%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO006-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 09:51:08 AM UTC 2026
% Result : Unsatisfiable 4.13s 1.53s
% Output : Refutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 13 unt; 5 def)
% Number of atoms : 128 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 135 ( 64 ~; 66 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-5 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ between(X0,X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| between(X0,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_betweeness) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X0,X1,X3)
| X0 = X1
| between(X0,X2,X3)
| between(X0,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectivity_for_betweeness) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4] :
( between(X0,outer_pasch(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch1) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4] :
( between(X4,X1,outer_pasch(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch2) ).
fof(f21,axiom,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_c) ).
fof(f23,axiom,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_not_d) ).
fof(f24,axiom,
between(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_between_a_and_d) ).
fof(f25,negated_conjecture,
( between(c,a,d)
| between(a,d,c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_not_between_others) ).
fof(f27,definition,
( spl0_1
<=> between(a,d,c) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f29,plain,
( between(a,d,c)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f31,definition,
( spl0_2
<=> between(c,a,d) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f33,plain,
( between(c,a,d)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f34,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f25,f31,f27]) ).
fof(f35,plain,
( ! [X0] :
( ~ between(a,X0,d)
| between(c,a,X0) )
| ~ spl0_2 ),
inference(resolution,[],[f2,f33]) ).
fof(f39,plain,
( between(c,a,c)
| ~ spl0_2 ),
inference(resolution,[],[f35,f24]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( outer_pasch(X3,X0,X0,X2,X1) = X0
| ~ between(X0,X3,X1)
| ~ between(X0,X1,X2) ),
inference(resolution,[],[f7,f1]) ).
fof(f43,plain,
( a = c
| ~ spl0_2 ),
inference(resolution,[],[f39,f1]) ).
fof(f45,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f43,f21]) ).
fof(f46,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f45]) ).
fof(f54,plain,
! [X0] :
( ~ between(a,c,X0)
| a = c
| between(a,d,X0)
| between(a,X0,d) ),
inference(resolution,[],[f3,f24]) ).
fof(f57,plain,
! [X0] :
( between(a,X0,d)
| between(a,d,X0)
| ~ between(a,c,X0) ),
inference(forward_subsumption_resolution,[],[f54,f21]) ).
fof(f164,definition,
( spl0_11
<=> between(a,d,d) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f165,plain,
( ~ between(a,d,d)
| spl0_11 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f166,plain,
( between(a,d,d)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f198,plain,
! [X2,X3,X0,X1] :
( between(X1,X2,X0)
| ~ between(X0,X3,X1)
| ~ between(X0,X2,X3)
| ~ between(X0,X2,X3)
| ~ between(X0,X3,X1) ),
inference(superposition,[],[f8,f40]) ).
fof(f201,plain,
! [X2,X3,X0,X1] :
( ~ between(X0,X3,X1)
| between(X1,X2,X0)
| ~ between(X0,X2,X3) ),
inference(duplicate_literal_removal,[],[f198]) ).
fof(f556,plain,
( ! [X0] :
( between(c,X0,a)
| ~ between(a,X0,d) )
| ~ spl0_1 ),
inference(resolution,[],[f201,f29]) ).
fof(f813,definition,
( spl0_36
<=> between(c,d,a) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f814,plain,
( ~ between(c,d,a)
| spl0_36 ),
inference(avatar_component_clause,[],[f813]) ).
fof(f815,plain,
( between(c,d,a)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f813]) ).
fof(f1131,plain,
( ~ between(a,d,d)
| ~ spl0_1
| spl0_36 ),
inference(resolution,[],[f814,f556]) ).
fof(f1140,plain,
( ~ spl0_11
| ~ spl0_1
| spl0_36 ),
inference(avatar_split_clause,[],[f1131,f813,f27,f164]) ).
fof(f1171,plain,
( ! [X0] :
( ~ between(d,X0,a)
| between(c,d,X0) )
| ~ spl0_36 ),
inference(resolution,[],[f815,f2]) ).
fof(f1178,plain,
( ! [X0] :
( between(d,X0,a)
| ~ between(a,X0,d) )
| ~ spl0_11 ),
inference(resolution,[],[f166,f201]) ).
fof(f1374,plain,
( ! [X0] :
( ~ between(a,X0,d)
| between(c,d,X0) )
| ~ spl0_11
| ~ spl0_36 ),
inference(resolution,[],[f1178,f1171]) ).
fof(f1513,plain,
( between(c,d,c)
| ~ spl0_11
| ~ spl0_36 ),
inference(resolution,[],[f1374,f24]) ).
fof(f1522,definition,
( spl0_47
<=> between(c,d,c) ),
introduced(definition,[new_symbols(definition,[spl0_47])],[avatar_definition]) ).
fof(f1524,plain,
( between(c,d,c)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1522]) ).
fof(f1526,plain,
( spl0_47
| ~ spl0_11
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f1513,f813,f164,f1522]) ).
fof(f1545,plain,
( between(a,d,d)
| ~ between(a,c,d)
| spl0_11 ),
inference(resolution,[],[f165,f57]) ).
fof(f1550,plain,
( ~ between(a,c,d)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f1545,f165]) ).
fof(f1553,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f1550,f24]) ).
fof(f1554,plain,
spl0_11,
inference(avatar_contradiction_clause,[],[f1553]) ).
fof(f1648,plain,
( c = d
| ~ spl0_47 ),
inference(resolution,[],[f1524,f1]) ).
fof(f1654,plain,
( $false
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1648,f23]) ).
fof(f1655,plain,
~ spl0_47,
inference(avatar_contradiction_clause,[],[f1654]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f34]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f46]) ).
cnf(s52,plain,
( ~ spl0_1
| ~ spl0_11
| spl0_36 ),
inference(sat_conversion,[],[f1140]) ).
cnf(s66,plain,
( ~ spl0_11
| ~ spl0_36
| spl0_47 ),
inference(sat_conversion,[],[f1526]) ).
cnf(s72,plain,
spl0_11,
inference(sat_conversion,[],[f1554]) ).
cnf(s81,plain,
~ spl0_47,
inference(sat_conversion,[],[f1655]) ).
cnf(s83,plain,
~ spl0_36,
inference(rat,[],[s66,s81,s72]) ).
cnf(s84,plain,
~ spl0_1,
inference(rat,[],[s52,s83,s72]) ).
cnf(s88,plain,
$false,
inference(rat,[],[s1,s2,s84]) ).
fof(f1658,plain,
$false,
inference(avatar_sat_refutation,[],[s88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO006-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 06:29:07 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 4.13/1.52 % (3143390)Input is clausal, will run a generic CNF schedule.
% 4.13/1.52 % (3143522)lrs+10_1_sil=8000:sp=occurrence:random_seed=3960495767:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.13/1.52 % (3143522)Refutation not found, incomplete strategy
% 4.13/1.52 % (3143522)------------------------------
% 4.13/1.52 % (3143522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.52 % (3143522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.52 % (3143522)CaDiCaL version: 2.1.3
% 4.13/1.52 % (3143522)Termination reason: Refutation not found, incomplete strategy
% 4.13/1.52 % (3143522)Time elapsed: 0.001 s
% 4.13/1.52 % (3143522)Peak memory usage: 88 MB
% 4.13/1.52 % (3143522)Instructions burned: 1 (million)
% 4.13/1.52 % (3143523)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=907534520:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.13/1.52 % (3143524)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3814495274:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.13/1.52 % (3143518)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=959963915:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.13/1.52 % (3143520)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1449009843:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.13/1.52 % (3143521)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=923870392:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.13/1.52 % (3143525)dis-21_1_sil=8000:lcm=predicate:random_seed=3155126230: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)
% 4.13/1.52 % (3143523)Instruction limit reached!
% 4.13/1.52 % (3143523)------------------------------
% 4.13/1.52 % (3143523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.52 % (3143523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.52 % (3143523)CaDiCaL version: 2.1.3
% 4.13/1.52 % (3143523)Termination reason: Instruction limit
% 4.13/1.52 % (3143523)Termination phase: Saturation
% 4.13/1.52 % (3143523)Time elapsed: 0.072 s
% 4.13/1.52 % (3143523)Peak memory usage: 88 MB
% 4.13/1.52 % (3143523)Instructions burned: 115 (million)
% 4.13/1.52 % (3143525)Instruction limit reached!
% 4.13/1.52 % (3143525)------------------------------
% 4.13/1.52 % (3143525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.52 % (3143525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.52 % (3143525)CaDiCaL version: 2.1.3
% 4.13/1.52 % (3143525)Termination reason: Instruction limit
% 4.13/1.52 % (3143525)Termination phase: Saturation
% 4.13/1.52 % (3143525)Time elapsed: 0.070 s
% 4.13/1.52 % (3143525)Peak memory usage: 89 MB
% 4.13/1.52 % (3143525)Instructions burned: 118 (million)
% 4.13/1.52 % (3143524)First to succeed.
% 4.13/1.52 % (3143524)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3143390"
% 4.13/1.52 % (3143522)------------------------------
% 4.13/1.52 % (3143522)------------------------------
% 4.13/1.52 % (3143533)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3599738853:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.13/1.52 % (3143534)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3783066225:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 4.13/1.52 % (3143535)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1916503350:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.13/1.52 % (3143535)Refutation not found, incomplete strategy
% 4.13/1.52 % (3143535)------------------------------
% 4.13/1.52 % (3143535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.52 % (3143535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.52 % (3143535)CaDiCaL version: 2.1.3
% 4.13/1.52 % (3143535)Termination reason: Refutation not found, incomplete strategy
% 4.13/1.52 % (3143535)Time elapsed: 0.0000 s
% 4.13/1.52 % (3143535)Peak memory usage: 88 MB
% 4.13/1.52 % (3143533)Instruction limit reached!
% 4.13/1.53 % (3143533)------------------------------
% 4.13/1.53 % (3143533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.53 % (3143533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.53 % (3143533)CaDiCaL version: 2.1.3
% 4.13/1.53 % (3143533)Termination reason: Instruction limit
% 4.13/1.53 % (3143533)Termination phase: Saturation
% 4.13/1.53 % (3143533)Time elapsed: 0.087 s
% 4.13/1.53 % (3143533)Peak memory usage: 88 MB
% 4.13/1.53 % (3143533)Instructions burned: 143 (million)
% 4.13/1.53 % (3143534)Instruction limit reached!
% 4.13/1.53 % (3143534)------------------------------
% 4.13/1.53 % (3143534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.53 % (3143534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.53 % (3143534)CaDiCaL version: 2.1.3
% 4.13/1.53 % (3143534)Termination reason: Instruction limit
% 4.13/1.53 % (3143534)Termination phase: Saturation
% 4.13/1.53 % (3143534)Time elapsed: 0.108 s
% 4.13/1.53 % (3143534)Peak memory usage: 90 MB
% 4.13/1.53 % (3143534)Instructions burned: 190 (million)
% 4.13/1.53 % (3143524)Refutation found. Thanks to Tanya!
% 4.13/1.53 % SZS status Unsatisfiable for theBenchmark
% 4.13/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 4.13/1.53 % (3143524)------------------------------
% 4.13/1.53 % (3143524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.53 % (3143524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.53 % (3143524)CaDiCaL version: 2.1.3
% 4.13/1.53 % (3143524)Termination reason: Refutation
% 4.13/1.53 % (3143524)Time elapsed: 0.103 s
% 4.13/1.53 % (3143524)Peak memory usage: 90 MB
% 4.13/1.53 % (3143524)Instructions burned: 162 (million)
% 4.13/1.53 % (3143524)------------------------------
% 4.13/1.53 % (3143524)------------------------------
% 4.13/1.53 % (3143390)Success in time 0.488 s
% 4.13/1.53 % Vampire exiting
%------------------------------------------------------------------------------