TSTP Solution File: SET986+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET986+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 18:26:16 EDT 2022
% Result : Theorem 1.42s 0.55s
% Output : Refutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 87 ( 12 unt; 0 def)
% Number of atoms : 364 ( 79 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 442 ( 165 ~; 174 |; 80 &)
% ( 14 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 171 ( 151 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f259,plain,
$false,
inference(subsumption_resolution,[],[f258,f255]) ).
fof(f255,plain,
~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),singleton(sK2)),
inference(resolution,[],[f249,f101]) ).
fof(f101,plain,
! [X3,X0,X1] :
( in(X3,set_union2(X1,X0))
| ~ in(X3,X1) ),
inference(equality_resolution,[],[f74]) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X1)
| set_union2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| set_union2(X1,X0) != X2 )
& ( set_union2(X1,X0) = X2
| ( ( ~ in(sK3(X0,X1,X2),X2)
| ( ~ in(sK3(X0,X1,X2),X1)
& ~ in(sK3(X0,X1,X2),X0) ) )
& ( in(sK3(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X1)
| in(sK3(X0,X1,X2),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f39,f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X2)
| in(X4,X1)
| in(X4,X0) ) )
=> ( ( ~ in(sK3(X0,X1,X2),X2)
| ( ~ in(sK3(X0,X1,X2),X1)
& ~ in(sK3(X0,X1,X2),X0) ) )
& ( in(sK3(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X1)
| in(sK3(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| set_union2(X1,X0) != X2 )
& ( set_union2(X1,X0) = X2
| ? [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X2)
| in(X4,X1)
| in(X4,X0) ) ) ) ),
inference(rectify,[],[f38]) ).
fof(f38,plain,
! [X2,X1,X0] :
( ( ! [X3] :
( ( in(X3,X1)
| in(X3,X2)
| ~ in(X3,X0) )
& ( in(X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X2) ) ) )
| set_union2(X1,X2) != X0 )
& ( set_union2(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X2) ) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) ) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
! [X2,X1,X0] :
( ( ! [X3] :
( ( in(X3,X1)
| in(X3,X2)
| ~ in(X3,X0) )
& ( in(X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X2) ) ) )
| set_union2(X1,X2) != X0 )
& ( set_union2(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X2) ) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X2,X1,X0] :
( ! [X3] :
( ( in(X3,X1)
| in(X3,X2) )
<=> in(X3,X0) )
<=> set_union2(X1,X2) = X0 ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X1)
| in(X3,X0) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f249,plain,
~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),
inference(subsumption_resolution,[],[f225,f68]) ).
fof(f68,plain,
in(sK2,sK1),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
( set_union2(set_difference(sK1,singleton(sK2)),singleton(sK2)) != sK1
& in(sK2,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f34,f35]) ).
fof(f35,plain,
( ? [X0,X1] :
( set_union2(set_difference(X0,singleton(X1)),singleton(X1)) != X0
& in(X1,X0) )
=> ( set_union2(set_difference(sK1,singleton(sK2)),singleton(sK2)) != sK1
& in(sK2,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
? [X0,X1] :
( set_union2(set_difference(X0,singleton(X1)),singleton(X1)) != X0
& in(X1,X0) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
? [X1,X0] :
( set_union2(set_difference(X1,singleton(X0)),singleton(X0)) != X1
& in(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> set_union2(set_difference(X1,singleton(X0)),singleton(X0)) = X1 ),
inference(negated_conjecture,[],[f14]) ).
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(f225,plain,
( ~ in(sK2,sK1)
| ~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))) ),
inference(backward_demodulation,[],[f171,f222]) ).
fof(f222,plain,
sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1) = sK2,
inference(subsumption_resolution,[],[f221,f196]) ).
fof(f196,plain,
( in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),sK1)
| sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1) = sK2 ),
inference(resolution,[],[f191,f109]) ).
fof(f109,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(equality_resolution,[],[f94]) ).
fof(f94,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ( ( sK7(X0,X1) != X0
| ~ in(sK7(X0,X1),X1) )
& ( sK7(X0,X1) = X0
| in(sK7(X0,X1),X1) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f59,f60]) ).
fof(f60,plain,
! [X0,X1] :
( ? [X3] :
( ( X0 != X3
| ~ in(X3,X1) )
& ( X0 = X3
| in(X3,X1) ) )
=> ( ( sK7(X0,X1) != X0
| ~ in(sK7(X0,X1),X1) )
& ( sK7(X0,X1) = X0
| in(sK7(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ? [X3] :
( ( X0 != X3
| ~ in(X3,X1) )
& ( X0 = X3
| in(X3,X1) ) ) ) ),
inference(rectify,[],[f58]) ).
fof(f58,plain,
! [X1,X0] :
( ( ! [X2] :
( ( in(X2,X0)
| X1 != X2 )
& ( X1 = X2
| ~ in(X2,X0) ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
<=> X1 = X2 )
<=> singleton(X1) = X0 ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( singleton(X0) = X1
<=> ! [X2] :
( X0 = X2
<=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f191,plain,
( in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),singleton(sK2))
| in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),sK1) ),
inference(subsumption_resolution,[],[f189,f172]) ).
fof(f172,plain,
( ~ in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),sK1)
| in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),sK1) ),
inference(resolution,[],[f169,f89]) ).
fof(f89,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f53,f54]) ).
fof(f54,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f52]) ).
fof(f52,plain,
! [X1,X0] :
( ( subset(X1,X0)
| ? [X2] :
( ~ in(X2,X0)
& in(X2,X1) ) )
& ( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ subset(X1,X0) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X1,X0] :
( subset(X1,X0)
<=> ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
=> in(X2,X0) )
<=> subset(X1,X0) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f169,plain,
( ~ subset(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))))
| ~ in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),sK1) ),
inference(resolution,[],[f166,f90]) ).
fof(f90,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f166,plain,
( ~ subset(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1)
| ~ subset(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))) ),
inference(forward_demodulation,[],[f165,f86]) ).
fof(f86,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f165,plain,
( ~ subset(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))))
| ~ subset(set_union2(set_difference(sK1,singleton(sK2)),singleton(sK2)),sK1) ),
inference(forward_demodulation,[],[f158,f86]) ).
fof(f158,plain,
( ~ subset(sK1,set_union2(set_difference(sK1,singleton(sK2)),singleton(sK2)))
| ~ subset(set_union2(set_difference(sK1,singleton(sK2)),singleton(sK2)),sK1) ),
inference(extensionality_resolution,[],[f99,f69]) ).
fof(f69,plain,
set_union2(set_difference(sK1,singleton(sK2)),singleton(sK2)) != sK1,
inference(cnf_transformation,[],[f36]) ).
fof(f99,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(rectify,[],[f63]) ).
fof(f63,plain,
! [X1,X0] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X1,X0] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f189,plain,
( in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),sK1)
| in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),sK1)
| in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),singleton(sK2)) ),
inference(resolution,[],[f183,f103]) ).
fof(f103,plain,
! [X2,X1,X4] :
( ~ in(X4,set_difference(X1,X2))
| in(X4,X1) ),
inference(equality_resolution,[],[f79]) ).
fof(f79,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| set_difference(X1,X2) != X0 ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( set_difference(X1,X2) = X0
| ( ( ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X2) )
& ( in(sK4(X0,X1,X2),X0)
| ( in(sK4(X0,X1,X2),X1)
& ~ in(sK4(X0,X1,X2),X2) ) ) ) )
& ( ! [X4] :
( ( ( in(X4,X1)
& ~ in(X4,X2) )
| ~ in(X4,X0) )
& ( in(X4,X0)
| ~ in(X4,X1)
| in(X4,X2) ) )
| set_difference(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f45,f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| in(X3,X2) )
& ( in(X3,X0)
| ( in(X3,X1)
& ~ in(X3,X2) ) ) )
=> ( ( ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X2) )
& ( in(sK4(X0,X1,X2),X0)
| ( in(sK4(X0,X1,X2),X1)
& ~ in(sK4(X0,X1,X2),X2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( set_difference(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| in(X3,X2) )
& ( in(X3,X0)
| ( in(X3,X1)
& ~ in(X3,X2) ) ) ) )
& ( ! [X4] :
( ( ( in(X4,X1)
& ~ in(X4,X2) )
| ~ in(X4,X0) )
& ( in(X4,X0)
| ~ in(X4,X1)
| in(X4,X2) ) )
| set_difference(X1,X2) != X0 ) ),
inference(rectify,[],[f44]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( in(X3,X2)
| ( in(X3,X0)
& ~ in(X3,X1) ) ) ) )
& ( ! [X3] :
( ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( in(X3,X2)
| ( in(X3,X0)
& ~ in(X3,X1) ) ) ) )
& ( ! [X3] :
( ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X0)
& ~ in(X3,X1) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f183,plain,
( in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),set_difference(sK1,singleton(sK2)))
| in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),sK1)
| in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),singleton(sK2)) ),
inference(resolution,[],[f100,f174]) ).
fof(f174,plain,
( in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))))
| in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),sK1) ),
inference(resolution,[],[f170,f89]) ).
fof(f170,plain,
( ~ subset(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))))
| in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))) ),
inference(resolution,[],[f166,f89]) ).
fof(f100,plain,
! [X3,X0,X1] :
( ~ in(X3,set_union2(X1,X0))
| in(X3,X1)
| in(X3,X0) ),
inference(equality_resolution,[],[f75]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2)
| set_union2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f221,plain,
( ~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),sK1)
| sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1) = sK2 ),
inference(subsumption_resolution,[],[f215,f203]) ).
fof(f203,plain,
( ~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),singleton(sK2))
| sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1) = sK2 ),
inference(resolution,[],[f198,f101]) ).
fof(f198,plain,
( ~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))))
| sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1) = sK2 ),
inference(resolution,[],[f195,f109]) ).
fof(f195,plain,
( in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),singleton(sK2))
| ~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))) ),
inference(subsumption_resolution,[],[f193,f171]) ).
fof(f193,plain,
( in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),sK1)
| ~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))))
| in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),singleton(sK2)) ),
inference(resolution,[],[f182,f103]) ).
fof(f182,plain,
( in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),set_difference(sK1,singleton(sK2)))
| ~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))))
| in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),singleton(sK2)) ),
inference(resolution,[],[f100,f173]) ).
fof(f173,plain,
( in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))))
| ~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))) ),
inference(resolution,[],[f170,f90]) ).
fof(f215,plain,
( sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1) = sK2
| in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),singleton(sK2))
| ~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),sK1) ),
inference(resolution,[],[f105,f202]) ).
fof(f202,plain,
( ~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),set_difference(sK1,singleton(sK2)))
| sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1) = sK2 ),
inference(resolution,[],[f198,f102]) ).
fof(f102,plain,
! [X3,X0,X1] :
( in(X3,set_union2(X1,X0))
| ~ in(X3,X0) ),
inference(equality_resolution,[],[f73]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X0)
| set_union2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f105,plain,
! [X2,X1,X4] :
( in(X4,set_difference(X1,X2))
| ~ in(X4,X1)
| in(X4,X2) ),
inference(equality_resolution,[],[f77]) ).
fof(f77,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X1)
| in(X4,X2)
| set_difference(X1,X2) != X0 ),
inference(cnf_transformation,[],[f47]) ).
fof(f171,plain,
( ~ in(sK5(set_union2(singleton(sK2),set_difference(sK1,singleton(sK2))),sK1),sK1)
| ~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))) ),
inference(resolution,[],[f169,f90]) ).
fof(f258,plain,
in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),singleton(sK2)),
inference(subsumption_resolution,[],[f257,f250]) ).
fof(f250,plain,
in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),sK1),
inference(subsumption_resolution,[],[f226,f68]) ).
fof(f226,plain,
( in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),sK1)
| ~ in(sK2,sK1) ),
inference(backward_demodulation,[],[f172,f222]) ).
fof(f257,plain,
( ~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),sK1)
| in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),singleton(sK2)) ),
inference(resolution,[],[f254,f105]) ).
fof(f254,plain,
~ in(sK5(sK1,set_union2(singleton(sK2),set_difference(sK1,singleton(sK2)))),set_difference(sK1,singleton(sK2))),
inference(resolution,[],[f249,f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET986+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 14:34:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.49 % (8529)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.49 % (8537)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.53 % (8517)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53 % (8521)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.53 % (8536)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.53 % (8515)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53 % (8516)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.53 % (8528)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.53 % (8543)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.53 % (8518)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53 % (8523)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53 % (8519)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.53 % (8524)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53 % (8541)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.42/0.54 % (8522)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.42/0.54 % (8522)Instruction limit reached!
% 1.42/0.54 % (8522)------------------------------
% 1.42/0.54 % (8522)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.42/0.54 % (8522)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.42/0.54 % (8522)Termination reason: Unknown
% 1.42/0.54 % (8522)Termination phase: Saturation
% 1.42/0.54
% 1.42/0.54 % (8522)Memory used [KB]: 5373
% 1.42/0.54 % (8522)Time elapsed: 0.003 s
% 1.42/0.54 % (8522)Instructions burned: 3 (million)
% 1.42/0.54 % (8522)------------------------------
% 1.42/0.54 % (8522)------------------------------
% 1.42/0.54 % (8533)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.42/0.54 % (8526)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.42/0.54 % (8536)First to succeed.
% 1.42/0.54 % (8531)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.42/0.54 % (8527)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.42/0.54 % (8532)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.42/0.55 % (8536)Refutation found. Thanks to Tanya!
% 1.42/0.55 % SZS status Theorem for theBenchmark
% 1.42/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 1.42/0.55 % (8536)------------------------------
% 1.42/0.55 % (8536)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.42/0.55 % (8536)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.42/0.55 % (8536)Termination reason: Refutation
% 1.42/0.55
% 1.42/0.55 % (8536)Memory used [KB]: 1151
% 1.42/0.55 % (8536)Time elapsed: 0.105 s
% 1.42/0.55 % (8536)Instructions burned: 11 (million)
% 1.42/0.55 % (8536)------------------------------
% 1.42/0.55 % (8536)------------------------------
% 1.42/0.55 % (8513)Success in time 0.192 s
%------------------------------------------------------------------------------