TSTP Solution File: SEU709_8 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU709_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.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 : Tue Apr 30 15:35:22 EDT 2024
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 24
% Syntax : Number of formulae : 146 ( 31 unt; 5 typ; 0 def)
% Number of atoms : 843 ( 160 equ)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 333 ( 106 ~; 118 |; 30 &)
% ( 18 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 604 ( 479 fml; 125 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 25 ( 22 usr; 19 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 4-4 aty)
% Number of variables : 174 ( 160 !; 14 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_2,type,
if: ( $i * $o * $i * $i ) > $i ).
tff(func_def_5,type,
bG0: $o > $o ).
tff(func_def_6,type,
bG1: $o > $o ).
tff(func_def_7,type,
bG2: $o > $o ).
tff(func_def_9,type,
sK4: $o ).
tff(f2011,plain,
$false,
inference(avatar_sat_refutation,[],[f373,f1644,f1711,f1717,f1719,f1745,f1747,f1751,f1787,f1984,f1999,f2010]) ).
tff(f2010,plain,
~ spl7_6,
inference(avatar_contradiction_clause,[],[f2009]) ).
tff(f2009,plain,
( $false
| ~ spl7_6 ),
inference(subsumption_resolution,[],[f2008,f77]) ).
tff(f77,plain,
! [X0: $i,X1: $i] : in(X1,setadjoin(X0,setadjoin(X1,emptyset))),
inference(global_subsumption,[],[f49,f68,f51,f69,f53,f70,f9,f8,f61,f60,f59,f58,f57,f56,f54,f62,f76,f63]) ).
tff(f63,plain,
! [X0: $i,X1: $i] :
( in(X1,setadjoin(X0,setadjoin(X1,emptyset)))
| ~ secondinupair ),
inference(cnf_transformation,[],[f35]) ).
tff(f35,plain,
( ! [X0,X1] : in(X1,setadjoin(X0,setadjoin(X1,emptyset)))
| ~ secondinupair ),
inference(ennf_transformation,[],[f29]) ).
tff(f29,plain,
( secondinupair
=> ! [X0,X1] : in(X1,setadjoin(X0,setadjoin(X1,emptyset))) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
tff(f14,plain,
( secondinupair
<=> ! [X0,X1] : in(X1,setadjoin(X0,setadjoin(X1,emptyset))) ),
inference(fool_elimination,[],[f3]) ).
tff(f3,axiom,
( secondinupair
= ( ! [X0,X1] : in(X1,setadjoin(X0,setadjoin(X1,emptyset))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
tff(f76,plain,
! [X0: $i,X1: $i] : in(X0,setadjoin(X0,X1)),
inference(global_subsumption,[],[f49,f68,f51,f69,f53,f70,f9,f8,f61,f60,f59,f58,f57,f56,f54,f62]) ).
tff(f62,plain,
! [X0: $i,X1: $i] :
( in(X0,setadjoin(X0,X1))
| ~ setadjoinIL ),
inference(cnf_transformation,[],[f34]) ).
tff(f34,plain,
( ! [X0,X1] : in(X0,setadjoin(X0,X1))
| ~ setadjoinIL ),
inference(ennf_transformation,[],[f31]) ).
tff(f31,plain,
( setadjoinIL
=> ! [X0,X1] : in(X0,setadjoin(X0,X1)) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
tff(f13,plain,
( setadjoinIL
<=> ! [X0,X1] : in(X0,setadjoin(X0,X1)) ),
inference(fool_elimination,[],[f1]) ).
tff(f1,axiom,
( setadjoinIL
= ( ! [X0,X1] : in(X0,setadjoin(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
tff(f54,plain,
setadjoinIL,
inference(cnf_transformation,[],[f46]) ).
tff(f46,plain,
( ~ in(if(sK3,bG0(sK4),sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset)))
& in(sK6,sK3)
& in(sK5,sK3)
& iffalse
& iftrue
& secondinupair
& in__Cong
& setadjoinIL ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f33,f45,f44]) ).
tff(f44,plain,
( ? [X0,X1: $o,X2] :
( ? [X3] :
( ~ in(if(X0,bG0((X1)),X2,X3),setadjoin(X2,setadjoin(X3,emptyset)))
& in(X3,X0) )
& in(X2,X0) )
=> ( ? [X3] :
( ~ in(if(sK3,bG0(sK4),sK5,X3),setadjoin(sK5,setadjoin(X3,emptyset)))
& in(X3,sK3) )
& in(sK5,sK3) ) ),
introduced(choice_axiom,[]) ).
tff(f45,plain,
( ? [X3] :
( ~ in(if(sK3,bG0(sK4),sK5,X3),setadjoin(sK5,setadjoin(X3,emptyset)))
& in(X3,sK3) )
=> ( ~ in(if(sK3,bG0(sK4),sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset)))
& in(sK6,sK3) ) ),
introduced(choice_axiom,[]) ).
tff(f33,plain,
( ? [X0,X1: $o,X2] :
( ? [X3] :
( ~ in(if(X0,bG0((X1)),X2,X3),setadjoin(X2,setadjoin(X3,emptyset)))
& in(X3,X0) )
& in(X2,X0) )
& iffalse
& iftrue
& secondinupair
& in__Cong
& setadjoinIL ),
inference(flattening,[],[f32]) ).
tff(f32,plain,
( ? [X0,X1: $o,X2] :
( ? [X3] :
( ~ in(if(X0,bG0((X1)),X2,X3),setadjoin(X2,setadjoin(X3,emptyset)))
& in(X3,X0) )
& in(X2,X0) )
& iffalse
& iftrue
& secondinupair
& in__Cong
& setadjoinIL ),
inference(ennf_transformation,[],[f12]) ).
tff(f12,plain,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X0,X1: $o,X2] :
( in(X2,X0)
=> ! [X3] :
( in(X3,X0)
=> in(if(X0,bG0((X1)),X2,X3),setadjoin(X2,setadjoin(X3,emptyset))) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f10,f11]) ).
tff(f11,plain,
! [X1: $o] :
( ( $true = (X1) )
<=> ( $true = bG0((X1)) ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG0])]) ).
tff(f10,plain,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X0,X1,X2] :
( in(X2,X0)
=> ! [X3] :
( in(X3,X0)
=> in(if(X0,X1,X2,X3),setadjoin(X2,setadjoin(X3,emptyset))) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
tff(f7,negated_conjecture,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X2,X4: $o,X0] :
( in(X0,X2)
=> ! [X1] :
( in(X1,X2)
=> in(if(X2,(X4),X0,X1),setadjoin(X0,setadjoin(X1,emptyset))) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f6]) ).
tff(f6,conjecture,
( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X2,X4: $o,X0] :
( in(X0,X2)
=> ! [X1] :
( in(X1,X2)
=> in(if(X2,(X4),X0,X1),setadjoin(X0,setadjoin(X1,emptyset))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueorfalse) ).
tff(f56,plain,
secondinupair,
inference(cnf_transformation,[],[f46]) ).
tff(f57,plain,
iftrue,
inference(cnf_transformation,[],[f46]) ).
tff(f58,plain,
iffalse,
inference(cnf_transformation,[],[f46]) ).
tff(f59,plain,
in(sK5,sK3),
inference(cnf_transformation,[],[f46]) ).
tff(f60,plain,
in(sK6,sK3),
inference(cnf_transformation,[],[f46]) ).
tff(f61,plain,
~ in(if(sK3,bG0(sK4),sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset))),
inference(cnf_transformation,[],[f46]) ).
tff(f8,plain,
$true != $false,
introduced(fool_axiom,[]) ).
tff(f9,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(fool_axiom,[]) ).
tff(f70,plain,
$true = bG0($true),
inference(equality_resolution,[],[f52]) ).
tff(f52,plain,
! [X0: $o] :
( ( $true = bG0((X0)) )
| ( $true != (X0) ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,plain,
! [X0: $o] :
( ( ( $true = (X0) )
| ( $true != bG0((X0)) ) )
& ( ( $true = bG0((X0)) )
| ( $true != (X0) ) ) ),
inference(nnf_transformation,[],[f25]) ).
tff(f25,plain,
! [X0: $o] :
( ( $true = (X0) )
<=> ( $true = bG0((X0)) ) ),
inference(rectify,[],[f11]) ).
tff(f53,plain,
! [X0: $o] :
( ( $true != bG0((X0)) )
| ( $true = (X0) ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f69,plain,
$true = bG1($true),
inference(equality_resolution,[],[f50]) ).
tff(f50,plain,
! [X0: $o] :
( ( $true = bG1((X0)) )
| ( $true != (X0) ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f42,plain,
! [X0: $o] :
( ( ( $true = (X0) )
| ( $true != bG1((X0)) ) )
& ( ( $true = bG1((X0)) )
| ( $true != (X0) ) ) ),
inference(nnf_transformation,[],[f24]) ).
tff(f24,plain,
! [X0: $o] :
( ( $true = (X0) )
<=> ( $true = bG1((X0)) ) ),
inference(rectify,[],[f18]) ).
tff(f18,plain,
! [X1: $o] :
( ( $true = (X1) )
<=> ( $true = bG1((X1)) ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG1])]) ).
tff(f51,plain,
! [X0: $o] :
( ( $true != bG1((X0)) )
| ( $true = (X0) ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f68,plain,
$true = bG2($true),
inference(equality_resolution,[],[f48]) ).
tff(f48,plain,
! [X0: $o] :
( ( $true = bG2((X0)) )
| ( $true != (X0) ) ),
inference(cnf_transformation,[],[f41]) ).
tff(f41,plain,
! [X0: $o] :
( ( ( $true = (X0) )
| ( $true != bG2((X0)) ) )
& ( ( $true = bG2((X0)) )
| ( $true != (X0) ) ) ),
inference(nnf_transformation,[],[f23]) ).
tff(f23,plain,
! [X0: $o] :
( ( $true = (X0) )
<=> ( $true = bG2((X0)) ) ),
inference(rectify,[],[f21]) ).
tff(f21,plain,
! [X1: $o] :
( ( $true = (X1) )
<=> ( $true = bG2((X1)) ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG2])]) ).
tff(f49,plain,
! [X0: $o] :
( ( $true != bG2((X0)) )
| ( $true = (X0) ) ),
inference(cnf_transformation,[],[f41]) ).
tff(f2008,plain,
( ~ in(sK6,setadjoin(sK5,setadjoin(sK6,emptyset)))
| ~ spl7_6 ),
inference(forward_demodulation,[],[f616,f1983]) ).
tff(f1983,plain,
( ( sK6 = if(sK3,$false,sK5,sK6) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f1981]) ).
tff(f1981,plain,
( spl7_6
<=> ( sK6 = if(sK3,$false,sK5,sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).
tff(f616,plain,
~ in(if(sK3,$false,sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset))),
inference(superposition,[],[f61,f605]) ).
tff(f605,plain,
$false = bG0(sK4),
inference(subsumption_resolution,[],[f604,f76]) ).
tff(f604,plain,
( ~ in(sK5,setadjoin(sK5,setadjoin(sK6,emptyset)))
| ( $false = bG0(sK4) ) ),
inference(superposition,[],[f61,f586]) ).
tff(f586,plain,
! [X0: $o] :
( ( sK5 = if(sK3,(X0),sK5,sK6) )
| ( $false = (X0) ) ),
inference(superposition,[],[f584,f9]) ).
tff(f584,plain,
sK5 = if(sK3,$true,sK5,sK6),
inference(resolution,[],[f565,f59]) ).
tff(f565,plain,
! [X0: $i] :
( ~ in(X0,sK3)
| ( if(sK3,$true,X0,sK6) = X0 ) ),
inference(resolution,[],[f434,f60]) ).
tff(f434,plain,
! [X2: $i,X3: $i,X0: $i] :
( ~ in(X3,X0)
| ( if(X0,$true,X2,X3) = X2 )
| ~ in(X2,X0) ),
inference(forward_demodulation,[],[f79,f68]) ).
tff(f79,plain,
! [X2: $i,X3: $i,X0: $i] :
( ( if(X0,bG2($true),X2,X3) = X2 )
| ~ in(X3,X0)
| ~ in(X2,X0) ),
inference(global_subsumption,[],[f49,f68,f51,f69,f53,f70,f9,f8,f61,f60,f59,f58,f57,f56,f54,f62,f76,f63,f77,f66,f78,f75]) ).
tff(f75,plain,
! [X2: $i,X3: $i,X0: $i] :
( ( if(X0,bG2($true),X2,X3) = X2 )
| ~ in(X3,X0)
| ~ in(X2,X0)
| ~ iftrue ),
inference(equality_resolution,[],[f67]) ).
tff(f67,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( if(X0,bG2((X1)),X2,X3) = X2 )
| ( $true != (X1) )
| ~ in(X3,X0)
| ~ in(X2,X0)
| ~ iftrue ),
inference(cnf_transformation,[],[f40]) ).
tff(f40,plain,
( ! [X0,X1: $o,X2] :
( ! [X3] :
( ( if(X0,bG2((X1)),X2,X3) = X2 )
| ( $true != (X1) )
| ~ in(X3,X0) )
| ~ in(X2,X0) )
| ~ iftrue ),
inference(flattening,[],[f39]) ).
tff(f39,plain,
( ! [X0,X1: $o,X2] :
( ! [X3] :
( ( if(X0,bG2((X1)),X2,X3) = X2 )
| ( $true != (X1) )
| ~ in(X3,X0) )
| ~ in(X2,X0) )
| ~ iftrue ),
inference(ennf_transformation,[],[f28]) ).
tff(f28,plain,
( iftrue
=> ! [X0,X1: $o,X2] :
( in(X2,X0)
=> ! [X3] :
( in(X3,X0)
=> ( ( $true = (X1) )
=> ( if(X0,bG2((X1)),X2,X3) = X2 ) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
tff(f22,plain,
( iftrue
<=> ! [X0,X1: $o,X2] :
( in(X2,X0)
=> ! [X3] :
( in(X3,X0)
=> ( ( $true = (X1) )
=> ( if(X0,bG2((X1)),X2,X3) = X2 ) ) ) ) ),
inference(fool_elimination,[],[f20,f21]) ).
tff(f20,plain,
( iftrue
= ( ! [X0,X1: $o,X2] :
( in(X2,X0)
=> ! [X3] :
( in(X3,X0)
=> ( (X1)
=> ( if(X0,(X1),X2,X3) = X2 ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
( iftrue
= ( ! [X2,X4: $o,X0] :
( in(X0,X2)
=> ! [X1] :
( in(X1,X2)
=> ( (X4)
=> ( if(X2,(X4),X0,X1) = X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrue) ).
tff(f78,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ~ in(X3,X0)
| ( $true = (X1) )
| ( if(X0,bG1((X1)),X2,X3) = X3 )
| ~ in(X2,X0) ),
inference(global_subsumption,[],[f49,f68,f51,f69,f53,f70,f9,f8,f61,f60,f59,f58,f57,f56,f54,f62,f76,f63,f77,f66]) ).
tff(f66,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( if(X0,bG1((X1)),X2,X3) = X3 )
| ( $true = (X1) )
| ~ in(X3,X0)
| ~ in(X2,X0)
| ~ iffalse ),
inference(cnf_transformation,[],[f38]) ).
tff(f38,plain,
( ! [X0,X1: $o,X2] :
( ! [X3] :
( ( if(X0,bG1((X1)),X2,X3) = X3 )
| ( $true = (X1) )
| ~ in(X3,X0) )
| ~ in(X2,X0) )
| ~ iffalse ),
inference(flattening,[],[f37]) ).
tff(f37,plain,
( ! [X0,X1: $o,X2] :
( ! [X3] :
( ( if(X0,bG1((X1)),X2,X3) = X3 )
| ( $true = (X1) )
| ~ in(X3,X0) )
| ~ in(X2,X0) )
| ~ iffalse ),
inference(ennf_transformation,[],[f27]) ).
tff(f27,plain,
( iffalse
=> ! [X0,X1: $o,X2] :
( in(X2,X0)
=> ! [X3] :
( in(X3,X0)
=> ( ( $true != (X1) )
=> ( if(X0,bG1((X1)),X2,X3) = X3 ) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f26]) ).
tff(f26,plain,
( iffalse
<=> ! [X0,X1: $o,X2] :
( in(X2,X0)
=> ! [X3] :
( in(X3,X0)
=> ( ( $true != (X1) )
=> ( if(X0,bG1((X1)),X2,X3) = X3 ) ) ) ) ),
inference(flattening,[],[f19]) ).
tff(f19,plain,
( iffalse
<=> ! [X0,X1: $o,X2] :
( in(X2,X0)
=> ! [X3] :
( in(X3,X0)
=> ( ( $true != (X1) )
=> ( if(X0,bG1((X1)),X2,X3) = X3 ) ) ) ) ),
inference(fool_elimination,[],[f17,f18]) ).
tff(f17,plain,
( iffalse
= ( ! [X0,X1: $o,X2] :
( in(X2,X0)
=> ! [X3] :
( in(X3,X0)
=> ( ~ (X1)
=> ( if(X0,(X1),X2,X3) = X3 ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
( iffalse
= ( ! [X2,X4: $o,X0] :
( in(X0,X2)
=> ! [X1] :
( in(X1,X2)
=> ( ~ (X4)
=> ( if(X2,(X4),X0,X1) = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalse) ).
tff(f1999,plain,
( spl7_3
| spl7_7 ),
inference(avatar_split_clause,[],[f1978,f1996,f1638]) ).
tff(f1638,plain,
( spl7_3
<=> ! [X0: $o] : ( $true = (X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
tff(f1996,plain,
( spl7_7
<=> ( sK6 = if(sK3,$false,sK6,sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_7])]) ).
tff(f1978,plain,
! [X0: $o] :
( ( sK6 = if(sK3,$false,sK6,sK6) )
| ( $true = (X0) ) ),
inference(duplicate_literal_removal,[],[f1961]) ).
tff(f1961,plain,
! [X0: $o] :
( ( sK6 = if(sK3,$false,sK6,sK6) )
| ( $true = (X0) )
| ( $true = (X0) ) ),
inference(superposition,[],[f915,f91]) ).
tff(f91,plain,
! [X0: $o] :
( ( $false = bG1((X0)) )
| ( $true = (X0) ) ),
inference(trivial_inequality_removal,[],[f90]) ).
tff(f90,plain,
! [X0: $o] :
( ( $true != $true )
| ( $true = (X0) )
| ( $false = bG1((X0)) ) ),
inference(superposition,[],[f51,f9]) ).
tff(f915,plain,
! [X0: $o] :
( ( sK6 = if(sK3,bG1((X0)),sK6,sK6) )
| ( $true = (X0) ) ),
inference(resolution,[],[f601,f60]) ).
tff(f601,plain,
! [X0: $o,X1: $i] :
( ~ in(X1,sK3)
| ( sK6 = if(sK3,bG1((X0)),X1,sK6) )
| ( $true = (X0) ) ),
inference(resolution,[],[f78,f60]) ).
tff(f1984,plain,
( spl7_3
| spl7_6 ),
inference(avatar_split_clause,[],[f1954,f1981,f1638]) ).
tff(f1954,plain,
! [X0: $o] :
( ( sK6 = if(sK3,$false,sK5,sK6) )
| ( $true = (X0) ) ),
inference(duplicate_literal_removal,[],[f1935]) ).
tff(f1935,plain,
! [X0: $o] :
( ( sK6 = if(sK3,$false,sK5,sK6) )
| ( $true = (X0) )
| ( $true = (X0) ) ),
inference(superposition,[],[f914,f91]) ).
tff(f914,plain,
! [X0: $o] :
( ( sK6 = if(sK3,bG1((X0)),sK5,sK6) )
| ( $true = (X0) ) ),
inference(resolution,[],[f601,f59]) ).
tff(f1787,plain,
( spl7_3
| spl7_5 ),
inference(avatar_split_clause,[],[f1781,f1784,f1638]) ).
tff(f1784,plain,
( spl7_5
<=> ( sK5 = if(sK3,$false,sK6,sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).
tff(f1781,plain,
! [X0: $o] :
( ( sK5 = if(sK3,$false,sK6,sK5) )
| ( $true = (X0) ) ),
inference(duplicate_literal_removal,[],[f1763]) ).
tff(f1763,plain,
! [X0: $o] :
( ( sK5 = if(sK3,$false,sK6,sK5) )
| ( $true = (X0) )
| ( $true = (X0) ) ),
inference(superposition,[],[f913,f91]) ).
tff(f913,plain,
! [X0: $o] :
( ( sK5 = if(sK3,bG1((X0)),sK6,sK5) )
| ( $true = (X0) ) ),
inference(resolution,[],[f600,f60]) ).
tff(f600,plain,
! [X0: $o,X1: $i] :
( ~ in(X1,sK3)
| ( sK5 = if(sK3,bG1((X0)),X1,sK5) )
| ( $true = (X0) ) ),
inference(resolution,[],[f78,f59]) ).
tff(f1751,plain,
~ spl7_3,
inference(avatar_contradiction_clause,[],[f1750]) ).
tff(f1750,plain,
( $false
| ~ spl7_3 ),
inference(subsumption_resolution,[],[f1749,f76]) ).
tff(f1749,plain,
( ~ in(sK5,setadjoin(sK5,setadjoin(sK6,emptyset)))
| ~ spl7_3 ),
inference(forward_demodulation,[],[f1748,f584]) ).
tff(f1748,plain,
( ~ in(if(sK3,$true,sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset)))
| ~ spl7_3 ),
inference(forward_demodulation,[],[f1709,f70]) ).
tff(f1709,plain,
( ~ in(if(sK3,bG0($true),sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset)))
| ~ spl7_3 ),
inference(superposition,[],[f61,f1639]) ).
tff(f1639,plain,
( ! [X0: $o] : ( $true = (X0) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f1638]) ).
tff(f1747,plain,
( spl7_2
| ~ spl7_3 ),
inference(avatar_contradiction_clause,[],[f1746]) ).
tff(f1746,plain,
( $false
| spl7_2
| ~ spl7_3 ),
inference(subsumption_resolution,[],[f1708,f395]) ).
tff(f395,plain,
( ( $false != bG0($true) )
| spl7_2 ),
inference(subsumption_resolution,[],[f389,f372]) ).
tff(f372,plain,
( ( $false != bG2($true) )
| spl7_2 ),
inference(avatar_component_clause,[],[f370]) ).
tff(f370,plain,
( spl7_2
<=> ( $false = bG2($true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
tff(f389,plain,
( ( $false != bG0($true) )
| ( $false = bG2($true) )
| spl7_2 ),
inference(superposition,[],[f372,f218]) ).
tff(f218,plain,
! [X0: $o] :
( ( bG0($true) = (X0) )
| ( $false = (X0) ) ),
inference(trivial_inequality_removal,[],[f192]) ).
tff(f192,plain,
! [X0: $o] :
( ( $true = $false )
| ( bG0($true) = (X0) )
| ( $false = (X0) ) ),
inference(superposition,[],[f70,f80]) ).
tff(f80,plain,
! [X0: $o,X1: $o] :
( ( (X0) = (X1) )
| ( $false = (X1) )
| ( $false = (X0) ) ),
inference(superposition,[],[f9,f9]) ).
tff(f1708,plain,
( ( $false = bG0($true) )
| ~ spl7_3 ),
inference(superposition,[],[f605,f1639]) ).
tff(f1745,plain,
~ spl7_3,
inference(avatar_contradiction_clause,[],[f1744]) ).
tff(f1744,plain,
( $false
| ~ spl7_3 ),
inference(subsumption_resolution,[],[f1743,f76]) ).
tff(f1743,plain,
( ~ in(sK5,setadjoin(sK5,setadjoin(sK6,emptyset)))
| ~ spl7_3 ),
inference(forward_demodulation,[],[f1690,f584]) ).
tff(f1690,plain,
( ~ in(if(sK3,$true,sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset)))
| ~ spl7_3 ),
inference(superposition,[],[f61,f1639]) ).
tff(f1719,plain,
~ spl7_3,
inference(avatar_contradiction_clause,[],[f1718]) ).
tff(f1718,plain,
( $false
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f1685]) ).
tff(f1685,plain,
( ( $true = $false )
| ~ spl7_3 ),
inference(superposition,[],[f634,f1639]) ).
tff(f634,plain,
$false = bG0($false),
inference(superposition,[],[f605,f620]) ).
tff(f620,plain,
$false = sK4,
inference(duplicate_literal_removal,[],[f618]) ).
tff(f618,plain,
( ( $false = sK4 )
| ( $false = sK4 ) ),
inference(superposition,[],[f81,f605]) ).
tff(f81,plain,
! [X0: $o] :
( ( bG0((X0)) = (X0) )
| ( $false = (X0) ) ),
inference(superposition,[],[f70,f9]) ).
tff(f1717,plain,
~ spl7_3,
inference(avatar_contradiction_clause,[],[f1716]) ).
tff(f1716,plain,
( $false
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f1689]) ).
tff(f1689,plain,
( ( $true = $false )
| ~ spl7_3 ),
inference(superposition,[],[f605,f1639]) ).
tff(f1711,plain,
~ spl7_3,
inference(avatar_contradiction_clause,[],[f1710]) ).
tff(f1710,plain,
( $false
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f1707]) ).
tff(f1707,plain,
( ( $true = $false )
| ~ spl7_3 ),
inference(superposition,[],[f620,f1639]) ).
tff(f1644,plain,
( spl7_3
| spl7_4 ),
inference(avatar_split_clause,[],[f1635,f1641,f1638]) ).
tff(f1641,plain,
( spl7_4
<=> ( sK5 = if(sK3,$false,sK5,sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).
tff(f1635,plain,
! [X0: $o] :
( ( sK5 = if(sK3,$false,sK5,sK5) )
| ( $true = (X0) ) ),
inference(duplicate_literal_removal,[],[f1619]) ).
tff(f1619,plain,
! [X0: $o] :
( ( sK5 = if(sK3,$false,sK5,sK5) )
| ( $true = (X0) )
| ( $true = (X0) ) ),
inference(superposition,[],[f912,f91]) ).
tff(f912,plain,
! [X0: $o] :
( ( sK5 = if(sK3,bG1((X0)),sK5,sK5) )
| ( $true = (X0) ) ),
inference(resolution,[],[f600,f59]) ).
tff(f373,plain,
( spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f270,f370,f367]) ).
tff(f367,plain,
( spl7_1
<=> ! [X0: $o] : ( $false = (X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
tff(f270,plain,
! [X0: $o] :
( ( $false != bG2($true) )
| ( $false = (X0) ) ),
inference(equality_factoring,[],[f214]) ).
tff(f214,plain,
! [X0: $o] :
( ( bG2($true) = (X0) )
| ( $false = (X0) ) ),
inference(trivial_inequality_removal,[],[f198]) ).
tff(f198,plain,
! [X0: $o] :
( ( $true = $false )
| ( bG2($true) = (X0) )
| ( $false = (X0) ) ),
inference(superposition,[],[f68,f80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU709_8 : TPTP v8.1.2. Released v8.0.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 21:06:49 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (5644)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (5647)WARNING: value z3 for option sas not known
% 0.14/0.38 % (5646)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (5650)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (5648)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (5649)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (5647)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (5651)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 Detected minimum model sizes of [1,1]
% 0.14/0.38 Detected maximum model sizes of [max,2]
% 0.14/0.38 TRYING [1,1]
% 0.14/0.38 TRYING [1,2]
% 0.14/0.38 % (5645)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 TRYING [2,2]
% 0.14/0.38 TRYING [3,2]
% 0.14/0.39 TRYING [4,2]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [5,2]
% 0.14/0.39 TRYING [3]
% 0.14/0.40 TRYING [6,2]
% 0.14/0.41 TRYING [4]
% 0.20/0.42 TRYING [7,2]
% 0.20/0.43 % (5647)First to succeed.
% 0.20/0.43 % (5647)Refutation found. Thanks to Tanya!
% 0.20/0.43 % SZS status Theorem for theBenchmark
% 0.20/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.44 % (5647)------------------------------
% 0.20/0.44 % (5647)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.44 % (5647)Termination reason: Refutation
% 0.20/0.44
% 0.20/0.44 % (5647)Memory used [KB]: 1281
% 0.20/0.44 % (5647)Time elapsed: 0.053 s
% 0.20/0.44 % (5647)Instructions burned: 110 (million)
% 0.20/0.44 % (5647)------------------------------
% 0.20/0.44 % (5647)------------------------------
% 0.20/0.44 % (5644)Success in time 0.068 s
%------------------------------------------------------------------------------