TSTP Solution File: ANA096^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ANA096^1 : 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 18:41:48 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 28
% Syntax : Number of formulae : 56 ( 17 unt; 22 typ; 0 def)
% Number of atoms : 572 ( 61 equ; 0 cnn)
% Maximal formula atoms : 6 ( 16 avg)
% Number of connectives : 61 ( 21 ~; 12 |; 17 &; 0 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 103 ( 102 >; 1 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 2 con; 0-6 aty)
% Number of variables : 99 ( 0 ^ 74 !; 12 ?; 99 :)
% ( 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/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/DIFF':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_4,type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_5,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_6,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_7,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_8,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
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,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_17,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_18,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
vOR: $o > $o > $o ).
thf(func_def_20,type,
vIMP: $o > $o > $o ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(f108,plain,
$false,
inference(trivial_inequality_removal,[],[f105]) ).
thf(f105,plain,
vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK2),sK1) != vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK2),sK1),
inference(superposition,[],[f89,f96]) ).
thf(f96,plain,
! [X0: sK0 > 'type/realax/real'] : ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),sK2),sK3)),X0)),vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK3),X0)) = 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),X0) ),
inference(forward_demodulation,[],[f91,f25]) ).
thf(f25,plain,
! [X0: $tType] : ( 'const/iterate/sum'(X0) = vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real')),'const/iterate/iterate'(X0,'type/realax/real'),'const/realax/real_add') ),
inference(cnf_transformation,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType] : ( 'const/iterate/sum'(X0) = vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real')),'const/iterate/iterate'(X0,'type/realax/real'),'const/realax/real_add') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/sum_') ).
thf(f91,plain,
! [X0: sK0 > 'type/realax/real'] : ( 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,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real')),'const/iterate/iterate'(sK0,'type/realax/real'),'const/realax/real_add'),vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),sK2),sK3)),X0)),vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real')),'const/iterate/iterate'(sK0,'type/realax/real'),'const/realax/real_add'),sK3),X0)) = vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real')),'const/iterate/iterate'(sK0,'type/realax/real'),'const/realax/real_add'),sK2),X0) ),
inference(unit_resulting_resolution,[],[f28,f22,f23,f27]) ).
thf(f27,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X5),X4) != $true )
| ( vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),X2,vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X4),X5)),X3)),vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),X5),X3)) = vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),X4),X3) )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4) != $true )
| ( vAPP(sTfun(X1,sTfun(X1,X1)),$o,'const/iterate/monoidal'(X1),X2) != $true ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f19,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ! [X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ( vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),X2,vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X4),X5)),X3)),vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),X5),X3)) = vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),X4),X3) )
| ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X5),X4) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4) != $true ) )
| ( vAPP(sTfun(X1,sTfun(X1,X1)),$o,'const/iterate/monoidal'(X1),X2) != $true ) ),
inference(flattening,[],[f18]) ).
thf(f18,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ! [X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ( vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),X2,vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X4),X5)),X3)),vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),X5),X3)) = vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),X4),X3) )
| ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X5),X4) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4) != $true ) )
| ( vAPP(sTfun(X1,sTfun(X1,X1)),$o,'const/iterate/monoidal'(X1),X2) != $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( vAPP(sTfun(X1,sTfun(X1,X1)),$o,'const/iterate/monoidal'(X1),X2) = $true )
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X5),X4) = $true )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4) = $true ) )
=> ( vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),X2,vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X4),X5)),X3)),vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),X5),X3)) = vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),X4),X3) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( vAPP(sTfun(X1,sTfun(X1,X1)),$o,'const/iterate/monoidal'(X1),X2)
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X5),X4)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4) )
=> ( vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),X2,vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X4),X5)),X3)),vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),X5),X3)) = vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),X4),X3) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( vAPP(sTfun(X1,sTfun(X1,X1)),$o,'const/iterate/monoidal'(X1),X2)
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X5),X4)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4) )
=> ( vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),X2,vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X4),X5)),X3)),vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),X5),X3)) = vAPP(sTfun(X0,X1),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1),vAPP(sTfun(X1,sTfun(X1,X1)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X1),X1)),'const/iterate/iterate'(X0,X1),X2),X4),X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_DIFF_') ).
thf(f23,plain,
$true = vAPP(sTfun(sK0,$o),$o,vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),$o),'const/sets/SUBSET'(sK0),sK3),sK2),
inference(cnf_transformation,[],[f21]) ).
thf(f21,plain,
( ( vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),sK2),sK3)),sK1) != vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_sub',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)) )
& ( $true = vAPP(sTfun(sK0,$o),$o,vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),$o),'const/sets/SUBSET'(sK0),sK3),sK2) )
& ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f17,f20]) ).
thf(f20,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,$o)),'const/sets/DIFF'(X0),X2),X3)),X1) != vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_sub',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$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/SUBSET'(X0),X3),X2) = $true )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) = $true ) )
=> ( ( vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$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,$o)),'const/sets/DIFF'(sK0),sK2),sK3)),sK1) != vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_sub',vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$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)) )
& ( $true = vAPP(sTfun(sK0,$o),$o,vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),$o),'const/sets/SUBSET'(sK0),sK3),sK2) )
& ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK2) ) ) ),
introduced(choice_axiom,[]) ).
thf(f17,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,$o)),'const/sets/DIFF'(X0),X2),X3)),X1) != vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_sub',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$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/SUBSET'(X0),X3),X2) = $true )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) = $true ) ),
inference(flattening,[],[f16]) ).
thf(f16,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,$o)),'const/sets/DIFF'(X0),X2),X3)),X1) != vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_sub',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$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/SUBSET'(X0),X3),X2) = $true )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f10,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/SUBSET'(X0),X3),X2) = $true )
& ( vAPP(sTfun(X0,$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,$o)),'const/sets/DIFF'(X0),X2),X3)),X1) = vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_sub',vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$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,[],[f9]) ).
thf(f9,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/SUBSET'(X0),X3),X2)
& 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/DIFF'(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_sub',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,[],[f6]) ).
thf(f6,negated_conjecture,
~ ! [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/SUBSET'(X0),X3),X2)
& 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/DIFF'(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_sub',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(negated_conjecture,[],[f5]) ).
thf(f5,conjecture,
! [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/SUBSET'(X0),X3),X2)
& 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/DIFF'(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_sub',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/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_DIFF_') ).
thf(f22,plain,
$true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK2),
inference(cnf_transformation,[],[f21]) ).
thf(f28,plain,
vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o,'const/iterate/monoidal'('type/realax/real'),'const/realax/real_add') = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o,'const/iterate/monoidal'('type/realax/real'),'const/realax/real_add') = $true,
inference(fool_elimination,[],[f14]) ).
thf(f14,plain,
vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o,'const/iterate/monoidal'('type/realax/real'),'const/realax/real_add'),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o,'const/iterate/monoidal'('type/realax/real'),'const/realax/real_add'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(f89,plain,
vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),sK2),sK1) != 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,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),sK2),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),sK3),sK1)),
inference(unit_resulting_resolution,[],[f24,f34]) ).
thf(f34,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',X0),X2) != X1 )
| ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_sub',X1),X2) = X0 ) ),
inference(equality_proxy_clausification,[],[f33]) ).
thf(f33,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_sub',X1),X2) = X0 )
| ( $false = vAPP('type/realax/real',$o,vAPP('type/realax/real',sTfun('type/realax/real',$o),vEQ('type/realax/real'),vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',X0),X2)),X1) ) ),
inference(equality_proxy_clausification,[],[f29]) ).
thf(f29,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true = vAPP('type/realax/real',$o,vAPP('type/realax/real',sTfun('type/realax/real',$o),vEQ('type/realax/real'),vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_sub',X1),X2)),X0) )
| ( $false = vAPP('type/realax/real',$o,vAPP('type/realax/real',sTfun('type/realax/real',$o),vEQ('type/realax/real'),vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',X0),X2)),X1) ) ),
inference(binary_proxy_clausification,[],[f26]) ).
thf(f26,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] : ( vAPP('type/realax/real',$o,vAPP('type/realax/real',sTfun('type/realax/real',$o),vEQ('type/realax/real'),vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_sub',X1),X2)),X0) = vAPP('type/realax/real',$o,vAPP('type/realax/real',sTfun('type/realax/real',$o),vEQ('type/realax/real'),vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',X0),X2)),X1) ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] : ( vAPP('type/realax/real',$o,vAPP('type/realax/real',sTfun('type/realax/real',$o),vEQ('type/realax/real'),vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_sub',X1),X2)),X0) = vAPP('type/realax/real',$o,vAPP('type/realax/real',sTfun('type/realax/real',$o),vEQ('type/realax/real'),vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',X0),X2)),X1) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_sub',X1),X2) = X0 )
= ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_add',X0),X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/real/REAL_EQ_SUB_LADD_') ).
thf(f24,plain,
vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK0),vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),sK2),sK3)),sK1) != vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),'const/realax/real_sub',vAPP(sTfun(sK0,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK0,$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)),
inference(cnf_transformation,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ANA096^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n002.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 May 20 07:44:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (12544)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (12547)WARNING: value z3 for option sas not known
% 0.14/0.38 % (12548)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (12545)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (12546)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 % (12547)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 % (12549)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 % (12550)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 % (12551)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 % (12551)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.38 % Exception at run slice level% Exception at run slice level
% 0.14/0.38
% 0.14/0.38 % Exception at run slice levelUser error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsUser error:
% 0.14/0.38 Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38 % (12551)First to succeed.
% 0.14/0.38 % (12550)Also succeeded, but the first one will report.
% 0.14/0.39 % (12551)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-12544"
% 0.14/0.39 % (12551)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39 % (12551)------------------------------
% 0.14/0.39 % (12551)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (12551)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (12551)Memory used [KB]: 878
% 0.14/0.39 % (12551)Time elapsed: 0.010 s
% 0.14/0.39 % (12551)Instructions burned: 15 (million)
% 0.14/0.39 % (12544)Success in time 0.026 s
%------------------------------------------------------------------------------