%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO010-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:51:10 AM UTC 2026
% Result : Unsatisfiable 2.65s 1.24s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 100 ( 11 unt; 8 def)
% Number of atoms : 218 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 212 ( 94 ~; 110 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 9 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X2,X0,X1] :
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity1) ).
fof(f20,axiom,
! [X2,X0,X1] :
( colinear(X2,X0,X1)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity2) ).
fof(f21,axiom,
! [X2,X0,X1] :
( colinear(X1,X2,X0)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity3) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ colinear(X0,X1,X2)
| between(X0,X1,X2)
| between(X1,X2,X0)
| between(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity4) ).
fof(f97,axiom,
! [X2,X0,X1] :
( colinear(X2,X1,X0)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_1) ).
fof(f98,axiom,
! [X2,X0,X1] :
( colinear(X0,X2,X1)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_2) ).
fof(f99,axiom,
! [X2,X0,X1] :
( colinear(X1,X0,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_3) ).
fof(f100,axiom,
colinear(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abc_colinear) ).
fof(f101,negated_conjecture,
( ~ colinear(a,c,b)
| ~ colinear(b,a,c)
| ~ colinear(b,c,a)
| ~ colinear(c,a,b)
| ~ colinear(c,b,a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_colinear_in_all_orders) ).
fof(f152,definition,
( spl1_1
<=> colinear(c,b,a) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f153,plain,
( ~ colinear(c,b,a)
| spl1_1 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,definition,
( spl1_2
<=> colinear(c,a,b) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f156,plain,
( ~ colinear(c,a,b)
| spl1_2 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,definition,
( spl1_3
<=> colinear(b,c,a) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f159,plain,
( ~ colinear(b,c,a)
| spl1_3 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,definition,
( spl1_4
<=> colinear(b,a,c) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f162,plain,
( ~ colinear(b,a,c)
| spl1_4 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,definition,
( spl1_5
<=> colinear(a,c,b) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f165,plain,
( ~ colinear(a,c,b)
| spl1_5 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f166,plain,
( ~ spl1_1
| ~ spl1_2
| ~ spl1_3
| ~ spl1_4
| ~ spl1_5 ),
inference(avatar_split_clause,[],[f101,f164,f161,f158,f155,f152]) ).
fof(f429,plain,
( ~ between(c,a,b)
| spl1_5 ),
inference(resolution,[],[f165,f99]) ).
fof(f430,plain,
( ~ between(a,b,c)
| spl1_5 ),
inference(resolution,[],[f165,f98]) ).
fof(f431,plain,
( ~ between(b,c,a)
| spl1_5 ),
inference(resolution,[],[f165,f97]) ).
fof(f491,plain,
( ~ between(b,c,a)
| spl1_2 ),
inference(resolution,[],[f156,f21]) ).
fof(f492,plain,
( ~ between(a,b,c)
| spl1_2 ),
inference(resolution,[],[f156,f20]) ).
fof(f493,plain,
( ~ between(c,a,b)
| spl1_2 ),
inference(resolution,[],[f156,f19]) ).
fof(f1245,plain,
( ~ between(a,b,c)
| spl1_4 ),
inference(resolution,[],[f162,f99]) ).
fof(f1246,plain,
( ~ between(b,c,a)
| spl1_4 ),
inference(resolution,[],[f162,f98]) ).
fof(f1247,plain,
( ~ between(c,a,b)
| spl1_4 ),
inference(resolution,[],[f162,f97]) ).
fof(f2160,plain,
( ~ between(a,b,c)
| spl1_3 ),
inference(resolution,[],[f159,f21]) ).
fof(f2161,plain,
( ~ between(c,a,b)
| spl1_3 ),
inference(resolution,[],[f159,f20]) ).
fof(f2162,plain,
( ~ between(b,c,a)
| spl1_3 ),
inference(resolution,[],[f159,f19]) ).
fof(f3979,plain,
( ~ between(b,c,a)
| spl1_1 ),
inference(resolution,[],[f153,f99]) ).
fof(f3980,plain,
( ~ between(c,a,b)
| spl1_1 ),
inference(resolution,[],[f153,f98]) ).
fof(f3981,plain,
( ~ between(a,b,c)
| spl1_1 ),
inference(resolution,[],[f153,f97]) ).
fof(f4025,plain,
( between(a,b,c)
| between(b,c,a)
| between(c,a,b) ),
inference(resolution,[],[f22,f100]) ).
fof(f4033,definition,
( spl1_17
<=> between(c,a,b) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f4034,plain,
( between(c,a,b)
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f4033]) ).
fof(f4036,definition,
( spl1_18
<=> between(b,c,a) ),
introduced(definition,[new_symbols(definition,[spl1_18])],[avatar_definition]) ).
fof(f4037,plain,
( between(b,c,a)
| ~ spl1_18 ),
inference(avatar_component_clause,[],[f4036]) ).
fof(f4039,definition,
( spl1_19
<=> between(a,b,c) ),
introduced(definition,[new_symbols(definition,[spl1_19])],[avatar_definition]) ).
fof(f4040,plain,
( between(a,b,c)
| ~ spl1_19 ),
inference(avatar_component_clause,[],[f4039]) ).
fof(f4041,plain,
( spl1_17
| spl1_18
| spl1_19 ),
inference(avatar_split_clause,[],[f4025,f4039,f4036,f4033]) ).
fof(f4042,plain,
( $false
| spl1_1
| ~ spl1_17 ),
inference(resolution,[],[f4034,f3980]) ).
fof(f4043,plain,
( spl1_1
| ~ spl1_17 ),
inference(avatar_contradiction_clause,[],[f4042]) ).
fof(f4060,plain,
( $false
| spl1_4
| ~ spl1_17 ),
inference(resolution,[],[f1247,f4034]) ).
fof(f4066,plain,
( spl1_4
| ~ spl1_17 ),
inference(avatar_contradiction_clause,[],[f4060]) ).
fof(f4093,plain,
( $false
| spl1_3
| ~ spl1_17 ),
inference(resolution,[],[f2161,f4034]) ).
fof(f4099,plain,
( spl1_3
| ~ spl1_17 ),
inference(avatar_contradiction_clause,[],[f4093]) ).
fof(f4106,plain,
( $false
| spl1_5
| ~ spl1_17 ),
inference(resolution,[],[f429,f4034]) ).
fof(f4112,plain,
( spl1_5
| ~ spl1_17 ),
inference(avatar_contradiction_clause,[],[f4106]) ).
fof(f4144,plain,
( $false
| spl1_2
| ~ spl1_17 ),
inference(resolution,[],[f493,f4034]) ).
fof(f4150,plain,
( spl1_2
| ~ spl1_17 ),
inference(avatar_contradiction_clause,[],[f4144]) ).
fof(f4271,plain,
( $false
| spl1_3
| ~ spl1_18 ),
inference(resolution,[],[f4037,f2162]) ).
fof(f4272,plain,
( spl1_3
| ~ spl1_18 ),
inference(avatar_contradiction_clause,[],[f4271]) ).
fof(f4279,plain,
( $false
| spl1_3
| ~ spl1_19 ),
inference(resolution,[],[f4040,f2160]) ).
fof(f4280,plain,
( spl1_3
| ~ spl1_19 ),
inference(avatar_contradiction_clause,[],[f4279]) ).
fof(f4287,plain,
( $false
| spl1_4
| ~ spl1_19 ),
inference(resolution,[],[f1245,f4040]) ).
fof(f4294,plain,
( spl1_4
| ~ spl1_19 ),
inference(avatar_contradiction_clause,[],[f4287]) ).
fof(f4329,plain,
( $false
| spl1_2
| ~ spl1_19 ),
inference(resolution,[],[f492,f4040]) ).
fof(f4336,plain,
( spl1_2
| ~ spl1_19 ),
inference(avatar_contradiction_clause,[],[f4329]) ).
fof(f4378,plain,
( $false
| spl1_1
| ~ spl1_19 ),
inference(resolution,[],[f3981,f4040]) ).
fof(f4385,plain,
( spl1_1
| ~ spl1_19 ),
inference(avatar_contradiction_clause,[],[f4378]) ).
fof(f4400,plain,
( $false
| spl1_5
| ~ spl1_19 ),
inference(resolution,[],[f430,f4040]) ).
fof(f4407,plain,
( spl1_5
| ~ spl1_19 ),
inference(avatar_contradiction_clause,[],[f4400]) ).
fof(f4508,plain,
( $false
| spl1_4
| ~ spl1_18 ),
inference(resolution,[],[f4037,f1246]) ).
fof(f4509,plain,
( spl1_4
| ~ spl1_18 ),
inference(avatar_contradiction_clause,[],[f4508]) ).
fof(f4534,plain,
( $false
| spl1_5
| ~ spl1_18 ),
inference(resolution,[],[f431,f4037]) ).
fof(f4542,plain,
( spl1_5
| ~ spl1_18 ),
inference(avatar_contradiction_clause,[],[f4534]) ).
fof(f4576,plain,
( $false
| spl1_2
| ~ spl1_18 ),
inference(resolution,[],[f491,f4037]) ).
fof(f4584,plain,
( spl1_2
| ~ spl1_18 ),
inference(avatar_contradiction_clause,[],[f4576]) ).
fof(f4636,plain,
( $false
| spl1_1
| ~ spl1_18 ),
inference(resolution,[],[f3979,f4037]) ).
fof(f4645,plain,
( spl1_1
| ~ spl1_18 ),
inference(avatar_contradiction_clause,[],[f4636]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2
| ~ spl1_3
| ~ spl1_4
| ~ spl1_5 ),
inference(sat_conversion,[],[f166]) ).
cnf(s18,plain,
( spl1_17
| spl1_18
| spl1_19 ),
inference(sat_conversion,[],[f4041]) ).
cnf(s19,plain,
( spl1_1
| ~ spl1_17 ),
inference(sat_conversion,[],[f4043]) ).
cnf(s20,plain,
( spl1_4
| ~ spl1_17 ),
inference(sat_conversion,[],[f4066]) ).
cnf(s21,plain,
( spl1_3
| ~ spl1_17 ),
inference(sat_conversion,[],[f4099]) ).
cnf(s22,plain,
( spl1_5
| ~ spl1_17 ),
inference(sat_conversion,[],[f4112]) ).
cnf(s23,plain,
( spl1_2
| ~ spl1_17 ),
inference(sat_conversion,[],[f4150]) ).
cnf(s36,plain,
( spl1_3
| ~ spl1_18 ),
inference(sat_conversion,[],[f4272]) ).
cnf(s37,plain,
( spl1_3
| ~ spl1_19 ),
inference(sat_conversion,[],[f4280]) ).
cnf(s38,plain,
( spl1_4
| ~ spl1_19 ),
inference(sat_conversion,[],[f4294]) ).
cnf(s43,plain,
( spl1_2
| ~ spl1_19 ),
inference(sat_conversion,[],[f4336]) ).
cnf(s49,plain,
( spl1_1
| ~ spl1_19 ),
inference(sat_conversion,[],[f4385]) ).
cnf(s52,plain,
( spl1_5
| ~ spl1_19 ),
inference(sat_conversion,[],[f4407]) ).
cnf(s72,plain,
( spl1_4
| ~ spl1_18 ),
inference(sat_conversion,[],[f4509]) ).
cnf(s77,plain,
( spl1_5
| ~ spl1_18 ),
inference(sat_conversion,[],[f4542]) ).
cnf(s84,plain,
( spl1_2
| ~ spl1_18 ),
inference(sat_conversion,[],[f4584]) ).
cnf(s91,plain,
( spl1_1
| ~ spl1_18 ),
inference(sat_conversion,[],[f4645]) ).
cnf(s94,plain,
spl1_1,
inference(rat,[],[s18,s19,s49,s91]) ).
cnf(s95,plain,
spl1_2,
inference(rat,[],[s18,s23,s43,s84]) ).
cnf(s96,plain,
spl1_3,
inference(rat,[],[s18,s21,s36,s37]) ).
cnf(s97,plain,
spl1_4,
inference(rat,[],[s18,s20,s38,s72]) ).
cnf(s98,plain,
~ spl1_5,
inference(rat,[],[s1,s96,s95,s94,s97]) ).
cnf(s99,plain,
~ spl1_18,
inference(rat,[],[s77,s98]) ).
cnf(s100,plain,
~ spl1_19,
inference(rat,[],[s52,s98]) ).
cnf(s101,plain,
~ spl1_17,
inference(rat,[],[s22,s98]) ).
cnf(s103,plain,
$false,
inference(rat,[],[s18,s100,s99,s101]) ).
fof(f4648,plain,
$false,
inference(avatar_sat_refutation,[],[s103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO010-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 06:30:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.65/1.24 % (1673971)Input is clausal, will run a generic CNF schedule.
% 2.65/1.24 % (1673982)dis-21_1_sil=8000:lcm=predicate:random_seed=884523071:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.65/1.24 % (1673982)First to succeed.
% 2.65/1.24 % (1673982)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1673971"
% 2.65/1.24 % (1673981)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4278873837:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.65/1.24 % (1673979)lrs+10_1_sil=8000:sp=occurrence:random_seed=1047131372:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.65/1.24 % (1673980)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4216624989:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.65/1.24 % (1673977)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3770654676:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.65/1.24 % (1673976)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2246824170:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.65/1.24 % (1673978)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=182165881:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.65/1.24 % (1673981)Also succeeded, but the first one will report.
% 2.65/1.24 % (1673979)Also succeeded, but the first one will report.
% 2.65/1.24 % (1673980)Also succeeded, but the first one will report.
% 2.65/1.24 % (1673982)Refutation found. Thanks to Tanya!
% 2.65/1.24 % SZS status Unsatisfiable for theBenchmark
% 2.65/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.24 % (1673982)------------------------------
% 2.65/1.24 % (1673982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.24 % (1673982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.24 % (1673982)CaDiCaL version: 2.1.3
% 2.65/1.24 % (1673982)Termination reason: Refutation
% 2.65/1.24 % (1673982)Time elapsed: 0.035 s
% 2.65/1.24 % (1673982)Peak memory usage: 90 MB
% 2.65/1.24 % (1673982)Instructions burned: 119 (million)
% 2.65/1.24 % (1673982)------------------------------
% 2.65/1.24 % (1673982)------------------------------
% 2.65/1.24 % (1673971)Success in time 0.312 s
% 2.65/1.24 % Vampire exiting
%------------------------------------------------------------------------------