%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA102^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:55 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 389 ( 113 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 716 ( 46 ~; 36 |; 30 &; 593 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 97 ( 97 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 2 con; 0-4 aty)
% Number of variables : 133 ( 0 ^; 118 !; 15 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/UNION':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/INTER':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_3,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_5,type,
'const/sets/DISJOINT':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_7,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_11,type,
sK1: sK0 > $o ).
thf(func_def_12,type,
sK2: sK0 > $o ).
thf(func_def_13,type,
sK3: sK0 > 'type/realax/real' ).
thf(func_def_14,type,
sK4: sK0 > $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
sK5:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(f1,axiom,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_UNION_1') ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_UNION_0') ).
thf(f3,axiom,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( 'const/sets/FINITE' @ X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_') ).
thf(f4,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
= ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
= 'const/sets/EMPTY' )
@ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/DISJOINT_') ).
thf(f5,axiom,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
& ( 'const/sets/DISJOINT' @ X0 @ X2 @ X3 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_UNION_') ).
thf(f6,conjecture,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X4: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( ( ( 'const/sets/INTER' @ X0 @ X2 @ X3 )
= 'const/sets/EMPTY' )
@ X0 )
& ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 )
= X4 ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X4 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_UNION_EQ_') ).
thf(f7,negated_conjecture,
~ ! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X4: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( ( ( 'const/sets/INTER' @ X0 @ X2 @ X3 )
= 'const/sets/EMPTY' )
@ X0 )
& ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 )
= X4 ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X4 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
= 'const/sets/EMPTY' )
@ X0 )
<=> ( ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f4]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) )
=> ( 'const/sets/FINITE' @ X0 @ X2 ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( $true
= ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 ) )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) )
=> ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > $o,X4: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
& ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
= 'const/sets/EMPTY' )
@ X0 )
& ( ( 'const/sets/UNION' @ X0 @ X1 @ X2 )
= X3 ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X4 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X4 ) )
= ( 'const/iterate/sum' @ X0 @ X3 @ X4 ) ) ),
inference(rectify,[],[f7]) ).
thf(f14,plain,
~ ! [X0: $tType,X3: X0 > $o,X1: X0 > $o,X2: X0 > $o,X4: X0 > 'type/realax/real'] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
= 'const/sets/EMPTY' )
@ X0 )
& ( ( 'const/sets/UNION' @ X0 @ X1 @ X2 )
= X3 ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X4 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X4 ) )
= ( 'const/iterate/sum' @ X0 @ X3 @ X4 ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) @ X3 )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f16,plain,
! [X0: $tType,X3: X0 > 'type/realax/real',X1: X0 > $o,X2: X0 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ( ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
= $true ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) @ X3 )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ),
inference(rectify,[],[f1]) ).
thf(f18,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( $true
= ( 'const/sets/SUBSET' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
! [X0: $tType,X3: X0 > 'type/realax/real',X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) @ X3 )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f20,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > 'type/realax/real',X1: X0 > $o] :
( ( ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) @ X3 )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
| ( $true
!= ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f22,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( $true
!= ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f21]) ).
thf(f23,plain,
? [X0: $tType,X3: X0 > $o,X1: X0 > $o,X2: X0 > $o,X4: X0 > 'type/realax/real'] :
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X4 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X4 ) )
!= ( 'const/iterate/sum' @ X0 @ X3 @ X4 ) )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
= 'const/sets/EMPTY' )
@ X0 )
& ( ( 'const/sets/UNION' @ X0 @ X1 @ X2 )
= X3 ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f24,plain,
? [X0: $tType,X2: X0 > $o,X3: X0 > $o,X4: X0 > 'type/realax/real',X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ( ( 'const/sets/UNION' @ X0 @ X1 @ X2 )
= X3 )
& ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
= 'const/sets/EMPTY' )
@ X0 )
& ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X4 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X4 ) )
!= ( 'const/iterate/sum' @ X0 @ X3 @ X4 ) ) ),
inference(flattening,[],[f23]) ).
thf(f25,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/realax/real',X4: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/sets/UNION' @ X0 @ X4 @ X1 )
= X2 )
& ( 'const/sets/EMPTY'
@ ( X0
= ( 'const/sets/INTER' @ X0 @ X4 @ X1 ) ) )
& ( ( 'const/iterate/sum' @ X0 @ X2 @ X3 )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X4 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f26,plain,
( ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
& ( ( 'const/sets/UNION' @ sK0 @ sK4 @ sK1 )
= sK2 )
& ( ( ( 'const/sets/INTER' @ sK0 @ sK4 @ sK1 )
= 'const/sets/EMPTY' )
@ sK0 )
& ( ( 'const/iterate/sum' @ sK0 @ sK2 @ sK3 )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK4 @ sK3 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK3 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f25]) ).
thf(f27,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( $true
!= ( 'const/sets/DISJOINT' @ X0 @ X3 @ X1 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) )
= ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X3 @ X1 ) @ X2 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true ) ),
inference(rectify,[],[f20]) ).
thf(f28,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
= 'const/sets/EMPTY' )
@ X0 )
| ( ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
= $true )
| ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
!= 'const/sets/EMPTY' )
@ X0 ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f29,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( $true
!= ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f30,plain,
( ( 'const/iterate/sum' @ sK0 @ sK2 @ sK3 )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK4 @ sK3 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK3 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f31,plain,
( ( ( 'const/sets/INTER' @ sK0 @ sK4 @ sK1 )
= 'const/sets/EMPTY' )
@ sK0 ),
inference(cnf_transformation,[],[f26]) ).
thf(f32,plain,
( ( 'const/sets/UNION' @ sK0 @ sK4 @ sK1 )
= sK2 ),
inference(cnf_transformation,[],[f26]) ).
thf(f33,plain,
( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f34,plain,
! [X0: $tType,X2: X0 > 'type/realax/real',X3: X0 > $o,X1: X0 > $o] :
( ( $true
!= ( 'const/sets/DISJOINT' @ X0 @ X3 @ X1 ) )
| ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) )
= ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X3 @ X1 ) @ X2 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f35,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f36,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( $true
= ( 'const/sets/SUBSET' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f37,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
!= 'const/sets/EMPTY' )
@ X0 )
| ( ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f41,plain,
( $true
= ( 'const/sets/FINITE' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK4 @ sK1 ) ) ),
inference(definition_unfolding,[],[f33,f32]) ).
thf(f42,plain,
( ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK4 @ sK1 ) @ sK3 )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK4 @ sK3 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK3 ) ) ),
inference(definition_unfolding,[],[f30,f32]) ).
thf(f48,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( $true != $true )
| ( $true
!= ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(constrained_superposition,[],[f29,f35]) ).
thf(f49,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( $true
!= ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f50,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( $true != $true )
| ( $true
!= ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f29,f36]) ).
thf(f51,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( $true
!= ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X1 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f52,plain,
( ( $true != $true )
| ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK4 ) ) ),
inference(constrained_superposition,[],[f49,f41]) ).
thf(f53,plain,
( $true
= ( 'const/sets/FINITE' @ sK0 @ sK4 ) ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f54,plain,
( ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK1 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f51,f41]) ).
thf(f55,plain,
( $true
= ( 'const/sets/FINITE' @ sK0 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f57,plain,
( ( 'const/sets/EMPTY' @ ( sK0 != 'const/sets/EMPTY' ) @ sK0 )
| ( $true
= ( 'const/sets/DISJOINT' @ sK0 @ sK4 @ sK1 ) ) ),
inference(constrained_superposition,[],[f37,f31]) ).
thf(f58,plain,
( $true
= ( 'const/sets/DISJOINT' @ sK0 @ sK4 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f79,plain,
! [X0: sK0 > 'type/realax/real'] :
( ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK1 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK4 ) )
| ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK4 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) )
= ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK4 @ sK1 ) @ X0 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f34,f58]) ).
thf(f80,plain,
! [X0: sK0 > 'type/realax/real'] :
( ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK4 ) )
| ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK4 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) )
= ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK4 @ sK1 ) @ X0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f81,plain,
! [X0: sK0 > 'type/realax/real'] :
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK4 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) )
= ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK4 @ sK1 ) @ X0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK1 ) ) ),
inference(forward_subsumption_resolution,[],[f80,f53]) ).
thf(f82,plain,
! [X0: sK0 > 'type/realax/real'] :
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK4 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) )
= ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK4 @ sK1 ) @ X0 ) ),
inference(forward_subsumption_resolution,[],[f81,f55]) ).
thf(f83,plain,
( ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK4 @ sK1 ) @ sK3 )
!= ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK4 @ sK1 ) @ sK3 ) ),
inference(constrained_superposition,[],[f42,f82]) ).
thf(f84,plain,
$false,
inference(trivial_inequality_removal,[],[f83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA102^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n002.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 17:44:07 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.29 % (1626685)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (1626695)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3596728680:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (1626696)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (1626696)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.29 % (1626690)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1420478003:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (1626691)lrs+10_16_si=on:nwc=1.5:random_seed=1259614102:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (1626692)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2374899692:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (1626694)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=817866303:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (1626693)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=569802781:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.29 % (1626696)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=956599784:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.29 % (1626692)Instruction limit reached!
% 0.22/0.29 % (1626692)------------------------------
% 0.22/0.29 % (1626692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (1626692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (1626692)CaDiCaL version: 2.1.3
% 0.22/0.29 % (1626692)Termination reason: Instruction limit
% 0.22/0.29 % (1626692)Termination phase: Saturation
% 0.22/0.29 % (1626692)Time elapsed: 0.002 s
% 0.22/0.29 % (1626692)Peak memory usage: 12 MB
% 0.22/0.29 % (1626692)Instructions burned: 4 (million)
% 0.22/0.29 % (1626690) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1626685-1626690"...
% 0.22/0.29 % (1626694) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1626685-1626694"...
% 0.22/0.29 % (1626693) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1626685-1626693"...
% 0.22/0.29 % (1626690)...printing done.
% 0.22/0.29 % (1626690)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (1626690)------------------------------
% 0.22/0.30 % (1626690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (1626690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (1626690)CaDiCaL version: 2.1.3
% 0.22/0.30 % (1626690)Termination reason: Refutation
% 0.22/0.30 % (1626690)Time elapsed: 0.007 s
% 0.22/0.30 % (1626690)Peak memory usage: 12 MB
% 0.22/0.30 % (1626690)Instructions burned: 11 (million)
% 0.22/0.30 % (1626685)Success in time 0.052 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------