%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n003.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 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 10 unt; 2 def)
% Number of atoms : 107 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 120 ( 58 ~; 60 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-5 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ between(X0,X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',identity_for_betweeness) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ between(X1,X3,X2)
| ~ between(X0,X1,X2)
| between(X0,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',transitivity_for_betweeness) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ between(X0,X1,X3)
| ~ between(X0,X1,X2)
| X0 = X1
| between(X0,X2,X3)
| between(X0,X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',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/Axioms/GEO001-0.ax',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/Axioms/GEO001-0.ax',outer_pasch2) ).
fof(f21,axiom,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_c) ).
fof(f22,axiom,
a != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_d) ).
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(f37,plain,
( ! [X0] :
( ~ between(X0,c,d)
| between(X0,c,a) )
| ~ spl0_2 ),
inference(resolution,[],[f2,f33]) ).
fof(f40,plain,
( between(a,c,a)
| ~ spl0_2 ),
inference(resolution,[],[f37,f24]) ).
fof(f43,plain,
( a = c
| ~ spl0_2 ),
inference(resolution,[],[f40,f1]) ).
fof(f45,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f43,f21]) ).
fof(f46,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f45]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ between(X0,X3,X1)
| ~ between(X0,X1,X2)
| outer_pasch(X3,X0,X0,X2,X1) = X0 ),
inference(resolution,[],[f7,f1]) ).
fof(f50,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ between(X5,X2,outer_pasch(X4,X3,X0,X2,X1))
| ~ between(X3,X4,X1)
| ~ between(X0,X1,X2)
| between(X5,X2,X4) ),
inference(resolution,[],[f8,f2]) ).
fof(f56,plain,
( ! [X0] :
( ~ between(a,d,X0)
| a = d
| between(a,X0,c)
| between(a,c,X0) )
| ~ spl0_1 ),
inference(resolution,[],[f3,f29]) ).
fof(f59,plain,
( ! [X0] :
( ~ between(a,d,X0)
| between(a,X0,c)
| between(a,c,X0) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f56,f22]) ).
fof(f62,plain,
( between(a,c,c)
| between(a,c,c)
| ~ spl0_1 ),
inference(resolution,[],[f59,f29]) ).
fof(f63,plain,
( between(a,c,c)
| ~ spl0_1 ),
inference(duplicate_literal_removal,[],[f62]) ).
fof(f168,plain,
( ! [X0] :
( ~ between(a,c,X0)
| a = outer_pasch(c,a,a,X0,c) )
| ~ spl0_1 ),
inference(resolution,[],[f48,f63]) ).
fof(f169,plain,
( ! [X0] :
( ~ between(a,c,X0)
| a = outer_pasch(d,a,a,X0,c) )
| ~ spl0_1 ),
inference(resolution,[],[f48,f29]) ).
fof(f177,plain,
( a = outer_pasch(d,a,a,c,c)
| ~ spl0_1 ),
inference(resolution,[],[f169,f63]) ).
fof(f197,plain,
( ! [X0] :
( ~ between(X0,c,a)
| ~ between(a,d,c)
| ~ between(a,c,c)
| between(X0,c,d) )
| ~ spl0_1 ),
inference(superposition,[],[f50,f177]) ).
fof(f201,plain,
( ! [X0] :
( ~ between(X0,c,a)
| ~ between(a,c,c)
| between(X0,c,d) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f197,f29]) ).
fof(f202,plain,
( ! [X0] :
( ~ between(X0,c,a)
| between(X0,c,d) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f201,f63]) ).
fof(f314,plain,
( a = outer_pasch(c,a,a,d,c)
| ~ spl0_1 ),
inference(resolution,[],[f168,f24]) ).
fof(f364,plain,
( between(d,c,a)
| ~ between(a,c,d)
| ~ between(a,c,c)
| ~ spl0_1 ),
inference(superposition,[],[f8,f314]) ).
fof(f372,plain,
( between(d,c,a)
| ~ between(a,c,c)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f364,f24]) ).
fof(f376,plain,
( between(d,c,a)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f372,f63]) ).
fof(f383,plain,
( between(d,c,d)
| ~ spl0_1 ),
inference(resolution,[],[f376,f202]) ).
fof(f399,plain,
( c = d
| ~ spl0_1 ),
inference(resolution,[],[f383,f1]) ).
fof(f404,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f399,f23]) ).
fof(f405,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f404]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f34]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f46]) ).
cnf(s4,plain,
~ spl0_1,
inference(sat_conversion,[],[f405]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s2,s4]) ).
fof(f406,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO006-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 06:30:55 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.16/0.48 % (142625)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (142632)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1604305844:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (142631)% WARNING: option uhcvi not known.
% 0.16/0.48 % (142630)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3691277087_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (142631)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2970002616:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (142633)dis+10_1_sil=32000:sp=arity:random_seed=1533549680:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (142634)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1483763772:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % Detected minimum model sizes of [3]
% 0.16/0.48 % Detected maximum model sizes of [max]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % (142635)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4030712528:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (142633) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-142625-142633"...
% 0.16/0.48 % (142636)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=833958006:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (142633)...printing done.
% 0.16/0.48 % (142633)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (142633)------------------------------
% 0.16/0.48 % (142633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (142633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (142633)CaDiCaL version: 2.1.3
% 0.16/0.48 % (142633)Termination reason: Refutation
% 0.16/0.48 % (142633)Time elapsed: 0.022 s
% 0.16/0.48 % (142633)Peak memory usage: 12 MB
% 0.16/0.48 % (142633)Instructions burned: 32 (million)
% 0.16/0.48 % (142625)Success in time 0.056 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------