%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA096^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 07:45:54 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 233 ( 78 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 642 ( 33 ~; 24 |; 15 &; 559 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 2 con; 0-5 aty)
% Number of variables : 100 ( 0 ^; 92 !; 8 ?; 100 :)
% 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/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/DIFF':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_3,type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_4,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_5,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_6,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_7,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
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,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/sum_') ).
thf(f2,axiom,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( 'const/sets/SUBSET' @ X0 @ X5 @ X4 ) )
=> ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DIFF' @ X0 @ X4 @ X5 ) @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_DIFF_') ).
thf(f3,axiom,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(f4,axiom,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( X0
= ( 'const/realax/real_sub' @ X1 @ X2 ) )
= ( ( 'const/realax/real_add' @ X0 @ X2 )
= X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/real/REAL_EQ_SUB_LADD_') ).
thf(f5,conjecture,
! [X0: $tType,X3: X0 > $o,X2: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/SUBSET' @ X0 @ X3 @ X2 ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X2 @ X3 ) @ X1 )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_DIFF_') ).
thf(f6,negated_conjecture,
~ ! [X0: $tType,X3: X0 > $o,X2: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/SUBSET' @ X0 @ X3 @ X2 ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X2 @ X3 ) @ X1 )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ X2 @ X0 )
= X1 )
= ( ( 'const/realax/real_add' @ X1 @ X0 )
= X2 ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
! [X2: 'type/realax/real',X1: 'type/realax/real',X0: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ X2 @ X0 )
= X1 )
<=> ( ( 'const/realax/real_add' @ X1 @ X0 )
= X2 ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
inference(rectify,[],[f3]) ).
thf(f10,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0] :
( ( 'const/iterate/monoidal' @ X0 @ X2 )
=> ! [X3: X1 > X0,X4: X1 > $o,X5: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X4 )
& ( 'const/sets/SUBSET' @ X1 @ X5 @ X4 ) )
=> ( ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X4 @ X3 )
= ( X2 @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ ( 'const/sets/DIFF' @ X1 @ X4 @ X5 ) @ X3 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X3 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f12,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X2 )
= $true )
=> ! [X3: X1 > X0,X5: X1 > $o,X4: X1 > $o] :
( ( ( ( 'const/sets/FINITE' @ X1 @ X4 )
= $true )
& ( $true
= ( 'const/sets/SUBSET' @ X1 @ X5 @ X4 ) ) )
=> ( ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X4 @ X3 )
= ( X2 @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ ( 'const/sets/DIFF' @ X1 @ X4 @ X5 ) @ X3 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X3 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X2 @ X1 ) @ X3 )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f14,plain,
~ ! [X0: $tType,X2: X0 > $o,X1: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X2 @ X1 ) @ X3 )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
? [X0: $tType,X2: X0 > $o,X1: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X2 @ X1 ) @ X3 )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) ) )
& ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f16,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
& ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X2 @ X1 ) @ X3 )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0] :
( ! [X3: X1 > X0,X5: X1 > $o,X4: X1 > $o] :
( ( ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X4 @ X3 )
= ( X2 @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ ( 'const/sets/DIFF' @ X1 @ X4 @ X5 ) @ X3 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X3 ) ) )
| ( ( 'const/sets/FINITE' @ X1 @ X4 )
!= $true )
| ( $true
!= ( 'const/sets/SUBSET' @ X1 @ X5 @ X4 ) ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f18,plain,
! [X1: $tType,X0: $tType,X2: X0 > X0 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X2 )
!= $true )
| ! [X5: X1 > $o,X4: X1 > $o,X3: X1 > X0] :
( ( ( 'const/sets/FINITE' @ X1 @ X4 )
!= $true )
| ( $true
!= ( 'const/sets/SUBSET' @ X1 @ X5 @ X4 ) )
| ( ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X4 @ X3 )
= ( X2 @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ ( 'const/sets/DIFF' @ X1 @ X4 @ X5 ) @ X3 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X3 ) ) ) ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $true )
& ( ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK2 @ sK1 ) @ sK3 )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK3 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK3 ) ) )
& ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f16]) ).
thf(f20,plain,
! [X2: 'type/realax/real',X1: 'type/realax/real',X0: 'type/realax/real'] :
( ( ( ( 'const/realax/real_sub' @ X2 @ X0 )
= X1 )
| ( ( 'const/realax/real_add' @ X1 @ X0 )
!= X2 ) )
& ( ( ( 'const/realax/real_add' @ X1 @ X0 )
= X2 )
| ( ( 'const/realax/real_sub' @ X2 @ X0 )
!= X1 ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f21,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_sub' @ X0 @ X2 )
= X1 )
| ( ( 'const/realax/real_add' @ X1 @ X2 )
!= X0 ) )
& ( ( ( 'const/realax/real_add' @ X1 @ X2 )
= X0 )
| ( ( 'const/realax/real_sub' @ X0 @ X2 )
!= X1 ) ) ),
inference(rectify,[],[f20]) ).
thf(f22,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ! [X3: X0 > $o,X4: X0 > $o,X5: X0 > X1] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X3 @ X4 )
!= $true )
| ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5 )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DIFF' @ X0 @ X4 @ X3 ) @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5 ) ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f23,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f24,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f19]) ).
thf(f25,plain,
( ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK2 @ sK1 ) @ sK3 )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK3 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK3 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f19]) ).
thf(f28,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ X0 @ X2 )
= X1 )
| ( ( 'const/realax/real_add' @ X1 @ X2 )
!= X0 ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f29,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > $o,X4: X0 > $o,X5: X0 > X1] :
( ( ( 'const/sets/SUBSET' @ X0 @ X3 @ X4 )
!= $true )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5 )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DIFF' @ X0 @ X4 @ X3 ) @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f30,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f33,plain,
( ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/DIFF' @ sK0 @ sK2 @ sK1 ) @ sK3 )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK3 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ sK3 ) ) ),
inference(definition_unfolding,[],[f25,f23,f23,f23]) ).
thf(f34,plain,
! [X2: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_sub' @ ( 'const/realax/real_add' @ X1 @ X2 ) @ X2 )
= X1 ),
inference(equality_resolution,[],[f28]) ).
thf(f36,plain,
! [X0: $tType,X2: sK0 > X0,X1: X0 > X0 > X0] :
( ( ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK2 @ X2 )
= ( X1 @ ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ ( 'const/sets/DIFF' @ sK0 @ sK2 @ sK1 ) @ X2 ) @ ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK1 @ X2 ) ) )
| ( $true != $true )
| ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true ) ),
inference(constrained_superposition,[],[f29,f26]) ).
thf(f37,plain,
! [X0: $tType,X2: sK0 > X0,X1: X0 > X0 > X0] :
( ( ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK2 @ X2 )
= ( X1 @ ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ ( 'const/sets/DIFF' @ sK0 @ sK2 @ sK1 ) @ X2 ) @ ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK1 @ X2 ) ) )
| ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true )
| ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f38,plain,
! [X0: $tType,X2: sK0 > X0,X1: X0 > X0 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true )
| ( ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK2 @ X2 )
= ( X1 @ ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ ( 'const/sets/DIFF' @ sK0 @ sK2 @ sK1 ) @ X2 ) @ ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK1 @ X2 ) ) ) ),
inference(forward_subsumption_resolution,[],[f37,f24]) ).
thf(f39,plain,
! [X0: sK0 > 'type/realax/real'] :
( ( ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ X0 )
= ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/DIFF' @ sK0 @ sK2 @ sK1 ) @ X0 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ X0 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f38,f30]) ).
thf(f40,plain,
! [X0: sK0 > 'type/realax/real'] :
( ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ X0 )
= ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/DIFF' @ sK0 @ sK2 @ sK1 ) @ X0 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f41,plain,
! [X0: sK0 > 'type/realax/real'] :
( ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/DIFF' @ sK0 @ sK2 @ sK1 ) @ X0 )
= ( 'const/realax/real_sub' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ X0 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ X0 ) ) ),
inference(constrained_superposition,[],[f34,f40]) ).
thf(f42,plain,
( ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/DIFF' @ sK0 @ sK2 @ sK1 ) @ sK3 )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/DIFF' @ sK0 @ sK2 @ sK1 ) @ sK3 ) ),
inference(constrained_superposition,[],[f33,f41]) ).
thf(f44,plain,
$false,
inference(trivial_inequality_removal,[],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA096^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n003.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 17:43:14 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.26 % (2827305)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.26 % (2827312)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2317158020:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.26 % (2827312)Refutation not found, incomplete strategy
% 0.20/0.26 % (2827312)------------------------------
% 0.20/0.26 % (2827312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (2827312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (2827312)CaDiCaL version: 2.1.3
% 0.20/0.26 % (2827312)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.26 % (2827312)Time elapsed: 0.002 s
% 0.20/0.26 % (2827312)Peak memory usage: 12 MB
% 0.20/0.26 % (2827312)Instructions burned: 5 (million)
% 0.20/0.26 % (2827312)------------------------------
% 0.20/0.26 % (2827312)------------------------------
% 0.20/0.26 % (2827310)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=13193100:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.26 % (2827311)lrs+10_16_si=on:nwc=1.5:random_seed=3063740717:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.26 % (2827313)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=3517884944: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)
% 0.20/0.26 % (2827316)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.26 % (2827316)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
% 0.20/0.26 % (2827315)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1144446445:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.26 % (2827310) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2827305-2827310"...
% 0.20/0.26 % (2827316)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=1589257797:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.26 % (2827315) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2827305-2827315"...
% 0.20/0.26 % (2827310)...printing done.
% 0.20/0.26 % (2827313) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2827305-2827313"...
% 0.20/0.26 % (2827310)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.26 % (2827310)------------------------------
% 0.20/0.26 % (2827310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (2827310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (2827310)CaDiCaL version: 2.1.3
% 0.20/0.26 % (2827310)Termination reason: Refutation
% 0.20/0.26 % (2827310)Time elapsed: 0.005 s
% 0.20/0.26 % (2827310)Peak memory usage: 12 MB
% 0.20/0.26 % (2827310)Instructions burned: 8 (million)
% 0.20/0.26 % (2827305)Success in time 0.036 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------