%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN060+1 : 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 : n017.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 0.13s 0.44s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 7 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 95 ( 41 ~; 30 |; 24 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 91 ( 70 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( id(X1,X0)
& r1(X1) )
| ( ~ r1(X1)
& ~ id(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
fof(f5,axiom,
! [X0] : id(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(f12,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( id(X3,X2)
& ? [X4] :
( r2(X1,X4)
& r3(X0,X4,X3) ) )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1a) ).
fof(f19,conjecture,
? [X0,X1,X2] :
( id(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',greq4id) ).
fof(f20,negated_conjecture,
~ ? [X0,X1,X2] :
( id(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)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ id(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(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(f26,plain,
! [X0,X1] :
( id(sK5(X0,X1),sK4(X0,X1))
& r2(X1,sK6(X0,X1))
& r3(X0,sK6(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))],[f12]) ).
fof(f31,plain,
! [X1] :
( ~ id(X1,sK0)
| r1(X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f47,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f66,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f69,plain,
! [X0,X1] : r2(X1,sK6(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f89,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ r1(X7)
| ~ r3(X1,X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ id(X2,X0)
| ~ r2(X7,X6) ),
inference(cnf_transformation,[],[f21]) ).
fof(f93,plain,
r1(sK0),
inference(resolution,[],[f31,f47]) ).
fof(f95,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r2(X3,X1)
| ~ r3(X0,X1,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ id(X2,X6)
| ~ r2(sK0,X5) ),
inference(resolution,[],[f93,f89]) ).
fof(f100,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r2(X4,X2)
| ~ r3(X0,sK6(X1,X2),X3)
| ~ r2(X5,X4)
| ~ id(X3,X6)
| ~ r2(sK0,X5) ),
inference(resolution,[],[f69,f95]) ).
fof(f104,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r2(X5,X3)
| ~ r3(X0,sK6(X1,sK6(X2,X3)),X4)
| ~ id(X4,X6)
| ~ r2(sK0,X5) ),
inference(resolution,[],[f100,f69]) ).
fof(f110,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r2(sK0,X4)
| ~ id(X5,X6)
| ~ r3(X0,sK6(X1,sK6(X2,sK6(X3,X4))),X5) ),
inference(resolution,[],[f104,f69]) ).
fof(f112,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ id(X0,X1)
| ~ r3(X2,sK6(X3,sK6(X4,sK6(X5,sK6(X6,sK0)))),X0) ),
inference(resolution,[],[f110,f69]) ).
fof(f117,plain,
! [X2,X3,X0,X1,X4,X5] : ~ r3(X0,sK6(X1,sK6(X2,sK6(X3,sK6(X4,sK0)))),X5),
inference(resolution,[],[f112,f47]) ).
fof(f120,plain,
$false,
inference(resolution,[],[f117,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN060+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n017.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 21:47:35 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 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
% 0.13/0.44 % (2973945)Will run a generic schedule for satisfiability detection.
% 0.13/0.44 % (2973955)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=62936660:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.44 % (2973955) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2973945-2973955"...
% 0.13/0.44 % (2973955)...printing done.
% 0.13/0.44 % (2973955)Refutation found. Thanks to Tanya!
% 0.13/0.44 % SZS status Theorem for theBenchmark
% 0.13/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.44 % (2973955)------------------------------
% 0.13/0.44 % (2973955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.44 % (2973955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.44 % (2973955)CaDiCaL version: 2.1.3
% 0.13/0.44 % (2973955)Termination reason: Refutation
% 0.13/0.44 % (2973955)Time elapsed: 0.002 s
% 0.13/0.44 % (2973955)Peak memory usage: 11 MB
% 0.13/0.44 % (2973955)Instructions burned: 4 (million)
% 0.13/0.44 % (2973945)Success in time 0.028 s
% 0.13/0.44 % Vampire exiting
%------------------------------------------------------------------------------