%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KRS166+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 0.12s 0.46s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 80 ( 12 unt; 6 def)
% Number of atoms : 242 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 267 ( 105 ~; 130 |; 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; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 28 ( 0 sgn 22 !; 6 ?)
% 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] :
( cAutomobile(X0)
=> cCar(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f4,axiom,
! [X0] :
( cCar(X0)
=> cAutomobile(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f5,conjecture,
( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( cCar(X0)
<=> cAutomobile(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
fof(f6,negated_conjecture,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( cCar(X0)
<=> cAutomobile(X0) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) )
& ! [X2] :
( cCar(X2)
<=> cAutomobile(X2) ) ),
inference(rectify,[],[f6]) ).
fof(f8,plain,
! [X0] :
( cCar(X0)
| ~ cAutomobile(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f9,plain,
! [X0] :
( cAutomobile(X0)
| ~ cCar(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X2] :
( cCar(X2)
<~> cAutomobile(X2) ) ),
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] :
( ( ~ cAutomobile(X2)
| ~ cCar(X2) )
& ( cAutomobile(X2)
| cCar(X2) ) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f13,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ( ( xsd_integer(sK1)
| ~ xsd_string(sK1) )
& ( ~ xsd_integer(sK1)
| xsd_string(sK1) ) )
| ( ( ~ cAutomobile(sK2)
| ~ cCar(sK2) )
& ( cAutomobile(sK2)
| cCar(sK2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[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] :
( ~ cAutomobile(X0)
| cCar(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f19,plain,
! [X0] :
( ~ cCar(X0)
| cAutomobile(X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cAutomobile(sK2)
| cCar(sK2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| ~ cAutomobile(sK2)
| ~ cCar(sK2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cAutomobile(sK2)
| cCar(sK2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
( ~ cowlThing(sK0)
| cowlNothing(sK0)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| ~ cAutomobile(sK2)
| ~ cCar(sK2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,definition,
( spl3_1
<=> cCar(sK2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f26,plain,
( ~ cCar(sK2)
| spl3_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f27,plain,
( cCar(sK2)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f29,definition,
( spl3_2
<=> cAutomobile(sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f30,plain,
( ~ cAutomobile(sK2)
| spl3_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f31,plain,
( cAutomobile(sK2)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f33,definition,
( spl3_3
<=> xsd_string(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f34,plain,
( ~ xsd_string(sK1)
| spl3_3 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f35,plain,
( xsd_string(sK1)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f37,definition,
( spl3_4
<=> xsd_integer(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f38,plain,
( xsd_integer(sK1)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f39,plain,
( ~ xsd_integer(sK1)
| spl3_4 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f41,definition,
( spl3_5
<=> cowlNothing(sK0) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f43,plain,
( cowlNothing(sK0)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f45,definition,
( spl3_6
<=> cowlThing(sK0) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f47,plain,
( ~ cowlThing(sK0)
| spl3_6 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f48,plain,
( spl3_1
| spl3_2
| spl3_3
| ~ spl3_4
| spl3_5
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f20,f45,f41,f37,f33,f29,f25]) ).
fof(f49,plain,
( ~ spl3_1
| ~ spl3_2
| spl3_3
| ~ spl3_4
| spl3_5
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f21,f45,f41,f37,f33,f29,f25]) ).
fof(f50,plain,
( spl3_1
| spl3_2
| ~ spl3_3
| spl3_4
| spl3_5
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f22,f45,f41,f37,f33,f29,f25]) ).
fof(f51,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| spl3_4
| spl3_5
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f23,f45,f41,f37,f33,f29,f25]) ).
fof(f52,plain,
( $false
| spl3_6 ),
inference(forward_subsumption_resolution,[],[f47,f15]) ).
fof(f53,plain,
spl3_6,
inference(avatar_contradiction_clause,[],[f52]) ).
fof(f54,plain,
( xsd_string(sK1)
| spl3_4 ),
inference(resolution,[],[f17,f39]) ).
fof(f56,plain,
( $false
| spl3_3
| spl3_4 ),
inference(forward_subsumption_resolution,[],[f54,f34]) ).
fof(f57,plain,
( spl3_3
| spl3_4 ),
inference(avatar_contradiction_clause,[],[f56]) ).
fof(f58,plain,
( $false
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f43,f14]) ).
fof(f59,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f58]) ).
fof(f60,plain,
( ~ xsd_string(sK1)
| ~ spl3_4 ),
inference(resolution,[],[f38,f16]) ).
fof(f61,plain,
( cAutomobile(sK2)
| ~ spl3_1 ),
inference(resolution,[],[f19,f27]) ).
fof(f62,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f61,f30]) ).
fof(f63,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f62]) ).
fof(f64,plain,
( $false
| ~ spl3_3
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f60,f35]) ).
fof(f65,plain,
( ~ spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f64]) ).
fof(f66,plain,
( cCar(sK2)
| ~ spl3_2 ),
inference(resolution,[],[f31,f18]) ).
fof(f67,plain,
( $false
| spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f66,f26]) ).
fof(f68,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f67]) ).
cnf(s1,plain,
( spl3_1
| spl3_2
| spl3_3
| ~ spl3_4
| spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f48]) ).
cnf(s2,plain,
( ~ spl3_1
| ~ spl3_2
| spl3_3
| ~ spl3_4
| spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
( spl3_1
| spl3_2
| ~ spl3_3
| spl3_4
| spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f50]) ).
cnf(s4,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| spl3_4
| spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f51]) ).
cnf(s5,plain,
spl3_6,
inference(sat_conversion,[],[f53]) ).
cnf(s6,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f57]) ).
cnf(s7,plain,
~ spl3_5,
inference(sat_conversion,[],[f59]) ).
cnf(s8,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f63]) ).
cnf(s9,plain,
( ~ spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f65]) ).
cnf(s10,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f68]) ).
cnf(s11,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| spl3_4 ),
inference(rat,[],[s4,s5,s7]) ).
cnf(s12,plain,
( spl3_1
| spl3_2
| ~ spl3_3
| spl3_4 ),
inference(rat,[],[s3,s5,s7]) ).
cnf(s13,plain,
( ~ spl3_1
| ~ spl3_2
| spl3_3
| ~ spl3_4 ),
inference(rat,[],[s2,s5,s7]) ).
cnf(s14,plain,
( spl3_1
| spl3_2
| spl3_3
| ~ spl3_4 ),
inference(rat,[],[s1,s5,s7]) ).
cnf(s15,plain,
( spl3_3
| spl3_1 ),
inference(rat,[],[s14,s6,s10]) ).
cnf(s16,plain,
spl3_1,
inference(rat,[],[s12,s9,s15,s10]) ).
cnf(s17,plain,
spl3_2,
inference(rat,[],[s8,s16]) ).
cnf(s18,plain,
spl3_3,
inference(rat,[],[s13,s6,s16,s17]) ).
cnf(s19,plain,
~ spl3_4,
inference(rat,[],[s9,s18]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s11,s17,s16,s19,s18]) ).
fof(f69,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS166+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n016.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 13:37:47 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.46 % (2656602)Will run a generic schedule for satisfiability detection.
% 0.12/0.46 % (2656612)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2637925159:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.46 % (2656612) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2656602-2656612"...
% 0.12/0.46 % (2656612)...printing done.
% 0.12/0.46 % (2656612)Refutation found. Thanks to Tanya!
% 0.12/0.46 % SZS status Theorem for theBenchmark
% 0.12/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.47 % (2656612)------------------------------
% 0.12/0.47 % (2656612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.47 % (2656612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.47 % (2656612)CaDiCaL version: 2.1.3
% 0.12/0.47 % (2656612)Termination reason: Refutation
% 0.12/0.47 % (2656612)Time elapsed: 0.002 s
% 0.12/0.47 % (2656612)Peak memory usage: 12 MB
% 0.12/0.47 % (2656612)Instructions burned: 2 (million)
% 0.12/0.47 % (2656602)Success in time 0.029 s
% 0.12/0.47 % Vampire exiting
%------------------------------------------------------------------------------