%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS142+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 : n013.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 11:41:45 AM UTC 2026
% Result : Theorem 3.52s 1.39s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 5 unt; 1 def)
% Number of atoms : 246 ( 20 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 297 ( 107 ~; 121 |; 49 &)
% ( 4 <=>; 13 =>; 0 <=; 3 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 88 ( 54 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
fof(f9,axiom,
! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f10,axiom,
! [X0] :
( cc(X0)
=> ( ? [X1] : rp(X0,X1)
& ! [X1,X2] :
( ( rp(X0,X1)
& rp(X0,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f11,conjecture,
( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( cc(X0)
=> ? [X1] : rp(X0,X1) )
& ! [X0] :
( cc(X0)
=> ! [X1,X2] :
( ( rp(X0,X1)
& rp(X0,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
fof(f12,negated_conjecture,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( cc(X0)
=> ? [X1] : rp(X0,X1) )
& ! [X0] :
( cc(X0)
=> ! [X1,X2] :
( ( rp(X0,X1)
& rp(X0,X2) )
=> X1 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) )
& ! [X2] :
( cc(X2)
=> ? [X3] : rp(X2,X3) )
& ! [X4] :
( cc(X4)
=> ! [X5,X6] :
( ( rp(X4,X5)
& rp(X4,X6) )
=> X5 = X6 ) ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
! [X0] :
( cc(X0)
=> ( ? [X1] : rp(X0,X1)
& ! [X2,X3] :
( ( rp(X0,X2)
& rp(X0,X3) )
=> X2 = X3 ) ) ),
inference(rectify,[],[f10]) ).
fof(f15,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X2] :
( ! [X3] : ~ rp(X2,X3)
& cc(X2) )
| ? [X4] :
( ? [X5,X6] :
( X5 != X6
& rp(X4,X5)
& rp(X4,X6) )
& cc(X4) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X2] :
( ! [X3] : ~ rp(X2,X3)
& cc(X2) )
| ? [X4] :
( ? [X5,X6] :
( X5 != X6
& rp(X4,X5)
& rp(X4,X6) )
& cc(X4) ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0] :
( ( ? [X1] : rp(X0,X1)
& ! [X2,X3] :
( X2 = X3
| ~ rp(X0,X2)
| ~ rp(X0,X3) ) )
| ~ cc(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0] :
( ( ? [X1] : rp(X0,X1)
& ! [X2,X3] :
( X2 = X3
| ~ rp(X0,X2)
| ~ rp(X0,X3) ) )
| ~ cc(X0) ),
inference(flattening,[],[f17]) ).
fof(f33,definition,
( ? [X4] :
( ? [X5,X6] :
( X5 != X6
& rp(X4,X5)
& rp(X4,X6) )
& cc(X4) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f34,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X2] :
( ! [X3] : ~ rp(X2,X3)
& cc(X2) )
| sP0 ),
inference(definition_folding,[],[f16,f33]) ).
fof(f35,plain,
( ? [X4] :
( ? [X5,X6] :
( X5 != X6
& rp(X4,X5)
& rp(X4,X6) )
& cc(X4) )
| ~ sP0 ),
inference(nnf_transformation,[],[f33]) ).
fof(f36,plain,
( ? [X0] :
( ? [X1,X2] :
( X1 != X2
& rp(X0,X1)
& rp(X0,X2) )
& cc(X0) )
| ~ sP0 ),
inference(rectify,[],[f35]) ).
fof(f37,plain,
( ( sK2 != sK3
& rp(sK1,sK2)
& rp(sK1,sK3)
& cc(sK1) )
| ~ sP0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f36]) ).
fof(f38,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( ( xsd_integer(X1)
| ~ xsd_string(X1) )
& ( ~ xsd_integer(X1)
| xsd_string(X1) ) )
| ? [X2] :
( ! [X3] : ~ rp(X2,X3)
& cc(X2) )
| sP0 ),
inference(nnf_transformation,[],[f34]) ).
fof(f39,plain,
( ~ cowlThing(sK4)
| cowlNothing(sK4)
| ( ( xsd_integer(sK5)
| ~ xsd_string(sK5) )
& ( ~ xsd_integer(sK5)
| xsd_string(sK5) ) )
| ( ! [X3] : ~ rp(sK6,X3)
& cc(sK6) )
| sP0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f38]) ).
fof(f40,plain,
! [X0] :
( ( rp(X0,sK7(X0))
& ! [X2,X3] :
( X2 = X3
| ~ rp(X0,X2)
| ~ rp(X0,X3) ) )
| ~ cc(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f18]) ).
fof(f41,plain,
! [X0] :
( ( xsd_string(X0)
| xsd_integer(X0) )
& ( ~ xsd_integer(X0)
| ~ xsd_string(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f42,plain,
( cc(sK1)
| ~ sP0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f43,plain,
( rp(sK1,sK3)
| ~ sP0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f44,plain,
( rp(sK1,sK2)
| ~ sP0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f45,plain,
( sK2 != sK3
| ~ sP0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f46,plain,
( xsd_string(sK5)
| cowlNothing(sK4)
| ~ xsd_integer(sK5)
| ~ cowlThing(sK4)
| cc(sK6)
| sP0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f47,plain,
! [X3] :
( ~ rp(sK6,X3)
| cowlNothing(sK4)
| ~ xsd_integer(sK5)
| xsd_string(sK5)
| ~ cowlThing(sK4)
| sP0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f48,plain,
( xsd_integer(sK5)
| cowlNothing(sK4)
| ~ cowlThing(sK4)
| ~ xsd_string(sK5)
| cc(sK6)
| sP0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f49,plain,
! [X3] :
( ~ rp(sK6,X3)
| cowlNothing(sK4)
| xsd_integer(sK5)
| ~ xsd_string(sK5)
| ~ cowlThing(sK4)
| sP0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f50,plain,
! [X2,X3,X0] :
( ~ rp(X0,X3)
| ~ rp(X0,X2)
| X2 = X3
| ~ cc(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f51,plain,
! [X0] :
( rp(X0,sK7(X0))
| ~ cc(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f53,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f54,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0] :
( ~ xsd_string(X0)
| ~ xsd_integer(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f60,plain,
! [X0] :
( xsd_string(X0)
| xsd_integer(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f70,plain,
( ~ xsd_integer(sK5)
| cowlNothing(sK4)
| ~ xsd_integer(sK5)
| ~ cowlThing(sK4)
| cc(sK6)
| sP0 ),
inference(resolution,[],[f59,f46]) ).
fof(f71,plain,
( ~ xsd_integer(sK5)
| cowlNothing(sK4)
| ~ cowlThing(sK4)
| cc(sK6)
| sP0 ),
inference(duplicate_literal_removal,[],[f70]) ).
fof(f72,plain,
( ~ xsd_integer(sK5)
| ~ cowlThing(sK4)
| cc(sK6)
| sP0 ),
inference(forward_subsumption_resolution,[],[f71,f53]) ).
fof(f73,plain,
( cc(sK6)
| ~ xsd_integer(sK5)
| sP0 ),
inference(forward_subsumption_resolution,[],[f72,f54]) ).
fof(f75,plain,
( ~ cc(sK6)
| cowlNothing(sK4)
| xsd_integer(sK5)
| ~ xsd_string(sK5)
| ~ cowlThing(sK4)
| sP0 ),
inference(resolution,[],[f51,f49]) ).
fof(f76,plain,
( ~ cc(sK6)
| cowlNothing(sK4)
| ~ xsd_integer(sK5)
| xsd_string(sK5)
| ~ cowlThing(sK4)
| sP0 ),
inference(resolution,[],[f51,f47]) ).
fof(f77,plain,
( ~ cc(sK6)
| cowlNothing(sK4)
| ~ xsd_integer(sK5)
| ~ cowlThing(sK4)
| sP0 ),
inference(forward_subsumption_resolution,[],[f76,f59]) ).
fof(f78,plain,
( cowlNothing(sK4)
| xsd_integer(sK5)
| ~ xsd_string(sK5)
| ~ cowlThing(sK4)
| sP0 ),
inference(forward_subsumption_resolution,[],[f75,f48]) ).
fof(f79,plain,
( cowlNothing(sK4)
| ~ xsd_integer(sK5)
| ~ cowlThing(sK4)
| sP0 ),
inference(forward_subsumption_resolution,[],[f77,f73]) ).
fof(f80,plain,
( xsd_integer(sK5)
| ~ xsd_string(sK5)
| ~ cowlThing(sK4)
| sP0 ),
inference(forward_subsumption_resolution,[],[f78,f53]) ).
fof(f81,plain,
( ~ xsd_integer(sK5)
| ~ cowlThing(sK4)
| sP0 ),
inference(forward_subsumption_resolution,[],[f79,f53]) ).
fof(f82,plain,
( ~ xsd_string(sK5)
| ~ cowlThing(sK4)
| sP0 ),
inference(forward_subsumption_resolution,[],[f80,f59]) ).
fof(f83,plain,
( ~ xsd_integer(sK5)
| sP0 ),
inference(forward_subsumption_resolution,[],[f81,f54]) ).
fof(f84,plain,
( ~ xsd_string(sK5)
| sP0 ),
inference(forward_subsumption_resolution,[],[f82,f54]) ).
fof(f90,plain,
( sP0
| xsd_integer(sK5) ),
inference(resolution,[],[f84,f60]) ).
fof(f92,plain,
sP0,
inference(forward_subsumption_resolution,[],[f90,f83]) ).
fof(f94,plain,
! [X0] :
( ~ rp(sK1,X0)
| sK2 = X0
| ~ cc(sK1)
| ~ sP0 ),
inference(resolution,[],[f50,f44]) ).
fof(f98,plain,
! [X0] :
( ~ rp(sK1,X0)
| sK2 = X0
| ~ sP0 ),
inference(forward_subsumption_resolution,[],[f94,f42]) ).
fof(f100,plain,
! [X0] :
( ~ rp(sK1,X0)
| sK2 = X0 ),
inference(forward_subsumption_resolution,[],[f98,f92]) ).
fof(f101,plain,
( sK2 = sK3
| ~ sP0 ),
inference(resolution,[],[f100,f43]) ).
fof(f104,plain,
~ sP0,
inference(forward_subsumption_resolution,[],[f101,f45]) ).
fof(f105,plain,
$false,
inference(forward_subsumption_resolution,[],[f104,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS142+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 : n013.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 13:28:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 3.52/1.39 % (231480)Detected formulas, will run a generic FOF schedule.
% 3.52/1.39 % (231487)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=2726312552:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.52/1.39 % (231485)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=2940199369:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.52/1.39 % (231486)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=345170146:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.52/1.39 % (231489)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2153739967:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.52/1.39 % (231488)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=896963474:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.52/1.39 % (231491)dis-21_1_sil=8000:lcm=predicate:random_seed=2971645890: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)
% 3.52/1.39 % (231490)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1576674622:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.52/1.39 % (231488)Refutation not found, incomplete strategy
% 3.52/1.39 % (231488)------------------------------
% 3.52/1.39 % (231488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.39 % (231489)First to succeed.
% 3.52/1.39 % (231488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.39 % (231488)CaDiCaL version: 2.1.3
% 3.52/1.39 % (231488)Termination reason: Refutation not found, incomplete strategy
% 3.52/1.39 % (231488)Time elapsed: 0.002 s
% 3.52/1.39 % (231488)Peak memory usage: 88 MB
% 3.52/1.39 % (231488)Instructions burned: 1 (million)
% 3.52/1.39 % (231491)Also succeeded, but the first one will report.
% 3.52/1.39 % (231490)Also succeeded, but the first one will report.
% 3.52/1.39 % (231489)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-231480"
% 3.52/1.39 % (231488)------------------------------
% 3.52/1.39 % (231488)------------------------------
% 3.52/1.39 % (231489)Refutation found. Thanks to Tanya!
% 3.52/1.39 % SZS status Theorem for theBenchmark
% 3.52/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.39 % (231489)------------------------------
% 3.52/1.39 % (231489)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.39 % (231489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.39 % (231489)CaDiCaL version: 2.1.3
% 3.52/1.39 % (231489)Termination reason: Refutation
% 3.52/1.39 % (231489)Time elapsed: 0.003 s
% 3.52/1.39 % (231489)Peak memory usage: 88 MB
% 3.52/1.39 % (231489)Instructions burned: 3 (million)
% 3.52/1.39 % (231489)------------------------------
% 3.52/1.39 % (231489)------------------------------
% 3.52/1.39 % (231480)Success in time 0.436 s
% 3.52/1.39 % Vampire exiting
%------------------------------------------------------------------------------