%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KRS106+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 11:42:17 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 76 ( 9 unt; 2 def)
% Number of atoms : 227 ( 18 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 255 ( 104 ~; 98 |; 42 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 130 ( 0 sgn 109 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rf3(X0,X1)
& cp2(X1) )
& ? [X1] :
( rf1(X0,X1)
& cp1(X1) )
& ? [X1] :
( rf2(X0,X1)
& cp1xcomp(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f20,axiom,
! [X0] :
( cp1(X0)
<=> ~ ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f21,axiom,
! [X0] :
( cp1xcomp(X0)
<=> ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( rf1(X0,X1)
& rf1(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f23,axiom,
! [X0,X1,X2] :
( ( rf2(X0,X1)
& rf2(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f25,axiom,
cUnsatisfiable(i2003_11_14_17_20_57644),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f26,axiom,
! [X0,X1] :
( rf3(X0,X1)
=> rf1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
fof(f27,axiom,
! [X0,X1] :
( rf3(X0,X1)
=> rf2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
fof(f28,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rf3(X0,X1)
& cp2(X1) )
& ? [X2] :
( rf1(X0,X2)
& cp1(X2) )
& ? [X3] :
( rf2(X0,X3)
& cp1xcomp(X3) ) ) ),
inference(rectify,[],[f19]) ).
fof(f61,plain,
! [X0] :
( cp1(X0)
<=> ! [X1] : ~ ra_Px1(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f62,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf1(X0,X1)
| ~ rf1(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f63,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf1(X0,X1)
| ~ rf1(X0,X2) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf2(X0,X1)
| ~ rf2(X0,X2) ),
inference(ennf_transformation,[],[f23]) ).
fof(f65,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf2(X0,X1)
| ~ rf2(X0,X2) ),
inference(flattening,[],[f64]) ).
fof(f68,plain,
! [X0,X1] :
( rf1(X0,X1)
| ~ rf3(X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f69,plain,
! [X0,X1] :
( rf2(X0,X1)
| ~ rf3(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f71,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf3(X0,X1)
| ~ cp2(X1) )
| ! [X2] :
( ~ rf1(X0,X2)
| ~ cp1(X2) )
| ! [X3] :
( ~ rf2(X0,X3)
| ~ cp1xcomp(X3) ) )
& ( ( ? [X1] :
( rf3(X0,X1)
& cp2(X1) )
& ? [X2] :
( rf1(X0,X2)
& cp1(X2) )
& ? [X3] :
( rf2(X0,X3)
& cp1xcomp(X3) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f72,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf3(X0,X1)
| ~ cp2(X1) )
| ! [X2] :
( ~ rf1(X0,X2)
| ~ cp1(X2) )
| ! [X3] :
( ~ rf2(X0,X3)
| ~ cp1xcomp(X3) ) )
& ( ( ? [X1] :
( rf3(X0,X1)
& cp2(X1) )
& ? [X2] :
( rf1(X0,X2)
& cp1(X2) )
& ? [X3] :
( rf2(X0,X3)
& cp1xcomp(X3) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf3(X0,X1)
| ~ cp2(X1) )
| ! [X2] :
( ~ rf1(X0,X2)
| ~ cp1(X2) )
| ! [X3] :
( ~ rf2(X0,X3)
| ~ cp1xcomp(X3) ) )
& ( ( ? [X4] :
( rf3(X0,X4)
& cp2(X4) )
& ? [X5] :
( rf1(X0,X5)
& cp1(X5) )
& ? [X6] :
( rf2(X0,X6)
& cp1xcomp(X6) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf3(X0,X1)
| ~ cp2(X1) )
| ! [X2] :
( ~ rf1(X0,X2)
| ~ cp1(X2) )
| ! [X3] :
( ~ rf2(X0,X3)
| ~ cp1xcomp(X3) ) )
& ( ( rf3(X0,sK0(X0))
& cp2(sK0(X0))
& rf1(X0,sK1(X0))
& cp1(sK1(X0))
& rf2(X0,sK2(X0))
& cp1xcomp(sK2(X0)) )
| ~ cUnsatisfiable(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X4,sK0(X0)),skolemize(X5,sK1(X0)),skolemize(X6,sK2(X0))],[f73]) ).
fof(f75,plain,
! [X0] :
( ( cp1(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X1] : ~ ra_Px1(X0,X1)
| ~ cp1(X0) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f76,plain,
! [X0] :
( ( cp1(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ cp1(X0) ) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0] :
( ( cp1(X0)
| ra_Px1(X0,sK3(X0)) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ cp1(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f76]) ).
fof(f78,plain,
! [X0] :
( ( cp1xcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ? [X1] : ra_Px1(X0,X1)
| ~ cp1xcomp(X0) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f79,plain,
! [X0] :
( ( cp1xcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ? [X2] : ra_Px1(X0,X2)
| ~ cp1xcomp(X0) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ( cp1xcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ra_Px1(X0,sK4(X0))
| ~ cp1xcomp(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0))],[f79]) ).
fof(f101,plain,
! [X0] :
( cp1xcomp(sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f102,plain,
! [X0] :
( rf2(X0,sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f103,plain,
! [X0] :
( cp1(sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f104,plain,
! [X0] :
( rf1(X0,sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f106,plain,
! [X0] :
( rf3(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f108,plain,
! [X2,X0] :
( ~ ra_Px1(X0,X2)
| ~ cp1(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f110,plain,
! [X0] :
( ra_Px1(X0,sK4(X0))
| ~ cp1xcomp(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f112,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ rf1(X0,X1)
| ~ rf1(X0,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f113,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ rf2(X0,X1)
| ~ rf2(X0,X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f115,plain,
cUnsatisfiable(i2003_11_14_17_20_57644),
inference(cnf_transformation,[],[f25]) ).
fof(f116,plain,
! [X0,X1] :
( rf1(X0,X1)
| ~ rf3(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
! [X0,X1] :
( rf2(X0,X1)
| ~ rf3(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f149,plain,
! [X0] :
( ~ rf3(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(consistent_polarity_flipping,[],[f106]) ).
fof(f150,plain,
! [X0] :
( ~ rf1(X0,sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(consistent_polarity_flipping,[],[f104]) ).
fof(f151,plain,
! [X0] :
( ~ cp1(sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(consistent_polarity_flipping,[],[f103]) ).
fof(f152,plain,
! [X0] :
( ~ rf2(X0,sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(consistent_polarity_flipping,[],[f102]) ).
fof(f153,plain,
! [X0] :
( ~ cp1xcomp(sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(consistent_polarity_flipping,[],[f101]) ).
fof(f155,plain,
! [X2,X0] :
( cp1(X0)
| ra_Px1(X0,X2) ),
inference(consistent_polarity_flipping,[],[f108]) ).
fof(f157,plain,
! [X0] :
( ~ ra_Px1(X0,sK4(X0))
| cp1xcomp(X0) ),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f158,plain,
! [X2,X0,X1] :
( rf1(X0,X2)
| rf1(X0,X1)
| X1 = X2 ),
inference(consistent_polarity_flipping,[],[f112]) ).
fof(f159,plain,
! [X2,X0,X1] :
( rf2(X0,X2)
| rf2(X0,X1)
| X1 = X2 ),
inference(consistent_polarity_flipping,[],[f113]) ).
fof(f161,plain,
! [X0,X1] :
( rf3(X0,X1)
| ~ rf1(X0,X1) ),
inference(consistent_polarity_flipping,[],[f116]) ).
fof(f162,plain,
! [X0,X1] :
( rf3(X0,X1)
| ~ rf2(X0,X1) ),
inference(consistent_polarity_flipping,[],[f117]) ).
fof(f164,plain,
! [X0,X1] :
( ra_Px1(sK1(X0),X1)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f155,f151]) ).
fof(f167,plain,
! [X0] :
( ~ rf1(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f161,f149]) ).
fof(f168,plain,
! [X0] :
( ~ rf2(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f162,f149]) ).
fof(f169,plain,
! [X0,X1] :
( rf1(X0,X1)
| sK1(X0) = X1
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f158,f150]) ).
fof(f171,plain,
! [X0] :
( cp1xcomp(sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f164,f157]) ).
fof(f174,plain,
! [X0,X1] :
( rf2(X0,X1)
| sK2(X0) = X1
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f159,f152]) ).
fof(f178,plain,
! [X0] :
( sK0(X0) = sK1(X0)
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f169,f167]) ).
fof(f179,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sK0(X0) = sK1(X0) ),
inference(duplicate_literal_removal,[],[f178]) ).
fof(f181,plain,
sK0(i2003_11_14_17_20_57644) = sK1(i2003_11_14_17_20_57644),
inference(resolution,[],[f179,f115]) ).
fof(f182,plain,
( cp1xcomp(sK0(i2003_11_14_17_20_57644))
| ~ cUnsatisfiable(i2003_11_14_17_20_57644) ),
inference(superposition,[],[f171,f181]) ).
fof(f187,definition,
( spl5_1
<=> cUnsatisfiable(i2003_11_14_17_20_57644) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f189,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_57644)
| spl5_1 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f200,definition,
( spl5_4
<=> cp1xcomp(sK0(i2003_11_14_17_20_57644)) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f203,plain,
( ~ spl5_1
| spl5_4 ),
inference(avatar_split_clause,[],[f182,f200,f187]) ).
fof(f204,plain,
( $false
| spl5_1 ),
inference(resolution,[],[f189,f115]) ).
fof(f205,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f204]) ).
fof(f211,plain,
! [X0] :
( sK0(X0) = sK2(X0)
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f174,f168]) ).
fof(f212,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sK0(X0) = sK2(X0) ),
inference(duplicate_literal_removal,[],[f211]) ).
fof(f214,plain,
sK0(i2003_11_14_17_20_57644) = sK2(i2003_11_14_17_20_57644),
inference(resolution,[],[f212,f115]) ).
fof(f216,plain,
( ~ cp1xcomp(sK0(i2003_11_14_17_20_57644))
| ~ cUnsatisfiable(i2003_11_14_17_20_57644) ),
inference(superposition,[],[f153,f214]) ).
fof(f217,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f216,f200,f187]) ).
cnf(s3,plain,
( ~ spl5_1
| spl5_4 ),
inference(sat_conversion,[],[f203]) ).
cnf(s4,plain,
spl5_1,
inference(sat_conversion,[],[f205]) ).
cnf(s5,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(sat_conversion,[],[f217]) ).
cnf(s6,plain,
~ spl5_4,
inference(rat,[],[s5,s4]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s3,s6,s4]) ).
fof(f218,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS106+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/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 13:28:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.44 % (2650967)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (2650978)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=845031313:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.44 % (2650978) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2650967-2650978"...
% 0.11/0.44 % (2650978)...printing done.
% 0.11/0.44 % (2650978)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.44 % (2650978)------------------------------
% 0.11/0.44 % (2650978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.44 % (2650978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.44 % (2650978)CaDiCaL version: 2.1.3
% 0.11/0.44 % (2650978)Termination reason: Refutation
% 0.11/0.44 % (2650978)Time elapsed: 0.002 s
% 0.11/0.44 % (2650978)Peak memory usage: 12 MB
% 0.11/0.44 % (2650978)Instructions burned: 4 (million)
% 0.11/0.44 % (2650967)Success in time 0.027 s
% 0.11/0.44 % Vampire exiting
%------------------------------------------------------------------------------