%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KRS178+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 11:42:28 AM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 24 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 98 ( 45 ~; 20 |; 26 &)
% ( 2 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 19 con; 0-2 aty)
% Number of variables : 74 ( 48 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
=> status(X2,X3,X1) )
<=> isa(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax',isa) ).
fof(f6,axiom,
! [X0,X1] :
( model(X0,X1)
<~> model(X0,not(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax',completeness) ).
fof(f7,axiom,
! [X0,X1] :
( model(X0,X1)
<=> ~ model(X0,not(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax',not) ).
fof(f8,axiom,
? [X0] :
! [X1] : model(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax',tautology) ).
fof(f9,axiom,
? [X0] :
( ? [X1] : model(X1,X0)
& ? [X2] : ~ model(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax',satisfiable) ).
fof(f10,axiom,
? [X0] :
! [X1] : ~ model(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax',contradiction) ).
fof(f11,axiom,
? [X0,X1] :
( ? [X2] :
( model(X2,X0)
& model(X2,X1) )
& ? [X3] :
( ~ model(X3,X0)
| ~ model(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax',sat_non_taut_pair) ).
fof(f12,axiom,
? [X0,X1] :
( ? [X2] : model(X2,X0)
& ! [X3] :
( model(X3,X0)
=> model(X3,X1) )
& ? [X4] :
( ~ model(X4,X0)
& model(X4,X1) )
& ? [X5] : ~ model(X5,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax',mixed_pair) ).
fof(f13,axiom,
? [X0,X1,X2] :
( model(X0,X1)
& ~ model(X0,X2)
& ? [X3] : model(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax',non_thm_spt) ).
fof(f14,conjecture,
! [X0] : isa(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isa_reflexive) ).
fof(f15,negated_conjecture,
~ ! [X0] : isa(X0,X0),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
=> status(X2,X3,X1) )
=> isa(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f17,plain,
! [X0,X1] :
( isa(X0,X1)
| ? [X2,X3] :
( ~ status(X2,X3,X1)
& status(X2,X3,X0) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f18,plain,
? [X0,X1] :
( ? [X2] : model(X2,X0)
& ! [X3] :
( model(X3,X1)
| ~ model(X3,X0) )
& ? [X4] :
( ~ model(X4,X0)
& model(X4,X1) )
& ? [X5] : ~ model(X5,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f19,plain,
? [X0] : ~ isa(X0,X0),
inference(ennf_transformation,[],[f15]) ).
fof(f20,plain,
! [X0,X1] :
( isa(X0,X1)
| ( ~ status(sK0(X0,X1),sK1(X0,X1),X1)
& status(sK0(X0,X1),sK1(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f17]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ model(X0,not(X1))
| ~ model(X0,X1) )
& ( model(X0,not(X1))
| model(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f22,plain,
! [X0,X1] :
( ( model(X0,X1)
| model(X0,not(X1)) )
& ( ~ model(X0,not(X1))
| ~ model(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f23,plain,
! [X1] : model(X1,sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f8]) ).
fof(f24,plain,
( model(sK4,sK3)
& ~ model(sK5,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f9]) ).
fof(f25,plain,
! [X1] : ~ model(X1,sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f10]) ).
fof(f26,plain,
( model(sK9,sK7)
& model(sK9,sK8)
& ( ~ model(sK10,sK7)
| ~ model(sK10,sK8) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10)],[f11]) ).
fof(f27,plain,
( model(sK13,sK11)
& ! [X3] :
( model(X3,sK12)
| ~ model(X3,sK11) )
& ~ model(sK14,sK11)
& model(sK14,sK12)
& ~ model(sK15,sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X4,sK14),skolemize(X5,sK15)],[f18]) ).
fof(f28,plain,
( model(sK16,sK17)
& ~ model(sK16,sK18)
& model(sK19,sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18),skolemize(X3,sK19)],[f13]) ).
fof(f29,plain,
~ isa(sK20,sK20),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X0,sK20)],[f19]) ).
fof(f30,plain,
! [X0,X1] :
( isa(X0,X1)
| status(sK0(X0,X1),sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
! [X0,X1] :
( isa(X0,X1)
| ~ status(sK0(X0,X1),sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( model(X0,not(X1))
| model(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
! [X0,X1] :
( ~ model(X0,not(X1))
| ~ model(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
! [X0,X1] :
( ~ model(X0,not(X1))
| ~ model(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X0,X1] :
( model(X0,X1)
| model(X0,not(X1)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X1] : model(X1,sK2),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
~ model(sK5,sK3),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
model(sK4,sK3),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
! [X1] : ~ model(X1,sK6),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
( ~ model(sK10,sK7)
| ~ model(sK10,sK8) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
model(sK9,sK8),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
model(sK9,sK7),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
~ model(sK15,sK12),
inference(cnf_transformation,[],[f27]) ).
fof(f44,plain,
model(sK14,sK12),
inference(cnf_transformation,[],[f27]) ).
fof(f45,plain,
~ model(sK14,sK11),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
! [X3] :
( model(X3,sK12)
| ~ model(X3,sK11) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
model(sK13,sK11),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
model(sK19,sK18),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
~ model(sK16,sK18),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
model(sK16,sK17),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
~ isa(sK20,sK20),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
! [X0,X1] :
( ~ isa(X0,X1)
| status(sK0(X0,X1),sK1(X0,X1),X1) ),
inference(consistent_polarity_flipping,[],[f31]) ).
fof(f53,plain,
! [X0,X1] :
( ~ isa(X0,X1)
| ~ status(sK0(X0,X1),sK1(X0,X1),X0) ),
inference(consistent_polarity_flipping,[],[f30]) ).
fof(f54,plain,
isa(sK20,sK20),
inference(consistent_polarity_flipping,[],[f51]) ).
fof(f83,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f52,f53,f33,f32,f35,f34,f36,f38,f37,f39,f42,f41,f40,f47,f46,f45,f44,f43,f50,f49,f48,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS178+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n014.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % 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 13:34:01 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.17/0.47 % (821172)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (821177)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=527563207_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % TRYING [4]
% 0.17/0.47 % (821177) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-821172-821177"...
% 0.17/0.47 % (821177)...printing done.
% 0.17/0.47 % (821178)% WARNING: option uhcvi not known.
% 0.17/0.47 % (821177)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (821177)------------------------------
% 0.17/0.47 % (821177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (821177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (821177)CaDiCaL version: 2.1.3
% 0.17/0.47 % (821177)Termination reason: Refutation
% 0.17/0.47 % (821177)Time elapsed: 0.002 s
% 0.17/0.47 % (821177)Peak memory usage: 11 MB
% 0.17/0.47 % (821177)Instructions burned: 7 (million)
% 0.17/0.47 % (821172)Success in time 0.038 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------