TSTP Solution File: SEU242+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU242+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_sat --cores 0 -t %d %s
% Computer : n027.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 18:32:47 EDT 2022
% Result : Theorem 1.44s 0.58s
% Output : Refutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 8
% Syntax : Number of formulae : 104 ( 13 unt; 0 def)
% Number of atoms : 454 ( 95 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 564 ( 214 ~; 255 |; 81 &)
% ( 6 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 136 ( 113 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f570,plain,
$false,
inference(subsumption_resolution,[],[f568,f509]) ).
fof(f509,plain,
~ connected(sK1),
inference(trivial_inequality_removal,[],[f498]) ).
fof(f498,plain,
( ~ connected(sK1)
| sK2 != sK2 ),
inference(superposition,[],[f102,f493]) ).
fof(f493,plain,
sK3 = sK2,
inference(subsumption_resolution,[],[f492,f428]) ).
fof(f428,plain,
( connected(sK1)
| sK3 = sK2 ),
inference(resolution,[],[f427,f210]) ).
fof(f210,plain,
( ~ is_connected_in(sK1,relation_field(sK1))
| connected(sK1) ),
inference(resolution,[],[f124,f105]) ).
fof(f105,plain,
relation(sK1),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
( relation(sK1)
& ( ~ connected(sK1)
| ( ~ in(ordered_pair(sK3,sK2),sK1)
& in(sK2,relation_field(sK1))
& sK3 != sK2
& in(sK3,relation_field(sK1))
& ~ in(ordered_pair(sK2,sK3),sK1) ) )
& ( connected(sK1)
| ! [X3,X4] :
( in(ordered_pair(X4,X3),sK1)
| ~ in(X3,relation_field(sK1))
| X3 = X4
| ~ in(X4,relation_field(sK1))
| in(ordered_pair(X3,X4),sK1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f68,f70,f69]) ).
fof(f69,plain,
( ? [X0] :
( relation(X0)
& ( ~ connected(X0)
| ? [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
& in(X1,relation_field(X0))
& X1 != X2
& in(X2,relation_field(X0))
& ~ in(ordered_pair(X1,X2),X0) ) )
& ( connected(X0)
| ! [X3,X4] :
( in(ordered_pair(X4,X3),X0)
| ~ in(X3,relation_field(X0))
| X3 = X4
| ~ in(X4,relation_field(X0))
| in(ordered_pair(X3,X4),X0) ) ) )
=> ( relation(sK1)
& ( ~ connected(sK1)
| ? [X2,X1] :
( ~ in(ordered_pair(X2,X1),sK1)
& in(X1,relation_field(sK1))
& X1 != X2
& in(X2,relation_field(sK1))
& ~ in(ordered_pair(X1,X2),sK1) ) )
& ( connected(sK1)
| ! [X4,X3] :
( in(ordered_pair(X4,X3),sK1)
| ~ in(X3,relation_field(sK1))
| X3 = X4
| ~ in(X4,relation_field(sK1))
| in(ordered_pair(X3,X4),sK1) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
( ? [X2,X1] :
( ~ in(ordered_pair(X2,X1),sK1)
& in(X1,relation_field(sK1))
& X1 != X2
& in(X2,relation_field(sK1))
& ~ in(ordered_pair(X1,X2),sK1) )
=> ( ~ in(ordered_pair(sK3,sK2),sK1)
& in(sK2,relation_field(sK1))
& sK3 != sK2
& in(sK3,relation_field(sK1))
& ~ in(ordered_pair(sK2,sK3),sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
? [X0] :
( relation(X0)
& ( ~ connected(X0)
| ? [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
& in(X1,relation_field(X0))
& X1 != X2
& in(X2,relation_field(X0))
& ~ in(ordered_pair(X1,X2),X0) ) )
& ( connected(X0)
| ! [X3,X4] :
( in(ordered_pair(X4,X3),X0)
| ~ in(X3,relation_field(X0))
| X3 = X4
| ~ in(X4,relation_field(X0))
| in(ordered_pair(X3,X4),X0) ) ) ),
inference(rectify,[],[f67]) ).
fof(f67,plain,
? [X0] :
( relation(X0)
& ( ~ connected(X0)
| ? [X2,X1] :
( ~ in(ordered_pair(X1,X2),X0)
& in(X2,relation_field(X0))
& X1 != X2
& in(X1,relation_field(X0))
& ~ in(ordered_pair(X2,X1),X0) ) )
& ( connected(X0)
| ! [X2,X1] :
( in(ordered_pair(X1,X2),X0)
| ~ in(X2,relation_field(X0))
| X1 = X2
| ~ in(X1,relation_field(X0))
| in(ordered_pair(X2,X1),X0) ) ) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
? [X0] :
( relation(X0)
& ( ~ connected(X0)
| ? [X2,X1] :
( ~ in(ordered_pair(X1,X2),X0)
& in(X2,relation_field(X0))
& X1 != X2
& in(X1,relation_field(X0))
& ~ in(ordered_pair(X2,X1),X0) ) )
& ( connected(X0)
| ! [X2,X1] :
( in(ordered_pair(X1,X2),X0)
| ~ in(X2,relation_field(X0))
| X1 = X2
| ~ in(X1,relation_field(X0))
| in(ordered_pair(X2,X1),X0) ) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
? [X0] :
( relation(X0)
& ( ! [X2,X1] :
( in(ordered_pair(X1,X2),X0)
| ~ in(X2,relation_field(X0))
| X1 = X2
| ~ in(X1,relation_field(X0))
| in(ordered_pair(X2,X1),X0) )
<~> connected(X0) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( connected(X0)
<=> ! [X2,X1] :
~ ( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2 ) ) ),
inference(negated_conjecture,[],[f25]) ).
fof(f25,conjecture,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> ! [X2,X1] :
~ ( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_wellord1) ).
fof(f124,plain,
! [X0] :
( ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ~ relation(X0)
| ( ( connected(X0)
| ~ is_connected_in(X0,relation_field(X0)) )
& ( is_connected_in(X0,relation_field(X0))
| ~ connected(X0) ) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ~ relation(X0)
| ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_2) ).
fof(f427,plain,
( is_connected_in(sK1,relation_field(sK1))
| sK3 = sK2 ),
inference(subsumption_resolution,[],[f426,f105]) ).
fof(f426,plain,
( is_connected_in(sK1,relation_field(sK1))
| ~ relation(sK1)
| sK3 = sK2 ),
inference(trivial_inequality_removal,[],[f425]) ).
fof(f425,plain,
( is_connected_in(sK1,relation_field(sK1))
| sK3 = sK2
| sK5(sK1,relation_field(sK1)) != sK5(sK1,relation_field(sK1))
| ~ relation(sK1) ),
inference(superposition,[],[f113,f416]) ).
fof(f416,plain,
( sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1))
| sK3 = sK2 ),
inference(subsumption_resolution,[],[f415,f354]) ).
fof(f354,plain,
( connected(sK1)
| sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1)) ),
inference(subsumption_resolution,[],[f353,f210]) ).
fof(f353,plain,
( connected(sK1)
| sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1))
| is_connected_in(sK1,relation_field(sK1)) ),
inference(resolution,[],[f338,f223]) ).
fof(f223,plain,
! [X1] :
( in(sK5(sK1,X1),X1)
| is_connected_in(sK1,X1) ),
inference(resolution,[],[f115,f105]) ).
fof(f115,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ( ~ in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
& in(sK5(X0,X1),X1)
& ~ in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
& sK5(X0,X1) != sK6(X0,X1)
& in(sK6(X0,X1),X1) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| ~ in(X4,X1)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1) )
| ~ is_connected_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f77,f78]) ).
fof(f78,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& in(X2,X1)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1) )
=> ( ~ in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
& in(sK5(X0,X1),X1)
& ~ in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
& sK5(X0,X1) != sK6(X0,X1)
& in(sK6(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& in(X2,X1)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| ~ in(X4,X1)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1) )
| ~ is_connected_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ? [X3,X2] :
( ~ in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& ~ in(ordered_pair(X3,X2),X0)
& X2 != X3
& in(X2,X1) ) )
& ( ! [X3,X2] :
( in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X2),X0)
| X2 = X3
| ~ in(X2,X1) )
| ~ is_connected_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X3,X2] :
( in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X2),X0)
| X2 = X3
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( ! [X3,X2] :
~ ( ~ in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& X2 != X3
& in(X2,X1)
& ~ in(ordered_pair(X3,X2),X0) )
<=> is_connected_in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_2) ).
fof(f338,plain,
( ~ in(sK5(sK1,relation_field(sK1)),relation_field(sK1))
| connected(sK1)
| sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1)) ),
inference(subsumption_resolution,[],[f337,f210]) ).
fof(f337,plain,
( connected(sK1)
| is_connected_in(sK1,relation_field(sK1))
| ~ in(sK5(sK1,relation_field(sK1)),relation_field(sK1))
| sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1)) ),
inference(duplicate_literal_removal,[],[f336]) ).
fof(f336,plain,
( sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1))
| is_connected_in(sK1,relation_field(sK1))
| is_connected_in(sK1,relation_field(sK1))
| ~ in(sK5(sK1,relation_field(sK1)),relation_field(sK1))
| connected(sK1) ),
inference(resolution,[],[f335,f217]) ).
fof(f217,plain,
! [X1] :
( in(sK6(sK1,X1),X1)
| is_connected_in(sK1,X1) ),
inference(resolution,[],[f112,f105]) ).
fof(f112,plain,
! [X0,X1] :
( ~ relation(X0)
| is_connected_in(X0,X1)
| in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f335,plain,
! [X0] :
( ~ in(sK6(sK1,X0),relation_field(sK1))
| connected(sK1)
| is_connected_in(sK1,X0)
| ~ in(sK5(sK1,X0),relation_field(sK1))
| sK5(sK1,X0) = sK6(sK1,X0) ),
inference(subsumption_resolution,[],[f327,f250]) ).
fof(f250,plain,
! [X1] :
( ~ in(unordered_pair(singleton(sK5(sK1,X1)),unordered_pair(sK5(sK1,X1),sK6(sK1,X1))),sK1)
| is_connected_in(sK1,X1) ),
inference(forward_demodulation,[],[f243,f98]) ).
fof(f98,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f243,plain,
! [X1] :
( is_connected_in(sK1,X1)
| ~ in(unordered_pair(unordered_pair(sK5(sK1,X1),sK6(sK1,X1)),singleton(sK5(sK1,X1))),sK1) ),
inference(resolution,[],[f142,f105]) ).
fof(f142,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK5(X0,X1),sK6(X0,X1)),singleton(sK5(X0,X1))),X0)
| is_connected_in(X0,X1) ),
inference(definition_unfolding,[],[f114,f118]) ).
fof(f118,plain,
! [X0,X1] : unordered_pair(unordered_pair(X1,X0),singleton(X1)) = ordered_pair(X1,X0),
inference(cnf_transformation,[],[f81]) ).
fof(f81,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/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f114,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f327,plain,
! [X0] :
( is_connected_in(sK1,X0)
| sK5(sK1,X0) = sK6(sK1,X0)
| connected(sK1)
| in(unordered_pair(singleton(sK5(sK1,X0)),unordered_pair(sK5(sK1,X0),sK6(sK1,X0))),sK1)
| ~ in(sK6(sK1,X0),relation_field(sK1))
| ~ in(sK5(sK1,X0),relation_field(sK1)) ),
inference(resolution,[],[f168,f241]) ).
fof(f241,plain,
! [X1] :
( ~ in(unordered_pair(singleton(sK6(sK1,X1)),unordered_pair(sK5(sK1,X1),sK6(sK1,X1))),sK1)
| is_connected_in(sK1,X1) ),
inference(forward_demodulation,[],[f240,f98]) ).
fof(f240,plain,
! [X1] :
( is_connected_in(sK1,X1)
| ~ in(unordered_pair(singleton(sK6(sK1,X1)),unordered_pair(sK6(sK1,X1),sK5(sK1,X1))),sK1) ),
inference(forward_demodulation,[],[f231,f98]) ).
fof(f231,plain,
! [X1] :
( is_connected_in(sK1,X1)
| ~ in(unordered_pair(unordered_pair(sK6(sK1,X1),sK5(sK1,X1)),singleton(sK6(sK1,X1))),sK1) ),
inference(resolution,[],[f141,f105]) ).
fof(f141,plain,
! [X0,X1] :
( ~ relation(X0)
| is_connected_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK6(X0,X1),sK5(X0,X1)),singleton(sK6(X0,X1))),X0) ),
inference(definition_unfolding,[],[f116,f118]) ).
fof(f116,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f168,plain,
! [X2,X3] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),sK1)
| in(unordered_pair(singleton(X2),unordered_pair(X3,X2)),sK1)
| ~ in(X3,relation_field(sK1))
| connected(sK1)
| ~ in(X2,relation_field(sK1))
| X2 = X3 ),
inference(forward_demodulation,[],[f167,f98]) ).
fof(f167,plain,
! [X2,X3] :
( connected(sK1)
| in(unordered_pair(singleton(X2),unordered_pair(X3,X2)),sK1)
| X2 = X3
| ~ in(X2,relation_field(sK1))
| in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),sK1)
| ~ in(X3,relation_field(sK1)) ),
inference(forward_demodulation,[],[f161,f98]) ).
fof(f161,plain,
! [X2,X3] :
( in(unordered_pair(unordered_pair(X3,X2),singleton(X2)),sK1)
| in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),sK1)
| ~ in(X3,relation_field(sK1))
| ~ in(X2,relation_field(sK1))
| X2 = X3
| connected(sK1) ),
inference(superposition,[],[f139,f98]) ).
fof(f139,plain,
! [X3,X4] :
( in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),sK1)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK1)
| ~ in(X3,relation_field(sK1))
| ~ in(X4,relation_field(sK1))
| connected(sK1)
| X3 = X4 ),
inference(definition_unfolding,[],[f99,f118,f118]) ).
fof(f99,plain,
! [X3,X4] :
( connected(sK1)
| in(ordered_pair(X4,X3),sK1)
| ~ in(X3,relation_field(sK1))
| X3 = X4
| ~ in(X4,relation_field(sK1))
| in(ordered_pair(X3,X4),sK1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f415,plain,
( ~ connected(sK1)
| sK3 = sK2
| sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1)) ),
inference(resolution,[],[f412,f103]) ).
fof(f103,plain,
( in(sK2,relation_field(sK1))
| ~ connected(sK1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f412,plain,
( ~ in(sK2,relation_field(sK1))
| sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1))
| sK3 = sK2 ),
inference(subsumption_resolution,[],[f411,f354]) ).
fof(f411,plain,
( sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1))
| ~ connected(sK1)
| sK3 = sK2
| ~ in(sK2,relation_field(sK1)) ),
inference(resolution,[],[f410,f101]) ).
fof(f101,plain,
( in(sK3,relation_field(sK1))
| ~ connected(sK1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f410,plain,
( ~ in(sK3,relation_field(sK1))
| sK3 = sK2
| ~ in(sK2,relation_field(sK1))
| sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1)) ),
inference(subsumption_resolution,[],[f408,f354]) ).
fof(f408,plain,
( ~ connected(sK1)
| sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1))
| ~ in(sK2,relation_field(sK1))
| ~ in(sK3,relation_field(sK1))
| sK3 = sK2 ),
inference(resolution,[],[f405,f170]) ).
fof(f170,plain,
( ~ in(unordered_pair(singleton(sK3),unordered_pair(sK2,sK3)),sK1)
| ~ connected(sK1) ),
inference(forward_demodulation,[],[f155,f98]) ).
fof(f155,plain,
( ~ connected(sK1)
| ~ in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK2)),sK1) ),
inference(superposition,[],[f137,f98]) ).
fof(f137,plain,
( ~ in(unordered_pair(unordered_pair(sK3,sK2),singleton(sK3)),sK1)
| ~ connected(sK1) ),
inference(definition_unfolding,[],[f104,f118]) ).
fof(f104,plain,
( ~ connected(sK1)
| ~ in(ordered_pair(sK3,sK2),sK1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f405,plain,
( in(unordered_pair(singleton(sK3),unordered_pair(sK2,sK3)),sK1)
| ~ in(sK2,relation_field(sK1))
| sK3 = sK2
| ~ in(sK3,relation_field(sK1))
| sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1)) ),
inference(forward_demodulation,[],[f404,f98]) ).
fof(f404,plain,
( ~ in(sK3,relation_field(sK1))
| ~ in(sK2,relation_field(sK1))
| sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1))
| in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK2)),sK1)
| sK3 = sK2 ),
inference(subsumption_resolution,[],[f390,f354]) ).
fof(f390,plain,
( in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK2)),sK1)
| ~ in(sK3,relation_field(sK1))
| ~ connected(sK1)
| sK3 = sK2
| sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1))
| ~ in(sK2,relation_field(sK1)) ),
inference(resolution,[],[f360,f156]) ).
fof(f156,plain,
( ~ in(unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)),sK1)
| ~ connected(sK1) ),
inference(superposition,[],[f138,f98]) ).
fof(f138,plain,
( ~ in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),sK1)
| ~ connected(sK1) ),
inference(definition_unfolding,[],[f100,f118]) ).
fof(f100,plain,
( ~ connected(sK1)
| ~ in(ordered_pair(sK2,sK3),sK1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f360,plain,
! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK1)
| sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1))
| X0 = X1
| ~ in(X1,relation_field(sK1))
| ~ in(X0,relation_field(sK1)) ),
inference(resolution,[],[f356,f262]) ).
fof(f262,plain,
! [X3,X4,X5] :
( ~ is_connected_in(sK1,X4)
| X3 = X5
| ~ in(X3,X4)
| ~ in(X5,X4)
| in(unordered_pair(singleton(X3),unordered_pair(X3,X5)),sK1)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X3)),sK1) ),
inference(forward_demodulation,[],[f261,f98]) ).
fof(f261,plain,
! [X3,X4,X5] :
( ~ is_connected_in(sK1,X4)
| in(unordered_pair(unordered_pair(X5,X3),singleton(X5)),sK1)
| X3 = X5
| ~ in(X5,X4)
| ~ in(X3,X4)
| in(unordered_pair(singleton(X3),unordered_pair(X3,X5)),sK1) ),
inference(forward_demodulation,[],[f254,f98]) ).
fof(f254,plain,
! [X3,X4,X5] :
( in(unordered_pair(unordered_pair(X3,X5),singleton(X3)),sK1)
| X3 = X5
| ~ in(X5,X4)
| in(unordered_pair(unordered_pair(X5,X3),singleton(X5)),sK1)
| ~ in(X3,X4)
| ~ is_connected_in(sK1,X4) ),
inference(resolution,[],[f143,f105]) ).
fof(f143,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| X4 = X5
| ~ is_connected_in(X0,X1)
| ~ in(X4,X1)
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X0) ),
inference(definition_unfolding,[],[f111,f118,f118]) ).
fof(f111,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| ~ in(X4,X1)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f356,plain,
( is_connected_in(sK1,relation_field(sK1))
| sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1)) ),
inference(subsumption_resolution,[],[f355,f105]) ).
fof(f355,plain,
( sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1))
| ~ relation(sK1)
| is_connected_in(sK1,relation_field(sK1)) ),
inference(resolution,[],[f354,f123]) ).
fof(f123,plain,
! [X0] :
( ~ connected(X0)
| ~ relation(X0)
| is_connected_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f113,plain,
! [X0,X1] :
( sK5(X0,X1) != sK6(X0,X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f492,plain,
( sK3 = sK2
| ~ connected(sK1) ),
inference(resolution,[],[f487,f103]) ).
fof(f487,plain,
( ~ in(sK2,relation_field(sK1))
| sK3 = sK2 ),
inference(subsumption_resolution,[],[f486,f428]) ).
fof(f486,plain,
( ~ in(sK2,relation_field(sK1))
| ~ connected(sK1)
| sK3 = sK2 ),
inference(resolution,[],[f485,f101]) ).
fof(f485,plain,
( ~ in(sK3,relation_field(sK1))
| ~ in(sK2,relation_field(sK1))
| sK3 = sK2 ),
inference(subsumption_resolution,[],[f483,f428]) ).
fof(f483,plain,
( ~ connected(sK1)
| ~ in(sK2,relation_field(sK1))
| sK3 = sK2
| ~ in(sK3,relation_field(sK1)) ),
inference(resolution,[],[f478,f170]) ).
fof(f478,plain,
( in(unordered_pair(singleton(sK3),unordered_pair(sK2,sK3)),sK1)
| ~ in(sK2,relation_field(sK1))
| ~ in(sK3,relation_field(sK1))
| sK3 = sK2 ),
inference(forward_demodulation,[],[f477,f98]) ).
fof(f477,plain,
( ~ in(sK3,relation_field(sK1))
| sK3 = sK2
| ~ in(sK2,relation_field(sK1))
| in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK2)),sK1) ),
inference(subsumption_resolution,[],[f475,f428]) ).
fof(f475,plain,
( sK3 = sK2
| ~ connected(sK1)
| ~ in(sK2,relation_field(sK1))
| in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK2)),sK1)
| ~ in(sK3,relation_field(sK1)) ),
inference(duplicate_literal_removal,[],[f463]) ).
fof(f463,plain,
( sK3 = sK2
| ~ in(sK3,relation_field(sK1))
| ~ connected(sK1)
| sK3 = sK2
| ~ in(sK2,relation_field(sK1))
| in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK2)),sK1) ),
inference(resolution,[],[f429,f156]) ).
fof(f429,plain,
! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK1)
| X0 = X1
| ~ in(X0,relation_field(sK1))
| sK3 = sK2
| ~ in(X1,relation_field(sK1)) ),
inference(resolution,[],[f427,f262]) ).
fof(f102,plain,
( sK3 != sK2
| ~ connected(sK1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f568,plain,
connected(sK1),
inference(resolution,[],[f567,f210]) ).
fof(f567,plain,
is_connected_in(sK1,relation_field(sK1)),
inference(subsumption_resolution,[],[f566,f105]) ).
fof(f566,plain,
( is_connected_in(sK1,relation_field(sK1))
| ~ relation(sK1) ),
inference(trivial_inequality_removal,[],[f565]) ).
fof(f565,plain,
( sK5(sK1,relation_field(sK1)) != sK5(sK1,relation_field(sK1))
| is_connected_in(sK1,relation_field(sK1))
| ~ relation(sK1) ),
inference(superposition,[],[f113,f533]) ).
fof(f533,plain,
sK5(sK1,relation_field(sK1)) = sK6(sK1,relation_field(sK1)),
inference(resolution,[],[f509,f354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU242+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.35 % Computer : n027.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue Aug 30 15:11:46 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.20/0.45 % (3117)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.45 TRYING [1]
% 0.20/0.47 TRYING [2]
% 0.20/0.47 TRYING [3]
% 0.20/0.48 % (3140)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.49 % (3127)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.50 % (3118)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)
% 0.20/0.50 % (3127)Instruction limit reached!
% 0.20/0.50 % (3127)------------------------------
% 0.20/0.50 % (3127)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (3127)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (3127)Termination reason: Unknown
% 0.20/0.50 % (3127)Termination phase: Property scanning
% 0.20/0.50
% 0.20/0.50 % (3127)Memory used [KB]: 895
% 0.20/0.50 % (3127)Time elapsed: 0.004 s
% 0.20/0.50 % (3127)Instructions burned: 3 (million)
% 0.20/0.50 % (3127)------------------------------
% 0.20/0.50 % (3127)------------------------------
% 0.20/0.51 % (3128)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)
% 0.20/0.51 % (3143)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)
% 0.20/0.51 % (3134)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)
% 0.20/0.51 % (3135)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)
% 0.20/0.51 % (3149)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)
% 1.28/0.52 TRYING [4]
% 1.28/0.52 % (3118)Refutation not found, incomplete strategy% (3118)------------------------------
% 1.28/0.52 % (3118)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.28/0.52 % (3126)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.28/0.52 % (3141)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.28/0.53 % (3123)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.28/0.53 % (3120)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)
% 1.28/0.53 % (3121)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)
% 1.28/0.53 % (3125)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.28/0.53 % (3146)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)
% 1.28/0.53 % (3118)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.28/0.53 % (3118)Termination reason: Refutation not found, incomplete strategy
% 1.28/0.53
% 1.28/0.53 % (3118)Memory used [KB]: 5500
% 1.28/0.53 % (3118)Time elapsed: 0.104 s
% 1.28/0.53 % (3118)Instructions burned: 6 (million)
% 1.28/0.53 % (3118)------------------------------
% 1.28/0.53 % (3118)------------------------------
% 1.28/0.53 TRYING [1]
% 1.44/0.53 % (3124)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)
% 1.44/0.54 % (3148)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.44/0.54 % (3132)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.44/0.54 % (3145)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.44/0.54 % (3142)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)
% 1.44/0.54 % (3147)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)
% 1.44/0.54 % (3126)Instruction limit reached!
% 1.44/0.54 % (3126)------------------------------
% 1.44/0.54 % (3126)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.44/0.54 % (3126)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.44/0.54 % (3126)Termination reason: Unknown
% 1.44/0.54 % (3126)Termination phase: Saturation
% 1.44/0.54
% 1.44/0.54 % (3126)Memory used [KB]: 5500
% 1.44/0.54 % (3126)Time elapsed: 0.103 s
% 1.44/0.54 % (3126)Instructions burned: 7 (million)
% 1.44/0.54 % (3126)------------------------------
% 1.44/0.54 % (3126)------------------------------
% 1.44/0.54 % (3138)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.44/0.54 % (3144)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.44/0.55 % (3137)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.44/0.55 TRYING [2]
% 1.44/0.55 TRYING [3]
% 1.44/0.55 % (3129)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.44/0.55 % (3131)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.44/0.55 % (3133)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.44/0.55 % (3139)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)
% 1.44/0.56 % (3136)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.44/0.57 % (3120)First to succeed.
% 1.44/0.57 TRYING [1]
% 1.44/0.57 TRYING [2]
% 1.44/0.57 TRYING [3]
% 1.44/0.58 TRYING [4]
% 1.44/0.58 % (3129)Also succeeded, but the first one will report.
% 1.44/0.58 % (3120)Refutation found. Thanks to Tanya!
% 1.44/0.58 % SZS status Theorem for theBenchmark
% 1.44/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.44/0.58 % (3120)------------------------------
% 1.44/0.58 % (3120)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.44/0.58 % (3120)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.44/0.58 % (3120)Termination reason: Refutation
% 1.44/0.58
% 1.44/0.58 % (3120)Memory used [KB]: 1151
% 1.44/0.58 % (3120)Time elapsed: 0.159 s
% 1.44/0.58 % (3120)Instructions burned: 24 (million)
% 1.44/0.58 % (3120)------------------------------
% 1.44/0.58 % (3120)------------------------------
% 1.44/0.58 % (3113)Success in time 0.226 s
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