%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN073+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 : n008.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 12:27:03 PM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 20 unt; 0 def)
% Number of atoms : 89 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 94 ( 44 ~; 32 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 48 ( 41 !; 7 ?)
% 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(f7,axiom,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( ~ r2(X0,X3)
| X3 != X2 )
| ~ r2(X1,X2) )
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3a) ).
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] :
( ~ r1(X2)
| ~ r2(X2,X1) )
| X1 != X0 )
| ! [X3] :
( ! [X4] :
( ~ r1(X4)
| ~ r2(X4,X3) )
| ~ r2(X3,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oneuneqtwo) ).
fof(f13,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( ! [X2] :
( ~ r1(X2)
| ~ r2(X2,X1) )
| X1 != X0 )
| ! [X3] :
( ! [X4] :
( ~ r1(X4)
| ~ r2(X4,X3) )
| ~ r2(X3,X0) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( r1(X2)
& r2(X2,X1) )
& X0 = X1 )
& ? [X3] :
( ? [X4] :
( r1(X4)
& r2(X4,X3) )
& r2(X3,X0) ) ),
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(f24,plain,
( r1(sK22)
& r2(sK22,sK21)
& sK20 = sK21
& r1(sK24)
& r2(sK24,sK23)
& r2(sK23,sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23),skolemize(X4,sK24)],[f14]) ).
fof(f26,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X1] :
( ~ r1(X1)
| sK0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| sK1(X0) = X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( ~ r2(X0,X3)
| X2 != X3
| ~ r2(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f7]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ r1(X2)
| X1 != X2
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f64,plain,
r2(sK23,sK20),
inference(cnf_transformation,[],[f24]) ).
fof(f65,plain,
r2(sK24,sK23),
inference(cnf_transformation,[],[f24]) ).
fof(f66,plain,
r1(sK24),
inference(cnf_transformation,[],[f24]) ).
fof(f67,plain,
sK20 = sK21,
inference(cnf_transformation,[],[f24]) ).
fof(f68,plain,
r2(sK22,sK21),
inference(cnf_transformation,[],[f24]) ).
fof(f69,plain,
r1(sK22),
inference(cnf_transformation,[],[f24]) ).
fof(f73,plain,
r2(sK23,sK21),
inference(definition_unfolding,[],[f64,f67]) ).
fof(f74,plain,
r1(sK0),
inference(equality_resolution,[],[f26]) ).
fof(f82,plain,
! [X3,X0,X1] :
( ~ r2(X1,X3)
| ~ r2(X0,X3)
| X0 = X1 ),
inference(equality_resolution,[],[f51]) ).
fof(f83,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f63]) ).
fof(f88,plain,
sK0 = sK22,
inference(resolution,[],[f27,f69]) ).
fof(f89,plain,
sK0 = sK24,
inference(resolution,[],[f27,f66]) ).
fof(f98,plain,
~ r1(sK21),
inference(resolution,[],[f83,f68]) ).
fof(f112,plain,
sK21 = sK1(sK22),
inference(resolution,[],[f31,f68]) ).
fof(f114,plain,
sK23 = sK1(sK24),
inference(resolution,[],[f31,f65]) ).
fof(f115,plain,
sK23 = sK1(sK0),
inference(forward_demodulation,[],[f114,f89]) ).
fof(f116,plain,
sK21 = sK1(sK0),
inference(forward_demodulation,[],[f112,f88]) ).
fof(f124,plain,
sK21 = sK23,
inference(superposition,[],[f116,f115]) ).
fof(f169,plain,
! [X0] :
( ~ r2(X0,sK21)
| sK23 = X0 ),
inference(resolution,[],[f82,f73]) ).
fof(f172,plain,
! [X0] :
( ~ r2(X0,sK21)
| sK21 = X0 ),
inference(forward_demodulation,[],[f169,f124]) ).
fof(f178,plain,
sK21 = sK22,
inference(resolution,[],[f172,f68]) ).
fof(f180,plain,
sK0 = sK21,
inference(forward_demodulation,[],[f178,f88]) ).
fof(f188,plain,
~ r1(sK0),
inference(superposition,[],[f98,f180]) ).
fof(f193,plain,
$false,
inference(forward_subsumption_resolution,[],[f188,f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN073+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n008.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 21:55:39 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.46 % (1641891)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (1641899)dis+10_1_sil=32000:sp=arity:random_seed=3364899735:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (1641899) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1641891-1641899"...
% 0.11/0.46 % (1641899)...printing done.
% 0.11/0.46 % (1641897)% WARNING: option uhcvi not known.
% 0.11/0.46 % (1641899)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Theorem for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (1641899)------------------------------
% 0.11/0.46 % (1641899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (1641899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (1641899)CaDiCaL version: 2.1.3
% 0.11/0.46 % (1641899)Termination reason: Refutation
% 0.11/0.46 % (1641899)Time elapsed: 0.003 s
% 0.11/0.46 % (1641899)Peak memory usage: 12 MB
% 0.11/0.46 % (1641899)Instructions burned: 5 (million)
% 0.11/0.46 % (1641891)Success in time 0.032 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------