%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN088+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 12:27:07 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 13 unt; 2 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 54 ~; 40 |; 18 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 52 ( 0 sgn 45 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( id(X1,X0)
& r1(X1) )
| ( ~ r1(X1)
& ~ id(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
fof(f6,axiom,
! [X0,X1] :
( ~ id(X0,X1)
| id(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(f8,axiom,
! [X0,X1] :
( ~ id(X0,X1)
| ( ~ r1(X0)
& ~ r1(X1) )
| ( r1(X0)
& r1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( ~ id(X0,X2)
| ~ id(X1,X3)
| ( ~ r2(X0,X1)
& ~ r2(X2,X3) )
| ( r2(X0,X1)
& r2(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_9) ).
fof(f17,axiom,
! [X0] :
( ? [X1] :
( id(X0,X1)
& r1(X1) )
| ? [X2,X3] :
( id(X0,X3)
& r2(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6a) ).
fof(f18,axiom,
! [X0,X1] :
( ! [X2] :
( ~ id(X2,X1)
| ~ r1(X2) )
| ~ r2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).
fof(f19,conjecture,
! [X0] :
( ! [X1] :
( ~ id(X1,X0)
| ~ r1(X1) )
| ! [X2] :
( ~ r1(X2)
| ~ r2(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zerounidone) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( ~ id(X1,X0)
| ~ r1(X1) )
| ! [X2] :
( ~ r1(X2)
| ~ r2(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0] :
( ? [X1] :
( id(X1,X0)
& r1(X1) )
& ? [X2] :
( r1(X2)
& r2(X2,X0) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f22,plain,
! [X1] :
( ( id(X1,sK0)
& r1(X1) )
| ( ~ r1(X1)
& ~ id(X1,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f30,plain,
! [X0] :
( ( id(X0,sK17(X0))
& r1(sK17(X0)) )
| ( id(X0,sK19(X0))
& r2(sK18(X0),sK19(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X1,sK17(X0)),skolemize(X2,sK18(X0)),skolemize(X3,sK19(X0))],[f17]) ).
fof(f31,plain,
( id(sK21,sK20)
& r1(sK21)
& r1(sK22)
& r2(sK22,sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22)],[f21]) ).
fof(f35,plain,
! [X1] :
( ~ r1(X1)
| id(X1,sK0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f49,plain,
! [X0,X1] :
( ~ id(X0,X1)
| id(X1,X0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0,X1] :
( ~ r1(X1)
| ~ id(X0,X1)
| r1(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f57,plain,
! [X2,X3,X0,X1] :
( ~ r2(X0,X1)
| ~ id(X1,X3)
| ~ id(X0,X2)
| r2(X2,X3) ),
inference(cnf_transformation,[],[f9]) ).
fof(f88,plain,
! [X0] :
( id(X0,sK19(X0))
| id(X0,sK17(X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ r1(X2)
| ~ id(X2,X1)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f90,plain,
r2(sK22,sK20),
inference(cnf_transformation,[],[f31]) ).
fof(f91,plain,
r1(sK22),
inference(cnf_transformation,[],[f31]) ).
fof(f92,plain,
r1(sK21),
inference(cnf_transformation,[],[f31]) ).
fof(f93,plain,
id(sK21,sK20),
inference(cnf_transformation,[],[f31]) ).
fof(f101,plain,
id(sK22,sK0),
inference(resolution,[],[f35,f91]) ).
fof(f110,plain,
id(sK20,sK21),
inference(resolution,[],[f49,f93]) ).
fof(f133,plain,
! [X0] :
( ~ id(X0,sK21)
| r1(X0) ),
inference(resolution,[],[f52,f92]) ).
fof(f146,plain,
r1(sK20),
inference(resolution,[],[f133,f110]) ).
fof(f186,plain,
! [X0,X1] :
( ~ id(sK20,X0)
| ~ r2(X1,X0) ),
inference(resolution,[],[f89,f146]) ).
fof(f278,plain,
! [X0,X1] :
( ~ id(sK20,X0)
| ~ id(sK22,X1)
| r2(X1,X0) ),
inference(resolution,[],[f57,f90]) ).
fof(f279,plain,
! [X0,X1] :
( ~ id(sK20,X0)
| ~ id(sK22,X1) ),
inference(forward_subsumption_resolution,[],[f278,f186]) ).
fof(f281,definition,
( spl23_5
<=> ! [X1] : ~ id(sK22,X1) ),
introduced(definition,[new_symbols(definition,[spl23_5])],[avatar_definition]) ).
fof(f282,plain,
( ! [X1] : ~ id(sK22,X1)
| ~ spl23_5 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f284,definition,
( spl23_6
<=> ! [X0] : ~ id(sK20,X0) ),
introduced(definition,[new_symbols(definition,[spl23_6])],[avatar_definition]) ).
fof(f285,plain,
( ! [X0] : ~ id(sK20,X0)
| ~ spl23_6 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f286,plain,
( spl23_5
| spl23_6 ),
inference(avatar_split_clause,[],[f279,f284,f281]) ).
fof(f287,plain,
( $false
| ~ spl23_5 ),
inference(resolution,[],[f282,f101]) ).
fof(f295,plain,
~ spl23_5,
inference(avatar_contradiction_clause,[],[f287]) ).
fof(f306,plain,
( id(sK20,sK17(sK20))
| ~ spl23_6 ),
inference(resolution,[],[f285,f88]) ).
fof(f312,plain,
( $false
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f306,f285]) ).
fof(f313,plain,
~ spl23_6,
inference(avatar_contradiction_clause,[],[f312]) ).
cnf(s3,plain,
( spl23_5
| spl23_6 ),
inference(sat_conversion,[],[f286]) ).
cnf(s7,plain,
~ spl23_5,
inference(sat_conversion,[],[f295]) ).
cnf(s13,plain,
~ spl23_6,
inference(sat_conversion,[],[f313]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s3,s13,s7]) ).
fof(f314,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN088+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 22:01:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.10/0.44 % (956153)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (956163)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=171246379:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.44 % (956163) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-956153-956163"...
% 0.10/0.44 % (956163)...printing done.
% 0.10/0.44 % (956159)% WARNING: option uhcvi not known.
% 0.10/0.44 % (956163)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (956163)------------------------------
% 0.10/0.44 % (956163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (956163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (956163)CaDiCaL version: 2.1.3
% 0.10/0.44 % (956163)Termination reason: Refutation
% 0.10/0.44 % (956163)Time elapsed: 0.003 s
% 0.10/0.44 % (956163)Peak memory usage: 12 MB
% 0.10/0.44 % (956163)Instructions burned: 7 (million)
% 0.10/0.44 % (956153)Success in time 0.028 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------