TSTP Solution File: ANA102^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ANA102^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.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 : Mon May 20 18:41:49 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 31
% Syntax : Number of formulae : 79 ( 22 unt; 23 typ; 0 def)
% Number of atoms : 823 ( 117 equ; 0 cnn)
% Maximal formula atoms : 8 ( 14 avg)
% Number of connectives : 125 ( 45 ~; 37 |; 32 &; 0 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 137 ( 136 >; 1 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 2 con; 0-6 aty)
% Number of variables : 136 ( 0 ^ 108 !; 15 ?; 136 :)
% ( 13 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
'type/realax/real': $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/sets/UNION':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_2,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/INTER':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_4,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_6,type,
'const/sets/DISJOINT':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_8,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_12,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_13,type,
sK1: sK0 > 'type/realax/real' ).
thf(func_def_14,type,
sK2: sK0 > $o ).
thf(func_def_15,type,
sK3: sK0 > $o ).
thf(func_def_16,type,
sK4: sK0 > $o ).
thf(func_def_18,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_19,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
vOR: $o > $o > $o ).
thf(func_def_22,type,
vIMP: $o > $o > $o ).
thf(func_def_23,type,
vNOT: $o > $o ).
thf(f189,plain,
$false,
inference(subsumption_resolution,[],[f188,f144]) ).
thf(f144,plain,
$true != vAPP(sTfun(sK0,$o),$o,vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),$o),'const/sets/DISJOINT'(sK0),sK2),sK3),
inference(trivial_inequality_removal,[],[f143]) ).
thf(f143,plain,
( ( vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK4),sK1) != vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK4),sK1) )
| ( $true != vAPP(sTfun(sK0,$o),$o,vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),$o),'const/sets/DISJOINT'(sK0),sK2),sK3) ) ),
inference(forward_demodulation,[],[f142,f31]) ).
thf(f31,plain,
sK4 = vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/UNION'(sK0),sK2),sK3),
inference(cnf_transformation,[],[f28]) ).
thf(f28,plain,
( ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK2),sK1)),vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK3),sK1)) != vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK4),sK1) )
& ( sK4 = vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/UNION'(sK0),sK2),sK3) )
& ( 'const/sets/EMPTY'(sK0) = vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/INTER'(sK0),sK2),sK3) )
& ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f22,f27]) ).
thf(f27,plain,
( ? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X2),X1)),vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),X1)) != vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X4),X1) )
& ( vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X3) = X4 )
& ( 'const/sets/EMPTY'(X0) = vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/INTER'(X0),X2),X3) )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4) = $true ) )
=> ( ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK2),sK1)),vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK3),sK1)) != vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK4),sK1) )
& ( sK4 = vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/UNION'(sK0),sK2),sK3) )
& ( 'const/sets/EMPTY'(sK0) = vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/INTER'(sK0),sK2),sK3) )
& ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK4) ) ) ),
introduced(choice_axiom,[]) ).
thf(f22,plain,
? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X2),X1)),vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),X1)) != vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X4),X1) )
& ( vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X3) = X4 )
& ( 'const/sets/EMPTY'(X0) = vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/INTER'(X0),X2),X3) )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4) = $true ) ),
inference(flattening,[],[f21]) ).
thf(f21,plain,
? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X2),X1)),vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),X1)) != vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X4),X1) )
& ( vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X3) = X4 )
& ( 'const/sets/EMPTY'(X0) = vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/INTER'(X0),X2),X3) )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4) = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( ( vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X3) = X4 )
& ( 'const/sets/EMPTY'(X0) = vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/INTER'(X0),X2),X3) )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4) = $true ) )
=> ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X2),X1)),vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),X1)) = vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X4),X1) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( ( vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X3) = X4 )
& ( 'const/sets/EMPTY'(X0) = vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/INTER'(X0),X2),X3) )
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4) )
=> ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X2),X1)),vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),X1)) = vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X4),X1) ) ),
inference(rectify,[],[f7]) ).
thf(f7,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( ( vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X3) = X4 )
& ( 'const/sets/EMPTY'(X0) = vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/INTER'(X0),X2),X3) )
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4) )
=> ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X2),X1)),vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),X1)) = vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X4),X1) ) ),
inference(negated_conjecture,[],[f6]) ).
thf(f6,conjecture,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( ( vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X3) = X4 )
& ( 'const/sets/EMPTY'(X0) = vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/INTER'(X0),X2),X3) )
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4) )
=> ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X2),X1)),vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),X1)) = vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X4),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_UNION_EQ_') ).
thf(f142,plain,
( ( vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK4),sK1) != vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/UNION'(sK0),sK2),sK3)),sK1) )
| ( $true != vAPP(sTfun(sK0,$o),$o,vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),$o),'const/sets/DISJOINT'(sK0),sK2),sK3) ) ),
inference(subsumption_resolution,[],[f141,f105]) ).
thf(f105,plain,
$true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK2),
inference(subsumption_resolution,[],[f104,f29]) ).
thf(f29,plain,
$true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK4),
inference(cnf_transformation,[],[f28]) ).
thf(f104,plain,
( ( $true != vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK4) )
| ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK2) ) ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f99,plain,
( ( $true = $false )
| ( $true != vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK4) )
| ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK2) ) ),
inference(superposition,[],[f92,f71]) ).
thf(f71,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) = $false )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true ) ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f70,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( $true != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true )
| ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) = $false ) ),
inference(superposition,[],[f34,f9]) ).
thf(f9,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f34,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
| ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true ) ),
inference(flattening,[],[f23]) ).
thf(f23,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
| ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) = $true )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) = $true ) )
=> ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) )
=> vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) )
=> vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_') ).
thf(f92,plain,
$true = vAPP(sTfun(sK0,$o),$o,vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),$o),'const/sets/SUBSET'(sK0),sK2),sK4),
inference(superposition,[],[f36,f31]) ).
thf(f36,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] : ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X1),X2)) = $true ),
inference(cnf_transformation,[],[f18]) ).
thf(f18,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X1),X2)) = $true ),
inference(fool_elimination,[],[f17]) ).
thf(f17,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X1),X2)),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_UNION_0') ).
thf(f141,plain,
( ( vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK4),sK1) != vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/UNION'(sK0),sK2),sK3)),sK1) )
| ( $true != vAPP(sTfun(sK0,$o),$o,vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),$o),'const/sets/DISJOINT'(sK0),sK2),sK3) )
| ( $true != vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK2) ) ),
inference(subsumption_resolution,[],[f136,f89]) ).
thf(f89,plain,
$true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK3),
inference(subsumption_resolution,[],[f88,f29]) ).
thf(f88,plain,
( ( $true != vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK4) )
| ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK3) ) ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f83,plain,
( ( $true = $false )
| ( $true != vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK4) )
| ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK3) ) ),
inference(superposition,[],[f76,f71]) ).
thf(f76,plain,
$true = vAPP(sTfun(sK0,$o),$o,vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),$o),'const/sets/SUBSET'(sK0),sK3),sK4),
inference(superposition,[],[f35,f31]) ).
thf(f35,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] : ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X1)) = $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f16,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X1)) = $true ),
inference(fool_elimination,[],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X1)),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_UNION_1') ).
thf(f136,plain,
( ( vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK4),sK1) != vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/UNION'(sK0),sK2),sK3)),sK1) )
| ( $true != vAPP(sTfun(sK0,$o),$o,vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),$o),'const/sets/DISJOINT'(sK0),sK2),sK3) )
| ( $true != vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK3) )
| ( $true != vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK2) ) ),
inference(superposition,[],[f32,f37]) ).
thf(f37,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X3)),X1) = vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X2),X1)),vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),X1)) )
| ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/DISJOINT'(X0),X2),X3) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X3) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f26,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X3)),X1) = vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X2),X1)),vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),X1)) )
| ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/DISJOINT'(X0),X2),X3) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X3) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true ) ),
inference(flattening,[],[f25]) ).
thf(f25,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X3)),X1) = vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X2),X1)),vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),X1)) )
| ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/DISJOINT'(X0),X2),X3) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X3) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f20,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/DISJOINT'(X0),X2),X3) = $true )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X3) = $true )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) = $true ) )
=> ( vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X3)),X1) = vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X2),X1)),vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),X1)) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f19,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/DISJOINT'(X0),X2),X3)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X3)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) )
=> ( vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X3)),X1) = vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X2),X1)),vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),X1)) ) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/DISJOINT'(X0),X2),X3)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X3)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) )
=> ( vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/UNION'(X0),X2),X3)),X1) = vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X2),X1)),vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_UNION_') ).
thf(f32,plain,
vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK2),sK1)),vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK3),sK1)) != vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK4),sK1),
inference(cnf_transformation,[],[f28]) ).
thf(f188,plain,
$true = vAPP(sTfun(sK0,$o),$o,vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),$o),'const/sets/DISJOINT'(sK0),sK2),sK3),
inference(trivial_inequality_removal,[],[f185]) ).
thf(f185,plain,
( ( 'const/sets/EMPTY'(sK0) != 'const/sets/EMPTY'(sK0) )
| ( $true = vAPP(sTfun(sK0,$o),$o,vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),$o),'const/sets/DISJOINT'(sK0),sK2),sK3) ) ),
inference(superposition,[],[f41,f30]) ).
thf(f30,plain,
'const/sets/EMPTY'(sK0) = vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/INTER'(sK0),sK2),sK3),
inference(cnf_transformation,[],[f28]) ).
thf(f41,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/INTER'(X0),X1),X2) != 'const/sets/EMPTY'(X0) )
| ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/DISJOINT'(X0),X1),X2) = $true ) ),
inference(equality_proxy_clausification,[],[f38]) ).
thf(f38,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/DISJOINT'(X0),X1),X2) = $true )
| ( $false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/INTER'(X0),X1),X2)),'const/sets/EMPTY'(X0)) ) ),
inference(binary_proxy_clausification,[],[f33]) ).
thf(f33,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] : ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/DISJOINT'(X0),X1),X2) = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/INTER'(X0),X1),X2)),'const/sets/EMPTY'(X0)) ),
inference(cnf_transformation,[],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/DISJOINT'(X0),X1),X2) = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/INTER'(X0),X1),X2)),'const/sets/EMPTY'(X0)) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/DISJOINT'(X0),X1),X2)
= ( vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/INTER'(X0),X1),X2) = 'const/sets/EMPTY'(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/DISJOINT_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA102^1 : TPTP v8.2.0. Released v7.0.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 07:52:52 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (3308)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (3311)WARNING: value z3 for option sas not known
% 0.13/0.37 % (3311)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)
% 0.13/0.37 % (3310)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (3309)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (3312)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (3313)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)
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % (3315)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)
% 0.13/0.37 % (3314)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)
% 0.13/0.37 % (3315)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37 % (3311)First to succeed.
% 0.13/0.38 % (3311)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3308"
% 0.13/0.38 % (3311)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38 % (3311)------------------------------
% 0.13/0.38 % (3311)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.38 % (3311)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (3311)Memory used [KB]: 886
% 0.13/0.38 % (3311)Time elapsed: 0.012 s
% 0.13/0.38 % (3311)Instructions burned: 25 (million)
% 0.13/0.38 % (3308)Success in time 0.016 s
%------------------------------------------------------------------------------