%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN060+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:27:00 PM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 10 unt; 1 def)
% Number of atoms : 94 ( 16 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 116 ( 52 ~; 35 |; 28 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 56 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X2 != X1 )
| ( r2(X0,X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(f5,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X1,X4)
& r3(X0,X4,X3) )
& X3 = X2 )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
fof(f12,conjecture,
? [X0,X1,X2] :
( X2 = X0
& ? [X3] :
( r3(X1,X3,X2)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r2(X6,X5)
& ? [X7] :
( r1(X7)
& r2(X7,X6) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greq4) ).
fof(f13,negated_conjecture,
~ ? [X0,X1,X2] :
( X2 = X0
& ? [X3] :
( r3(X1,X3,X2)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r2(X6,X5)
& ? [X7] :
( r1(X7)
& r2(X7,X6) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( X0 != X2
| ! [X3] :
( ~ r3(X1,X3,X2)
| ! [X4] :
( ~ r2(X4,X3)
| ! [X5] :
( ~ r2(X5,X4)
| ! [X6] :
( ~ r2(X6,X5)
| ! [X7] :
( ~ r1(X7)
| ~ r2(X7,X6) ) ) ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X1] :
( ( ~ r1(X1)
& sK0 != X1 )
| ( r1(X1)
& sK0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f16,plain,
! [X0,X2] :
( ( ~ r2(X0,X2)
& sK1(X0) != X2 )
| ( r2(X0,X2)
& sK1(X0) = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f2]) ).
fof(f19,plain,
! [X0,X1] :
( r2(X1,sK6(X0,X1))
& r3(X0,sK6(X0,X1),sK5(X0,X1))
& sK4(X0,X1) = sK5(X0,X1)
& r2(sK7(X0,X1),sK4(X0,X1))
& r3(X0,X1,sK7(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X2,sK4(X0,X1)),skolemize(X3,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X5,sK7(X0,X1))],[f5]) ).
fof(f25,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0] :
( sK1(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X0 != X2
| ~ r3(X1,X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6) ),
inference(cnf_transformation,[],[f14]) ).
fof(f67,plain,
r1(sK0),
inference(equality_resolution,[],[f25]) ).
fof(f69,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f29]) ).
fof(f77,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( ~ r3(X1,X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6) ),
inference(equality_resolution,[],[f63]) ).
fof(f85,definition,
( spl20_3
<=> ! [X7] : ~ r1(X7) ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
fof(f86,plain,
( ! [X7] : ~ r1(X7)
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( $false
| ~ spl20_3 ),
inference(resolution,[],[f86,f67]) ).
fof(f88,plain,
~ spl20_3,
inference(avatar_contradiction_clause,[],[f87]) ).
fof(f116,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2(X4,X3)
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r2(X0,X1) ),
inference(resolution,[],[f40,f77]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( ~ r2(sK1(X2),X0)
| ~ r2(X0,X1)
| ~ r1(X2)
| ~ r2(X1,X3) ),
inference(resolution,[],[f116,f69]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ r2(sK1(sK1(X0)),X1)
| ~ r1(X0)
| ~ r2(X1,X2) ),
inference(resolution,[],[f117,f69]) ).
fof(f135,plain,
! [X0,X1] :
( ~ r2(sK1(sK1(sK1(X0))),X1)
| ~ r1(X0) ),
inference(resolution,[],[f123,f69]) ).
fof(f147,plain,
! [X0] : ~ r1(X0),
inference(resolution,[],[f135,f69]) ).
fof(f150,plain,
spl20_3,
inference(avatar_split_clause,[],[f147,f85]) ).
cnf(s36,plain,
~ spl20_3,
inference(sat_conversion,[],[f88]) ).
cnf(s101,plain,
spl20_3,
inference(sat_conversion,[],[f150]) ).
cnf(s102,plain,
$false,
inference(rat,[],[s36,s101]) ).
fof(f151,plain,
$false,
inference(avatar_sat_refutation,[],[s102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN060+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n009.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 21:52:00 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.40 Running first-order model finding
% 0.15/0.40 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
% 0.15/0.44 % (2435946)Will run a generic schedule for satisfiability detection.
% 0.15/0.44 % (2435953)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3824630820:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.44 % (2435953) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2435946-2435953"...
% 0.15/0.44 % (2435953)...printing done.
% 0.15/0.44 % (2435953)Refutation found. Thanks to Tanya!
% 0.15/0.44 % SZS status Theorem for theBenchmark
% 0.15/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.44 % (2435953)------------------------------
% 0.15/0.44 % (2435953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.44 % (2435953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.44 % (2435953)CaDiCaL version: 2.1.3
% 0.15/0.44 % (2435953)Termination reason: Refutation
% 0.15/0.44 % (2435953)Time elapsed: 0.003 s
% 0.15/0.44 % (2435953)Peak memory usage: 12 MB
% 0.15/0.44 % (2435953)Instructions burned: 4 (million)
% 0.15/0.44 % (2435946)Success in time 0.03 s
% 0.15/0.44 % Vampire exiting
%------------------------------------------------------------------------------