%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO010-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 09:53:15 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.46s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 84 ( 11 unt; 8 def)
% Number of atoms : 174 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 168 ( 78 ~; 82 |; 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] :
( ~ between(X0,X1,X2)
| colinear(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity1) ).
fof(f20,axiom,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| colinear(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity2) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| colinear(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',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/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity4) ).
fof(f97,axiom,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| colinear(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_1) ).
fof(f98,axiom,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| colinear(X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_2) ).
fof(f99,axiom,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| colinear(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_3) ).
fof(f100,axiom,
colinear(a,b,c),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',prove_colinear_in_all_orders) ).
fof(f118,definition,
( spl0_1
<=> colinear(c,b,a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f120,plain,
( ~ colinear(c,b,a)
| spl0_1 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f122,definition,
( spl0_2
<=> colinear(c,a,b) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f126,definition,
( spl0_3
<=> colinear(b,c,a) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f130,definition,
( spl0_4
<=> colinear(b,a,c) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f134,definition,
( spl0_5
<=> colinear(a,c,b) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f137,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f101,f134,f130,f126,f122,f118]) ).
fof(f404,plain,
( between(a,b,c)
| between(b,c,a)
| between(c,a,b) ),
inference(resolution,[],[f22,f100]) ).
fof(f415,definition,
( spl0_6
<=> between(c,a,b) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f417,plain,
( between(c,a,b)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f419,definition,
( spl0_7
<=> between(b,c,a) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f421,plain,
( between(b,c,a)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f423,definition,
( spl0_8
<=> between(a,b,c) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f425,plain,
( between(a,b,c)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f426,plain,
( spl0_6
| spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f404,f423,f419,f415]) ).
fof(f427,plain,
( colinear(c,a,b)
| ~ spl0_6 ),
inference(resolution,[],[f417,f19]) ).
fof(f428,plain,
( colinear(b,c,a)
| ~ spl0_6 ),
inference(resolution,[],[f417,f20]) ).
fof(f439,plain,
( colinear(b,a,c)
| ~ spl0_6 ),
inference(resolution,[],[f417,f97]) ).
fof(f440,plain,
( colinear(c,b,a)
| ~ spl0_6 ),
inference(resolution,[],[f417,f98]) ).
fof(f441,plain,
( colinear(a,c,b)
| ~ spl0_6 ),
inference(resolution,[],[f417,f99]) ).
fof(f443,plain,
( spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f441,f415,f134]) ).
fof(f444,plain,
( $false
| spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f440,f120]) ).
fof(f445,plain,
( spl0_1
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f444]) ).
fof(f446,plain,
( spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f439,f415,f130]) ).
fof(f478,plain,
( spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f428,f415,f126]) ).
fof(f479,plain,
( spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f427,f415,f122]) ).
fof(f488,plain,
( colinear(b,c,a)
| ~ spl0_7 ),
inference(resolution,[],[f421,f19]) ).
fof(f490,plain,
( colinear(c,a,b)
| ~ spl0_7 ),
inference(resolution,[],[f421,f21]) ).
fof(f502,plain,
( colinear(a,c,b)
| ~ spl0_7 ),
inference(resolution,[],[f421,f97]) ).
fof(f503,plain,
( colinear(b,a,c)
| ~ spl0_7 ),
inference(resolution,[],[f421,f98]) ).
fof(f504,plain,
( colinear(c,b,a)
| ~ spl0_7 ),
inference(resolution,[],[f421,f99]) ).
fof(f506,plain,
( $false
| spl0_1
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f504,f120]) ).
fof(f507,plain,
( spl0_1
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f506]) ).
fof(f508,plain,
( spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f503,f419,f130]) ).
fof(f509,plain,
( spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f502,f419,f134]) ).
fof(f534,plain,
( spl0_2
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f490,f419,f122]) ).
fof(f535,plain,
( spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f488,f419,f126]) ).
fof(f564,plain,
( colinear(c,a,b)
| ~ spl0_8 ),
inference(resolution,[],[f425,f20]) ).
fof(f565,plain,
( colinear(b,c,a)
| ~ spl0_8 ),
inference(resolution,[],[f425,f21]) ).
fof(f578,plain,
( colinear(c,b,a)
| ~ spl0_8 ),
inference(resolution,[],[f425,f97]) ).
fof(f579,plain,
( colinear(a,c,b)
| ~ spl0_8 ),
inference(resolution,[],[f425,f98]) ).
fof(f580,plain,
( colinear(b,a,c)
| ~ spl0_8 ),
inference(resolution,[],[f425,f99]) ).
fof(f582,plain,
( spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f580,f423,f130]) ).
fof(f583,plain,
( spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f579,f423,f134]) ).
fof(f584,plain,
( $false
| spl0_1
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f578,f120]) ).
fof(f585,plain,
( spl0_1
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f584]) ).
fof(f602,plain,
( spl0_3
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f565,f423,f126]) ).
fof(f603,plain,
( spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f564,f423,f122]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f137]) ).
cnf(s2,plain,
( spl0_6
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f426]) ).
cnf(s3,plain,
( spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f443]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f445]) ).
cnf(s5,plain,
( spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f446]) ).
cnf(s11,plain,
( spl0_3
| ~ spl0_6 ),
inference(sat_conversion,[],[f478]) ).
cnf(s12,plain,
( spl0_2
| ~ spl0_6 ),
inference(sat_conversion,[],[f479]) ).
cnf(s13,plain,
( spl0_1
| ~ spl0_7 ),
inference(sat_conversion,[],[f507]) ).
cnf(s14,plain,
( spl0_4
| ~ spl0_7 ),
inference(sat_conversion,[],[f508]) ).
cnf(s15,plain,
( spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f509]) ).
cnf(s22,plain,
( spl0_2
| ~ spl0_7 ),
inference(sat_conversion,[],[f534]) ).
cnf(s23,plain,
( spl0_3
| ~ spl0_7 ),
inference(sat_conversion,[],[f535]) ).
cnf(s24,plain,
( spl0_4
| ~ spl0_8 ),
inference(sat_conversion,[],[f582]) ).
cnf(s25,plain,
( spl0_5
| ~ spl0_8 ),
inference(sat_conversion,[],[f583]) ).
cnf(s26,plain,
( spl0_1
| ~ spl0_8 ),
inference(sat_conversion,[],[f585]) ).
cnf(s33,plain,
( spl0_3
| ~ spl0_8 ),
inference(sat_conversion,[],[f602]) ).
cnf(s34,plain,
( spl0_2
| ~ spl0_8 ),
inference(sat_conversion,[],[f603]) ).
cnf(s35,plain,
spl0_1,
inference(rat,[],[s2,s4,s13,s26]) ).
cnf(s36,plain,
spl0_2,
inference(rat,[],[s2,s12,s22,s34]) ).
cnf(s37,plain,
spl0_3,
inference(rat,[],[s2,s11,s23,s33]) ).
cnf(s38,plain,
spl0_4,
inference(rat,[],[s2,s5,s14,s24]) ).
cnf(s39,plain,
~ spl0_5,
inference(rat,[],[s1,s37,s36,s35,s38]) ).
cnf(s40,plain,
~ spl0_8,
inference(rat,[],[s25,s39]) ).
cnf(s41,plain,
~ spl0_7,
inference(rat,[],[s15,s39]) ).
cnf(s42,plain,
~ spl0_6,
inference(rat,[],[s3,s39]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s2,s40,s41,s42]) ).
fof(f604,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO010-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 06:30:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.46 % (449451)Will run a generic schedule for satisfiability detection.
% 0.09/0.46 % (449460)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4151480962:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.46 % (449456)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3740025604_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.46 % (449461)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2290781384:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.46 % (449458)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1280828215:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.46 % (449459)dis+10_1_sil=32000:sp=arity:random_seed=1068566171:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.46 % (449462)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1319094920:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.46 % (449457)% WARNING: option uhcvi not known.
% 0.09/0.46 % (449457)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1819761111:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.46 % Detected minimum model sizes of [3]
% 0.09/0.46 % Detected maximum model sizes of [max]
% 0.09/0.46 % TRYING [3]
% 0.09/0.46 % (449459) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-449451-449459"...
% 0.09/0.46 % (449459)...printing done.
% 0.09/0.46 % (449459)Refutation found. Thanks to Tanya!
% 0.09/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.46 % (449459)------------------------------
% 0.09/0.46 % (449459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.46 % (449459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.46 % (449459)CaDiCaL version: 2.1.3
% 0.09/0.46 % (449459)Termination reason: Refutation
% 0.09/0.46 % (449459)Time elapsed: 0.011 s
% 0.09/0.46 % (449459)Peak memory usage: 12 MB
% 0.09/0.46 % (449459)Instructions burned: 16 (million)
% 0.09/0.46 % (449451)Success in time 0.05 s
% 0.09/0.46 % Vampire exiting
%------------------------------------------------------------------------------