%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS134+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 : n002.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 11:41:44 AM UTC 2026
% Result : Theorem 3.58s 6.69s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 8 unt; 4 def)
% Number of atoms : 178 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 196 ( 80 ~; 81 |; 19 &)
% ( 8 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 33 ( 0 sgn 25 !; 8 ?)
% 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,X1] :
( rprop(X0,X1)
=> cA(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f4,conjecture,
( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( cowlThing(X0)
=> ! [X1] :
( rprop(X0,X1)
=> cA(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
fof(f5,negated_conjecture,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( cowlThing(X0)
=> ! [X1] :
( rprop(X0,X1)
=> cA(X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) )
& ! [X2] :
( cowlThing(X2)
=> ! [X3] :
( rprop(X2,X3)
=> cA(X3) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X2] :
( ? [X3] :
( ~ cA(X3)
& rprop(X2,X3) )
& cowlThing(X2) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( cA(X1)
| ~ rprop(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f9,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( ( xsd_integer(X1)
| ~ xsd_string(X1) )
& ( ~ xsd_integer(X1)
| xsd_string(X1) ) )
| ? [X2] :
( ? [X3] :
( ~ cA(X3)
& rprop(X2,X3) )
& cowlThing(X2) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f10,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ( ( xsd_integer(sK1)
| ~ xsd_string(sK1) )
& ( ~ xsd_integer(sK1)
| xsd_string(sK1) ) )
| ( ~ cA(sK3)
& rprop(sK2,sK3)
& cowlThing(sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f9]) ).
fof(f11,plain,
! [X0] :
( ( xsd_string(X0)
| xsd_integer(X0) )
& ( ~ xsd_integer(X0)
| ~ xsd_string(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f13,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| rprop(sK2,sK3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f14,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| ~ cA(sK3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| rprop(sK2,sK3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| ~ cA(sK3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[],[f1]) ).
fof(f19,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[],[f1]) ).
fof(f20,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
! [X0,X1] :
( ~ rprop(X0,X1)
| cA(X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f23,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| rprop(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f13,f20]) ).
fof(f24,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| ~ cA(sK3) ),
inference(forward_subsumption_resolution,[],[f14,f20]) ).
fof(f25,plain,
( cowlNothing(sK0)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| rprop(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f16,f19]) ).
fof(f26,plain,
( cowlNothing(sK0)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| ~ cA(sK3) ),
inference(forward_subsumption_resolution,[],[f17,f19]) ).
fof(f27,plain,
( cowlNothing(sK0)
| ~ xsd_integer(sK1)
| rprop(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f23,f19]) ).
fof(f28,plain,
( cowlNothing(sK0)
| ~ xsd_integer(sK1)
| ~ cA(sK3) ),
inference(forward_subsumption_resolution,[],[f24,f19]) ).
fof(f29,plain,
( xsd_integer(sK1)
| ~ xsd_string(sK1)
| rprop(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f25,f18]) ).
fof(f30,plain,
( xsd_integer(sK1)
| ~ xsd_string(sK1)
| ~ cA(sK3) ),
inference(forward_subsumption_resolution,[],[f26,f18]) ).
fof(f31,plain,
( ~ xsd_integer(sK1)
| rprop(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f27,f18]) ).
fof(f32,plain,
( ~ xsd_integer(sK1)
| ~ cA(sK3) ),
inference(forward_subsumption_resolution,[],[f28,f18]) ).
fof(f33,plain,
( ~ xsd_string(sK1)
| rprop(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f29,f20]) ).
fof(f34,plain,
( ~ xsd_string(sK1)
| ~ cA(sK3) ),
inference(forward_subsumption_resolution,[],[f30,f20]) ).
fof(f36,definition,
( spl4_1
<=> rprop(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f38,plain,
( rprop(sK2,sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f40,definition,
( spl4_2
<=> xsd_integer(sK1) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f42,plain,
( ~ xsd_integer(sK1)
| spl4_2 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f43,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f31,f40,f36]) ).
fof(f45,definition,
( spl4_3
<=> cA(sK3) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f47,plain,
( ~ cA(sK3)
| spl4_3 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f48,plain,
( ~ spl4_3
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f32,f40,f45]) ).
fof(f50,definition,
( spl4_4
<=> xsd_string(sK1) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f52,plain,
( ~ xsd_string(sK1)
| spl4_4 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,plain,
( spl4_1
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f33,f50,f36]) ).
fof(f54,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f34,f50,f45]) ).
fof(f55,plain,
( xsd_string(sK1)
| spl4_2 ),
inference(resolution,[],[f42,f21]) ).
fof(f56,plain,
( $false
| spl4_2
| spl4_4 ),
inference(forward_subsumption_resolution,[],[f55,f52]) ).
fof(f57,plain,
( spl4_2
| spl4_4 ),
inference(avatar_contradiction_clause,[],[f56]) ).
fof(f58,plain,
( cA(sK3)
| ~ spl4_1 ),
inference(resolution,[],[f38,f22]) ).
fof(f59,plain,
( $false
| ~ spl4_1
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f58,f47]) ).
fof(f60,plain,
( ~ spl4_1
| spl4_3 ),
inference(avatar_contradiction_clause,[],[f59]) ).
cnf(s1,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s2,plain,
( ~ spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f48]) ).
cnf(s3,plain,
( spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f54]) ).
cnf(s5,plain,
( spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f57]) ).
cnf(s6,plain,
( ~ spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f60]) ).
cnf(s7,plain,
spl4_1,
inference(rat,[],[s5,s1,s3]) ).
cnf(s8,plain,
spl4_3,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
~ spl4_4,
inference(rat,[],[s4,s8]) ).
cnf(s10,plain,
~ spl4_2,
inference(rat,[],[s2,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s5,s9,s10]) ).
fof(f61,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS134+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.59 % Computer : n002.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.59 % CPULimit : 300
% 0.11/5.59 % WCLimit : 300
% 0.11/5.59 % DateTime : Sun Sep 27 13:30:59 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.63 Running first-order theorem proving
% 0.15/5.63 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
% 3.58/6.69 % (3531164)Detected formulas, will run a generic FOF schedule.
% 3.58/6.69 % (3531201)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=121006668:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.58/6.69 % (3531202)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=2834500477:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.58/6.69 % (3531200)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=69140932:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.58/6.69 % (3531203)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2460812787:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.58/6.69 % (3531203)First to succeed.
% 3.58/6.69 % (3531203)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3531164"
% 3.58/6.69 % (3531205)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2890106485:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.58/6.69 % (3531206)dis-21_1_sil=8000:lcm=predicate:random_seed=2466427274: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)
% 3.58/6.69 % (3531204)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2412768328:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.58/6.69 % (3531204)Also succeeded, but the first one will report.
% 3.58/6.69 % (3531205)Also succeeded, but the first one will report.
% 3.58/6.69 % (3531206)Also succeeded, but the first one will report.
% 3.58/6.69 % (3531203)Refutation found. Thanks to Tanya!
% 3.58/6.69 % SZS status Theorem for theBenchmark
% 3.58/6.69 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/6.69 % (3531203)------------------------------
% 3.58/6.69 % (3531203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/6.69 % (3531203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/6.69 % (3531203)CaDiCaL version: 2.1.3
% 3.58/6.69 % (3531203)Termination reason: Refutation
% 3.58/6.69 % (3531203)Time elapsed: 0.003 s
% 3.58/6.69 % (3531203)Peak memory usage: 89 MB
% 3.58/6.69 % (3531203)Instructions burned: 2 (million)
% 3.58/6.69 % (3531203)------------------------------
% 3.58/6.69 % (3531203)------------------------------
% 3.58/6.69 % (3531164)Success in time 0.43 s
% 3.58/6.69 % Vampire exiting
%------------------------------------------------------------------------------