%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KRS169+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 11:42:26 AM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 68 ( 23 unt; 7 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 168 ( 71 ~; 67 |; 16 &)
% ( 12 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 22 ( 0 sgn 20 !; 2 ?)
% 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,
cowlThing(iX),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f4,axiom,
rhasLeader(iX,iY),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f5,axiom,
cowlThing(iY),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f6,axiom,
! [X0,X1] :
( rhasLeader(X0,X1)
<=> rhasHead(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f7,conjecture,
( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).
fof(f8,negated_conjecture,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) )
& cowlThing(iX)
& rhasHead(iX,iY)
& cowlThing(iY) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( rhasLeader(X0,X1)
=> rhasHead(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f11,plain,
! [X0,X1] :
( rhasHead(X0,X1)
| ~ rhasLeader(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f12,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ~ cowlThing(iX)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iY) ),
inference(ennf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[],[f2]) ).
fof(f17,plain,
cowlThing(iX),
inference(cnf_transformation,[],[f3]) ).
fof(f18,plain,
rhasLeader(iX,iY),
inference(cnf_transformation,[],[f4]) ).
fof(f19,plain,
cowlThing(iY),
inference(cnf_transformation,[],[f5]) ).
fof(f20,plain,
! [X0,X1] :
( ~ rhasLeader(X0,X1)
| rhasHead(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| xsd_integer(sK0)
| ~ xsd_string(sK0)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f22,plain,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| ~ xsd_integer(sK0)
| xsd_string(sK0)
| cowlNothing(sK1)
| ~ cowlThing(sK1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,definition,
( spl2_1
<=> cowlThing(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f26,plain,
( ~ cowlThing(sK1)
| spl2_1 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f28,definition,
( spl2_2
<=> cowlNothing(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f30,plain,
( cowlNothing(sK1)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f32,definition,
( spl2_3
<=> xsd_string(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f33,plain,
( xsd_string(sK0)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f34,plain,
( ~ xsd_string(sK0)
| spl2_3 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f36,definition,
( spl2_4
<=> xsd_integer(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f37,plain,
( ~ xsd_integer(sK0)
| spl2_4 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f38,plain,
( xsd_integer(sK0)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f40,definition,
( spl2_5
<=> cowlThing(iX) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f44,definition,
( spl2_6
<=> rhasHead(iX,iY) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f46,plain,
( ~ rhasHead(iX,iY)
| spl2_6 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f48,definition,
( spl2_7
<=> cowlThing(iY) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f51,plain,
( ~ spl2_1
| spl2_2
| ~ spl2_3
| spl2_4
| ~ spl2_5
| ~ spl2_6
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f21,f48,f44,f40,f36,f32,f28,f24]) ).
fof(f52,plain,
( ~ spl2_1
| spl2_2
| spl2_3
| ~ spl2_4
| ~ spl2_5
| ~ spl2_6
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f22,f48,f44,f40,f36,f32,f28,f24]) ).
fof(f53,plain,
spl2_7,
inference(avatar_split_clause,[],[f19,f48]) ).
fof(f54,plain,
spl2_5,
inference(avatar_split_clause,[],[f17,f40]) ).
fof(f55,plain,
( $false
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f26,f14]) ).
fof(f56,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f55]) ).
fof(f58,plain,
rhasHead(iX,iY),
inference(resolution,[],[f20,f18]) ).
fof(f59,plain,
( $false
| spl2_6 ),
inference(forward_subsumption_resolution,[],[f58,f46]) ).
fof(f60,plain,
spl2_6,
inference(avatar_contradiction_clause,[],[f59]) ).
fof(f61,plain,
( xsd_string(sK0)
| spl2_4 ),
inference(resolution,[],[f37,f15]) ).
fof(f62,plain,
( $false
| spl2_3
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f61,f34]) ).
fof(f63,plain,
( spl2_3
| spl2_4 ),
inference(avatar_contradiction_clause,[],[f62]) ).
fof(f64,plain,
( ~ xsd_string(sK0)
| ~ spl2_4 ),
inference(resolution,[],[f38,f16]) ).
fof(f65,plain,
( $false
| ~ spl2_3
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f64,f33]) ).
fof(f66,plain,
( ~ spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f65]) ).
fof(f67,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f30,f13]) ).
fof(f68,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f67]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2
| ~ spl2_3
| spl2_4
| ~ spl2_5
| ~ spl2_6
| ~ spl2_7 ),
inference(sat_conversion,[],[f51]) ).
cnf(s2,plain,
( ~ spl2_1
| spl2_2
| spl2_3
| ~ spl2_4
| ~ spl2_5
| ~ spl2_6
| ~ spl2_7 ),
inference(sat_conversion,[],[f52]) ).
cnf(s3,plain,
spl2_7,
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
spl2_5,
inference(sat_conversion,[],[f54]) ).
cnf(s5,plain,
spl2_1,
inference(sat_conversion,[],[f56]) ).
cnf(s6,plain,
spl2_6,
inference(sat_conversion,[],[f60]) ).
cnf(s7,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f63]) ).
cnf(s8,plain,
( ~ spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f66]) ).
cnf(s9,plain,
~ spl2_2,
inference(sat_conversion,[],[f68]) ).
cnf(s10,plain,
( spl2_3
| ~ spl2_4 ),
inference(rat,[],[s2,s3,s6,s4,s9,s5]) ).
cnf(s11,plain,
( ~ spl2_3
| spl2_4 ),
inference(rat,[],[s1,s3,s6,s4,s9,s5]) ).
cnf(s12,plain,
spl2_3,
inference(rat,[],[s10,s7]) ).
cnf(s13,plain,
~ spl2_4,
inference(rat,[],[s8,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s11,s13,s12]) ).
fof(f69,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS169+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 13:33:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.43 % (2040769)Will run a generic schedule for satisfiability detection.
% 0.10/0.43 % (2040778)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2020428029:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.43 % (2040778) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2040769-2040778"...
% 0.10/0.43 % (2040778)...printing done.
% 0.10/0.43 % (2040778)Refutation found. Thanks to Tanya!
% 0.10/0.43 % SZS status Theorem for theBenchmark
% 0.10/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.43 % (2040778)------------------------------
% 0.10/0.43 % (2040778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.43 % (2040778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.43 % (2040778)CaDiCaL version: 2.1.3
% 0.10/0.43 % (2040778)Termination reason: Refutation
% 0.10/0.43 % (2040778)Time elapsed: 0.001 s
% 0.10/0.43 % (2040778)Peak memory usage: 12 MB
% 0.10/0.43 % (2040778)Instructions burned: 1 (million)
% 0.10/0.43 % (2040769)Success in time 0.025 s
% 0.10/0.43 % Vampire exiting
%------------------------------------------------------------------------------