%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n014.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 11:41:39 AM UTC 2026
% Result : Unsatisfiable 3.44s 1.45s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 8 unt; 3 def)
% Number of atoms : 261 ( 35 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 352 ( 141 ~; 126 |; 70 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 130 ( 0 sgn 97 !; 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] :
( cc(X4)
| ~ rs(X4,X6)
| X5 = X6
| ~ rs(X4,X5)
| ~ 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] :
( sP0(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f79,plain,
! [X0,X5] :
( cd(X5)
| ~ rr(X0,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(f95,plain,
! [X0,X1] :
( ~ cc(X1)
| ~ cUnsatisfiable(X0)
| ~ rr(X0,X1) ),
inference(resolution,[],[f79,f82]) ).
fof(f97,plain,
! [X2,X3,X0,X1,X4] :
( ~ cUnsatisfiable(X0)
| ~ rr(X0,X1)
| ~ rs(X1,X2)
| X2 = X3
| ~ rs(X1,X3)
| ~ rr(X4,X1)
| ~ sP0(X4) ),
inference(resolution,[],[f95,f68]) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( ~ rr(i2003_11_14_17_20_36582,X0)
| ~ rs(X0,X1)
| X1 = X2
| ~ rs(X0,X2)
| ~ rr(X3,X0)
| ~ sP0(X3) ),
inference(resolution,[],[f97,f83]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ rs(sK5(i2003_11_14_17_20_36582),X0)
| X0 = X1
| ~ rs(sK5(i2003_11_14_17_20_36582),X1)
| ~ rr(X2,sK5(i2003_11_14_17_20_36582))
| ~ sP0(X2)
| ~ cUnsatisfiable(i2003_11_14_17_20_36582) ),
inference(resolution,[],[f98,f77]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ rs(sK5(i2003_11_14_17_20_36582),X0)
| X0 = X1
| ~ rs(sK5(i2003_11_14_17_20_36582),X1)
| ~ rr(X2,sK5(i2003_11_14_17_20_36582))
| ~ sP0(X2) ),
inference(forward_subsumption_resolution,[],[f100,f83]) ).
fof(f113,definition,
( spl8_3
<=> ! [X2] :
( ~ rr(X2,sK5(i2003_11_14_17_20_36582))
| ~ sP0(X2) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
fof(f114,plain,
( ! [X2] :
( ~ rr(X2,sK5(i2003_11_14_17_20_36582))
| ~ sP0(X2) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,definition,
( spl8_4
<=> ! [X0,X1] :
( ~ rs(sK5(i2003_11_14_17_20_36582),X0)
| ~ rs(sK5(i2003_11_14_17_20_36582),X1)
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
fof(f117,plain,
( ! [X0,X1] :
( ~ rs(sK5(i2003_11_14_17_20_36582),X0)
| ~ rs(sK5(i2003_11_14_17_20_36582),X1)
| X0 = X1 )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f118,plain,
( spl8_3
| spl8_4 ),
inference(avatar_split_clause,[],[f111,f116,f113]) ).
fof(f132,plain,
( ~ sP0(i2003_11_14_17_20_36582)
| ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ spl8_3 ),
inference(resolution,[],[f114,f77]) ).
fof(f133,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f132,f78]) ).
fof(f134,plain,
( $false
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f133,f83]) ).
fof(f135,plain,
~ spl8_3,
inference(avatar_contradiction_clause,[],[f134]) ).
fof(f137,plain,
( ! [X0] :
( ~ rs(sK5(i2003_11_14_17_20_36582),X0)
| sK6(i2003_11_14_17_20_36582) = X0
| ~ cUnsatisfiable(i2003_11_14_17_20_36582) )
| ~ spl8_4 ),
inference(resolution,[],[f117,f75]) ).
fof(f139,plain,
( ! [X0] :
( ~ rs(sK5(i2003_11_14_17_20_36582),X0)
| sK6(i2003_11_14_17_20_36582) = X0 )
| ~ spl8_4 ),
inference(forward_subsumption_resolution,[],[f137,f83]) ).
fof(f143,plain,
( sK7(i2003_11_14_17_20_36582) = sK6(i2003_11_14_17_20_36582)
| ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ spl8_4 ),
inference(resolution,[],[f139,f74]) ).
fof(f145,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ spl8_4 ),
inference(forward_subsumption_resolution,[],[f143,f76]) ).
fof(f146,plain,
( $false
| ~ spl8_4 ),
inference(forward_subsumption_resolution,[],[f145,f83]) ).
fof(f147,plain,
~ spl8_4,
inference(avatar_contradiction_clause,[],[f146]) ).
cnf(s2,plain,
( spl8_3
| spl8_4 ),
inference(sat_conversion,[],[f118]) ).
cnf(s5,plain,
~ spl8_3,
inference(sat_conversion,[],[f135]) ).
cnf(s6,plain,
~ spl8_4,
inference(sat_conversion,[],[f147]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f148,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS101+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.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 13:22:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.44/1.45 % (816929)Detected formulas, will run a generic FOF schedule.
% 3.44/1.45 % (816936)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3169556506:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.45 % (816939)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3710979087:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.45 % (816934)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=615355786:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.45 % (816938)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2970005778:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.45 % (816935)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1152104998:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.45 % (816940)dis-21_1_sil=8000:lcm=predicate:random_seed=1336549473:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.44/1.45 % (816937)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=21418808:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.45 % (816938)Refutation not found, incomplete strategy
% 3.44/1.45 % (816938)------------------------------
% 3.44/1.45 % (816938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.45 % (816938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.45 % (816938)CaDiCaL version: 2.1.3
% 3.44/1.45 % (816938)Termination reason: Refutation not found, incomplete strategy
% 3.44/1.45 % (816938)Time elapsed: 0.0000 s
% 3.44/1.45 % (816938)Peak memory usage: 86 MB
% 3.44/1.45 % (816937)Refutation not found, incomplete strategy
% 3.44/1.45 % (816937)------------------------------
% 3.44/1.45 % (816937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.45 % (816937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.45 % (816937)CaDiCaL version: 2.1.3
% 3.44/1.45 % (816937)Termination reason: Refutation not found, incomplete strategy
% 3.44/1.45 % (816937)Time elapsed: 0.0000 s
% 3.44/1.45 % (816937)Peak memory usage: 86 MB
% 3.44/1.45 % (816939)First to succeed.
% 3.44/1.45 % (816940)Also succeeded, but the first one will report.
% 3.44/1.45 % (816939)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-816929"
% 3.44/1.45 % (816937)------------------------------
% 3.44/1.45 % (816937)------------------------------
% 3.44/1.45 % (816938)------------------------------
% 3.44/1.45 % (816938)------------------------------
% 3.44/1.45 % (816939)Refutation found. Thanks to Tanya!
% 3.44/1.45 % SZS status Unsatisfiable for theBenchmark
% 3.44/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.45 % (816939)------------------------------
% 3.44/1.45 % (816939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.45 % (816939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.45 % (816939)CaDiCaL version: 2.1.3
% 3.44/1.45 % (816939)Termination reason: Refutation
% 3.44/1.45 % (816939)Time elapsed: 0.005 s
% 3.44/1.45 % (816939)Peak memory usage: 90 MB
% 3.44/1.45 % (816939)Instructions burned: 5 (million)
% 3.44/1.45 % (816939)------------------------------
% 3.44/1.45 % (816939)------------------------------
% 3.44/1.45 % (816929)Success in time 0.402 s
% 3.44/1.45 % Vampire exiting
%------------------------------------------------------------------------------