%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS105+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 : n019.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 11:41:40 AM UTC 2026
% Result : Unsatisfiable 3.70s 1.44s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 10 unt; 2 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 93 ( 42 ~; 34 |; 2 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 46 ( 0 sgn 40 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( cUnsatisfiable(X0)
=> cdxcomp(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f4,axiom,
! [X0] :
( cUnsatisfiable(X0)
=> cc(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f5,axiom,
! [X0] :
( cc(X0)
=> ! [X1] :
( rr(X0,X1)
=> cc(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f6,axiom,
! [X0] :
( cd(X0)
<=> ~ ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f7,axiom,
! [X0] :
( cdxcomp(X0)
<=> ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
fof(f8,axiom,
! [X0] :
( ca_Ax2(X0)
<=> ! [X1] :
( rr(X0,X1)
=> cc(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
fof(f9,axiom,
! [X0] :
( ca_Ax2(X0)
=> cd(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
fof(f10,axiom,
cUnsatisfiable(i2003_11_14_17_20_53634),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
fof(f11,plain,
! [X0] :
( ! [X1] :
( rr(X0,X1)
=> cc(X1) )
=> ca_Ax2(X0) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f12,plain,
! [X0] :
( cd(X0)
=> ~ ? [X1] : ra_Px1(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f13,plain,
! [X0] :
( cdxcomp(X0)
=> ? [X1] : ra_Px1(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f16,plain,
! [X0] :
( cdxcomp(X0)
| ~ cUnsatisfiable(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0] :
( cc(X0)
| ~ cUnsatisfiable(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f18,plain,
! [X0] :
( ! [X1] :
( cc(X1)
| ~ rr(X0,X1) )
| ~ cc(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f19,plain,
! [X0] :
( ! [X1] : ~ ra_Px1(X0,X1)
| ~ cd(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f20,plain,
! [X0] :
( ? [X1] : ra_Px1(X0,X1)
| ~ cdxcomp(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0] :
( ca_Ax2(X0)
| ? [X1] :
( ~ cc(X1)
& rr(X0,X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f22,plain,
! [X0] :
( cd(X0)
| ~ ca_Ax2(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f23,plain,
! [X0] :
( ra_Px1(X0,sK0(X0))
| ~ cdxcomp(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f20]) ).
fof(f24,plain,
! [X0] :
( ca_Ax2(X0)
| ( ~ cc(sK1(X0))
& rr(X0,sK1(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f21]) ).
fof(f25,plain,
! [X0] :
( cdxcomp(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| cc(X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X0,X1] :
( ~ rr(X0,X1)
| cc(X1)
| ~ cc(X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cd(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X0] :
( ra_Px1(X0,sK0(X0))
| ~ cdxcomp(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f30,plain,
! [X0] :
( rr(X0,sK1(X0))
| ca_Ax2(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f31,plain,
! [X0] :
( ca_Ax2(X0)
| ~ cc(sK1(X0)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f32,plain,
! [X0] :
( cd(X0)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
cUnsatisfiable(i2003_11_14_17_20_53634),
inference(cnf_transformation,[],[f10]) ).
fof(f34,plain,
cc(i2003_11_14_17_20_53634),
inference(resolution,[],[f26,f33]) ).
fof(f35,plain,
! [X0] :
( ~ cd(X0)
| ~ cdxcomp(X0) ),
inference(resolution,[],[f29,f28]) ).
fof(f36,plain,
! [X0] :
( ~ cdxcomp(X0)
| ~ ca_Ax2(X0) ),
inference(resolution,[],[f35,f32]) ).
fof(f37,plain,
! [X0] :
( ~ ca_Ax2(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f36,f25]) ).
fof(f38,plain,
! [X0] :
( ca_Ax2(X0)
| ~ cc(X0)
| cc(sK1(X0)) ),
inference(resolution,[],[f27,f30]) ).
fof(f39,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ~ cc(sK1(X0)) ),
inference(resolution,[],[f37,f31]) ).
fof(f40,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| cc(sK1(X0))
| ~ cc(X0) ),
inference(resolution,[],[f38,f37]) ).
fof(f41,plain,
~ cc(sK1(i2003_11_14_17_20_53634)),
inference(resolution,[],[f39,f33]) ).
fof(f42,plain,
( cc(sK1(i2003_11_14_17_20_53634))
| ~ cc(i2003_11_14_17_20_53634) ),
inference(resolution,[],[f40,f33]) ).
fof(f44,definition,
( spl2_1
<=> cc(i2003_11_14_17_20_53634) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f45,plain,
( ~ cc(i2003_11_14_17_20_53634)
| spl2_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,definition,
( spl2_2
<=> cc(sK1(i2003_11_14_17_20_53634)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f48,plain,
( cc(sK1(i2003_11_14_17_20_53634))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f49,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f42,f47,f44]) ).
fof(f50,plain,
( $false
| spl2_1 ),
inference(resolution,[],[f45,f34]) ).
fof(f51,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f50]) ).
fof(f52,plain,
( $false
| ~ spl2_2 ),
inference(resolution,[],[f48,f41]) ).
fof(f53,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f52]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f51]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f54,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS105+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n019.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 27 13:24:34 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 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
% 3.70/1.44 % (3097560)Detected formulas, will run a generic FOF schedule.
% 3.70/1.44 % (3097569)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2516214351:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.70/1.44 % (3097569)Refutation not found, incomplete strategy
% 3.70/1.44 % (3097569)------------------------------
% 3.70/1.44 % (3097569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.44 % (3097569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.44 % (3097569)CaDiCaL version: 2.1.3
% 3.70/1.44 % (3097569)Termination reason: Refutation not found, incomplete strategy
% 3.70/1.44 % (3097569)Time elapsed: 0.0000 s
% 3.70/1.44 % (3097569)Peak memory usage: 86 MB
% 3.70/1.44 % (3097568)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=37688261:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.70/1.44 % (3097567)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=202980943:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.70/1.44 % (3097565)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=167200772:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.70/1.44 % (3097566)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=3386526493:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.70/1.44 % (3097568)Refutation not found, incomplete strategy
% 3.70/1.44 % (3097568)------------------------------
% 3.70/1.44 % (3097568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.44 % (3097568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.44 % (3097568)CaDiCaL version: 2.1.3
% 3.70/1.44 % (3097568)Termination reason: Refutation not found, incomplete strategy
% 3.70/1.44 % (3097568)Time elapsed: 0.0000 s
% 3.70/1.44 % (3097568)Peak memory usage: 86 MB
% 3.70/1.44 % (3097571)dis-21_1_sil=8000:lcm=predicate:random_seed=1681811708: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)
% 3.70/1.44 % (3097571)First to succeed.
% 3.70/1.44 % (3097571)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3097560"
% 3.70/1.44 % (3097570)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=646727518:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.70/1.44 % (3097570)Also succeeded, but the first one will report.
% 3.70/1.44 % (3097569)------------------------------
% 3.70/1.44 % (3097569)------------------------------
% 3.70/1.44 % (3097568)------------------------------
% 3.70/1.44 % (3097568)------------------------------
% 3.70/1.44 % (3097579)lrs+10_1_sil=8000:sp=occurrence:random_seed=3256637234:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.70/1.44 % (3097579)Refutation not found, incomplete strategy
% 3.70/1.44 % (3097579)------------------------------
% 3.70/1.44 % (3097579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.44 % (3097579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.44 % (3097579)CaDiCaL version: 2.1.3
% 3.70/1.44 % (3097579)Termination reason: Refutation not found, incomplete strategy
% 3.70/1.44 % (3097579)Time elapsed: 0.0000 s
% 3.70/1.44 % (3097579)Peak memory usage: 86 MB
% 3.70/1.44 % (3097571)Refutation found. Thanks to Tanya!
% 3.70/1.44 % SZS status Unsatisfiable for theBenchmark
% 3.70/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.70/1.44 % (3097571)------------------------------
% 3.70/1.44 % (3097571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.44 % (3097571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.44 % (3097571)CaDiCaL version: 2.1.3
% 3.70/1.44 % (3097571)Termination reason: Refutation
% 3.70/1.44 % (3097571)Time elapsed: 0.003 s
% 3.70/1.44 % (3097571)Peak memory usage: 89 MB
% 3.70/1.44 % (3097571)Instructions burned: 1 (million)
% 3.70/1.44 % (3097571)------------------------------
% 3.70/1.44 % (3097571)------------------------------
% 3.70/1.44 % (3097560)Success in time 0.454 s
% 3.70/1.44 % Vampire exiting
%------------------------------------------------------------------------------