%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS171+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 : 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 11:41:49 AM UTC 2026
% Result : Theorem 2.54s 1.34s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 12 unt; 6 def)
% Number of atoms : 222 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 247 ( 97 ~; 118 |; 15 &)
% ( 13 <=>; 2 =>; 0 <=; 2 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 39 ( 0 sgn 31 !; 8 ?)
% 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,axiom,
! [X0,X1] :
( rhasHead(X0,X1)
=> rhasLeader(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f4,axiom,
! [X0,X1] :
( rhasLeader(X0,X1)
=> rhasHead(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f5,conjecture,
( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0,X1] :
( rhasLeader(X0,X1)
<=> rhasHead(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).
fof(f6,negated_conjecture,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0,X1] :
( rhasLeader(X0,X1)
<=> rhasHead(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) )
& ! [X2,X3] :
( rhasLeader(X2,X3)
<=> rhasHead(X2,X3) ) ),
inference(rectify,[],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( rhasLeader(X0,X1)
| ~ rhasHead(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f9,plain,
! [X0,X1] :
( rhasHead(X0,X1)
| ~ rhasLeader(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X2,X3] :
( rhasLeader(X2,X3)
<~> rhasHead(X2,X3) ) ),
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] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( ( xsd_integer(X1)
| ~ xsd_string(X1) )
& ( ~ xsd_integer(X1)
| xsd_string(X1) ) )
| ? [X2,X3] :
( ( ~ rhasHead(X2,X3)
| ~ rhasLeader(X2,X3) )
& ( rhasHead(X2,X3)
| rhasLeader(X2,X3) ) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f13,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ( ( xsd_integer(sK1)
| ~ xsd_string(sK1) )
& ( ~ xsd_integer(sK1)
| xsd_string(sK1) ) )
| ( ( ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3) )
& ( rhasHead(sK2,sK3)
| rhasLeader(sK2,sK3) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f12]) ).
fof(f14,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f17,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0,X1] :
( rhasLeader(X0,X1)
| ~ rhasHead(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f19,plain,
! [X0,X1] :
( ~ rhasLeader(X0,X1)
| rhasHead(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| rhasHead(sK2,sK3)
| rhasLeader(sK2,sK3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| rhasHead(sK2,sK3)
| rhasLeader(sK2,sK3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| ~ rhasHead(sK2,sK3)
| ~ rhasLeader(sK2,sK3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,definition,
( spl4_1
<=> rhasLeader(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f26,plain,
( rhasLeader(sK2,sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f28,definition,
( spl4_2
<=> rhasHead(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f31,definition,
( spl4_3
<=> xsd_string(sK1) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f34,definition,
( spl4_4
<=> xsd_integer(sK1) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f35,plain,
( ~ xsd_integer(sK1)
| spl4_4 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f37,definition,
( spl4_5
<=> cowlNothing(sK0) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f38,plain,
( cowlNothing(sK0)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f40,definition,
( spl4_6
<=> cowlThing(sK0) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f41,plain,
( ~ cowlThing(sK0)
| spl4_6 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f42,plain,
( spl4_1
| spl4_2
| spl4_3
| ~ spl4_4
| spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f20,f40,f37,f34,f31,f28,f25]) ).
fof(f43,plain,
( ~ rhasLeader(sK2,sK3)
| spl4_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f45,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_3
| ~ spl4_4
| spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f21,f40,f37,f34,f31,f28,f25]) ).
fof(f47,plain,
( xsd_integer(sK1)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f48,plain,
( spl4_1
| spl4_2
| ~ spl4_3
| spl4_4
| spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f22,f40,f37,f34,f31,f28,f25]) ).
fof(f49,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| spl4_4
| spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f23,f40,f37,f34,f31,f28,f25]) ).
fof(f50,plain,
( $false
| spl4_6 ),
inference(resolution,[],[f15,f41]) ).
fof(f51,plain,
spl4_6,
inference(avatar_contradiction_clause,[],[f50]) ).
fof(f52,plain,
( xsd_string(sK1)
| spl4_4 ),
inference(resolution,[],[f17,f35]) ).
fof(f54,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f52,f34,f31]) ).
fof(f55,plain,
( $false
| ~ spl4_5 ),
inference(resolution,[],[f38,f14]) ).
fof(f56,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f55]) ).
fof(f57,plain,
( ~ xsd_string(sK1)
| ~ spl4_4 ),
inference(resolution,[],[f47,f16]) ).
fof(f58,plain,
( rhasHead(sK2,sK3)
| ~ spl4_1 ),
inference(resolution,[],[f19,f26]) ).
fof(f60,plain,
( spl4_2
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f58,f25,f28]) ).
fof(f61,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f57,f34,f31]) ).
fof(f62,plain,
( ~ rhasHead(sK2,sK3)
| spl4_1 ),
inference(resolution,[],[f43,f18]) ).
fof(f63,plain,
( ~ spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f62,f25,f28]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3
| ~ spl4_4
| spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_3
| ~ spl4_4
| spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f45]) ).
cnf(s3,plain,
( spl4_1
| spl4_2
| ~ spl4_3
| spl4_4
| spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f48]) ).
cnf(s4,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,[],[f51]) ).
cnf(s6,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f54]) ).
cnf(s7,plain,
~ spl4_5,
inference(sat_conversion,[],[f56]) ).
cnf(s8,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f60]) ).
cnf(s9,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f61]) ).
cnf(s10,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f63]) ).
cnf(s11,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| spl4_4 ),
inference(rat,[],[s4,s5,s7]) ).
cnf(s12,plain,
( spl4_1
| spl4_2
| ~ spl4_3
| spl4_4 ),
inference(rat,[],[s3,s5,s7]) ).
cnf(s13,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_3
| ~ spl4_4 ),
inference(rat,[],[s2,s5,s7]) ).
cnf(s14,plain,
( spl4_1
| spl4_2
| spl4_3
| ~ spl4_4 ),
inference(rat,[],[s1,s5,s7]) ).
cnf(s15,plain,
( spl4_3
| spl4_1 ),
inference(rat,[],[s14,s6,s10]) ).
cnf(s16,plain,
spl4_1,
inference(rat,[],[s12,s9,s15,s10]) ).
cnf(s17,plain,
spl4_2,
inference(rat,[],[s8,s16]) ).
cnf(s18,plain,
spl4_3,
inference(rat,[],[s13,s6,s16,s17]) ).
cnf(s19,plain,
~ spl4_4,
inference(rat,[],[s9,s18]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s11,s17,s16,s19,s18]) ).
fof(f64,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS171+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 : n002.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
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 13:36:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.54/1.34 % (3532404)Detected formulas, will run a generic FOF schedule.
% 2.54/1.34 % (3532415)dis-21_1_sil=8000:lcm=predicate:random_seed=3836061032: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)
% 2.54/1.34 % (3532415)First to succeed.
% 2.54/1.34 % (3532415)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3532404"
% 2.54/1.34 % (3532413)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3961481090:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.54/1.34 % (3532411)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=4071417864:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.54/1.34 % (3532412)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=559933835:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.54/1.34 % (3532409)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=3395124198:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.54/1.34 % (3532410)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=942590585:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.54/1.34 % (3532413)Also succeeded, but the first one will report.
% 2.54/1.34 % (3532412)Also succeeded, but the first one will report.
% 2.54/1.34 % (3532414)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2501890506:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.54/1.34 % (3532414)Also succeeded, but the first one will report.
% 2.54/1.34 % (3532415)Refutation found. Thanks to Tanya!
% 2.54/1.34 % SZS status Theorem for theBenchmark
% 2.54/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/1.34 % (3532415)------------------------------
% 2.54/1.34 % (3532415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.34 % (3532415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.34 % (3532415)CaDiCaL version: 2.1.3
% 2.54/1.34 % (3532415)Termination reason: Refutation
% 2.54/1.34 % (3532415)Time elapsed: 0.002 s
% 2.54/1.34 % (3532415)Peak memory usage: 89 MB
% 2.54/1.34 % (3532415)Instructions burned: 2 (million)
% 2.54/1.34 % (3532415)------------------------------
% 2.54/1.34 % (3532415)------------------------------
% 2.54/1.34 % (3532404)Success in time 0.271 s
% 2.54/1.34 % Vampire exiting
%------------------------------------------------------------------------------