%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS130+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 11:41:43 AM UTC 2026
% Result : Theorem 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 15 unt; 6 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 181 ( 74 ~; 75 |; 15 &)
% ( 13 <=>; 2 =>; 0 <=; 2 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn 27 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
fof(f2,axiom,
! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f3,axiom,
! [X0] :
( cNothing(X0)
=> ~ ? [X1] : rp(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f4,axiom,
! [X0] :
( cNothing(X0)
=> ? [X1] : rp(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f5,conjecture,
( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( cNothing(X0)
<=> cowlNothing(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
fof(f6,negated_conjecture,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( cNothing(X0)
<=> cowlNothing(X0) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) )
& ! [X2] :
( cNothing(X2)
<=> cowlNothing(X2) ) ),
inference(rectify,[],[f6]) ).
fof(f8,plain,
! [X0] :
( ! [X1] : ~ rp(X0,X1)
| ~ cNothing(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f9,plain,
! [X0] :
( ? [X1] : rp(X0,X1)
| ~ cNothing(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X2] :
( cNothing(X2)
<~> cowlNothing(X2) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f11,plain,
! [X0] :
( ( xsd_string(X0)
| xsd_integer(X0) )
& ( ~ xsd_integer(X0)
| ~ xsd_string(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0] :
( rp(X0,sK0(X0))
| ~ cNothing(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f9]) ).
fof(f13,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( ( xsd_integer(X1)
| ~ xsd_string(X1) )
& ( ~ xsd_integer(X1)
| xsd_string(X1) ) )
| ? [X2] :
( ( ~ cowlNothing(X2)
| ~ cNothing(X2) )
& ( cowlNothing(X2)
| cNothing(X2) ) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f14,plain,
( ~ cowlThing(sK1)
| cowlNothing(sK1)
| ( ( xsd_integer(sK2)
| ~ xsd_string(sK2) )
& ( ~ xsd_integer(sK2)
| xsd_string(sK2) ) )
| ( ( ~ cowlNothing(sK3)
| ~ cNothing(sK3) )
& ( cowlNothing(sK3)
| cNothing(sK3) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f13]) ).
fof(f15,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[],[f1]) ).
fof(f17,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f19,plain,
! [X0,X1] :
( ~ rp(X0,X1)
| ~ cNothing(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f20,plain,
! [X0] :
( rp(X0,sK0(X0))
| ~ cNothing(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
( ~ cowlThing(sK1)
| cowlNothing(sK1)
| ~ xsd_integer(sK2)
| xsd_string(sK2)
| cowlNothing(sK3)
| cNothing(sK3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
( ~ cowlThing(sK1)
| cowlNothing(sK1)
| xsd_integer(sK2)
| ~ xsd_string(sK2)
| cowlNothing(sK3)
| cNothing(sK3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,definition,
( spl4_1
<=> cNothing(sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f27,plain,
( cNothing(sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f29,definition,
( spl4_2
<=> cowlNothing(sK3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f30,plain,
( cowlNothing(sK3)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,definition,
( spl4_3
<=> xsd_string(sK2) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f35,definition,
( spl4_4
<=> xsd_integer(sK2) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f36,plain,
( ~ xsd_integer(sK2)
| spl4_4 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f38,definition,
( spl4_5
<=> cowlNothing(sK1) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f39,plain,
( cowlNothing(sK1)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f41,definition,
( spl4_6
<=> cowlThing(sK1) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f42,plain,
( ~ cowlThing(sK1)
| spl4_6 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f43,plain,
( spl4_1
| spl4_2
| spl4_3
| ~ spl4_4
| spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f21,f41,f38,f35,f32,f29,f26]) ).
fof(f48,plain,
( xsd_integer(sK2)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f49,plain,
( spl4_1
| spl4_2
| ~ spl4_3
| spl4_4
| spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f23,f41,f38,f35,f32,f29,f26]) ).
fof(f51,plain,
( $false
| spl4_6 ),
inference(resolution,[],[f16,f42]) ).
fof(f52,plain,
spl4_6,
inference(avatar_contradiction_clause,[],[f51]) ).
fof(f53,plain,
( xsd_string(sK2)
| spl4_4 ),
inference(resolution,[],[f18,f36]) ).
fof(f55,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f53,f35,f32]) ).
fof(f56,plain,
( $false
| ~ spl4_5 ),
inference(resolution,[],[f39,f15]) ).
fof(f57,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f56]) ).
fof(f58,plain,
( ~ xsd_string(sK2)
| ~ spl4_4 ),
inference(resolution,[],[f48,f17]) ).
fof(f59,plain,
! [X0] :
( ~ cNothing(X0)
| ~ cNothing(X0) ),
inference(resolution,[],[f20,f19]) ).
fof(f60,plain,
! [X0] : ~ cNothing(X0),
inference(duplicate_literal_removal,[],[f59]) ).
fof(f61,plain,
( $false
| ~ spl4_1 ),
inference(resolution,[],[f60,f27]) ).
fof(f62,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f61]) ).
fof(f63,plain,
( $false
| ~ spl4_2 ),
inference(resolution,[],[f30,f15]) ).
fof(f64,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f63]) ).
fof(f65,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f58,f35,f32]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3
| ~ spl4_4
| spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
( spl4_1
| spl4_2
| ~ spl4_3
| spl4_4
| spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f49]) ).
cnf(s5,plain,
spl4_6,
inference(sat_conversion,[],[f52]) ).
cnf(s6,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f55]) ).
cnf(s7,plain,
~ spl4_5,
inference(sat_conversion,[],[f57]) ).
cnf(s8,plain,
~ spl4_1,
inference(sat_conversion,[],[f62]) ).
cnf(s9,plain,
~ spl4_2,
inference(sat_conversion,[],[f64]) ).
cnf(s10,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f65]) ).
cnf(s11,plain,
( ~ spl4_3
| spl4_4 ),
inference(rat,[],[s3,s5,s7,s9,s8]) ).
cnf(s12,plain,
( spl4_3
| ~ spl4_4 ),
inference(rat,[],[s1,s5,s7,s9,s8]) ).
cnf(s13,plain,
spl4_3,
inference(rat,[],[s12,s6]) ).
cnf(s14,plain,
~ spl4_4,
inference(rat,[],[s10,s13]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s11,s14,s13]) ).
fof(f66,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS130+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.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 13:27:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/1.50 % (3988935)Detected formulas, will run a generic FOF schedule.
% 0.17/1.50 % (3988943)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=741334647:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.50 % (3988943)Refutation not found, incomplete strategy
% 0.17/1.50 % (3988943)------------------------------
% 0.17/1.50 % (3988943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3988943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3988943)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3988943)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (3988943)Time elapsed: 0.001 s
% 0.17/1.50 % (3988943)Peak memory usage: 87 MB
% 0.17/1.50 % (3988944)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4200157602:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.50 % (3988941)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=1076618737:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.50 % (3988940)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=458438556:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.50 % (3988945)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3134848138:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.50 % (3988942)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=3520260309:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.50 % (3988946)dis-21_1_sil=8000:lcm=predicate:random_seed=2132733585: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)
% 0.17/1.50 % (3988944)Refutation not found, incomplete strategy
% 0.17/1.50 % (3988944)------------------------------
% 0.17/1.50 % (3988944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3988944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3988944)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3988944)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (3988944)Time elapsed: 0.001 s
% 0.17/1.50 % (3988944)Peak memory usage: 88 MB
% 0.17/1.50 % (3988945)Also succeeded, but the first one will report.
% 0.17/1.50 % (3988946)First to succeed.
% 0.17/1.50 % (3988946)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3988935"
% 0.17/1.50 % (3988943)------------------------------
% 0.17/1.50 % (3988943)------------------------------
% 0.17/1.50 % (3988944)------------------------------
% 0.17/1.50 % (3988944)------------------------------
% 0.17/1.50 % (3988946)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Theorem for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (3988946)------------------------------
% 0.17/1.50 % (3988946)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3988946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3988946)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3988946)Termination reason: Refutation
% 0.17/1.50 % (3988946)Time elapsed: 0.003 s
% 0.17/1.50 % (3988946)Peak memory usage: 89 MB
% 0.17/1.50 % (3988946)Instructions burned: 1 (million)
% 0.17/1.50 % (3988946)------------------------------
% 0.17/1.50 % (3988946)------------------------------
% 0.17/1.50 % (3988935)Success in time 0.434 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------