%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO006-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 09:53:13 AM UTC 2026
% Result : Unsatisfiable 0.83s 0.60s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 65 ( 17 unt; 4 def)
% Number of atoms : 140 ( 19 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 148 ( 73 ~; 71 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
fof(f7,axiom,
! [X0,X1] :
( ~ between(X0,X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4] :
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4] :
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
fof(f19,axiom,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_c) ).
fof(f21,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_not_d) ).
fof(f22,axiom,
between(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_between_a_and_d) ).
fof(f23,negated_conjecture,
( between(c,a,d)
| between(a,d,c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_between_others) ).
fof(f25,definition,
( spl0_1
<=> between(a,d,c) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f27,plain,
( between(a,d,c)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f29,definition,
( spl0_2
<=> between(c,a,d) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f31,plain,
( between(c,a,d)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f23,f29,f25]) ).
fof(f93,plain,
! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0,
inference(resolution,[],[f5,f3]) ).
fof(f95,plain,
! [X0,X1] : between(X1,X0,X0),
inference(superposition,[],[f4,f93]) ).
fof(f1945,plain,
! [X2,X3,X0,X1] :
( ~ between(X3,X0,X2)
| ~ between(X0,X1,X2)
| inner_pasch(X3,X0,X2,X1,X0) = X0 ),
inference(resolution,[],[f8,f7]) ).
fof(f3082,plain,
! [X0] :
( ~ between(c,X0,d)
| c = inner_pasch(a,c,d,X0,c) ),
inference(resolution,[],[f1945,f22]) ).
fof(f4103,plain,
c = inner_pasch(a,c,d,d,c),
inference(resolution,[],[f3082,f95]) ).
fof(f4537,plain,
( ! [X0] :
( ~ between(a,X0,d)
| a = inner_pasch(c,a,d,X0,a) )
| ~ spl0_2 ),
inference(resolution,[],[f31,f1945]) ).
fof(f4557,plain,
( a = inner_pasch(c,a,d,c,a)
| ~ spl0_2 ),
inference(resolution,[],[f4537,f22]) ).
fof(f4589,plain,
( between(c,a,c)
| ~ between(a,c,d)
| ~ between(c,a,d)
| ~ spl0_2 ),
inference(superposition,[],[f9,f4557]) ).
fof(f4591,plain,
( between(c,a,c)
| ~ between(c,a,d)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f4589,f22]) ).
fof(f4592,plain,
( between(c,a,c)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f4591,f31]) ).
fof(f4593,plain,
( a = c
| ~ spl0_2 ),
inference(resolution,[],[f4592,f7]) ).
fof(f4595,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f4593,f19]) ).
fof(f4596,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f4595]) ).
fof(f4597,plain,
( ! [X0] :
( ~ between(d,X0,c)
| d = inner_pasch(a,d,c,X0,d) )
| ~ spl0_1 ),
inference(resolution,[],[f27,f1945]) ).
fof(f4598,plain,
( d = inner_pasch(a,d,c,c,d)
| ~ spl0_1 ),
inference(resolution,[],[f4597,f95]) ).
fof(f4601,plain,
( between(c,d,a)
| ~ between(d,c,c)
| ~ between(a,d,c)
| ~ spl0_1 ),
inference(superposition,[],[f9,f4598]) ).
fof(f4603,plain,
( between(c,d,a)
| ~ between(a,d,c)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f4601,f95]) ).
fof(f4604,plain,
( between(c,d,a)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f4603,f27]) ).
fof(f4605,plain,
( ! [X0] :
( ~ between(d,X0,a)
| d = inner_pasch(c,d,a,X0,d) )
| ~ spl0_1 ),
inference(resolution,[],[f4604,f1945]) ).
fof(f4611,definition,
( spl0_99
<=> between(c,d,c) ),
introduced(definition,[new_symbols(definition,[spl0_99])],[avatar_definition]) ).
fof(f4612,plain,
( between(c,d,c)
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f4611]) ).
fof(f4613,plain,
( ~ between(c,d,c)
| spl0_99 ),
inference(avatar_component_clause,[],[f4611]) ).
fof(f4673,plain,
( ! [X2,X0,X1] :
( ~ between(a,X0,X1)
| ~ between(X2,d,X1)
| d = inner_pasch(c,d,a,inner_pasch(a,X0,X1,d,X2),d) )
| ~ spl0_1 ),
inference(resolution,[],[f4605,f9]) ).
fof(f4979,plain,
( ! [X0] :
( ~ between(X0,d,d)
| d = inner_pasch(c,d,a,inner_pasch(a,c,d,d,X0),d) )
| ~ spl0_1 ),
inference(resolution,[],[f4673,f22]) ).
fof(f4990,plain,
( ! [X0] : d = inner_pasch(c,d,a,inner_pasch(a,c,d,d,X0),d)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f4979,f95]) ).
fof(f7587,definition,
( spl0_149
<=> between(d,c,a) ),
introduced(definition,[new_symbols(definition,[spl0_149])],[avatar_definition]) ).
fof(f7588,plain,
( between(d,c,a)
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f7587]) ).
fof(f7589,plain,
( ~ between(d,c,a)
| spl0_149 ),
inference(avatar_component_clause,[],[f7587]) ).
fof(f7649,plain,
( d = inner_pasch(c,d,a,c,d)
| ~ spl0_1 ),
inference(superposition,[],[f4990,f4103]) ).
fof(f7655,plain,
( between(d,c,a)
| ~ between(c,d,d)
| ~ between(a,c,d) ),
inference(superposition,[],[f9,f4103]) ).
fof(f7657,plain,
( ~ between(c,d,d)
| ~ between(a,c,d)
| spl0_149 ),
inference(forward_subsumption_resolution,[],[f7655,f7589]) ).
fof(f7662,plain,
( ~ between(a,c,d)
| spl0_149 ),
inference(forward_subsumption_resolution,[],[f7657,f95]) ).
fof(f7663,plain,
( $false
| spl0_149 ),
inference(forward_subsumption_resolution,[],[f7662,f22]) ).
fof(f7664,plain,
spl0_149,
inference(avatar_contradiction_clause,[],[f7663]) ).
fof(f7683,plain,
( c = d
| ~ spl0_99 ),
inference(resolution,[],[f4612,f7]) ).
fof(f7685,plain,
( $false
| ~ spl0_99 ),
inference(forward_subsumption_resolution,[],[f7683,f21]) ).
fof(f7686,plain,
~ spl0_99,
inference(avatar_contradiction_clause,[],[f7685]) ).
fof(f7692,plain,
( between(c,d,c)
| ~ between(d,c,a)
| ~ between(c,d,a)
| ~ spl0_1 ),
inference(superposition,[],[f9,f7649]) ).
fof(f7694,plain,
( ~ between(d,c,a)
| ~ between(c,d,a)
| ~ spl0_1
| spl0_99 ),
inference(forward_subsumption_resolution,[],[f7692,f4613]) ).
fof(f7695,plain,
( ~ between(c,d,a)
| ~ spl0_1
| spl0_99
| ~ spl0_149 ),
inference(forward_subsumption_resolution,[],[f7694,f7588]) ).
fof(f7696,plain,
( $false
| ~ spl0_1
| spl0_99
| ~ spl0_149 ),
inference(forward_subsumption_resolution,[],[f7695,f4604]) ).
fof(f7697,plain,
( ~ spl0_1
| spl0_99
| ~ spl0_149 ),
inference(avatar_contradiction_clause,[],[f7696]) ).
cnf(s31,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f32]) ).
cnf(s2421,plain,
~ spl0_2,
inference(sat_conversion,[],[f4596]) ).
cnf(s3894,plain,
spl0_149,
inference(sat_conversion,[],[f7664]) ).
cnf(s3912,plain,
~ spl0_99,
inference(sat_conversion,[],[f7686]) ).
cnf(s3919,plain,
( ~ spl0_1
| spl0_99
| ~ spl0_149 ),
inference(sat_conversion,[],[f7697]) ).
cnf(s3921,plain,
~ spl0_1,
inference(rat,[],[s3919,s3912,s3894]) ).
cnf(s3966,plain,
$false,
inference(rat,[],[s31,s2421,s3921]) ).
fof(f7698,plain,
$false,
inference(avatar_sat_refutation,[],[s3966]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n019.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 06:29:19 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.83/0.60 % (2742351)Will run a generic schedule for satisfiability detection.
% 0.83/0.60 % (2742358)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3769636007:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.83/0.60 % (2742357)% WARNING: option uhcvi not known.
% 0.83/0.60 % (2742357)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3935410953:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.83/0.60 % (2742356)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2866633661_2999 on theBenchmark for (2999ds/0Mi)
% 0.83/0.60 % (2742361)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4039613634:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.83/0.60 % (2742359)dis+10_1_sil=32000:sp=arity:random_seed=740531537:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.83/0.60 % (2742360)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2931329190:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.83/0.60 % (2742362)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3847172662:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.83/0.60 % Detected minimum model sizes of [3]
% 0.83/0.60 % Detected maximum model sizes of [max]
% 0.83/0.60 % TRYING [3]
% 0.83/0.60 % TRYING [4]
% 0.83/0.60 % (2742360)Instruction limit reached!
% 0.83/0.60 % (2742360)------------------------------
% 0.83/0.60 % (2742360)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.60 % (2742360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.60 % (2742360)CaDiCaL version: 2.1.3
% 0.83/0.60 % (2742360)Termination reason: Instruction limit
% 0.83/0.60 % (2742360)Termination phase: Saturation
% 0.83/0.60 % (2742360)Time elapsed: 0.059 s
% 0.83/0.60 % (2742360)Peak memory usage: 12 MB
% 0.83/0.60 % (2742360)Instructions burned: 117 (million)
% 0.83/0.60 % (2742359)Instruction limit reached!
% 0.83/0.60 % (2742359)------------------------------
% 0.83/0.60 % (2742359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.60 % (2742359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.60 % (2742359)CaDiCaL version: 2.1.3
% 0.83/0.60 % (2742359)Termination reason: Instruction limit
% 0.83/0.60 % (2742359)Termination phase: Saturation
% 0.83/0.60 % (2742359)Time elapsed: 0.067 s
% 0.83/0.60 % (2742359)Peak memory usage: 12 MB
% 0.83/0.60 % (2742359)Instructions burned: 103 (million)
% 0.83/0.60 % (2742370)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=913814708:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.83/0.60 % Detected minimum model sizes of [3]
% 0.83/0.60 % Detected maximum model sizes of [max]
% 0.83/0.60 % TRYING [3]
% 0.83/0.60 % (2742371)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1933312958:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.83/0.60 % (2742361)Instruction limit reached!
% 0.83/0.60 % (2742361)------------------------------
% 0.83/0.60 % (2742361)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.60 % (2742361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.60 % (2742361)CaDiCaL version: 2.1.3
% 0.83/0.60 % (2742361)Termination reason: Instruction limit
% 0.83/0.60 % (2742361)Termination phase: Saturation
% 0.83/0.60 % (2742361)Time elapsed: 0.088 s
% 0.83/0.60 % (2742361)Peak memory usage: 13 MB
% 0.83/0.60 % (2742361)Instructions burned: 132 (million)
% 0.83/0.60 % (2742362)Instruction limit reached!
% 0.83/0.60 % (2742362)------------------------------
% 0.83/0.60 % (2742362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.60 % (2742362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.60 % (2742362)CaDiCaL version: 2.1.3
% 0.83/0.60 % (2742362)Termination reason: Instruction limit
% 0.83/0.60 % (2742362)Termination phase: Saturation
% 0.83/0.60 % (2742362)Time elapsed: 0.100 s
% 0.83/0.60 % (2742362)Peak memory usage: 14 MB
% 0.83/0.60 % (2742362)Instructions burned: 159 (million)
% 0.83/0.60 % (2742374)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3581504336:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.83/0.60 % (2742375)ott-21_1_sil=16000:fs=off:random_seed=3483372036:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.83/0.60 % (2742358) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2742351-2742358"...
% 0.83/0.60 % (2742358)...printing done.
% 0.83/0.60 % (2742358)Refutation found. Thanks to Tanya!
% 0.83/0.60 % SZS status Unsatisfiable for theBenchmark
% 0.83/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.83/0.60 % (2742358)------------------------------
% 0.83/0.60 % (2742358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.60 % (2742358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.60 % (2742358)CaDiCaL version: 2.1.3
% 0.83/0.60 % (2742358)Termination reason: Refutation
% 0.83/0.60 % (2742358)Time elapsed: 0.131 s
% 0.83/0.60 % (2742358)Peak memory usage: 16 MB
% 0.83/0.60 % (2742358)Instructions burned: 360 (million)
% 0.83/0.60 % (2742351)Success in time 0.165 s
% 0.83/0.60 % Vampire exiting
%------------------------------------------------------------------------------