%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS168+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 : n010.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 11:41:49 AM UTC 2026
% Result : Theorem 3.38s 1.34s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 6 unt; 0 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 265 ( 108 ~; 120 |; 28 &)
% ( 7 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 25 ( 16 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
fof(f2,axiom,
! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f3,conjecture,
( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( ( ~ cB(X0)
& ~ cA(X0) )
<=> ~ ( cA(X0)
| cB(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).
fof(f4,negated_conjecture,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( ( ~ cB(X0)
& ~ cA(X0) )
<=> ~ ( cA(X0)
| cB(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) )
& ! [X2] :
( ( ~ cB(X2)
& ~ cA(X2) )
<=> ~ ( cA(X2)
| cB(X2) ) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X2] :
( ( ~ cB(X2)
& ~ cA(X2) )
<~> ( ~ cA(X2)
& ~ cB(X2) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f7,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( ( xsd_integer(X1)
| ~ xsd_string(X1) )
& ( ~ xsd_integer(X1)
| xsd_string(X1) ) )
| ? [X2] :
( ( cA(X2)
| cB(X2)
| cB(X2)
| cA(X2) )
& ( ( ~ cA(X2)
& ~ cB(X2) )
| ( ~ cB(X2)
& ~ cA(X2) ) ) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f8,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( ( xsd_integer(X1)
| ~ xsd_string(X1) )
& ( ~ xsd_integer(X1)
| xsd_string(X1) ) )
| ? [X2] :
( ( cA(X2)
| cB(X2)
| cB(X2)
| cA(X2) )
& ( ( ~ cA(X2)
& ~ cB(X2) )
| ( ~ cB(X2)
& ~ cA(X2) ) ) ) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ( ( xsd_integer(sK1)
| ~ xsd_string(sK1) )
& ( ~ xsd_integer(sK1)
| xsd_string(sK1) ) )
| ( ( cA(sK2)
| cB(sK2)
| cB(sK2)
| cA(sK2) )
& ( ( ~ cA(sK2)
& ~ cB(sK2) )
| ( ~ cB(sK2)
& ~ cA(sK2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
fof(f10,plain,
! [X0] :
( ( xsd_string(X0)
| xsd_integer(X0) )
& ( ~ xsd_integer(X0)
| ~ xsd_string(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f12,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| ~ cB(sK2)
| ~ cB(sK2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f13,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| ~ cA(sK2)
| ~ cA(sK2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cA(sK2)
| cB(sK2)
| cB(sK2)
| cA(sK2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| ~ cB(sK2)
| ~ cB(sK2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f18,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| ~ cA(sK2)
| ~ cA(sK2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cA(sK2)
| cB(sK2)
| cB(sK2)
| cA(sK2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f21,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[],[f1]) ).
fof(f22,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[],[f1]) ).
fof(f23,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f25,plain,
( xsd_string(sK1)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0)
| ~ cB(sK2) ),
inference(duplicate_literal_removal,[],[f12]) ).
fof(f26,plain,
( xsd_string(sK1)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0)
| ~ cA(sK2) ),
inference(duplicate_literal_removal,[],[f13]) ).
fof(f27,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cA(sK2)
| cB(sK2) ),
inference(duplicate_literal_removal,[],[f15]) ).
fof(f28,plain,
( xsd_integer(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0)
| ~ xsd_string(sK1)
| ~ cB(sK2) ),
inference(duplicate_literal_removal,[],[f17]) ).
fof(f29,plain,
( xsd_integer(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0)
| ~ xsd_string(sK1)
| ~ cA(sK2) ),
inference(duplicate_literal_removal,[],[f18]) ).
fof(f30,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cA(sK2)
| cB(sK2) ),
inference(duplicate_literal_removal,[],[f20]) ).
fof(f31,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cB(sK2) ),
inference(forward_subsumption_resolution,[],[f27,f26]) ).
fof(f32,plain,
( xsd_string(sK1)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0) ),
inference(forward_subsumption_resolution,[],[f31,f25]) ).
fof(f33,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cB(sK2) ),
inference(forward_subsumption_resolution,[],[f30,f29]) ).
fof(f34,plain,
( xsd_integer(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0)
| ~ xsd_string(sK1) ),
inference(forward_subsumption_resolution,[],[f33,f28]) ).
fof(f35,plain,
( ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0)
| ~ xsd_string(sK1) ),
inference(resolution,[],[f23,f34]) ).
fof(f40,plain,
( ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(duplicate_literal_removal,[],[f35]) ).
fof(f43,plain,
( ~ xsd_string(sK1)
| ~ cowlThing(sK0) ),
inference(forward_subsumption_resolution,[],[f40,f21]) ).
fof(f46,plain,
~ xsd_string(sK1),
inference(forward_subsumption_resolution,[],[f43,f22]) ).
fof(f47,plain,
( cowlNothing(sK0)
| ~ xsd_integer(sK1)
| ~ cowlThing(sK0) ),
inference(resolution,[],[f46,f32]) ).
fof(f52,plain,
( ~ xsd_integer(sK1)
| ~ cowlThing(sK0) ),
inference(forward_subsumption_resolution,[],[f47,f21]) ).
fof(f55,plain,
~ xsd_integer(sK1),
inference(forward_subsumption_resolution,[],[f52,f22]) ).
fof(f60,plain,
xsd_string(sK1),
inference(resolution,[],[f55,f24]) ).
fof(f61,plain,
$false,
inference(forward_subsumption_resolution,[],[f60,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS168+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 : n010.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 13:33:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.38/1.34 % (972019)Detected formulas, will run a generic FOF schedule.
% 3.38/1.34 % (972026)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=992643215:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.38/1.34 % (972025)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=3899521035:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.38/1.34 % (972029)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=77421998:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.38/1.34 % (972028)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1148684770:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.38/1.34 % (972024)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=3524398990:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.38/1.34 % (972027)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1400806713:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.38/1.34 % (972030)dis-21_1_sil=8000:lcm=predicate:random_seed=1100302864: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)
% 3.38/1.34 % (972028)First to succeed.
% 3.38/1.34 % (972030)Also succeeded, but the first one will report.
% 3.38/1.34 % (972029)Also succeeded, but the first one will report.
% 3.38/1.34 % (972027)Also succeeded, but the first one will report.
% 3.38/1.34 % (972028)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-972019"
% 3.38/1.34 % (972028)Refutation found. Thanks to Tanya!
% 3.38/1.34 % SZS status Theorem for theBenchmark
% 3.38/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/1.34 % (972028)------------------------------
% 3.38/1.34 % (972028)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.34 % (972028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.34 % (972028)CaDiCaL version: 2.1.3
% 3.38/1.34 % (972028)Termination reason: Refutation
% 3.38/1.34 % (972028)Time elapsed: 0.002 s
% 3.38/1.34 % (972028)Peak memory usage: 88 MB
% 3.38/1.34 % (972028)Instructions burned: 1 (million)
% 3.38/1.34 % (972028)------------------------------
% 3.38/1.34 % (972028)------------------------------
% 3.38/1.34 % (972019)Success in time 0.409 s
% 3.38/1.34 % Vampire exiting
%------------------------------------------------------------------------------