%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET986+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 12:45:08 PM UTC 2026
% Result : Theorem 2.30s 1.00s
% Output : Refutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 113 ( 27 unt; 6 def)
% Number of atoms : 376 ( 108 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 417 ( 154 ~; 194 |; 57 &)
% ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 174 ( 1 sgn 164 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f7,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f10,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f14,conjecture,
! [X0,X1] :
( in(X0,X1)
=> set_union2(set_difference(X1,singleton(X0)),singleton(X0)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_zfmisc_1) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> set_union2(set_difference(X1,singleton(X0)),singleton(X0)) = X1 ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,axiom,
! [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<=> ( in(X0,X1)
& X0 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_zfmisc_1) ).
fof(f17,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f10]) ).
fof(f23,plain,
? [X0,X1] :
( set_union2(set_difference(X1,singleton(X0)),singleton(X0)) != X1
& in(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f27,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK1(X0,X1,X2),X0)
& ~ in(sK1(X0,X1,X2),X1) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f31]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK3(X0,X1,X2),X0)
| in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),X0)
& ~ in(sK3(X0,X1,X2),X1) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f38]) ).
fof(f42,plain,
( sK7 != set_union2(set_difference(sK7,singleton(sK6)),singleton(sK6))
& in(sK6,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f23]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( in(X0,set_difference(X1,singleton(X2)))
| ~ in(X0,X1)
| X0 = X2 )
& ( ( in(X0,X1)
& X0 != X2 )
| ~ in(X0,set_difference(X1,singleton(X2))) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( in(X0,set_difference(X1,singleton(X2)))
| ~ in(X0,X1)
| X0 = X2 )
& ( ( in(X0,X1)
& X0 != X2 )
| ~ in(X0,set_difference(X1,singleton(X2))) ) ),
inference(flattening,[],[f43]) ).
fof(f46,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f50,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f28]) ).
fof(f54,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f55,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f56,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f57,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f64,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f39]) ).
fof(f65,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f39]) ).
fof(f67,plain,
! [X2,X0,X1] :
( in(sK3(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f39]) ).
fof(f71,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f17]) ).
fof(f75,plain,
in(sK6,sK7),
inference(cnf_transformation,[],[f42]) ).
fof(f76,plain,
sK7 != set_union2(set_difference(sK7,singleton(sK6)),singleton(sK6)),
inference(cnf_transformation,[],[f42]) ).
fof(f77,plain,
! [X2,X0,X1] :
( X0 != X2
| ~ in(X0,set_difference(X1,singleton(X2))) ),
inference(cnf_transformation,[],[f44]) ).
fof(f79,plain,
! [X2,X0,X1] :
( in(X0,set_difference(X1,singleton(X2)))
| ~ in(X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f44]) ).
fof(f82,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f51]) ).
fof(f83,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f82]) ).
fof(f84,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f50]) ).
fof(f85,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f56]) ).
fof(f86,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f55]) ).
fof(f87,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f54]) ).
fof(f88,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| ~ in(X4,X0)
| in(X4,X1) ),
inference(equality_resolution,[],[f65]) ).
fof(f89,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f64]) ).
fof(f91,plain,
! [X2,X1] : ~ in(X2,set_difference(X1,singleton(X2))),
inference(equality_resolution,[],[f77]) ).
fof(f92,definition,
sF8 = singleton(sK6),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f93,plain,
singleton(sK6) = sF8,
inference(reorient_equations,[],[f92]) ).
fof(f94,definition,
sF9 = set_difference(sK7,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f95,plain,
set_difference(sK7,sF8) = sF9,
inference(reorient_equations,[],[f94]) ).
fof(f96,definition,
sF10 = set_union2(sF9,sF8),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f97,plain,
set_union2(sF9,sF8) = sF10,
inference(reorient_equations,[],[f96]) ).
fof(f98,plain,
sK7 != sF10,
inference(definition_folding,[],[f76,f97,f93,f95,f93]) ).
fof(f99,plain,
sF10 = set_union2(sF8,sF9),
inference(forward_demodulation,[],[f97,f46]) ).
fof(f100,plain,
in(sK6,sF8),
inference(superposition,[],[f83,f93]) ).
fof(f117,plain,
! [X0] : ~ in(sK6,set_difference(X0,sF8)),
inference(superposition,[],[f91,f93]) ).
fof(f125,plain,
! [X0] :
( ~ in(X0,sF8)
| sK6 = X0 ),
inference(superposition,[],[f84,f93]) ).
fof(f149,plain,
! [X0] :
( ~ in(X0,sF9)
| in(X0,sK7) ),
inference(superposition,[],[f89,f95]) ).
fof(f166,plain,
! [X0] :
( ~ in(X0,sF10)
| in(X0,sF9)
| in(X0,sF8) ),
inference(superposition,[],[f87,f99]) ).
fof(f183,plain,
! [X0] :
( ~ in(X0,sK7)
| in(X0,sF9)
| in(X0,sF8) ),
inference(superposition,[],[f88,f95]) ).
fof(f192,plain,
! [X0,X1] :
( in(X0,set_difference(X1,sF8))
| ~ in(X0,X1)
| sK6 = X0 ),
inference(superposition,[],[f79,f93]) ).
fof(f225,plain,
! [X2,X3,X0,X1] :
( ~ in(sK1(X0,X1,set_union2(X2,X3)),X3)
| set_union2(X0,X1) = set_union2(X2,X3)
| ~ in(sK1(X0,X1,set_union2(X2,X3)),X0) ),
inference(resolution,[],[f59,f86]) ).
fof(f226,plain,
! [X2,X3,X0,X1] :
( ~ in(sK1(X0,X1,set_union2(X2,X3)),X2)
| set_union2(X0,X1) = set_union2(X2,X3)
| ~ in(sK1(X0,X1,set_union2(X2,X3)),X0) ),
inference(resolution,[],[f59,f85]) ).
fof(f271,plain,
! [X0,X1] :
( in(sK3(X0,X1,X0),X0)
| set_difference(X0,X1) = X0 ),
inference(factoring,[],[f67]) ).
fof(f316,plain,
! [X0,X1] :
( in(sK1(X0,X0,X1),X1)
| in(sK1(X0,X0,X1),X0)
| set_union2(X0,X0) = X1 ),
inference(factoring,[],[f57]) ).
fof(f319,plain,
! [X0,X1] :
( in(sK1(X0,X0,X1),X1)
| in(sK1(X0,X0,X1),X0)
| X0 = X1 ),
inference(forward_demodulation,[],[f316,f71]) ).
fof(f400,plain,
! [X0] :
( ~ in(X0,sK7)
| in(X0,sF9)
| sK6 = X0 ),
inference(superposition,[],[f192,f95]) ).
fof(f441,plain,
! [X0] :
( sF8 = set_difference(sF8,X0)
| sK6 = sK3(sF8,X0,sF8) ),
inference(resolution,[],[f271,f125]) ).
fof(f572,plain,
! [X0] :
( in(sK1(X0,X0,sF10),sF9)
| in(sK1(X0,X0,sF10),X0)
| sF10 = X0
| in(sK1(X0,X0,sF10),sF8) ),
inference(resolution,[],[f319,f166]) ).
fof(f970,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1,sF10),sF9)
| set_union2(X0,X1) = sF10
| ~ in(sK1(X0,X1,sF10),X0) ),
inference(superposition,[],[f225,f99]) ).
fof(f984,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1,sF10),sF8)
| set_union2(X0,X1) = sF10
| ~ in(sK1(X0,X1,sF10),X0) ),
inference(superposition,[],[f226,f99]) ).
fof(f3106,plain,
( ~ in(sK6,sF8)
| sK6 = sK3(sF8,sF8,sF8) ),
inference(superposition,[],[f117,f441]) ).
fof(f3107,plain,
sK6 = sK3(sF8,sF8,sF8),
inference(forward_subsumption_resolution,[],[f3106,f100]) ).
fof(f3247,plain,
in(sK3(sF8,sF8,sF8),sK7),
inference(superposition,[],[f75,f3107]) ).
fof(f14003,plain,
( in(sK1(sK7,sK7,sF10),sF9)
| sK7 = sF10
| in(sK1(sK7,sK7,sF10),sF8)
| in(sK1(sK7,sK7,sF10),sF9)
| sK6 = sK1(sK7,sK7,sF10) ),
inference(resolution,[],[f572,f400]) ).
fof(f14004,plain,
( in(sK1(sK7,sK7,sF10),sF9)
| sK7 = sF10
| in(sK1(sK7,sK7,sF10),sF8)
| in(sK1(sK7,sK7,sF10),sF9)
| in(sK1(sK7,sK7,sF10),sF8) ),
inference(resolution,[],[f572,f183]) ).
fof(f14008,plain,
( in(sK1(sK7,sK7,sF10),sF9)
| sK7 = sF10
| in(sK1(sK7,sK7,sF10),sF8) ),
inference(duplicate_literal_removal,[],[f14004]) ).
fof(f14009,plain,
( in(sK1(sK7,sK7,sF10),sF9)
| sK7 = sF10
| in(sK1(sK7,sK7,sF10),sF8)
| sK6 = sK1(sK7,sK7,sF10) ),
inference(duplicate_literal_removal,[],[f14003]) ).
fof(f14010,plain,
( in(sK1(sK7,sK7,sF10),sF9)
| in(sK1(sK7,sK7,sF10),sF8) ),
inference(forward_subsumption_resolution,[],[f14008,f98]) ).
fof(f14011,plain,
( in(sK1(sK7,sK7,sF10),sF9)
| in(sK1(sK7,sK7,sF10),sF8)
| sK6 = sK1(sK7,sK7,sF10) ),
inference(forward_subsumption_resolution,[],[f14009,f98]) ).
fof(f14014,definition,
( spl11_127
<=> in(sK1(sK7,sK7,sF10),sF8) ),
introduced(definition,[new_symbols(definition,[spl11_127])],[avatar_definition]) ).
fof(f14016,plain,
( in(sK1(sK7,sK7,sF10),sF8)
| ~ spl11_127 ),
inference(avatar_component_clause,[],[f14014]) ).
fof(f14018,definition,
( spl11_128
<=> in(sK1(sK7,sK7,sF10),sF9) ),
introduced(definition,[new_symbols(definition,[spl11_128])],[avatar_definition]) ).
fof(f14020,plain,
( in(sK1(sK7,sK7,sF10),sF9)
| ~ spl11_128 ),
inference(avatar_component_clause,[],[f14018]) ).
fof(f14021,plain,
( spl11_127
| spl11_128 ),
inference(avatar_split_clause,[],[f14010,f14018,f14014]) ).
fof(f14022,plain,
( in(sK1(sK7,sK7,sF10),sF9)
| sK6 = sK1(sK7,sK7,sF10) ),
inference(forward_subsumption_resolution,[],[f14011,f125]) ).
fof(f14023,plain,
( sK3(sF8,sF8,sF8) = sK1(sK7,sK7,sF10)
| in(sK1(sK7,sK7,sF10),sF9) ),
inference(forward_demodulation,[],[f14022,f3107]) ).
fof(f14025,definition,
( spl11_129
<=> sK3(sF8,sF8,sF8) = sK1(sK7,sK7,sF10) ),
introduced(definition,[new_symbols(definition,[spl11_129])],[avatar_definition]) ).
fof(f14027,plain,
( sK3(sF8,sF8,sF8) = sK1(sK7,sK7,sF10)
| ~ spl11_129 ),
inference(avatar_component_clause,[],[f14025]) ).
fof(f14028,plain,
( spl11_128
| spl11_129 ),
inference(avatar_split_clause,[],[f14023,f14025,f14018]) ).
fof(f14029,plain,
( sF10 = set_union2(sK7,sK7)
| ~ in(sK1(sK7,sK7,sF10),sK7)
| ~ spl11_128 ),
inference(resolution,[],[f14020,f970]) ).
fof(f14032,plain,
( in(sK1(sK7,sK7,sF10),sK7)
| ~ spl11_128 ),
inference(resolution,[],[f14020,f149]) ).
fof(f14037,plain,
( sF10 = set_union2(sK7,sK7)
| ~ spl11_128 ),
inference(forward_subsumption_resolution,[],[f14029,f14032]) ).
fof(f14039,plain,
( sK7 = sF10
| ~ spl11_128 ),
inference(forward_demodulation,[],[f14037,f71]) ).
fof(f14042,plain,
( $false
| ~ spl11_128 ),
inference(forward_subsumption_resolution,[],[f14039,f98]) ).
fof(f14043,plain,
~ spl11_128,
inference(avatar_contradiction_clause,[],[f14042]) ).
fof(f14075,plain,
( sF10 = set_union2(sK7,sK7)
| ~ in(sK1(sK7,sK7,sF10),sK7)
| ~ spl11_127 ),
inference(resolution,[],[f14016,f984]) ).
fof(f14086,plain,
( sK7 = sF10
| ~ in(sK1(sK7,sK7,sF10),sK7)
| ~ spl11_127 ),
inference(forward_demodulation,[],[f14075,f71]) ).
fof(f14088,plain,
( ~ in(sK1(sK7,sK7,sF10),sK7)
| ~ spl11_127 ),
inference(forward_subsumption_resolution,[],[f14086,f98]) ).
fof(f14090,plain,
( ~ in(sK3(sF8,sF8,sF8),sK7)
| ~ spl11_127
| ~ spl11_129 ),
inference(forward_demodulation,[],[f14088,f14027]) ).
fof(f14093,plain,
( $false
| ~ spl11_127
| ~ spl11_129 ),
inference(forward_subsumption_resolution,[],[f14090,f3247]) ).
fof(f14094,plain,
( ~ spl11_127
| ~ spl11_129 ),
inference(avatar_contradiction_clause,[],[f14093]) ).
cnf(s133,plain,
( spl11_127
| spl11_128 ),
inference(sat_conversion,[],[f14021]) ).
cnf(s134,plain,
( spl11_128
| spl11_129 ),
inference(sat_conversion,[],[f14028]) ).
cnf(s137,plain,
~ spl11_128,
inference(sat_conversion,[],[f14043]) ).
cnf(s139,plain,
( ~ spl11_127
| ~ spl11_129 ),
inference(sat_conversion,[],[f14094]) ).
cnf(s140,plain,
spl11_129,
inference(rat,[],[s134,s137]) ).
cnf(s141,plain,
~ spl11_127,
inference(rat,[],[s139,s140]) ).
cnf(s142,plain,
$false,
inference(rat,[],[s133,s137,s141]) ).
fof(f14095,plain,
$false,
inference(avatar_sat_refutation,[],[s142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET986+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n016.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 : Mon Sep 28 03:24:03 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 2.30/1.00 % (3229284)Will run a generic schedule for satisfiability detection.
% 2.30/1.00 % (3229293)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3663773436:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.30/1.00 % (3229290)% WARNING: option uhcvi not known.
% 2.30/1.00 % (3229289)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2233004107_2999 on theBenchmark for (2999ds/0Mi)
% 2.30/1.00 % (3229291)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1112299012:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.30/1.00 % (3229290)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=860571811:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.30/1.00 % (3229292)dis+10_1_sil=32000:sp=arity:random_seed=3257500621:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.30/1.00 % (3229295)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2818561990:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.30/1.00 % (3229294)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3557417808:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.30/1.00 % TRYING [1]
% 2.30/1.00 % TRYING [2]
% 2.30/1.00 % TRYING [3]
% 2.30/1.00 % TRYING [4]
% 2.30/1.00 % TRYING [5]
% 2.30/1.00 % (3229293)Instruction limit reached!
% 2.30/1.00 % (3229293)------------------------------
% 2.30/1.00 % (3229293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/1.00 % (3229293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.00 % (3229293)CaDiCaL version: 2.1.3
% 2.30/1.00 % (3229293)Termination reason: Instruction limit
% 2.30/1.00 % (3229293)Termination phase: Saturation
% 2.30/1.00 % (3229293)Time elapsed: 0.038 s
% 2.30/1.00 % (3229293)Peak memory usage: 12 MB
% 2.30/1.00 % (3229293)Instructions burned: 116 (million)
% 2.30/1.00 % TRYING [6]
% 2.30/1.00 % (3229303)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3119619594:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.30/1.00 % TRYING [1]
% 2.30/1.00 % TRYING [2]
% 2.30/1.00 % TRYING [3]
% 2.30/1.00 % TRYING [4]
% 2.30/1.00 % TRYING [5]
% 2.30/1.00 % (3229292)Instruction limit reached!
% 2.30/1.00 % (3229292)------------------------------
% 2.30/1.00 % (3229292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/1.00 % (3229292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.00 % (3229292)CaDiCaL version: 2.1.3
% 2.30/1.00 % (3229292)Termination reason: Instruction limit
% 2.30/1.00 % (3229292)Termination phase: Saturation
% 2.30/1.00 % (3229292)Time elapsed: 0.062 s
% 2.30/1.00 % (3229292)Peak memory usage: 12 MB
% 2.30/1.00 % (3229292)Instructions burned: 103 (million)
% 2.30/1.00 % TRYING [6]
% 2.30/1.00 % (3229294)Instruction limit reached!
% 2.30/1.00 % (3229294)------------------------------
% 2.30/1.00 % (3229294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/1.00 % (3229294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.00 % (3229294)CaDiCaL version: 2.1.3
% 2.30/1.00 % (3229294)Termination reason: Instruction limit
% 2.30/1.00 % (3229294)Termination phase: Saturation
% 2.30/1.00 % (3229294)Time elapsed: 0.076 s
% 2.30/1.00 % (3229294)Peak memory usage: 12 MB
% 2.30/1.00 % (3229294)Instructions burned: 133 (million)
% 2.30/1.00 % (3229305)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3958729898:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.30/1.00 % (3229306)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1102426163:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.30/1.00 % (3229295)Instruction limit reached!
% 2.30/1.00 % (3229295)------------------------------
% 2.30/1.00 % (3229295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/1.00 % (3229295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.00 % (3229295)CaDiCaL version: 2.1.3
% 2.30/1.00 % (3229295)Termination reason: Instruction limit
% 2.30/1.00 % (3229295)Termination phase: Saturation
% 2.30/1.00 % (3229295)Time elapsed: 0.097 s
% 2.30/1.00 % (3229295)Peak memory usage: 13 MB
% 2.30/1.00 % (3229295)Instructions burned: 159 (million)
% 2.30/1.00 % (3229309)ott-21_1_sil=16000:fs=off:random_seed=3318966715:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.30/1.00 % TRYING [7]
% 2.30/1.00 % TRYING [7]
% 2.30/1.00 % (3229305)Instruction limit reached!
% 2.30/1.00 % (3229305)------------------------------
% 2.30/1.00 % (3229305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/1.00 % (3229305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.00 % (3229305)CaDiCaL version: 2.1.3
% 2.30/1.00 % (3229305)Termination reason: Instruction limit
% 2.30/1.00 % (3229305)Termination phase: Saturation
% 2.30/1.00 % (3229305)Time elapsed: 0.086 s
% 2.30/1.00 % (3229305)Peak memory usage: 13 MB
% 2.30/1.00 % (3229305)Instructions burned: 131 (million)
% 2.30/1.00 % (3229311)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3766399238:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.30/1.00 % (3229309)Instruction limit reached!
% 2.30/1.00 % (3229309)------------------------------
% 2.30/1.00 % (3229309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/1.00 % (3229309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.00 % (3229309)CaDiCaL version: 2.1.3
% 2.30/1.00 % (3229309)Termination reason: Instruction limit
% 2.30/1.00 % (3229309)Termination phase: Saturation
% 2.30/1.00 % (3229309)Time elapsed: 0.098 s
% 2.30/1.00 % (3229309)Peak memory usage: 13 MB
% 2.30/1.00 % (3229309)Instructions burned: 181 (million)
% 2.30/1.00 % (3229303)Instruction limit reached!
% 2.30/1.00 % (3229303)------------------------------
% 2.30/1.00 % (3229303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/1.00 % (3229303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.00 % (3229303)CaDiCaL version: 2.1.3
% 2.30/1.00 % (3229303)Termination reason: Instruction limit
% 2.30/1.00 % (3229303)Termination phase: Finite model building SAT solving
% 2.30/1.00 % (3229303)Time elapsed: 0.181 s
% 2.30/1.00 % (3229303)Peak memory usage: 24 MB
% 2.30/1.00 % (3229303)Instructions burned: 716 (million)
% 2.30/1.00 % (3229313)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=206408433:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.30/1.00 % (3229314)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=530505099:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 2.30/1.00 % TRYING [1]
% 2.30/1.00 % TRYING [2]
% 2.30/1.00 % TRYING [3]
% 2.30/1.00 % TRYING [4]
% 2.30/1.00 % TRYING [5]
% 2.30/1.00 % TRYING [8]
% 2.30/1.00 % TRYING [6]
% 2.30/1.00 % TRYING [7]
% 2.30/1.00 % (3229306)Instruction limit reached!
% 2.30/1.00 % (3229306)------------------------------
% 2.30/1.00 % (3229306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/1.00 % (3229306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.00 % (3229306)CaDiCaL version: 2.1.3
% 2.30/1.00 % (3229306)Termination reason: Instruction limit
% 2.30/1.00 % (3229306)Termination phase: Saturation
% 2.30/1.00 % (3229306)Time elapsed: 0.390 s
% 2.30/1.00 % (3229306)Peak memory usage: 18 MB
% 2.30/1.00 % (3229306)Instructions burned: 685 (million)
% 2.30/1.00 % (3229311)Instruction limit reached!
% 2.30/1.00 % (3229311)------------------------------
% 2.30/1.00 % (3229311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/1.00 % (3229311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.00 % (3229311)CaDiCaL version: 2.1.3
% 2.30/1.00 % (3229311)Termination reason: Instruction limit
% 2.30/1.00 % (3229311)Termination phase: Saturation
% 2.30/1.00 % (3229311)Time elapsed: 0.318 s
% 2.30/1.00 % (3229311)Peak memory usage: 14 MB
% 2.30/1.00 % (3229311)Instructions burned: 477 (million)
% 2.30/1.00 % (3229317)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3614969607:i=889:ins=1_2994 on theBenchmark for (2994ds/889Mi)
% 2.30/1.00 % (3229319)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2304153156:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 2.30/1.00 % (3229314) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3229284-3229314"...
% 2.30/1.00 % (3229314)...printing done.
% 2.30/1.00 % (3229314)Refutation found. Thanks to Tanya!
% 2.30/1.00 % SZS status Theorem for theBenchmark
% 2.30/1.00 % SZS output start Proof for theBenchmark
% See solution above
% 2.30/1.00 % (3229314)------------------------------
% 2.30/1.00 % (3229314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/1.00 % (3229314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/1.00 % (3229314)CaDiCaL version: 2.1.3
% 2.30/1.00 % (3229314)Termination reason: Refutation
% 2.30/1.00 % (3229314)Time elapsed: 0.296 s
% 2.30/1.00 % (3229314)Peak memory usage: 21 MB
% 2.30/1.00 % (3229314)Instructions burned: 958 (million)
% 2.30/1.00 % (3229284)Success in time 0.569 s
% 2.30/1.00 % Vampire exiting
%------------------------------------------------------------------------------