%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KRS002-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 11:42:03 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.43s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 32 ( 15 unt; 1 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 27 ~; 23 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
e(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f2,axiom,
! [X0] :
( ~ c(X0)
| s2least(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f4,axiom,
! [X0] :
( ~ s2least(X0)
| ~ equalish(u1r2(X0),u1r1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f5,axiom,
! [X0] :
( ~ s2least(X0)
| s(X0,u1r1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
fof(f6,axiom,
! [X0] :
( ~ s2least(X0)
| s(X0,u1r2(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
fof(f8,axiom,
! [X0] :
( ~ d(X0)
| s1most(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ s1most(X2)
| equalish(X0,X1)
| ~ s(X2,X0)
| ~ s(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
fof(f14,axiom,
! [X0] :
( ~ e(X0)
| r(X0,u4r2(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
fof(f15,axiom,
! [X0,X1] :
( ~ e(X1)
| d(X0)
| ~ r(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
fof(f16,axiom,
! [X0,X1] :
( ~ e(X1)
| c(X0)
| ~ r(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
fof(f21,plain,
r(exist,u4r2(exist)),
inference(resolution,[],[f14,f1]) ).
fof(f24,plain,
! [X0] :
( ~ r(exist,X0)
| d(X0) ),
inference(resolution,[],[f15,f1]) ).
fof(f25,plain,
d(u4r2(exist)),
inference(resolution,[],[f24,f21]) ).
fof(f26,plain,
! [X0] :
( ~ r(exist,X0)
| c(X0) ),
inference(resolution,[],[f16,f1]) ).
fof(f27,plain,
s1most(u4r2(exist)),
inference(resolution,[],[f25,f8]) ).
fof(f30,plain,
c(u4r2(exist)),
inference(resolution,[],[f26,f21]) ).
fof(f33,plain,
! [X0,X1] :
( ~ s(u4r2(exist),X0)
| equalish(X0,X1)
| ~ s(u4r2(exist),X1) ),
inference(resolution,[],[f10,f27]) ).
fof(f34,plain,
s2least(u4r2(exist)),
inference(resolution,[],[f30,f2]) ).
fof(f37,plain,
~ equalish(u1r2(u4r2(exist)),u1r1(u4r2(exist))),
inference(resolution,[],[f34,f4]) ).
fof(f38,plain,
s(u4r2(exist),u1r2(u4r2(exist))),
inference(resolution,[],[f34,f6]) ).
fof(f39,plain,
s(u4r2(exist),u1r1(u4r2(exist))),
inference(resolution,[],[f34,f5]) ).
fof(f48,definition,
( spl0_2
<=> ! [X0] :
( equalish(u1r2(u4r2(exist)),X0)
| ~ s(u4r2(exist),X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f49,plain,
( ! [X0] :
( ~ s(u4r2(exist),X0)
| equalish(u1r2(u4r2(exist)),X0) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f65,plain,
( equalish(u1r2(u4r2(exist)),u1r1(u4r2(exist)))
| ~ spl0_2 ),
inference(resolution,[],[f49,f39]) ).
fof(f66,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f65,f37]) ).
fof(f67,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f66]) ).
fof(f69,plain,
! [X0] :
( equalish(u1r2(u4r2(exist)),X0)
| ~ s(u4r2(exist),X0) ),
inference(resolution,[],[f33,f38]) ).
fof(f71,plain,
spl0_2,
inference(avatar_split_clause,[],[f69,f48]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f67]) ).
cnf(s6,plain,
spl0_2,
inference(sat_conversion,[],[f71]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s4,s6]) ).
fof(f72,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS002-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n016.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 13:19:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.43 % (2639593)Will run a generic schedule for satisfiability detection.
% 0.11/0.43 % (2639605)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2858682097:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.11/0.43 % (2639605) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2639593-2639605"...
% 0.11/0.43 % (2639605)...printing done.
% 0.11/0.43 % (2639605)Refutation found. Thanks to Tanya!
% 0.11/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.43 % (2639605)------------------------------
% 0.11/0.43 % (2639605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.43 % (2639605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.43 % (2639605)CaDiCaL version: 2.1.3
% 0.11/0.43 % (2639605)Termination reason: Refutation
% 0.11/0.43 % (2639605)Time elapsed: 0.001 s
% 0.11/0.43 % (2639605)Peak memory usage: 12 MB
% 0.11/0.43 % (2639605)Instructions burned: 2 (million)
% 0.11/0.43 % (2639593)Success in time 0.016 s
% 0.11/0.43 % Vampire exiting
%------------------------------------------------------------------------------