%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN072+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:26:44 PM UTC 2026
% Result : Theorem 6.39s 1.96s
% Output : Refutation 8.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 106 ( 56 unt; 3 def)
% Number of atoms : 286 ( 65 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 324 ( 144 ~; 117 |; 60 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-2 aty)
% Number of variables : 231 ( 0 sgn 196 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X2 != X1 )
| ( r2(X0,X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ r3(X0,X1,X3)
& X3 != X2 )
| ( r3(X0,X1,X3)
& X3 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f4,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ r4(X0,X1,X3)
& X3 != X2 )
| ( r4(X0,X1,X3)
& X3 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
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/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
fof(f6,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X1,X4)
& r4(X0,X4,X3) )
& X3 = X2 )
& ? [X5] :
( r3(X5,X0,X2)
& r4(X0,X1,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r3(X0,X2,X1) )
& X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
fof(f9,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,X1) )
& ? [X3] :
( r1(X3)
& X1 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
fof(f12,conjecture,
? [X0] :
( ? [X1] :
( ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r1(X3)
& r2(X3,X2) ) )
& ? [X4] :
( r4(X4,X1,X0)
& ? [X5] :
( r1(X5)
& r2(X5,X4) ) ) )
& ? [X6] :
( X0 = X6
& ? [X7] :
( r2(X7,X6)
& ? [X8] :
( r1(X8)
& r2(X8,X7) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',onetimestwoeqtwo) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ? [X1] :
( ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r1(X3)
& r2(X3,X2) ) )
& ? [X4] :
( r4(X4,X1,X0)
& ? [X5] :
( r1(X5)
& r2(X5,X4) ) ) )
& ? [X6] :
( X0 = X6
& ? [X7] :
( r2(X7,X6)
& ? [X8] :
( r1(X8)
& r2(X8,X7) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ r2(X2,X1)
| ! [X3] :
( ~ r1(X3)
| ~ r2(X3,X2) ) )
| ! [X4] :
( ~ r4(X4,X1,X0)
| ! [X5] :
( ~ r1(X5)
| ~ r2(X5,X4) ) ) )
| ! [X6] :
( X0 != X6
| ! [X7] :
( ~ r2(X7,X6)
| ! [X8] :
( ~ r1(X8)
| ~ r2(X8,X7) ) ) ) ),
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(f17,plain,
! [X0,X1,X3] :
( ( ~ r3(X0,X1,X3)
& sK2(X0,X1) != X3 )
| ( r3(X0,X1,X3)
& sK2(X0,X1) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f3]) ).
fof(f18,plain,
! [X0,X1,X3] :
( ( ~ r4(X0,X1,X3)
& sK3(X0,X1) != X3 )
| ( r4(X0,X1,X3)
& sK3(X0,X1) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f4]) ).
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(f20,plain,
! [X0,X1] :
( r2(X1,sK10(X0,X1))
& r4(X0,sK10(X0,X1),sK9(X0,X1))
& sK8(X0,X1) = sK9(X0,X1)
& r3(sK11(X0,X1),X0,sK8(X0,X1))
& r4(X0,X1,sK11(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1)),skolemize(X4,sK10(X0,X1)),skolemize(X5,sK11(X0,X1))],[f6]) ).
fof(f21,plain,
! [X0] :
( r1(sK13(X0))
& r3(X0,sK13(X0),sK12(X0))
& sK12(X0) = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0))],[f8]) ).
fof(f22,plain,
! [X0] :
( r1(sK15(X0))
& r4(X0,sK15(X0),sK14(X0))
& r1(sK16(X0))
& sK14(X0) = sK16(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X1,sK14(X0)),skolemize(X2,sK15(X0)),skolemize(X3,sK16(X0))],[f9]) ).
fof(f25,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X1] :
( ~ r1(X1)
| sK0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0] :
( sK1(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| sK1(X0) = X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| sK2(X0,X1) = X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
! [X3,X0,X1] :
( ~ r4(X0,X1,X3)
| sK3(X0,X1) = X3 ),
inference(cnf_transformation,[],[f18]) ).
fof(f40,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
! [X0,X1] : r2(sK7(X0,X1),sK4(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0,X1] : sK4(X0,X1) = sK5(X0,X1),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0,X1] : r3(X0,sK6(X0,X1),sK5(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0,X1] : r2(X1,sK6(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f45,plain,
! [X0,X1] : r4(X0,X1,sK11(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
! [X0,X1] : r3(sK11(X0,X1),X0,sK8(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f47,plain,
! [X0,X1] : sK8(X0,X1) = sK9(X0,X1),
inference(cnf_transformation,[],[f20]) ).
fof(f48,plain,
! [X0,X1] : r4(X0,sK10(X0,X1),sK9(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f49,plain,
! [X0,X1] : r2(X1,sK10(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f51,plain,
! [X0] : sK12(X0) = X0,
inference(cnf_transformation,[],[f21]) ).
fof(f52,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f53,plain,
! [X0] : r1(sK13(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f54,plain,
! [X0] : sK14(X0) = sK16(X0),
inference(cnf_transformation,[],[f22]) ).
fof(f55,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f56,plain,
! [X0] : r4(X0,sK15(X0),sK14(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f57,plain,
! [X0] : r1(sK15(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ r2(X2,X1)
| ~ r1(X3)
| ~ r2(X3,X2)
| ~ r4(X4,X1,X0)
| ~ r1(X5)
| ~ r2(X5,X4)
| X0 != X6
| ~ r2(X7,X6)
| ~ r1(X8)
| ~ r2(X8,X7) ),
inference(cnf_transformation,[],[f14]) ).
fof(f64,plain,
! [X0,X1] : r2(sK7(X0,X1),sK5(X0,X1)),
inference(definition_unfolding,[],[f41,f42]) ).
fof(f65,plain,
! [X0,X1] : r3(sK11(X0,X1),X0,sK9(X0,X1)),
inference(definition_unfolding,[],[f46,f47]) ).
fof(f66,plain,
! [X0] : r4(X0,sK15(X0),sK16(X0)),
inference(definition_unfolding,[],[f56,f54]) ).
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,X8,X6,X7,X4,X5] :
( ~ r4(X4,X1,X6)
| ~ r1(X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| ~ r1(X5)
| ~ r2(X5,X4)
| ~ r2(X7,X6)
| ~ r1(X8)
| ~ r2(X8,X7) ),
inference(equality_resolution,[],[f63]) ).
fof(f78,plain,
! [X0] : r3(X0,sK13(X0),X0),
inference(forward_demodulation,[],[f52,f51]) ).
fof(f82,plain,
! [X0] : sK16(X0) = sK3(X0,sK15(X0)),
inference(resolution,[],[f38,f66]) ).
fof(f84,plain,
! [X0,X1] : sK3(X0,X1) = sK11(X0,X1),
inference(resolution,[],[f38,f45]) ).
fof(f89,plain,
! [X0,X1] : sK9(X0,X1) = sK3(X0,sK10(X0,X1)),
inference(resolution,[],[f48,f38]) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r2(X5,sK9(X2,X3))
| ~ r2(X0,X1)
| ~ r2(X1,sK10(X2,X3))
| ~ r1(X4)
| ~ r2(X4,X2)
| ~ r1(X0)
| ~ r1(X6)
| ~ r2(X6,X5) ),
inference(resolution,[],[f48,f77]) ).
fof(f95,plain,
! [X0] : sK0 = sK13(X0),
inference(resolution,[],[f26,f53]) ).
fof(f96,plain,
! [X0] : sK0 = sK15(X0),
inference(resolution,[],[f26,f57]) ).
fof(f97,plain,
! [X0] : sK0 = sK16(X0),
inference(resolution,[],[f26,f55]) ).
fof(f100,plain,
! [X0] : sK16(X0) = sK3(X0,sK0),
inference(superposition,[],[f82,f96]) ).
fof(f104,plain,
! [X0] : sK0 = sK3(X0,sK0),
inference(forward_demodulation,[],[f100,f97]) ).
fof(f121,plain,
! [X0] : sK2(X0,sK13(X0)) = X0,
inference(resolution,[],[f34,f78]) ).
fof(f123,plain,
! [X0,X1] : sK2(X0,X1) = sK7(X0,X1),
inference(resolution,[],[f34,f40]) ).
fof(f124,plain,
! [X0,X1] : sK9(X0,X1) = sK2(sK11(X0,X1),X0),
inference(resolution,[],[f34,f65]) ).
fof(f125,plain,
! [X0,X1] : sK9(X0,X1) = sK2(sK3(X0,X1),X0),
inference(forward_demodulation,[],[f124,f84]) ).
fof(f126,plain,
! [X0] : sK2(X0,sK0) = X0,
inference(forward_demodulation,[],[f121,f95]) ).
fof(f132,plain,
! [X0] : sK9(X0,sK0) = sK2(sK0,X0),
inference(superposition,[],[f125,f104]) ).
fof(f164,plain,
! [X0,X1] : sK5(X0,X1) = sK2(X0,sK6(X0,X1)),
inference(resolution,[],[f43,f34]) ).
fof(f180,plain,
! [X0,X1] : sK1(X0) = sK10(X1,X0),
inference(resolution,[],[f30,f49]) ).
fof(f181,plain,
! [X0,X1] : sK1(X0) = sK6(X1,X0),
inference(resolution,[],[f30,f44]) ).
fof(f182,plain,
! [X0,X1] : sK5(X0,X1) = sK1(sK7(X0,X1)),
inference(resolution,[],[f30,f64]) ).
fof(f183,plain,
! [X0,X1] : sK5(X0,X1) = sK1(sK2(X0,X1)),
inference(forward_demodulation,[],[f182,f123]) ).
fof(f185,plain,
! [X0,X1] : sK9(X1,X0) = sK3(X1,sK1(X0)),
inference(superposition,[],[f89,f180]) ).
fof(f199,plain,
! [X0,X1] : sK5(X1,X0) = sK2(X1,sK1(X0)),
inference(superposition,[],[f164,f181]) ).
fof(f202,plain,
! [X0] : sK1(X0) = sK5(X0,sK0),
inference(superposition,[],[f183,f126]) ).
fof(f203,plain,
! [X0,X1] : sK5(X0,sK6(X0,X1)) = sK1(sK5(X0,X1)),
inference(superposition,[],[f183,f164]) ).
fof(f206,plain,
! [X0,X1] : sK1(sK5(X0,X1)) = sK5(X0,sK1(X1)),
inference(forward_demodulation,[],[f203,f181]) ).
fof(f231,plain,
! [X0,X1] : sK9(sK1(X0),X1) = sK5(sK3(sK1(X0),X1),X0),
inference(superposition,[],[f125,f199]) ).
fof(f243,plain,
! [X0] : sK1(sK3(sK1(sK0),X0)) = sK9(sK1(sK0),X0),
inference(superposition,[],[f202,f231]) ).
fof(f253,plain,
! [X0] : sK9(sK1(sK0),sK1(X0)) = sK1(sK9(sK1(sK0),X0)),
inference(superposition,[],[f243,f185]) ).
fof(f274,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(X1,sK1(sK9(sK1(sK0),X0)))
| ~ r2(X2,X3)
| ~ r2(X3,sK10(sK1(sK0),sK1(X0)))
| ~ r1(X4)
| ~ r2(X4,sK1(sK0))
| ~ r1(X2)
| ~ r1(X5)
| ~ r2(X5,X1) ),
inference(superposition,[],[f90,f253]) ).
fof(f277,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(X3,sK1(sK1(X0)))
| ~ r2(X1,sK1(sK9(sK1(sK0),X0)))
| ~ r2(X2,X3)
| ~ r1(X4)
| ~ r2(X4,sK1(sK0))
| ~ r1(X2)
| ~ r1(X5)
| ~ r2(X5,X1) ),
inference(forward_demodulation,[],[f274,f180]) ).
fof(f280,definition,
( spl20_7
<=> ! [X4] :
( ~ r1(X4)
| ~ r2(X4,sK1(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
fof(f281,plain,
( ! [X4] :
( ~ r2(X4,sK1(sK0))
| ~ r1(X4) )
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f283,definition,
( spl20_8
<=> ! [X3,X0,X5,X2,X1] :
( ~ r2(X1,sK1(sK9(sK1(sK0),X0)))
| ~ r1(X5)
| ~ r2(X5,X1)
| ~ r1(X2)
| ~ r2(X2,X3)
| ~ r2(X3,sK1(sK1(X0))) ) ),
introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition]) ).
fof(f284,plain,
( ! [X2,X3,X0,X1,X5] :
( ~ r2(X1,sK1(sK9(sK1(sK0),X0)))
| ~ r1(X5)
| ~ r2(X5,X1)
| ~ r1(X2)
| ~ r2(X2,X3)
| ~ r2(X3,sK1(sK1(X0))) )
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f288,plain,
( spl20_7
| spl20_8 ),
inference(avatar_split_clause,[],[f277,f283,f280]) ).
fof(f290,plain,
( ~ r1(sK0)
| ~ spl20_7 ),
inference(resolution,[],[f281,f69]) ).
fof(f291,plain,
( $false
| ~ spl20_7 ),
inference(forward_subsumption_resolution,[],[f290,f67]) ).
fof(f292,plain,
~ spl20_7,
inference(avatar_contradiction_clause,[],[f291]) ).
fof(f295,plain,
( ! [X2,X3,X0,X1] :
( ~ r2(X0,sK1(sK2(sK0,sK1(sK0))))
| ~ r1(X1)
| ~ r2(X1,X0)
| ~ r1(X2)
| ~ r2(X2,X3)
| ~ r2(X3,sK1(sK1(sK0))) )
| ~ spl20_8 ),
inference(superposition,[],[f284,f132]) ).
fof(f298,plain,
( ! [X2,X3,X0,X1] :
( ~ r2(X0,sK5(sK0,sK1(sK0)))
| ~ r1(X1)
| ~ r2(X1,X0)
| ~ r1(X2)
| ~ r2(X2,X3)
| ~ r2(X3,sK1(sK1(sK0))) )
| ~ spl20_8 ),
inference(forward_demodulation,[],[f295,f183]) ).
fof(f300,plain,
( ! [X2,X3,X0,X1] :
( ~ r2(X0,sK1(sK5(sK0,sK0)))
| ~ r1(X1)
| ~ r2(X1,X0)
| ~ r1(X2)
| ~ r2(X2,X3)
| ~ r2(X3,sK1(sK1(sK0))) )
| ~ spl20_8 ),
inference(forward_demodulation,[],[f298,f206]) ).
fof(f302,plain,
( ! [X2,X3,X0,X1] :
( ~ r2(X0,sK1(sK1(sK0)))
| ~ r1(X1)
| ~ r2(X1,X0)
| ~ r1(X2)
| ~ r2(X2,X3)
| ~ r2(X3,sK1(sK1(sK0))) )
| ~ spl20_8 ),
inference(forward_demodulation,[],[f300,f202]) ).
fof(f305,definition,
( spl20_9
<=> ! [X2,X3] :
( ~ r1(X2)
| ~ r2(X3,sK1(sK1(sK0)))
| ~ r2(X2,X3) ) ),
introduced(definition,[new_symbols(definition,[spl20_9])],[avatar_definition]) ).
fof(f306,plain,
( ! [X2,X3] :
( ~ r2(X3,sK1(sK1(sK0)))
| ~ r1(X2)
| ~ r2(X2,X3) )
| ~ spl20_9 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f307,plain,
( spl20_9
| spl20_9
| ~ spl20_8 ),
inference(avatar_split_clause,[],[f302,f283,f305,f305]) ).
fof(f308,plain,
( ! [X0] :
( ~ r1(X0)
| ~ r2(X0,sK1(sK0)) )
| ~ spl20_9 ),
inference(resolution,[],[f306,f69]) ).
fof(f309,plain,
( spl20_7
| ~ spl20_9 ),
inference(avatar_split_clause,[],[f308,f305,f280]) ).
cnf(s6,plain,
( spl20_7
| spl20_8 ),
inference(sat_conversion,[],[f288]) ).
cnf(s7,plain,
~ spl20_7,
inference(sat_conversion,[],[f292]) ).
cnf(s8,plain,
( spl20_9
| ~ spl20_8
| spl20_9 ),
inference(sat_conversion,[],[f307]) ).
cnf(s9,plain,
( ~ spl20_8
| spl20_9 ),
inference(rat,[],[s8]) ).
cnf(s10,plain,
( spl20_7
| ~ spl20_9 ),
inference(sat_conversion,[],[f309]) ).
cnf(s11,plain,
~ spl20_9,
inference(rat,[],[s10,s7]) ).
cnf(s12,plain,
~ spl20_8,
inference(rat,[],[s9,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s6,s12,s7]) ).
fof(f310,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN072+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 % Computer : n006.cluster.edu
% 0.09/0.41 % Model : x86_64 x86_64
% 0.09/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.41 % Memory : 8046.5625MB
% 0.09/0.41 % OS : Linux 6.8.0-71-generic
% 0.09/0.41 % CPULimit : 300
% 0.09/0.41 % WCLimit : 300
% 0.09/0.41 % DateTime : Sun Sep 27 21:55:26 UTC 2026
% 0.09/0.41 % CPUTime :
% 0.09/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.45 Running first-order theorem proving
% 0.09/0.45 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.39/1.96 % (3361710)Detected formulas, will run a generic FOF schedule.
% 6.39/1.96 % (3361717)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=104428444:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.39/1.96 % (3361720)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2177108586:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.39/1.96 % (3361719)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1839361109:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.39/1.96 % (3361716)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2230467111:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.39/1.96 % (3361715)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3853141831:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.39/1.96 % (3361718)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2288557115:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.39/1.96 % (3361721)dis-21_1_sil=8000:lcm=predicate:random_seed=147884183:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 6.39/1.96 % (3361718)Refutation not found, incomplete strategy
% 6.39/1.96 % (3361718)------------------------------
% 6.39/1.96 % (3361718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361718)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361718)Termination reason: Refutation not found, incomplete strategy
% 6.39/1.96 % (3361718)Time elapsed: 0.003 s
% 6.39/1.96 % (3361718)Peak memory usage: 88 MB
% 6.39/1.96 % (3361718)Instructions burned: 3 (million)
% 6.39/1.96 % (3361721)Instruction limit reached!
% 6.39/1.96 % (3361721)------------------------------
% 6.39/1.96 % (3361721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361721)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361721)Termination reason: Instruction limit
% 6.39/1.96 % (3361721)Termination phase: Saturation
% 6.39/1.96 % (3361721)Time elapsed: 0.058 s
% 6.39/1.96 % (3361721)Peak memory usage: 88 MB
% 6.39/1.96 % (3361721)Instructions burned: 129 (million)
% 6.39/1.96 % (3361719)Instruction limit reached!
% 6.39/1.96 % (3361719)------------------------------
% 6.39/1.96 % (3361719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361719)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361719)Termination reason: Instruction limit
% 6.39/1.96 % (3361719)Termination phase: Saturation
% 6.39/1.96 % (3361719)Time elapsed: 0.073 s
% 6.39/1.96 % (3361719)Peak memory usage: 88 MB
% 6.39/1.96 % (3361719)Instructions burned: 119 (million)
% 6.39/1.96 % (3361720)Instruction limit reached!
% 6.39/1.96 % (3361720)------------------------------
% 6.39/1.96 % (3361720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361720)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361720)Termination reason: Instruction limit
% 6.39/1.96 % (3361720)Termination phase: Saturation
% 6.39/1.96 % (3361720)Time elapsed: 0.089 s
% 6.39/1.96 % (3361720)Peak memory usage: 89 MB
% 6.39/1.96 % (3361720)Instructions burned: 139 (million)
% 6.39/1.96 % (3361729)lrs+10_1_sil=8000:sp=occurrence:random_seed=3232386075:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.39/1.96 % (3361730)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2188571025:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.39/1.96 % (3361731)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2529367573:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.39/1.96 % (3361718)------------------------------
% 6.39/1.96 % (3361718)------------------------------
% 6.39/1.96 % (3361730)Instruction limit reached!
% 6.39/1.96 % (3361730)------------------------------
% 6.39/1.96 % (3361730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361730)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361730)Termination reason: Instruction limit
% 6.39/1.96 % (3361730)Termination phase: Saturation
% 6.39/1.96 % (3361730)Time elapsed: 0.071 s
% 6.39/1.96 % (3361730)Peak memory usage: 90 MB
% 6.39/1.96 % (3361730)Instructions burned: 159 (million)
% 6.39/1.96 % (3361717)Refutation not found, incomplete strategy
% 6.39/1.96 % (3361717)------------------------------
% 6.39/1.96 % (3361717)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361717)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361717)Termination reason: Refutation not found, incomplete strategy
% 6.39/1.96 % (3361717)Time elapsed: 0.386 s
% 6.39/1.96 % (3361717)Peak memory usage: 128 MB
% 6.39/1.96 % (3361717)Instructions burned: 920 (million)
% 6.39/1.96 % (3361729)Instruction limit reached!
% 6.39/1.96 % (3361729)------------------------------
% 6.39/1.96 % (3361729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361729)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361729)Termination reason: Instruction limit
% 6.39/1.96 % (3361729)Termination phase: Saturation
% 6.39/1.96 % (3361729)Time elapsed: 0.157 s
% 6.39/1.96 % (3361729)Peak memory usage: 90 MB
% 6.39/1.96 % (3361729)Instructions burned: 287 (million)
% 6.39/1.96 % (3361735)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1099668151:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.39/1.96 % (3361736)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1118422433:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.39/1.96 % (3361736)Refutation not found, incomplete strategy
% 6.39/1.96 % (3361736)------------------------------
% 6.39/1.96 % (3361736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361736)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361736)Termination reason: Refutation not found, incomplete strategy
% 6.39/1.96 % (3361736)Time elapsed: 0.002 s
% 6.39/1.96 % (3361736)Peak memory usage: 88 MB
% 6.39/1.96 % (3361736)Instructions burned: 2 (million)
% 6.39/1.96 % (3361731)Instruction limit reached!
% 6.39/1.96 % (3361731)------------------------------
% 6.39/1.96 % (3361731)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361731)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361731)Termination reason: Instruction limit
% 6.39/1.96 % (3361731)Termination phase: Saturation
% 6.39/1.96 % (3361731)Time elapsed: 0.197 s
% 6.39/1.96 % (3361731)Peak memory usage: 91 MB
% 6.39/1.96 % (3361731)Instructions burned: 325 (million)
% 6.39/1.96 % (3361737)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=286599164:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.39/1.96 % (3361735)Instruction limit reached!
% 6.39/1.96 % (3361735)------------------------------
% 6.39/1.96 % (3361735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361735)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361735)Termination reason: Instruction limit
% 6.39/1.96 % (3361735)Termination phase: Saturation
% 6.39/1.96 % (3361735)Time elapsed: 0.118 s
% 6.39/1.96 % (3361735)Peak memory usage: 91 MB
% 6.39/1.96 % (3361735)Instructions burned: 248 (million)
% 6.39/1.96 % (3361717)------------------------------
% 6.39/1.96 % (3361717)------------------------------
% 6.39/1.96 % (3361740)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=436634419:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.39/1.96 % (3361740)Refutation not found, incomplete strategy
% 6.39/1.96 % (3361740)------------------------------
% 6.39/1.96 % (3361740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361740)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361740)Termination reason: Refutation not found, incomplete strategy
% 6.39/1.96 % (3361740)Time elapsed: 0.004 s
% 6.39/1.96 % (3361740)Peak memory usage: 88 MB
% 6.39/1.96 % (3361740)Instructions burned: 5 (million)
% 6.39/1.96 % (3361743)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=826366429:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.39/1.96 % (3361742)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1112963446:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.39/1.96 % (3361736)------------------------------
% 6.39/1.96 % (3361736)------------------------------
% 6.39/1.96 % (3361743)Instruction limit reached!
% 6.39/1.96 % (3361743)------------------------------
% 6.39/1.96 % (3361743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361743)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361743)Termination reason: Instruction limit
% 6.39/1.96 % (3361743)Termination phase: Saturation
% 6.39/1.96 % (3361743)Time elapsed: 0.041 s
% 6.39/1.96 % (3361743)Peak memory usage: 89 MB
% 6.39/1.96 % (3361743)Instructions burned: 116 (million)
% 6.39/1.96 % (3361715)First to succeed.
% 6.39/1.96 % (3361715)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3361710"
% 6.39/1.96 % (3361742)Instruction limit reached!
% 6.39/1.96 % (3361742)------------------------------
% 6.39/1.96 % (3361742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361742)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361742)Termination reason: Instruction limit
% 6.39/1.96 % (3361742)Termination phase: Saturation
% 6.39/1.96 % (3361742)Time elapsed: 0.067 s
% 6.39/1.96 % (3361742)Peak memory usage: 88 MB
% 6.39/1.96 % (3361742)Instructions burned: 128 (million)
% 6.39/1.96 % (3361747)lrs+10_1_sil=8000:sp=occurrence:random_seed=3352017113:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.39/1.96 % (3361748)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1363468034:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.39/1.96 % (3361748)Refutation not found, incomplete strategy
% 6.39/1.96 % (3361748)------------------------------
% 6.39/1.96 % (3361748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.96 % (3361748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.96 % (3361748)CaDiCaL version: 2.1.3
% 6.39/1.96 % (3361748)Termination reason: Refutation not found, incomplete strategy
% 6.39/1.96 % (3361748)Time elapsed: 0.002 s
% 6.39/1.96 % (3361748)Peak memory usage: 88 MB
% 6.39/1.96 % (3361748)Instructions burned: 2 (million)
% 6.39/1.96 % (3361716)Also succeeded, but the first one will report.
% 6.39/1.96 % (3361740)------------------------------
% 6.39/1.96 % (3361740)------------------------------
% 6.39/1.96 % (3361749)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2511681662:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.39/1.96 % (3361747)Also succeeded, but the first one will report.
% 6.39/1.96 % (3361715)Refutation found. Thanks to Tanya!
% 6.39/1.96 % SZS status Theorem for theBenchmark
% 6.39/1.96 % SZS output start Proof for theBenchmark
% See solution above
% 8.17/2.14 % (3361715)------------------------------
% 8.17/2.14 % (3361715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.17/2.14 % (3361715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.17/2.14 % (3361715)CaDiCaL version: 2.1.3
% 8.17/2.14 % (3361715)Termination reason: Refutation
% 8.17/2.14 % (3361715)Time elapsed: 0.650 s
% 8.17/2.14 % (3361715)Peak memory usage: 130 MB
% 8.17/2.14 % (3361715)Instructions burned: 958 (million)
% 8.17/2.14 % (3361715)------------------------------
% 8.17/2.14 % (3361715)------------------------------
% 8.17/2.14 % (3361710)Success in time 1.07 s
% 8.17/2.14 % Vampire exiting
%------------------------------------------------------------------------------