%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO067-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 09:51:25 AM UTC 2026
% Result : Unsatisfiable 2.60s 1.37s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 45 ( 18 unt; 5 def)
% Number of atoms : 86 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 76 ( 35 ~; 36 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
fof(f19,axiom,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| colinear(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity1) ).
fof(f20,axiom,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| colinear(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity2) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| colinear(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity3) ).
fof(f23,negated_conjecture,
( ~ colinear(x,x,y)
| ~ colinear(x,y,x)
| ~ colinear(y,x,x)
| x = y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_1) ).
fof(f24,negated_conjecture,
( ~ 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) ).
fof(f26,definition,
( spl0_1
<=> colinear(x,z,y) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f28,plain,
( ~ colinear(x,z,y)
| spl0_1 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f30,definition,
( spl0_2
<=> colinear(y,x,x) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f32,plain,
( ~ colinear(y,x,x)
| spl0_2 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f34,definition,
( spl0_3
<=> colinear(x,y,x) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f36,plain,
( ~ colinear(x,y,x)
| spl0_3 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f38,definition,
( spl0_4
<=> colinear(x,x,y) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f40,plain,
( ~ colinear(x,x,y)
| spl0_4 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f41,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f24,f38,f34,f30,f26]) ).
fof(f43,definition,
( spl0_5
<=> x = y ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f45,plain,
( x = y
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,plain,
( spl0_5
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f23,f38,f34,f30,f43]) ).
fof(f48,plain,
! [X2,X3,X0,X1] : colinear(X0,X1,extension(X0,X1,X2,X3)),
inference(resolution,[],[f19,f4]) ).
fof(f51,plain,
! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0,
inference(resolution,[],[f5,f3]) ).
fof(f53,plain,
! [X0,X1] : colinear(X1,X0,X0),
inference(superposition,[],[f48,f51]) ).
fof(f54,plain,
! [X0,X1] : between(X1,X0,X0),
inference(superposition,[],[f4,f51]) ).
fof(f57,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f53,f32]) ).
fof(f58,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f57]) ).
fof(f60,plain,
! [X0,X1] : colinear(X0,X0,X1),
inference(resolution,[],[f54,f21]) ).
fof(f61,plain,
! [X0,X1] : colinear(X0,X1,X0),
inference(resolution,[],[f54,f20]) ).
fof(f69,plain,
( $false
| spl0_3 ),
inference(resolution,[],[f61,f36]) ).
fof(f71,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f69]) ).
fof(f72,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f40,f60]) ).
fof(f73,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f72]) ).
fof(f74,plain,
( ~ colinear(x,z,x)
| spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f28,f45]) ).
fof(f75,plain,
( $false
| spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f74,f61]) ).
fof(f76,plain,
( spl0_1
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f75]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f41]) ).
cnf(s2,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f46]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f58]) ).
cnf(s4,plain,
spl0_3,
inference(sat_conversion,[],[f71]) ).
cnf(s5,plain,
spl0_4,
inference(sat_conversion,[],[f73]) ).
cnf(s6,plain,
( spl0_1
| ~ spl0_5 ),
inference(sat_conversion,[],[f76]) ).
cnf(s7,plain,
spl0_5,
inference(rat,[],[s2,s5,s4,s3]) ).
cnf(s8,plain,
spl0_1,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s5,s4,s3,s8]) ).
fof(f77,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO067-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 % Computer : n001.cluster.edu
% 0.09/0.41 % Model : x86_64 x86_64
% 0.09/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.41 % Memory : 8046.5625MB
% 0.09/0.41 % OS : Linux 6.8.0-71-generic
% 0.09/0.41 % CPULimit : 300
% 0.09/0.41 % WCLimit : 300
% 0.09/0.41 % DateTime : Sun Sep 27 06:55:00 UTC 2026
% 0.09/0.41 % CPUTime :
% 0.09/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.45 Running first-order theorem proving
% 0.09/0.45 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.60/1.37 % (3209481)Input is clausal, will run a generic CNF schedule.
% 2.60/1.37 % (3209489)lrs+10_1_sil=8000:sp=occurrence:random_seed=3034568399:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.60/1.37 % (3209489)First to succeed.
% 2.60/1.37 % (3209489)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3209481"
% 2.60/1.37 % (3209487)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=160619033:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.60/1.37 % (3209491)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2418653465:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.60/1.37 % (3209490)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3002567749:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.60/1.37 % (3209492)dis-21_1_sil=8000:lcm=predicate:random_seed=1293480503: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)
% 2.60/1.37 % (3209486)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=3511734495:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.60/1.37 % (3209488)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2263757438:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.60/1.37 % (3209492)Refutation not found, incomplete strategy
% 2.60/1.37 % (3209492)------------------------------
% 2.60/1.37 % (3209492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.37 % (3209492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.37 % (3209492)CaDiCaL version: 2.1.3
% 2.60/1.37 % (3209492)Termination reason: Refutation not found, incomplete strategy
% 2.60/1.37 % (3209492)Time elapsed: 0.002 s
% 2.60/1.37 % (3209492)Peak memory usage: 88 MB
% 2.60/1.37 % (3209492)Instructions burned: 1 (million)
% 2.60/1.37 % (3209491)Also succeeded, but the first one will report.
% 2.60/1.37 % (3209490)Instruction limit reached!
% 2.60/1.37 % (3209490)------------------------------
% 2.60/1.37 % (3209490)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.37 % (3209490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.37 % (3209490)CaDiCaL version: 2.1.3
% 2.60/1.37 % (3209490)Termination reason: Instruction limit
% 2.60/1.37 % (3209490)Termination phase: Saturation
% 2.60/1.37 % (3209490)Time elapsed: 0.063 s
% 2.60/1.37 % (3209490)Peak memory usage: 88 MB
% 2.60/1.37 % (3209490)Instructions burned: 114 (million)
% 2.60/1.37 % (3209489)Refutation found. Thanks to Tanya!
% 2.60/1.37 % SZS status Unsatisfiable for theBenchmark
% 2.60/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.60/1.38 % (3209489)------------------------------
% 2.60/1.38 % (3209489)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.38 % (3209489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.38 % (3209489)CaDiCaL version: 2.1.3
% 2.60/1.38 % (3209489)Termination reason: Refutation
% 2.60/1.38 % (3209489)Time elapsed: 0.002 s
% 2.60/1.38 % (3209489)Peak memory usage: 89 MB
% 2.60/1.38 % (3209489)Instructions burned: 3 (million)
% 2.60/1.38 % (3209489)------------------------------
% 2.60/1.38 % (3209489)------------------------------
% 2.60/1.38 % (3209481)Success in time 0.289 s
% 2.60/1.38 % Vampire exiting
%------------------------------------------------------------------------------