%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KRS097+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 : n017.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 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 15 unt; 1 def)
% Number of atoms : 156 ( 18 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 184 ( 65 ~; 56 |; 58 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 80 ( 49 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] : rr(X0,X1)
& ? [X2] :
( rr(X0,X2)
& cd(X2) )
& ~ ? [X1,X3] :
( rr(X0,X1)
& rr(X0,X3)
& X1 != X3 )
& ? [X2] :
( rr(X0,X2)
& cc(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f30,axiom,
cUnsatisfiable(i2003_11_14_17_20_21603),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f32,axiom,
! [X0] :
~ ( cd(X0)
& cc(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
fof(f40,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] : rr(X0,X1)
& ? [X2] :
( rr(X0,X2)
& cd(X2) )
& ~ ? [X3,X4] :
( rr(X0,X3)
& rr(X0,X4)
& X3 != X4 )
& ? [X5] :
( rr(X0,X5)
& cc(X5) ) ) ),
inference(rectify,[],[f28]) ).
fof(f91,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] : rr(X0,X1)
& ? [X2] :
( rr(X0,X2)
& cd(X2) )
& ! [X3,X4] :
( ~ rr(X0,X3)
| ~ rr(X0,X4)
| X3 = X4 )
& ? [X5] :
( rr(X0,X5)
& cc(X5) ) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f93,plain,
! [X0] :
( ~ cd(X0)
| ~ cc(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f101,definition,
! [X0] :
( sP0(X0)
<=> ( ? [X1] : rr(X0,X1)
& ? [X2] :
( rr(X0,X2)
& cd(X2) )
& ! [X3,X4] :
( ~ rr(X0,X3)
| ~ rr(X0,X4)
| X3 = X4 )
& ? [X5] :
( rr(X0,X5)
& cc(X5) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f102,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> sP0(X0) ),
inference(definition_folding,[],[f91,f101]) ).
fof(f104,plain,
! [X0] :
( ( sP0(X0)
| ! [X1] : ~ rr(X0,X1)
| ! [X2] :
( ~ rr(X0,X2)
| ~ cd(X2) )
| ? [X3,X4] :
( rr(X0,X3)
& rr(X0,X4)
& X3 != X4 )
| ! [X5] :
( ~ rr(X0,X5)
| ~ cc(X5) ) )
& ( ( ? [X1] : rr(X0,X1)
& ? [X2] :
( rr(X0,X2)
& cd(X2) )
& ! [X3,X4] :
( ~ rr(X0,X3)
| ~ rr(X0,X4)
| X3 = X4 )
& ? [X5] :
( rr(X0,X5)
& cc(X5) ) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f105,plain,
! [X0] :
( ( sP0(X0)
| ! [X1] : ~ rr(X0,X1)
| ! [X2] :
( ~ rr(X0,X2)
| ~ cd(X2) )
| ? [X3,X4] :
( rr(X0,X3)
& rr(X0,X4)
& X3 != X4 )
| ! [X5] :
( ~ rr(X0,X5)
| ~ cc(X5) ) )
& ( ( ? [X1] : rr(X0,X1)
& ? [X2] :
( rr(X0,X2)
& cd(X2) )
& ! [X3,X4] :
( ~ rr(X0,X3)
| ~ rr(X0,X4)
| X3 = X4 )
& ? [X5] :
( rr(X0,X5)
& cc(X5) ) )
| ~ sP0(X0) ) ),
inference(flattening,[],[f104]) ).
fof(f106,plain,
! [X0] :
( ( sP0(X0)
| ! [X1] : ~ rr(X0,X1)
| ! [X2] :
( ~ rr(X0,X2)
| ~ cd(X2) )
| ? [X3,X4] :
( rr(X0,X3)
& rr(X0,X4)
& X3 != X4 )
| ! [X5] :
( ~ rr(X0,X5)
| ~ cc(X5) ) )
& ( ( ? [X6] : rr(X0,X6)
& ? [X7] :
( rr(X0,X7)
& cd(X7) )
& ! [X8,X9] :
( ~ rr(X0,X8)
| ~ rr(X0,X9)
| X8 = X9 )
& ? [X10] :
( rr(X0,X10)
& cc(X10) ) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
! [X0] :
( ( sP0(X0)
| ! [X1] : ~ rr(X0,X1)
| ! [X2] :
( ~ rr(X0,X2)
| ~ cd(X2) )
| ( rr(X0,sK1(X0))
& rr(X0,sK2(X0))
& sK1(X0) != sK2(X0) )
| ! [X5] :
( ~ rr(X0,X5)
| ~ cc(X5) ) )
& ( ( rr(X0,sK3(X0))
& rr(X0,sK4(X0))
& cd(sK4(X0))
& ! [X8,X9] :
( ~ rr(X0,X8)
| ~ rr(X0,X9)
| X8 = X9 )
& rr(X0,sK5(X0))
& cc(sK5(X0)) )
| ~ sP0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5]),skolemize(X3,sK1(X0)),skolemize(X4,sK2(X0)),skolemize(X6,sK3(X0)),skolemize(X7,sK4(X0)),skolemize(X10,sK5(X0))],[f106]) ).
fof(f108,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f140,plain,
! [X0] :
( ~ sP0(X0)
| cc(sK5(X0)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f141,plain,
! [X0] :
( ~ sP0(X0)
| rr(X0,sK5(X0)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f142,plain,
! [X0,X8,X9] :
( ~ sP0(X0)
| ~ rr(X0,X9)
| X8 = X9
| ~ rr(X0,X8) ),
inference(cnf_transformation,[],[f107]) ).
fof(f143,plain,
! [X0] :
( ~ sP0(X0)
| cd(sK4(X0)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f144,plain,
! [X0] :
( ~ sP0(X0)
| rr(X0,sK4(X0)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f145,plain,
! [X0] :
( ~ sP0(X0)
| rr(X0,sK3(X0)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f149,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f154,plain,
cUnsatisfiable(i2003_11_14_17_20_21603),
inference(cnf_transformation,[],[f30]) ).
fof(f156,plain,
! [X0] :
( ~ cd(X0)
| ~ cc(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f165,plain,
sP0(i2003_11_14_17_20_21603),
inference(resolution,[],[f149,f154]) ).
fof(f167,plain,
cc(sK5(i2003_11_14_17_20_21603)),
inference(resolution,[],[f140,f165]) ).
fof(f169,plain,
cd(sK4(i2003_11_14_17_20_21603)),
inference(resolution,[],[f143,f165]) ).
fof(f170,plain,
~ cc(sK4(i2003_11_14_17_20_21603)),
inference(resolution,[],[f169,f156]) ).
fof(f172,plain,
rr(i2003_11_14_17_20_21603,sK5(i2003_11_14_17_20_21603)),
inference(resolution,[],[f141,f165]) ).
fof(f173,plain,
rr(i2003_11_14_17_20_21603,sK4(i2003_11_14_17_20_21603)),
inference(resolution,[],[f144,f165]) ).
fof(f174,plain,
rr(i2003_11_14_17_20_21603,sK3(i2003_11_14_17_20_21603)),
inference(resolution,[],[f145,f165]) ).
fof(f201,plain,
! [X0,X1] :
( ~ rr(i2003_11_14_17_20_21603,X0)
| X0 = X1
| ~ rr(i2003_11_14_17_20_21603,X1) ),
inference(resolution,[],[f142,f165]) ).
fof(f203,plain,
! [X0] :
( ~ rr(i2003_11_14_17_20_21603,X0)
| sK5(i2003_11_14_17_20_21603) = X0 ),
inference(resolution,[],[f201,f172]) ).
fof(f208,plain,
sK5(i2003_11_14_17_20_21603) = sK4(i2003_11_14_17_20_21603),
inference(resolution,[],[f203,f173]) ).
fof(f209,plain,
sK5(i2003_11_14_17_20_21603) = sK3(i2003_11_14_17_20_21603),
inference(resolution,[],[f203,f174]) ).
fof(f210,plain,
sK4(i2003_11_14_17_20_21603) = sK3(i2003_11_14_17_20_21603),
inference(forward_demodulation,[],[f208,f209]) ).
fof(f213,plain,
cc(sK3(i2003_11_14_17_20_21603)),
inference(superposition,[],[f167,f209]) ).
fof(f236,plain,
~ cc(sK3(i2003_11_14_17_20_21603)),
inference(superposition,[],[f170,f210]) ).
fof(f242,plain,
$false,
inference(forward_subsumption_resolution,[],[f236,f213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS097+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 13:18:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.44 % (2550037)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (2550047)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1012438964:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.44 % (2550047) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2550037-2550047"...
% 0.10/0.44 % (2550047)...printing done.
% 0.10/0.44 % (2550043)% WARNING: option uhcvi not known.
% 0.10/0.44 % (2550047)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (2550047)------------------------------
% 0.10/0.44 % (2550047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (2550047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (2550047)CaDiCaL version: 2.1.3
% 0.10/0.44 % (2550047)Termination reason: Refutation
% 0.10/0.44 % (2550047)Time elapsed: 0.003 s
% 0.10/0.44 % (2550047)Peak memory usage: 11 MB
% 0.10/0.44 % (2550047)Instructions burned: 5 (million)
% 0.10/0.44 % (2550037)Success in time 0.028 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------