%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS003-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 11:41:26 AM UTC 2026
% Result : Unsatisfiable 2.57s 1.31s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 33 ( 14 unt; 2 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 22 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
e(exist),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f2,negated_conjecture,
f(exist),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f3,axiom,
! [X0] :
( ~ c(X0)
| s2least(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f5,axiom,
! [X0] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ s2least(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f6,axiom,
! [X0] :
( ~ s2least(X0)
| s(X0,u1r1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f7,axiom,
! [X0] :
( ~ s2least(X0)
| s(X0,u1r2(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
fof(f9,axiom,
! [X0] :
( ~ d(X0)
| s1most(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
fof(f11,axiom,
! [X2,X0,X1] :
( equalish(X0,X1)
| ~ s1most(X2)
| ~ s(X2,X0)
| ~ s(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).
fof(f15,axiom,
! [X0] :
( ~ e(X0)
| c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_15) ).
fof(f16,axiom,
! [X0] :
( ~ f(X0)
| d(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16) ).
fof(f19,plain,
c(exist),
inference(resolution,[],[f15,f1]) ).
fof(f20,plain,
d(exist),
inference(resolution,[],[f16,f2]) ).
fof(f21,plain,
s2least(exist),
inference(resolution,[],[f19,f3]) ).
fof(f22,plain,
s1most(exist),
inference(resolution,[],[f20,f9]) ).
fof(f23,plain,
s(exist,u1r2(exist)),
inference(resolution,[],[f21,f7]) ).
fof(f24,plain,
s(exist,u1r1(exist)),
inference(resolution,[],[f21,f6]) ).
fof(f27,plain,
! [X0,X1] :
( ~ s1most(X0)
| ~ s(X0,u1r2(X1))
| ~ s(X0,u1r1(X1))
| ~ s2least(X1) ),
inference(resolution,[],[f11,f5]) ).
fof(f34,plain,
! [X0] :
( ~ s2least(X0)
| ~ s(exist,u1r1(X0))
| ~ s(exist,u1r2(X0)) ),
inference(resolution,[],[f27,f22]) ).
fof(f36,plain,
( ~ s(exist,u1r1(exist))
| ~ s(exist,u1r2(exist)) ),
inference(resolution,[],[f34,f21]) ).
fof(f39,definition,
( spl0_1
<=> s(exist,u1r2(exist)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f40,plain,
( ~ s(exist,u1r2(exist))
| spl0_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,definition,
( spl0_2
<=> s(exist,u1r1(exist)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f43,plain,
( ~ s(exist,u1r1(exist))
| spl0_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f44,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f36,f42,f39]) ).
fof(f45,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f40,f23]) ).
fof(f46,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f45]) ).
fof(f47,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f43,f24]) ).
fof(f48,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f47]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f46]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f48]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f49,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS003-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 13:14:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.57/1.31 % (2397975)Input is clausal, will run a generic CNF schedule.
% 2.57/1.31 % (2397986)dis-21_1_sil=8000:lcm=predicate:random_seed=3377371389: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)
% 2.57/1.31 % (2397986)First to succeed.
% 2.57/1.31 % (2397986)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2397975"
% 2.57/1.31 % (2397981)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=654421884:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.57/1.31 % (2397983)lrs+10_1_sil=8000:sp=occurrence:random_seed=4254311057:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.57/1.31 % (2397980)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=355550009:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.57/1.31 % (2397985)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2956383836:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.57/1.31 % (2397984)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3935322863:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.57/1.31 % (2397982)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3835344100:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.57/1.31 % (2397984)Refutation not found, incomplete strategy
% 2.57/1.31 % (2397984)------------------------------
% 2.57/1.31 % (2397984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.31 % (2397984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.31 % (2397984)CaDiCaL version: 2.1.3
% 2.57/1.31 % (2397984)Termination reason: Refutation not found, incomplete strategy
% 2.57/1.31 % (2397984)Time elapsed: 0.001 s
% 2.57/1.31 % (2397984)Peak memory usage: 87 MB
% 2.57/1.31 % (2397983)Also succeeded, but the first one will report.
% 2.57/1.31 % (2397985)Also succeeded, but the first one will report.
% 2.57/1.31 % (2397986)Refutation found. Thanks to Tanya!
% 2.57/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.57/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.31 % (2397986)------------------------------
% 2.57/1.31 % (2397986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.31 % (2397986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.31 % (2397986)CaDiCaL version: 2.1.3
% 2.57/1.31 % (2397986)Termination reason: Refutation
% 2.57/1.31 % (2397986)Time elapsed: 0.001 s
% 2.57/1.31 % (2397986)Peak memory usage: 89 MB
% 2.57/1.31 % (2397986)Instructions burned: 1 (million)
% 2.57/1.31 % (2397986)------------------------------
% 2.57/1.31 % (2397986)------------------------------
% 2.57/1.31 % (2397975)Success in time 0.274 s
% 2.57/1.31 % Vampire exiting
%------------------------------------------------------------------------------