%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KRS101+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 11:42:16 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 4 unt; 1 def)
% Number of atoms : 226 ( 30 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 306 ( 117 ~; 106 |; 70 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 123 ( 90 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X1] :
( rr(X0,X1)
=> cd(X1) )
& ! [X1] :
( rr(X0,X1)
=> ( ~ ? [X2,X3] :
( rs(X1,X2)
& rs(X1,X3)
& X2 != X3 )
| cc(X1) ) )
& ? [X1] :
( rr(X0,X1)
& ~ ! [X2,X3] :
( ( rs(X1,X2)
& rs(X1,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f15,axiom,
! [X0] :
( cc(X0)
=> ~ cd(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f16,axiom,
cUnsatisfiable(i2003_11_14_17_20_36582),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f17,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X1] :
( rr(X0,X1)
=> cd(X1) )
& ! [X2] :
( rr(X0,X2)
=> ( ~ ? [X3,X4] :
( rs(X2,X3)
& rs(X2,X4)
& X3 != X4 )
| cc(X2) ) )
& ? [X5] :
( rr(X0,X5)
& ~ ! [X6,X7] :
( ( rs(X5,X6)
& rs(X5,X7) )
=> X6 = X7 ) ) ) ),
inference(rectify,[],[f14]) ).
fof(f40,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X1] :
( cd(X1)
| ~ rr(X0,X1) )
& ! [X2] :
( ! [X3,X4] :
( ~ rs(X2,X3)
| ~ rs(X2,X4)
| X3 = X4 )
| cc(X2)
| ~ rr(X0,X2) )
& ? [X5] :
( rr(X0,X5)
& ? [X6,X7] :
( X6 != X7
& rs(X5,X6)
& rs(X5,X7) ) ) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f41,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X1] :
( cd(X1)
| ~ rr(X0,X1) )
& ! [X2] :
( ! [X3,X4] :
( ~ rs(X2,X3)
| ~ rs(X2,X4)
| X3 = X4 )
| cc(X2)
| ~ rr(X0,X2) )
& ? [X5] :
( rr(X0,X5)
& ? [X6,X7] :
( X6 != X7
& rs(X5,X6)
& rs(X5,X7) ) ) ) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0] :
( ~ cd(X0)
| ~ cc(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f43,definition,
! [X0] :
( sP0(X0)
<=> ! [X2] :
( ! [X3,X4] :
( ~ rs(X2,X3)
| ~ rs(X2,X4)
| X3 = X4 )
| cc(X2)
| ~ rr(X0,X2) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f44,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X1] :
( cd(X1)
| ~ rr(X0,X1) )
& sP0(X0)
& ? [X5] :
( rr(X0,X5)
& ? [X6,X7] :
( X6 != X7
& rs(X5,X6)
& rs(X5,X7) ) ) ) ),
inference(definition_folding,[],[f41,f43]) ).
fof(f46,plain,
! [X0] :
( ( sP0(X0)
| ? [X2] :
( ? [X3,X4] :
( rs(X2,X3)
& rs(X2,X4)
& X3 != X4 )
& ~ cc(X2)
& rr(X0,X2) ) )
& ( ! [X2] :
( ! [X3,X4] :
( ~ rs(X2,X3)
| ~ rs(X2,X4)
| X3 = X4 )
| cc(X2)
| ~ rr(X0,X2) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f47,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( ? [X2,X3] :
( rs(X1,X2)
& rs(X1,X3)
& X2 != X3 )
& ~ cc(X1)
& rr(X0,X1) ) )
& ( ! [X4] :
( ! [X5,X6] :
( ~ rs(X4,X5)
| ~ rs(X4,X6)
| X5 = X6 )
| cc(X4)
| ~ rr(X0,X4) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ( sP0(X0)
| ( rs(sK1(X0),sK2(X0))
& rs(sK1(X0),sK3(X0))
& sK2(X0) != sK3(X0)
& ~ cc(sK1(X0))
& rr(X0,sK1(X0)) ) )
& ( ! [X4] :
( ! [X5,X6] :
( ~ rs(X4,X5)
| ~ rs(X4,X6)
| X5 = X6 )
| cc(X4)
| ~ rr(X0,X4) )
| ~ sP0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0)),skolemize(X3,sK3(X0))],[f47]) ).
fof(f49,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ? [X1] :
( ~ cd(X1)
& rr(X0,X1) )
| ~ sP0(X0)
| ! [X5] :
( ~ rr(X0,X5)
| ! [X6,X7] :
( X6 = X7
| ~ rs(X5,X6)
| ~ rs(X5,X7) ) ) )
& ( ( ! [X1] :
( cd(X1)
| ~ rr(X0,X1) )
& sP0(X0)
& ? [X5] :
( rr(X0,X5)
& ? [X6,X7] :
( X6 != X7
& rs(X5,X6)
& rs(X5,X7) ) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f50,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ? [X1] :
( ~ cd(X1)
& rr(X0,X1) )
| ~ sP0(X0)
| ! [X5] :
( ~ rr(X0,X5)
| ! [X6,X7] :
( X6 = X7
| ~ rs(X5,X6)
| ~ rs(X5,X7) ) ) )
& ( ( ! [X1] :
( cd(X1)
| ~ rr(X0,X1) )
& sP0(X0)
& ? [X5] :
( rr(X0,X5)
& ? [X6,X7] :
( X6 != X7
& rs(X5,X6)
& rs(X5,X7) ) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ? [X1] :
( ~ cd(X1)
& rr(X0,X1) )
| ~ sP0(X0)
| ! [X2] :
( ~ rr(X0,X2)
| ! [X3,X4] :
( X3 = X4
| ~ rs(X2,X3)
| ~ rs(X2,X4) ) ) )
& ( ( ! [X5] :
( cd(X5)
| ~ rr(X0,X5) )
& sP0(X0)
& ? [X6] :
( rr(X0,X6)
& ? [X7,X8] :
( X7 != X8
& rs(X6,X7)
& rs(X6,X8) ) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(rectify,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ( ~ cd(sK4(X0))
& rr(X0,sK4(X0)) )
| ~ sP0(X0)
| ! [X2] :
( ~ rr(X0,X2)
| ! [X3,X4] :
( X3 = X4
| ~ rs(X2,X3)
| ~ rs(X2,X4) ) ) )
& ( ( ! [X5] :
( cd(X5)
| ~ rr(X0,X5) )
& sP0(X0)
& rr(X0,sK5(X0))
& sK6(X0) != sK7(X0)
& rs(sK5(X0),sK6(X0))
& rs(sK5(X0),sK7(X0)) )
| ~ cUnsatisfiable(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X1,sK4(X0)),skolemize(X6,sK5(X0)),skolemize(X7,sK6(X0)),skolemize(X8,sK7(X0))],[f51]) ).
fof(f68,plain,
! [X0,X6,X4,X5] :
( ~ rs(X4,X6)
| ~ rs(X4,X5)
| X5 = X6
| cc(X4)
| ~ rr(X0,X4)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f74,plain,
! [X0] :
( rs(sK5(X0),sK7(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f75,plain,
! [X0] :
( rs(sK5(X0),sK6(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f76,plain,
! [X0] :
( sK6(X0) != sK7(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f77,plain,
! [X0] :
( rr(X0,sK5(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f78,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f79,plain,
! [X0,X5] :
( ~ rr(X0,X5)
| cd(X5)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f82,plain,
! [X0] :
( ~ cd(X0)
| ~ cc(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f83,plain,
cUnsatisfiable(i2003_11_14_17_20_36582),
inference(cnf_transformation,[],[f16]) ).
fof(f98,plain,
! [X0] :
( cd(sK5(X0))
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f79,f77]) ).
fof(f99,plain,
! [X0] :
( cd(sK5(X0))
| ~ cUnsatisfiable(X0) ),
inference(duplicate_literal_removal,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ cc(sK5(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f99,f82]) ).
fof(f103,plain,
! [X2,X0,X1] :
( ~ rs(sK5(X0),X1)
| sK7(X0) = X1
| cc(sK5(X0))
| ~ rr(X2,sK5(X0))
| ~ sP0(X2)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f68,f74]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ rs(sK5(X0),X1)
| sK7(X0) = X1
| ~ rr(X2,sK5(X0))
| ~ sP0(X2)
| ~ cUnsatisfiable(X0) ),
inference(forward_subsumption_resolution,[],[f103,f100]) ).
fof(f124,plain,
! [X0,X1] :
( sK6(X0) = sK7(X0)
| ~ rr(X1,sK5(X0))
| ~ sP0(X1)
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f122,f75]) ).
fof(f125,plain,
! [X0,X1] :
( sK6(X0) = sK7(X0)
| ~ rr(X1,sK5(X0))
| ~ sP0(X1)
| ~ cUnsatisfiable(X0) ),
inference(duplicate_literal_removal,[],[f124]) ).
fof(f127,plain,
! [X0,X1] :
( ~ rr(X1,sK5(X0))
| ~ sP0(X1)
| ~ cUnsatisfiable(X0) ),
inference(forward_subsumption_resolution,[],[f125,f76]) ).
fof(f128,plain,
! [X0] :
( ~ sP0(X0)
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f127,f77]) ).
fof(f129,plain,
! [X0] :
( ~ sP0(X0)
| ~ cUnsatisfiable(X0) ),
inference(duplicate_literal_removal,[],[f128]) ).
fof(f130,plain,
! [X0] : ~ cUnsatisfiable(X0),
inference(forward_subsumption_resolution,[],[f129,f78]) ).
fof(f131,plain,
$false,
inference(resolution,[],[f130,f83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS101+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 13:20:40 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.10/0.45 % (1415660)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (1415668)dis+10_1_sil=32000:sp=arity:random_seed=1957060294:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (1415668) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1415660-1415668"...
% 0.10/0.45 % (1415668)...printing done.
% 0.10/0.45 % (1415668)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (1415668)------------------------------
% 0.10/0.45 % (1415668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (1415668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (1415668)CaDiCaL version: 2.1.3
% 0.10/0.45 % (1415668)Termination reason: Refutation
% 0.10/0.45 % (1415668)Time elapsed: 0.002 s
% 0.10/0.45 % (1415668)Peak memory usage: 11 MB
% 0.10/0.45 % (1415668)Instructions burned: 4 (million)
% 0.10/0.45 % (1415660)Success in time 0.025 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------