TSTP Solution File: GEO010-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO010-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:34:15 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO010-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 04:39:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(colinear_type, type, (
% 0.20/0.42 colinear: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(b_type, type, (
% 0.20/0.42 b: $i)).
% 0.20/0.42 tff(a_type, type, (
% 0.20/0.42 a: $i)).
% 0.20/0.42 tff(c_type, type, (
% 0.20/0.42 c: $i)).
% 0.20/0.42 tff(between_type, type, (
% 0.20/0.42 between: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(1,assumption,(between(c, a, b)), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (^[Z: $i, Y: $i, X: $i] : refl(((~between(X, Y, Z)) | colinear(X, Y, Z)) <=> ((~between(X, Y, Z)) | colinear(X, Y, Z)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(5,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')).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.42 tff(7,plain,(
% 0.20/0.42 ![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 0.20/0.42 inference(skolemize,[status(sab)],[6])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.42 tff(9,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(10,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(11,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)],[10, 9])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (colinear(c, a, b)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.20/0.42 tff(13,assumption,(~colinear(a, c, b)), introduced(assumption)).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (^[W: $i, V: $i, U: $i] : refl(((~between(V, U, W)) | colinear(U, V, W)) <=> ((~between(V, U, W)) | colinear(U, V, W)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(17,axiom,(![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c2_3')).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.42 tff(19,plain,(
% 0.20/0.42 ![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.20/0.42 inference(skolemize,[status(sab)],[18])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.42 tff(21,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(22,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(23,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)],[22, 21])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (~between(c, a, b)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[23, 20, 13])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (^[W: $i, V: $i, U: $i] : refl(((~between(W, V, U)) | colinear(U, V, W)) <=> ((~between(W, V, U)) | colinear(U, V, W)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(28,axiom,(![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c2_1')).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.42 tff(30,plain,(
% 0.20/0.42 ![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.20/0.42 inference(skolemize,[status(sab)],[29])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (((~![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(b, c, a)) | colinear(a, c, b))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(b, c, a)) | colinear(a, c, b)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (~between(b, c, a)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[34, 31, 13])).
% 0.20/0.42 tff(36,assumption,(~colinear(c, b, a)), introduced(assumption)).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (((~![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(a, b, c)) | colinear(c, b, a))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(a, b, c)) | colinear(c, b, a)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (~between(a, b, c)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[39, 31, 36])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (((~![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(b, c, a)) | colinear(c, b, a))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(b, c, a)) | colinear(c, b, a)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (~between(b, c, a)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[43, 20, 36])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (^[W: $i, V: $i, U: $i] : refl(((~between(U, W, V)) | colinear(U, V, W)) <=> ((~between(U, W, V)) | colinear(U, V, W)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(48,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c2_2')).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.43 tff(50,plain,(
% 0.20/0.43 ![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.20/0.43 inference(skolemize,[status(sab)],[49])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (((~![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(c, a, b)) | colinear(c, b, a))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(c, a, b)) | colinear(c, b, a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (~between(c, a, b)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[54, 51, 36])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (colinear(a, b, c) <=> colinear(a, b, c)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(57,axiom,(colinear(a, b, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abc_colinear')).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (colinear(a, b, c)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.43 tff(64,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')).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.20/0.43 tff(67,plain,(
% 0.20/0.43 ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[66])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 ((~![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)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | between(c, a, b) | between(b, c, a) | between(a, b, c) | (~colinear(a, b, c))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (between(c, a, b) | between(b, c, a) | between(a, b, c)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[71, 68, 58])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[72, 55, 44, 40])).
% 0.20/0.43 tff(74,plain,(colinear(c, b, a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(75,assumption,(between(a, b, c)), introduced(assumption)).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (^[Z: $i, Y: $i, X: $i] : refl(((~between(Y, Z, X)) | colinear(X, Y, Z)) <=> ((~between(Y, Z, X)) | colinear(X, Y, Z)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(79,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')).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.43 tff(81,plain,(
% 0.20/0.43 ![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 0.20/0.43 inference(skolemize,[status(sab)],[80])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.20/0.43 tff(83,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))) <=> ((~![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(84,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(85,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)],[84, 83])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (colinear(c, a, b)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[85, 82, 75])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (^[Z: $i, Y: $i, X: $i] : refl(((~between(Z, X, Y)) | colinear(X, Y, Z)) <=> ((~between(Z, X, Y)) | colinear(X, Y, Z)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(90,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')).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.43 tff(92,plain,(
% 0.20/0.43 ![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 0.20/0.43 inference(skolemize,[status(sab)],[91])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.20/0.43 tff(94,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(95,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(96,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)],[95, 94])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (colinear(b, c, a)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[96, 93, 75])).
% 0.20/0.43 tff(98,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(99,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(100,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)],[99, 98])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (colinear(b, a, c)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[100, 20, 75])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (((~![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(a, b, c)) | colinear(a, c, b))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(a, b, c)) | colinear(a, c, b)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (colinear(a, c, b)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[104, 51, 75])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (((~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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 ((((~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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 ((((~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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 ((((~colinear(a, c, b)) | (~colinear(b, a, c))) | (~colinear(b, c, a))) <=> ((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (((((~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)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[109])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (((((~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)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[110, 108])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 ((((((~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)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 ((((((~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)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[112, 107])).
% 0.20/0.44 tff(114,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')).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 ((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)) | (~colinear(c, a, b)) | (~colinear(c, b, a))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 ((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)) | (~colinear(c, a, b)) | (~colinear(c, b, a))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[115, 106])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[116, 105, 101, 97, 86, 74])).
% 0.20/0.44 tff(118,plain,(~between(a, b, c)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (between(c, a, b) | between(b, c, a)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[72, 118])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[119, 35, 24])).
% 0.20/0.44 tff(121,plain,(colinear(a, c, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (((~![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(c, a, b)) | colinear(b, a, c))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(c, a, b)) | colinear(b, a, c)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (colinear(b, a, c)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[124, 31, 1])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (((~![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | ((~between(c, a, b)) | colinear(b, c, a))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | (~between(c, a, b)) | colinear(b, c, a)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 (colinear(b, c, a)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[128, 82, 1])).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 ((~colinear(a, c, b)) | (~colinear(b, a, c)) | (~colinear(b, c, a)) | (~colinear(c, a, b))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[116, 74])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[130, 129, 125, 121, 12])).
% 0.20/0.44 tff(132,plain,(~between(c, a, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 (between(b, c, a)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[119, 132])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (((~![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))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | ((~between(b, c, a)) | colinear(c, a, b))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | (~between(b, c, a)) | colinear(c, a, b)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (colinear(c, a, b)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[136, 93, 133])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (((~![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))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(b, c, a)) | colinear(b, a, c))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(b, c, a)) | colinear(b, a, c)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (colinear(b, a, c)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[140, 51, 133])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (((~![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))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | ((~between(b, c, a)) | colinear(b, c, a))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | (~between(b, c, a)) | colinear(b, c, a)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 (colinear(b, c, a)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[144, 8, 133])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[130, 145, 141, 121, 137])).
% 0.20/0.45 % SZS output end Proof
%------------------------------------------------------------------------------