%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN062+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 12:27:01 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 61 ( 22 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 67 ( 29 ~; 20 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 58 ( 45 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
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(f11,axiom,
! [X0,X1] :
( ! [X2] :
( ~ r1(X2)
| X2 != X1 )
| ~ r2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
fof(f12,conjecture,
! [X0] :
? [X1,X2] :
( ! [X3] :
( ~ r1(X3)
| X2 != X3 )
& ? [X4] :
( r3(X0,X2,X4)
& X4 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infiniteNumbers) ).
fof(f13,negated_conjecture,
~ ! [X0] :
? [X1,X2] :
( ! [X3] :
( ~ r1(X3)
| X2 != X3 )
& ? [X4] :
( r3(X0,X2,X4)
& X4 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0] :
! [X1,X2] :
( ? [X3] :
( r1(X3)
& X2 = X3 )
| ! [X4] :
( ~ r3(X0,X2,X4)
| X1 != X4 ) ),
inference(ennf_transformation,[],[f13]) ).
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(f24,plain,
! [X1,X2] :
( ( r1(sK21(X2))
& sK21(X2) = X2 )
| ! [X4] :
( ~ r3(sK20,X2,X4)
| X1 != X4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21]),skolemize(X0,sK20),skolemize(X3,sK21(X2))],[f14]) ).
fof(f30,plain,
! [X2,X0] :
( sK1(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f41,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ r1(X2)
| X1 != X2
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f64,plain,
! [X2,X1,X4] :
( sK21(X2) = X2
| ~ r3(sK20,X2,X4)
| X1 != X4 ),
inference(cnf_transformation,[],[f24]) ).
fof(f65,plain,
! [X2,X1,X4] :
( r1(sK21(X2))
| ~ r3(sK20,X2,X4)
| X1 != X4 ),
inference(cnf_transformation,[],[f24]) ).
fof(f71,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f30]) ).
fof(f78,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f63]) ).
fof(f79,plain,
! [X2,X4] :
( ~ r3(sK20,X2,X4)
| r1(sK21(X2)) ),
inference(equality_resolution,[],[f65]) ).
fof(f80,plain,
! [X2,X4] :
( ~ r3(sK20,X2,X4)
| sK21(X2) = X2 ),
inference(equality_resolution,[],[f64]) ).
fof(f87,plain,
! [X0] : ~ r1(sK1(X0)),
inference(resolution,[],[f78,f71]) ).
fof(f90,plain,
! [X0] : sK21(X0) = X0,
inference(resolution,[],[f41,f80]) ).
fof(f91,plain,
! [X0] : r1(sK21(X0)),
inference(resolution,[],[f41,f79]) ).
fof(f93,plain,
! [X0] : r1(X0),
inference(superposition,[],[f91,f90]) ).
fof(f97,plain,
$false,
inference(resolution,[],[f93,f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN062+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/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 21:52:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.44 % (2436343)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (2436351)dis+10_1_sil=32000:sp=arity:random_seed=3377802735:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.44 % (2436351) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2436343-2436351"...
% 0.10/0.44 % (2436351)...printing done.
% 0.10/0.44 % (2436351)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 % (2436351)------------------------------
% 0.10/0.44 % (2436351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (2436351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (2436351)CaDiCaL version: 2.1.3
% 0.10/0.44 % (2436351)Termination reason: Refutation
% 0.10/0.44 % (2436351)Time elapsed: 0.001 s
% 0.10/0.44 % (2436351)Peak memory usage: 11 MB
% 0.10/0.44 % (2436351)Instructions burned: 2 (million)
% 0.10/0.44 % (2436343)Success in time 0.033 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------