%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO006-3 : 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 : n006.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 09:51:09 AM UTC 2026
% Result : Unsatisfiable 2.56s 1.31s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 9 unt; 2 def)
% Number of atoms : 43 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 20 ~; 17 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 6 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f55,axiom,
! [X2,X0,X1] :
( ~ between(X1,X0,X2)
| ~ between(X0,X1,X2)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
fof(f56,axiom,
! [X2,X0,X1] :
( ~ between(X0,X2,X1)
| ~ between(X0,X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).
fof(f57,axiom,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_c) ).
fof(f59,axiom,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_not_d) ).
fof(f60,axiom,
between(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_between_a_and_d) ).
fof(f61,negated_conjecture,
( between(c,a,d)
| between(a,d,c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_not_between_others) ).
fof(f64,definition,
( spl0_1
<=> between(a,d,c) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f65,plain,
( between(a,d,c)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,definition,
( spl0_2
<=> between(c,a,d) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f68,plain,
( between(c,a,d)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f69,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f61,f67,f64]) ).
fof(f94,plain,
( ~ between(a,c,d)
| a = c
| ~ spl0_2 ),
inference(resolution,[],[f55,f68]) ).
fof(f102,plain,
( a = c
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f94,f60]) ).
fof(f105,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f102,f57]) ).
fof(f106,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f105]) ).
fof(f116,plain,
( ~ between(a,c,d)
| c = d
| ~ spl0_1 ),
inference(resolution,[],[f56,f65]) ).
fof(f120,plain,
( c = d
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f116,f60]) ).
fof(f123,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f120,f59]) ).
fof(f124,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f123]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f69]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f106]) ).
cnf(s5,plain,
~ spl0_1,
inference(sat_conversion,[],[f124]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
fof(f125,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n006.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 06:28:56 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.56/1.31 % (2634050)Input is clausal, will run a generic CNF schedule.
% 2.56/1.31 % (2634132)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2294850054:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.56/1.31 % (2634132)First to succeed.
% 2.56/1.31 % (2634132)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2634050"
% 2.56/1.31 % (2634128)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=4014896785:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.56/1.31 % (2634129)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1148812271:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.56/1.31 % (2634130)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3396328325:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.56/1.31 % (2634131)lrs+10_1_sil=8000:sp=occurrence:random_seed=239603377:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.56/1.31 % (2634131)Also succeeded, but the first one will report.
% 2.56/1.31 % (2634134)dis-21_1_sil=8000:lcm=predicate:random_seed=696048813: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)
% 2.56/1.31 % (2634133)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2326797383:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.56/1.31 % (2634133)Also succeeded, but the first one will report.
% 2.56/1.31 % (2634134)Also succeeded, but the first one will report.
% 2.56/1.31 % (2634132)Refutation found. Thanks to Tanya!
% 2.56/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.56/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.31 % (2634132)------------------------------
% 2.56/1.31 % (2634132)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.31 % (2634132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.31 % (2634132)CaDiCaL version: 2.1.3
% 2.56/1.31 % (2634132)Termination reason: Refutation
% 2.56/1.31 % (2634132)Time elapsed: 0.002 s
% 2.56/1.31 % (2634132)Peak memory usage: 89 MB
% 2.56/1.31 % (2634132)Instructions burned: 3 (million)
% 2.56/1.31 % (2634132)------------------------------
% 2.56/1.31 % (2634132)------------------------------
% 2.56/1.31 % (2634050)Success in time 0.265 s
% 2.56/1.31 % Vampire exiting
%------------------------------------------------------------------------------