TSTP Solution File: GEO067-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO067-3 : 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 20:34:39 EDT 2022
% Result : Unsatisfiable 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO067-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 05:11:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.40 % SZS status Unsatisfiable
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(between_type, type, (
% 0.18/0.40 between: ( $i * $i * $i ) > $o)).
% 0.18/0.40 tff(insertion_type, type, (
% 0.18/0.40 insertion: ( $i * $i * $i * $i ) > $i)).
% 0.18/0.40 tff(x_type, type, (
% 0.18/0.40 x: $i)).
% 0.18/0.40 tff(y_type, type, (
% 0.18/0.40 y: $i)).
% 0.18/0.40 tff(z_type, type, (
% 0.18/0.40 z: $i)).
% 0.18/0.40 tff(colinear_type, type, (
% 0.18/0.40 colinear: ( $i * $i * $i ) > $o)).
% 0.18/0.40 tff(1,assumption,(~between(y, x, x)), introduced(assumption)).
% 0.18/0.40 tff(2,plain,
% 0.18/0.40 (^[V: $i, U: $i] : refl(between(U, V, V) <=> between(U, V, V))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(3,plain,
% 0.18/0.40 (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 0.18/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(5,axiom,(![V: $i, U: $i] : between(U, V, V)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3')).
% 0.18/0.40 tff(6,plain,
% 0.18/0.40 (![V: $i, U: $i] : between(U, V, V)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.40 tff(7,plain,(
% 0.18/0.40 ![V: $i, U: $i] : between(U, V, V)),
% 0.18/0.40 inference(skolemize,[status(sab)],[6])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 (![V: $i, U: $i] : between(U, V, V)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.40 tff(9,plain,
% 0.18/0.40 ((~![V: $i, U: $i] : between(U, V, V)) | between(y, x, x)),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.40 tff(11,plain,(between(y, x, x)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(12,plain,
% 0.18/0.40 (^[W: $i, V: $i, U: $i] : refl(((~between(V, U, W)) | colinear(U, V, W)) <=> ((~between(V, U, W)) | colinear(U, V, W)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(13,plain,
% 0.18/0.40 (![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))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.40 tff(14,plain,
% 0.18/0.40 (![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))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(15,axiom,(![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c2_3')).
% 0.18/0.40 tff(16,plain,
% 0.18/0.40 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.40 tff(17,plain,(
% 0.18/0.40 ![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.18/0.40 inference(skolemize,[status(sab)],[16])).
% 0.18/0.40 tff(18,plain,
% 0.18/0.40 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.18/0.40 tff(19,plain,
% 0.18/0.40 (((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(y, x, x)) | colinear(x, y, x))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(y, x, x)) | colinear(x, y, x))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(20,plain,
% 0.18/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(y, x, x)) | colinear(x, y, x))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(21,plain,
% 0.18/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(y, x, x)) | colinear(x, y, x)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.40 tff(22,plain,
% 0.18/0.40 (colinear(x, y, x)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.18/0.40 tff(23,plain,
% 0.18/0.40 (^[W: $i, V: $i, U: $i] : refl(((~between(U, W, V)) | colinear(U, V, W)) <=> ((~between(U, W, V)) | colinear(U, V, W)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(24,plain,
% 0.18/0.40 (![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))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.18/0.40 tff(25,plain,
% 0.18/0.40 (![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))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(26,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c2_2')).
% 0.18/0.40 tff(27,plain,
% 0.18/0.40 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.40 tff(28,plain,(
% 0.18/0.40 ![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.18/0.40 inference(skolemize,[status(sab)],[27])).
% 0.18/0.40 tff(29,plain,
% 0.18/0.40 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.18/0.40 tff(30,plain,
% 0.18/0.40 (((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(y, x, x)) | colinear(y, x, x))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(y, x, x)) | colinear(y, x, x))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(31,plain,
% 0.18/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(y, x, x)) | colinear(y, x, x))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(y, x, x)) | colinear(y, x, x)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 (colinear(y, x, x)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[32, 29, 11])).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 (^[W: $i, V: $i, U: $i] : refl(((~between(W, V, U)) | colinear(U, V, W)) <=> ((~between(W, V, U)) | colinear(U, V, W)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 (![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))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 (![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))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(37,axiom,(![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c2_1')).
% 0.18/0.40 tff(38,plain,
% 0.18/0.40 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.18/0.40 tff(39,plain,(
% 0.18/0.40 ![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.18/0.40 inference(skolemize,[status(sab)],[38])).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 (((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(y, x, x)) | colinear(x, x, y))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(y, x, x)) | colinear(x, x, y))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(y, x, x)) | colinear(x, x, y))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(y, x, x)) | colinear(x, x, y)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (colinear(x, x, y)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[43, 40, 11])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 (((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (x = y)) <=> ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (x = y))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 ((((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x))) | (x = y)) <=> ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (x = y))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 ((((~colinear(x, x, y)) | (~colinear(x, y, x))) | (~colinear(y, x, x))) <=> ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 (((((~colinear(x, x, y)) | (~colinear(x, y, x))) | (~colinear(y, x, x))) | (x = y)) <=> (((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x))) | (x = y))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[47])).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 (((((~colinear(x, x, y)) | (~colinear(x, y, x))) | (~colinear(y, x, x))) | (x = y)) <=> ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (x = y))),
% 0.18/0.40 inference(transitivity,[status(thm)],[48, 46])).
% 0.18/0.40 tff(50,axiom,((((~colinear(x, x, y)) | (~colinear(x, y, x))) | (~colinear(y, x, x))) | (x = y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','part_1')).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (x = y)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (x = y)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[51, 45])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 (x = y),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[52, 44, 33, 22])).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 (^[W: $i, V: $i, U: $i] : refl(((~between(U, V, W)) | (V = insertion(U, W, U, V))) <=> ((~between(U, V, W)) | (V = insertion(U, W, U, V))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V))) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V))) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(57,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i3')).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.18/0.40 tff(59,plain,(
% 0.18/0.40 ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[58])).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(y, x, x)) | (x = insertion(y, x, y, x)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(y, x, x)) | (x = insertion(y, x, y, x)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(y, x, x)) | (x = insertion(y, x, y, x)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(y, x, x)) | (x = insertion(y, x, y, x))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (x = insertion(y, x, y, x)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[63, 60, 11])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 (insertion(y, x, y, x) = x),
% 0.18/0.40 inference(symmetry,[status(thm)],[64])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (insertion(y, x, y, x) = y),
% 0.18/0.40 inference(transitivity,[status(thm)],[65, 53])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (colinear(insertion(y, x, y, x), z, insertion(y, x, y, x)) <=> colinear(x, z, y)),
% 0.18/0.40 inference(monotonicity,[status(thm)],[65, 66])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (colinear(x, z, y) <=> colinear(insertion(y, x, y, x), z, insertion(y, x, y, x))),
% 0.18/0.40 inference(symmetry,[status(thm)],[67])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 ((~colinear(x, z, y)) <=> (~colinear(insertion(y, x, y, x), z, insertion(y, x, y, x)))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[68])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (~colinear(x, z, y))) <=> ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (~colinear(x, z, y)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 ((((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x))) | (~colinear(x, z, y))) <=> ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (~colinear(x, z, y)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (((((~colinear(x, x, y)) | (~colinear(x, y, x))) | (~colinear(y, x, x))) | (~colinear(x, z, y))) <=> (((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x))) | (~colinear(x, z, y)))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[47])).
% 0.18/0.41 tff(73,plain,
% 0.18/0.41 (((((~colinear(x, x, y)) | (~colinear(x, y, x))) | (~colinear(y, x, x))) | (~colinear(x, z, y))) <=> ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (~colinear(x, z, y)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[72, 71])).
% 0.18/0.41 tff(74,axiom,((((~colinear(x, x, y)) | (~colinear(x, y, x))) | (~colinear(y, x, x))) | (~colinear(x, z, y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','part_2')).
% 0.18/0.41 tff(75,plain,
% 0.18/0.41 ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (~colinear(x, z, y))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.18/0.41 tff(76,plain,
% 0.18/0.41 ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (~colinear(x, z, y))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[75, 70])).
% 0.18/0.41 tff(77,plain,
% 0.18/0.41 ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (~colinear(x, z, y))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[76, 70])).
% 0.18/0.41 tff(78,plain,
% 0.18/0.41 ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (~colinear(x, z, y))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.18/0.41 tff(79,plain,
% 0.18/0.41 ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (~colinear(x, z, y))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[78, 70])).
% 0.18/0.41 tff(80,plain,
% 0.18/0.41 ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (~colinear(x, z, y))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[79, 70])).
% 0.18/0.41 tff(81,plain,
% 0.18/0.41 ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (~colinear(x, z, y))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.18/0.41 tff(82,plain,
% 0.18/0.41 ((~colinear(x, x, y)) | (~colinear(x, y, x)) | (~colinear(y, x, x)) | (~colinear(x, z, y))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[81, 70])).
% 0.18/0.41 tff(83,plain,
% 0.18/0.41 (~colinear(x, z, y)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[82, 44, 33, 22])).
% 0.18/0.41 tff(84,plain,
% 0.18/0.41 (~colinear(insertion(y, x, y, x), z, insertion(y, x, y, x))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[83, 69])).
% 0.18/0.41 tff(85,plain,
% 0.18/0.41 (((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(z, insertion(y, x, y, x), insertion(y, x, y, x))) | colinear(insertion(y, x, y, x), z, insertion(y, x, y, x)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(z, insertion(y, x, y, x), insertion(y, x, y, x))) | colinear(insertion(y, x, y, x), z, insertion(y, x, y, x)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(z, insertion(y, x, y, x), insertion(y, x, y, x))) | colinear(insertion(y, x, y, x), z, insertion(y, x, y, x)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(87,plain,
% 0.18/0.41 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(z, insertion(y, x, y, x), insertion(y, x, y, x))) | colinear(insertion(y, x, y, x), z, insertion(y, x, y, x))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 ((~between(z, insertion(y, x, y, x), insertion(y, x, y, x))) | colinear(insertion(y, x, y, x), z, insertion(y, x, y, x))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[87, 18])).
% 0.18/0.41 tff(89,plain,
% 0.18/0.41 (~between(z, insertion(y, x, y, x), insertion(y, x, y, x))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[88, 84])).
% 0.18/0.41 tff(90,plain,
% 0.18/0.41 ((~![V: $i, U: $i] : between(U, V, V)) | between(z, insertion(y, x, y, x), insertion(y, x, y, x))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(91,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[90, 8, 89])).
% 0.18/0.41 % SZS output end Proof
%------------------------------------------------------------------------------