TSTP Solution File: SEU205+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU205+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n001.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 18:27:22 EDT 2022
% Result : Theorem 1.40s 0.53s
% Output : Refutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 77 ( 13 unt; 0 def)
% Number of atoms : 342 ( 41 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 419 ( 154 ~; 166 |; 74 &)
% ( 13 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 201 ( 172 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f351,plain,
$false,
inference(subsumption_resolution,[],[f350,f273]) ).
fof(f273,plain,
in(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9),sK8),
inference(subsumption_resolution,[],[f265,f133]) ).
fof(f133,plain,
relation(sK9),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
( relation(sK9)
& relation_image(sK9,set_intersection2(relation_dom(sK9),sK8)) != relation_image(sK9,sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f88,f89]) ).
fof(f89,plain,
( ? [X0,X1] :
( relation(X1)
& relation_image(X1,X0) != relation_image(X1,set_intersection2(relation_dom(X1),X0)) )
=> ( relation(sK9)
& relation_image(sK9,set_intersection2(relation_dom(sK9),sK8)) != relation_image(sK9,sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
? [X0,X1] :
( relation(X1)
& relation_image(X1,X0) != relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
? [X1,X0] :
( relation(X0)
& relation_image(X0,X1) != relation_image(X0,set_intersection2(relation_dom(X0),X1)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,plain,
~ ! [X1,X0] :
( relation(X0)
=> relation_image(X0,X1) = relation_image(X0,set_intersection2(relation_dom(X0),X1)) ),
inference(rectify,[],[f32]) ).
fof(f32,negated_conjecture,
~ ! [X1,X0] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
inference(negated_conjecture,[],[f31]) ).
fof(f31,conjecture,
! [X1,X0] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
fof(f265,plain,
( in(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9),sK8)
| ~ relation(sK9) ),
inference(resolution,[],[f260,f110]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_image(X2,X1))
| ~ relation(X2)
| in(sK4(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ( in(ordered_pair(sK4(X0,X1,X2),X0),X2)
& in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) )
& ( in(X0,relation_image(X2,X1))
| ! [X4] :
( ~ in(ordered_pair(X4,X0),X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X2)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f75,f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ? [X3] :
( in(ordered_pair(X3,X0),X2)
& in(X3,X1)
& in(X3,relation_dom(X2)) )
=> ( in(ordered_pair(sK4(X0,X1,X2),X0),X2)
& in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),relation_dom(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ? [X3] :
( in(ordered_pair(X3,X0),X2)
& in(X3,X1)
& in(X3,relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) )
& ( in(X0,relation_image(X2,X1))
| ! [X4] :
( ~ in(ordered_pair(X4,X0),X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X2)) ) ) ) ),
inference(rectify,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ? [X3] :
( in(ordered_pair(X3,X0),X2)
& in(X3,X1)
& in(X3,relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) )
& ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,X1)
| ~ in(X3,relation_dom(X2)) ) ) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ? [X3] :
( in(ordered_pair(X3,X0),X2)
& in(X3,X1)
& in(X3,relation_dom(X2)) )
<=> in(X0,relation_image(X2,X1)) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X2,X1,X0] :
( relation(X2)
=> ( ? [X3] :
( in(ordered_pair(X3,X0),X2)
& in(X3,X1)
& in(X3,relation_dom(X2)) )
<=> in(X0,relation_image(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f260,plain,
in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8)),
inference(duplicate_literal_removal,[],[f258]) ).
fof(f258,plain,
( in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8))
| in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8))
| in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8)) ),
inference(resolution,[],[f218,f186]) ).
fof(f186,plain,
( in(sK3(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8)
| in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8)) ),
inference(resolution,[],[f184,f160]) ).
fof(f160,plain,
! [X2,X3,X1] :
( ~ in(X3,set_intersection2(X1,X2))
| in(X3,X2) ),
inference(equality_resolution,[],[f124]) ).
fof(f124,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X0)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X2) )
| ~ in(X3,X0) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ( ( ~ in(sK7(X0,X1,X2),X1)
| ~ in(sK7(X0,X1,X2),X2)
| ~ in(sK7(X0,X1,X2),X0) )
& ( ( in(sK7(X0,X1,X2),X1)
& in(sK7(X0,X1,X2),X2) )
| in(sK7(X0,X1,X2),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f85,f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X1)
| ~ in(X4,X2)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X2) )
| in(X4,X0) ) )
=> ( ( ~ in(sK7(X0,X1,X2),X1)
| ~ in(sK7(X0,X1,X2),X2)
| ~ in(sK7(X0,X1,X2),X0) )
& ( ( in(sK7(X0,X1,X2),X1)
& in(sK7(X0,X1,X2),X2) )
| in(sK7(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X2) )
| ~ in(X3,X0) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ? [X4] :
( ( ~ in(X4,X1)
| ~ in(X4,X2)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X2) )
| in(X4,X0) ) ) ) ),
inference(rectify,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X2) )
| ~ in(X3,X0) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X2) )
| in(X3,X0) ) ) ) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X2) )
| ~ in(X3,X0) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X2) )
| in(X3,X0) ) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ! [X3] :
( in(X3,X0)
<=> ( in(X3,X1)
& in(X3,X2) ) )
<=> set_intersection2(X1,X2) = X0 ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) )
<=> set_intersection2(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f184,plain,
( in(sK3(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),set_intersection2(relation_dom(sK9),sK8))
| in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8)) ),
inference(subsumption_resolution,[],[f180,f133]) ).
fof(f180,plain,
( in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8))
| in(sK3(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),set_intersection2(relation_dom(sK9),sK8))
| ~ relation(sK9) ),
inference(resolution,[],[f171,f163]) ).
fof(f163,plain,
! [X2,X0,X1] :
( sQ13_eqProxy(relation_image(X0,X1),X2)
| ~ relation(X0)
| in(sK3(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2) ),
inference(equality_proxy_replacement,[],[f101,f161]) ).
fof(f161,plain,
! [X0,X1] :
( sQ13_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ13_eqProxy])]) ).
fof(f101,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(sK3(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ! [X1,X2] :
( ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) )
& ( ( in(sK1(X0,X1,X3),X1)
& in(ordered_pair(sK1(X0,X1,X3),X3),X0) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 )
& ( relation_image(X0,X1) = X2
| ( ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,sK2(X0,X1,X2)),X0) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),X1)
& in(ordered_pair(sK3(X0,X1,X2),sK2(X0,X1,X2)),X0) )
| in(sK2(X0,X1,X2),X2) ) ) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f69,f72,f71,f70]) ).
fof(f70,plain,
! [X0,X1,X3] :
( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) )
=> ( in(sK1(X0,X1,X3),X1)
& in(ordered_pair(sK1(X0,X1,X3),X3),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ? [X6] :
( ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| ~ in(X6,X2) )
& ( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) )
| in(X6,X2) ) )
=> ( ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,sK2(X0,X1,X2)),X0) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,sK2(X0,X1,X2)),X0) )
| in(sK2(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,sK2(X0,X1,X2)),X0) )
=> ( in(sK3(X0,X1,X2),X1)
& in(ordered_pair(sK3(X0,X1,X2),sK2(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0] :
( ! [X1,X2] :
( ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 )
& ( relation_image(X0,X1) = X2
| ? [X6] :
( ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| ~ in(X6,X2) )
& ( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) )
| in(X6,X2) ) ) ) )
| ~ relation(X0) ),
inference(rectify,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ! [X2,X1] :
( ( ! [X3] :
( ( in(X3,X1)
| ! [X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X0) ) )
& ( ? [X4] :
( in(X4,X2)
& in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X1) ) )
| relation_image(X0,X2) != X1 )
& ( relation_image(X0,X2) = X1
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X1) )
& ( ? [X4] :
( in(X4,X2)
& in(ordered_pair(X4,X3),X0) )
| in(X3,X1) ) ) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ! [X2,X1] :
( ! [X3] :
( in(X3,X1)
<=> ? [X4] :
( in(X4,X2)
& in(ordered_pair(X4,X3),X0) ) )
<=> relation_image(X0,X2) = X1 )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( relation(X0)
=> ! [X2,X1] :
( ! [X3] :
( in(X3,X1)
<=> ? [X4] :
( in(X4,X2)
& in(ordered_pair(X4,X3),X0) ) )
<=> relation_image(X0,X2) = X1 ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X2,X1] :
( ! [X3] :
( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
<=> in(X3,X2) )
<=> relation_image(X0,X1) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f171,plain,
~ sQ13_eqProxy(relation_image(sK9,set_intersection2(relation_dom(sK9),sK8)),relation_image(sK9,sK8)),
inference(equality_proxy_replacement,[],[f132,f161]) ).
fof(f132,plain,
relation_image(sK9,set_intersection2(relation_dom(sK9),sK8)) != relation_image(sK9,sK8),
inference(cnf_transformation,[],[f90]) ).
fof(f218,plain,
! [X0] :
( ~ in(sK3(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),X0)
| in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,X0))
| in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8)) ),
inference(subsumption_resolution,[],[f216,f133]) ).
fof(f216,plain,
! [X0] :
( ~ in(sK3(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),X0)
| in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,X0))
| in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8))
| ~ relation(sK9) ),
inference(resolution,[],[f183,f155]) ).
fof(f155,plain,
! [X3,X0,X1,X4] :
( ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X0)
| ~ in(X4,X1)
| in(X3,relation_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f148]) ).
fof(f148,plain,
! [X2,X3,X0,X1,X4] :
( in(X3,X2)
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X0)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f105,f115]) ).
fof(f115,plain,
! [X0,X1] : unordered_pair(unordered_pair(X1,X0),singleton(X1)) = ordered_pair(X1,X0),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] : unordered_pair(unordered_pair(X1,X0),singleton(X1)) = ordered_pair(X1,X0),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f105,plain,
! [X2,X3,X0,X1,X4] :
( in(X3,X2)
| ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f183,plain,
( in(unordered_pair(unordered_pair(sK3(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8))),singleton(sK3(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)))),sK9)
| in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8)) ),
inference(subsumption_resolution,[],[f179,f133]) ).
fof(f179,plain,
( ~ relation(sK9)
| in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8))
| in(unordered_pair(unordered_pair(sK3(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8))),singleton(sK3(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)))),sK9) ),
inference(resolution,[],[f171,f164]) ).
fof(f164,plain,
! [X2,X0,X1] :
( sQ13_eqProxy(relation_image(X0,X1),X2)
| in(unordered_pair(unordered_pair(sK3(X0,X1,X2),sK2(X0,X1,X2)),singleton(sK3(X0,X1,X2))),X0)
| in(sK2(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(equality_proxy_replacement,[],[f151,f161]) ).
fof(f151,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK3(X0,X1,X2),sK2(X0,X1,X2)),singleton(sK3(X0,X1,X2))),X0)
| in(sK2(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f100,f115]) ).
fof(f100,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(ordered_pair(sK3(X0,X1,X2),sK2(X0,X1,X2)),X0)
| in(sK2(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f350,plain,
~ in(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9),sK8),
inference(subsumption_resolution,[],[f349,f272]) ).
fof(f272,plain,
in(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9),relation_dom(sK9)),
inference(subsumption_resolution,[],[f262,f133]) ).
fof(f262,plain,
( ~ relation(sK9)
| in(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9),relation_dom(sK9)) ),
inference(resolution,[],[f260,f109]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_image(X2,X1))
| in(sK4(X0,X1,X2),relation_dom(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f349,plain,
( ~ in(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9),relation_dom(sK9))
| ~ in(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9),sK8) ),
inference(resolution,[],[f337,f158]) ).
fof(f158,plain,
! [X2,X3,X1] :
( in(X3,set_intersection2(X1,X2))
| ~ in(X3,X1)
| ~ in(X3,X2) ),
inference(equality_resolution,[],[f126]) ).
fof(f126,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f87]) ).
fof(f337,plain,
~ in(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9),set_intersection2(relation_dom(sK9),sK8)),
inference(subsumption_resolution,[],[f336,f260]) ).
fof(f336,plain,
( ~ in(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9),set_intersection2(relation_dom(sK9),sK8))
| ~ in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8)) ),
inference(subsumption_resolution,[],[f335,f133]) ).
fof(f335,plain,
( ~ relation(sK9)
| ~ in(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9),set_intersection2(relation_dom(sK9),sK8))
| ~ in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8)) ),
inference(subsumption_resolution,[],[f328,f171]) ).
fof(f328,plain,
( sQ13_eqProxy(relation_image(sK9,set_intersection2(relation_dom(sK9),sK8)),relation_image(sK9,sK8))
| ~ in(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),relation_image(sK9,sK8))
| ~ in(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9),set_intersection2(relation_dom(sK9),sK8))
| ~ relation(sK9) ),
inference(resolution,[],[f270,f162]) ).
fof(f162,plain,
! [X2,X0,X1,X7] :
( ~ in(unordered_pair(unordered_pair(X7,sK2(X0,X1,X2)),singleton(X7)),X0)
| ~ relation(X0)
| ~ in(X7,X1)
| sQ13_eqProxy(relation_image(X0,X1),X2)
| ~ in(sK2(X0,X1,X2),X2) ),
inference(equality_proxy_replacement,[],[f150,f161]) ).
fof(f150,plain,
! [X2,X0,X1,X7] :
( relation_image(X0,X1) = X2
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,sK2(X0,X1,X2)),singleton(X7)),X0)
| ~ in(sK2(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f102,f115]) ).
fof(f102,plain,
! [X2,X0,X1,X7] :
( relation_image(X0,X1) = X2
| ~ in(X7,X1)
| ~ in(ordered_pair(X7,sK2(X0,X1,X2)),X0)
| ~ in(sK2(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f270,plain,
in(unordered_pair(unordered_pair(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9),sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8))),singleton(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9))),sK9),
inference(subsumption_resolution,[],[f264,f133]) ).
fof(f264,plain,
( ~ relation(sK9)
| in(unordered_pair(unordered_pair(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9),sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8))),singleton(sK4(sK2(sK9,set_intersection2(relation_dom(sK9),sK8),relation_image(sK9,sK8)),sK8,sK9))),sK9) ),
inference(resolution,[],[f260,f152]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_image(X2,X1))
| in(unordered_pair(unordered_pair(sK4(X0,X1,X2),X0),singleton(sK4(X0,X1,X2))),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f111,f115]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| in(ordered_pair(sK4(X0,X1,X2),X0),X2)
| ~ in(X0,relation_image(X2,X1)) ),
inference(cnf_transformation,[],[f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU205+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n001.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 15:12:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47 % (22205)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.20/0.50 % (22186)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.51 % (22182)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.51 % (22184)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.51 % (22184)Refutation not found, incomplete strategy% (22184)------------------------------
% 0.20/0.51 % (22184)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (22184)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (22184)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51
% 0.20/0.51 % (22184)Memory used [KB]: 6012
% 0.20/0.51 % (22184)Time elapsed: 0.105 s
% 0.20/0.51 % (22184)Instructions burned: 2 (million)
% 0.20/0.51 % (22184)------------------------------
% 0.20/0.51 % (22184)------------------------------
% 0.20/0.51 % (22187)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.51 % (22210)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.20/0.51 % (22185)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51 % (22207)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.20/0.51 % (22206)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52 % (22202)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.52 % (22186)Instruction limit reached!
% 0.20/0.52 % (22186)------------------------------
% 0.20/0.52 % (22186)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (22196)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.52 % (22194)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.20/0.52 % (22190)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.52 % (22202)Instruction limit reached!
% 0.20/0.52 % (22202)------------------------------
% 0.20/0.52 % (22202)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (22202)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (22202)Termination reason: Unknown
% 0.20/0.52 % (22202)Termination phase: Finite model building preprocessing
% 0.20/0.52
% 0.20/0.52 % (22202)Memory used [KB]: 1535
% 0.20/0.52 % (22202)Time elapsed: 0.004 s
% 0.20/0.52 % (22202)Instructions burned: 3 (million)
% 0.20/0.52 % (22202)------------------------------
% 0.20/0.52 % (22202)------------------------------
% 0.20/0.52 % (22192)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.52 % (22183)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.52 % (22195)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.52 % (22208)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.52 % (22203)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.52 % (22203)Instruction limit reached!
% 0.20/0.52 % (22203)------------------------------
% 0.20/0.52 % (22203)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (22203)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (22203)Termination reason: Unknown
% 0.20/0.53 % (22203)Termination phase: Preprocessing 3
% 0.20/0.53
% 0.20/0.53 % (22203)Memory used [KB]: 1407
% 0.20/0.53 % (22203)Time elapsed: 0.003 s
% 0.20/0.53 % (22203)Instructions burned: 2 (million)
% 0.20/0.53 % (22203)------------------------------
% 0.20/0.53 % (22203)------------------------------
% 0.20/0.53 % (22211)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.53 % (22200)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.53 % (22209)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53 % (22212)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.20/0.53 % (22194)Instruction limit reached!
% 0.20/0.53 % (22194)------------------------------
% 0.20/0.53 % (22194)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (22196)First to succeed.
% 1.40/0.53 % (22194)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.40/0.53 % (22194)Termination reason: Unknown
% 1.40/0.53 % (22194)Termination phase: Saturation
% 1.40/0.53
% 1.40/0.53 % (22194)Memory used [KB]: 6268
% 1.40/0.53 % (22194)Time elapsed: 0.136 s
% 1.40/0.53 % (22194)Instructions burned: 12 (million)
% 1.40/0.53 % (22194)------------------------------
% 1.40/0.53 % (22194)------------------------------
% 1.40/0.53 % (22188)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.40/0.53 % (22186)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.40/0.53 % (22196)Refutation found. Thanks to Tanya!
% 1.40/0.53 % SZS status Theorem for theBenchmark
% 1.40/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 1.40/0.53 % (22196)------------------------------
% 1.40/0.53 % (22196)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.40/0.53 % (22196)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.40/0.53 % (22196)Termination reason: Refutation
% 1.40/0.53
% 1.40/0.53 % (22196)Memory used [KB]: 1663
% 1.40/0.53 % (22196)Time elapsed: 0.134 s
% 1.40/0.53 % (22196)Instructions burned: 10 (million)
% 1.40/0.53 % (22196)------------------------------
% 1.40/0.53 % (22196)------------------------------
% 1.40/0.53 % (22179)Success in time 0.18 s
%------------------------------------------------------------------------------