 0.20/0.41 tff(53,plain,(colinear(c, b, a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(54,assumption,(between(b, c, a)), introduced(assumption)).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (^[Z: $i, Y: $i, X: $i] : refl(((~between(Z, X, Y)) | colinear(X, Y, Z)) <=> ((~between(Z, X, Y)) | colinear(X, Y, Z)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(58,axiom,(![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax','colinearity3')).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.41 tff(60,plain,(
% 0.20/0.41 ![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 0.20/0.41 inference(skolemize,[status(sab)],[59])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | ((~between(b, c, a)) | colinear(c, a, b))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | (~between(b, c, a)) | colinear(c, a, b))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | ((~between(b, c, a)) | colinear(c, a, b))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | (~between(b, c, a)) | colinear(c, a, b)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (colinear(c, a, b)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[64, 61, 54])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (^[Z: $i, Y: $i, X: $i] : refl(((~between(X, Y, Z)) | colinear(X, Y, Z)) <=> ((~between(X, Y, Z)) | colinear(X, Y, Z)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(69,axiom,(![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax','colinearity1')).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.41 tff(71,plain,(
% 0.20/0.41 ![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 0.20/0.41 inference(skolemize,[status(sab)],[70])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | ((~between(b, c, a)) | colinear(b, c, a))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | (~between(b, c, a)) | colinear(b, c, a))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | ((~between(b, c, a)) | colinear(b, c, a))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | (~between(b, c, a)) | colinear(b, c, a)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (colinear(b, c, a)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[75, 72, 54])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(b, c, a)) | colinear(b, a, c))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(b, c, a)) | colinear(b, a, c))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(b, c, a)) | colinear(b, a, c))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(b, c, a)) | colinear(b, a, c)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (colinear(b, a, c)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[79, 30, 54])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(b, c, a)) | colinear(a, c, b))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(b, c, a)) | colinear(a, c, b))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(b, c, a)) | colinear(a, c, b))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(b, c, a)) | colinear(a, c, b)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (colinear(a, c, b)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[83, 8, 54])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)) | (~colinear(c, a, b)) | (~colinear(c, b, a))) <=> ((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)) | (~colinear(c, a, b)) | (~colinear(c, b, a)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 ((((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)) | (~colinear(c, a, b))) | (~colinear(c, b, a))) <=> ((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)) | (~colinear(c, a, b)) | (~colinear(c, b, a)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 ((((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a))) | (~colinear(c, a, b))) <=> ((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)) | (~colinear(c, a, b)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 ((((~colinear(a, c, b)) | (~colinear(b, a, c))) | (~colinear(b, c, a))) <=> ((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (((((~colinear(a, c, b)) | (~colinear(b, a, c))) | (~colinear(b, c, a))) | (~colinear(c, a, b))) <=> (((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a))) | (~colinear(c, a, b)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (((((~colinear(a, c, b)) | (~colinear(b, a, c))) | (~colinear(b, c, a))) | (~colinear(c, a, b))) <=> ((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)) | (~colinear(c, a, b)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[89, 87])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 ((((((~colinear(a, c, b)) | (~colinear(b, a, c))) | (~colinear(b, c, a))) | (~colinear(c, a, b))) | (~colinear(c, b, a))) <=> (((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)) | (~colinear(c, a, b))) | (~colinear(c, b, a)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[90])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 ((((((~colinear(a, c, b)) | (~colinear(b, a, c))) | (~colinear(b, c, a))) | (~colinear(c, a, b))) | (~colinear(c, b, a))) <=> ((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)) | (~colinear(c, a, b)) | (~colinear(c, b, a)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[91, 86])).
% 0.20/0.42 tff(93,axiom,(((((~colinear(a, c, b)) | (~colinear(b, a, c))) | (~colinear(b, c, a))) | (~colinear(c, a, b))) | (~colinear(c, b, a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_colinear_in_all_orders')).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 ((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)) | (~colinear(c, a, b)) | (~colinear(c, b, a))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 ((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)) | (~colinear(c, a, b)) | (~colinear(c, b, a))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[94, 85])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[95, 84, 80, 76, 65, 53])).
% 0.20/0.42 tff(97,plain,(~between(b, c, a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(98,assumption,(between(c, a, b)), introduced(assumption)).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | ((~between(c, a, b)) | colinear(c, a, b))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | (~between(c, a, b)) | colinear(c, a, b))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | ((~between(c, a, b)) | colinear(c, a, b))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | (~between(c, a, b)) | colinear(c, a, b)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 (colinear(c, a, b)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[101, 72, 98])).
% 0.20/0.42 tff(103,assumption,(~colinear(a, c, b)), introduced(assumption)).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(c, a, b)) | colinear(a, c, b))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(c, a, b)) | colinear(a, c, b))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(c, a, b)) | colinear(a, c, b))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(c, a, b)) | colinear(a, c, b)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (~between(c, a, b)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[106, 19, 103])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 (((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(a, b, c)) | colinear(a, c, b))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(a, b, c)) | colinear(a, c, b))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(a, b, c)) | colinear(a, c, b))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(a, b, c)) | colinear(a, c, b)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (~between(a, b, c)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[110, 30, 103])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[51, 111, 107, 97])).
% 0.20/0.42 tff(113,plain,(colinear(a, c, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(c, a, b)) | colinear(b, a, c))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(c, a, b)) | colinear(b, a, c))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(c, a, b)) | colinear(b, a, c))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(c, a, b)) | colinear(b, a, c)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (colinear(b, a, c)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[116, 8, 98])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (^[Z: $i, Y: $i, X: $i] : refl(((~between(Y, Z, X)) | colinear(X, Y, Z)) <=> ((~between(Y, Z, X)) | colinear(X, Y, Z)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[118])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(121,axiom,(![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax','colinearity2')).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 (![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.42 tff(123,plain,(
% 0.20/0.42 ![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 0.20/0.42 inference(skolemize,[status(sab)],[122])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 (![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 (((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | ((~between(c, a, b)) | colinear(b, c, a))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | (~between(c, a, b)) | colinear(b, c, a))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | ((~between(c, a, b)) | colinear(b, c, a))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | (~between(c, a, b)) | colinear(b, c, a)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 (colinear(b, c, a)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[127, 124, 98])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[95, 128, 117, 113, 102, 53])).
% 0.20/0.42 tff(130,plain,(~between(c, a, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 (between(a, b, c)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[51, 130, 97])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | ((~between(a, b, c)) | colinear(c, a, b))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | (~between(a, b, c)) | colinear(c, a, b))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | ((~between(a, b, c)) | colinear(c, a, b))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | (~between(a, b, c)) | colinear(c, a, b)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (colinear(c, a, b)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[134, 124, 131])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(a, b, c)) | colinear(b, a, c))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(a, b, c)) | colinear(b, a, c))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(a, b, c)) | colinear(b, a, c))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(a, b, c)) | colinear(b, a, c)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 (colinear(b, a, c)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[138, 19, 131])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 (((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | ((~between(a, b, c)) | colinear(b, c, a))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | (~between(a, b, c)) | colinear(b, c, a))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | ((~between(a, b, c)) | colinear(b, c, a))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(142,plain,
% 0.20/0.43 ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | (~between(a, b, c)) | colinear(b, c, a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 (colinear(b, c, a)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[142, 61, 131])).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[95, 143, 139, 113, 135, 53])).
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------