TSTP Solution File: SEV510^1 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV510^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n017.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 Jun 24 16:04:11 EDT 2024
% Result : Theorem 0.13s 0.40s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 341 ( 92 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 742 ( 38 ~; 34 |; 22 &; 629 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 141 ( 26 ^ 100 !; 15 ?; 141 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
'type/realax/real': $tType ).
thf(type_def_8,type,
sK0: $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'type/nums/num': $tType ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/CARD':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' ) ).
thf(func_def_5,type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_6,type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_7,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_8,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_13,type,
sK1: sK0 > $o ).
thf(func_def_14,type,
sK2: sK0 > 'type/realax/real' ).
thf(func_def_15,type,
sK3: 'type/realax/real' ).
thf(func_def_16,type,
sK4:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > ( X0 > 'type/realax/real' ) > X0 ) ).
thf(func_def_18,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f47,plain,
$false,
inference(subsumption_resolution,[],[f45,f29]) ).
thf(f29,plain,
( $true
!= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) ) ),
inference(backward_demodulation,[],[f21,f28]) ).
thf(f28,plain,
! [X0: 'type/realax/real'] :
( ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : X0 )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ sK0 @ sK1 ) ) @ X0 ) ),
inference(trivial_inequality_removal,[],[f27]) ).
thf(f27,plain,
! [X0: 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : X0 )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ sK0 @ sK1 ) ) @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[],[f24,f23]) ).
thf(f23,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f18]) ).
thf(f18,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true )
& ! [X4: sK0] :
( ( ( 'const/realax/real_le' @ ( sK2 @ X4 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ X4 @ sK1 )
!= $true ) )
& ( $true
!= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ sK0 @ sK1 ) ) @ sK3 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f17]) ).
thf(f17,plain,
( ? [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ! [X4: X0] :
( ( ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
!= $true ) )
& ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) )
!= $true ) )
=> ( ( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true )
& ! [X4: sK0] :
( ( ( 'const/realax/real_le' @ ( sK2 @ X4 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ X4 @ sK1 )
!= $true ) )
& ( $true
!= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ sK0 @ sK1 ) ) @ sK3 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ! [X4: X0] :
( ( ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
!= $true ) )
& ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) )
!= $true ) ),
inference(flattening,[],[f13]) ).
thf(f13,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) )
!= $true )
& ! [X4: X0] :
( ( ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
!= $true ) )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ( ! [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true )
=> ( ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 )
= $true ) )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) )
=> ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) )
= $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
=> ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) ) ),
inference(rectify,[],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
=> ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) ) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
=> ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_BOUND_') ).
thf(f24,plain,
! [X0: $tType,X2: X0 > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) @ X1 )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : X1 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: 'type/realax/real',X2: X0 > $o] :
( ( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) @ X1 )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : X1 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: 'type/realax/real',X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
=> ( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) @ X1 )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : X1 ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: 'type/realax/real',X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( 'const/iterate/sum' @ X0 @ X2
@ ^ [X3: X0] : X1 )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: 'type/realax/real',X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( 'const/iterate/sum' @ X0 @ X2
@ ^ [X3: X0] : X1 )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_CONST_') ).
thf(f21,plain,
( $true
!= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ sK0 @ sK1 ) ) @ sK3 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f45,plain,
( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) ) ),
inference(beta_eta_normalization,[],[f44]) ).
thf(f44,plain,
( ( 'const/realax/real_le'
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] :
( sK2
@ ( ^ [Y1: sK0] : Y1
@ Y0 ) ) )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) )
= $true ),
inference(duplicate_literal_removal,[],[f42]) ).
thf(f42,plain,
( ( ( 'const/realax/real_le'
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] :
( sK2
@ ( ^ [Y1: sK0] : Y1
@ Y0 ) ) )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) )
= $true )
| ( ( 'const/realax/real_le'
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] :
( sK2
@ ( ^ [Y1: sK0] : Y1
@ Y0 ) ) )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) )
= $true ) ),
inference(equality_resolution,[],[f39]) ).
thf(f39,plain,
! [X2: sK0 > 'type/realax/real',X0: sK0 > sK0,X1: sK0 > 'type/realax/real'] :
( ( ( X0
@ ( sK4 @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3
@ ^ [Y0: sK0] : ( sK2 @ ( X0 @ Y0 ) ) ) )
!= ( sK4 @ sK0 @ sK1 @ X1 @ X2 ) )
| ( ( 'const/realax/real_le'
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : ( sK2 @ ( X0 @ Y0 ) ) )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X2 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f38]) ).
thf(f38,plain,
! [X2: sK0 > 'type/realax/real',X0: sK0 > sK0,X1: sK0 > 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X2 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) ) )
| ( ( 'const/realax/real_le'
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : ( sK2 @ ( X0 @ Y0 ) ) )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) )
= $true )
| ( $true != $true )
| ( ( X0
@ ( sK4 @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3
@ ^ [Y0: sK0] : ( sK2 @ ( X0 @ Y0 ) ) ) )
!= ( sK4 @ sK0 @ sK1 @ X1 @ X2 ) ) ),
inference(constrained_superposition,[],[f35,f33]) ).
thf(f33,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK2 @ ( sK4 @ sK0 @ sK1 @ X0 @ X1 ) ) @ sK3 ) )
| ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f32,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK2 @ ( sK4 @ sK0 @ sK1 @ X0 @ X1 ) ) @ sK3 ) )
| ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) )
= $true ) ),
inference(superposition,[],[f22,f31]) ).
thf(f31,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK4 @ sK0 @ sK1 @ X0 @ X1 ) @ sK1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f30,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK4 @ sK0 @ sK1 @ X0 @ X1 ) @ sK1 ) ) ),
inference(superposition,[],[f26,f23]) ).
thf(f26,plain,
! [X0: $tType,X2: X0 > 'type/realax/real',X3: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( $true
= ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) @ X3 ) )
| ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f20,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true )
| ( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) @ X3 ) )
& ( ( 'const/realax/real_le' @ ( X1 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) @ ( X2 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f16,f19]) ).
thf(f19,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
!= $true ) )
=> ( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) @ X3 ) )
& ( ( 'const/realax/real_le' @ ( X1 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) @ ( X2 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) )
!= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f16,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true )
| ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
!= $true ) ) ),
inference(flattening,[],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true )
| ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
!= $true ) )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ! [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
= $true )
=> ( ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
= $true ) )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true ) )
=> ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
& ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
=> ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
& ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
=> ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_LE_') ).
thf(f22,plain,
! [X4: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X4 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ ( sK2 @ X4 ) @ sK3 )
= $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f35,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( X0 @ ( sK4 @ sK0 @ sK1 @ X1 @ X0 ) ) @ ( X1 @ ( sK4 @ sK0 @ sK1 @ X1 @ X0 ) ) )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f34,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) ) )
| ( ( 'const/realax/real_le' @ ( X0 @ ( sK4 @ sK0 @ sK1 @ X1 @ X0 ) ) @ ( X1 @ ( sK4 @ sK0 @ sK1 @ X1 @ X0 ) ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f25,f23]) ).
thf(f25,plain,
! [X0: $tType,X2: X0 > 'type/realax/real',X3: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true )
| ( ( 'const/realax/real_le' @ ( X1 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) @ ( X2 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) )
!= $true ) ),
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEV510^1 : TPTP v8.2.0. Released v7.0.0.
% 0.08/0.13 % Command : run_vampire %s %d THM
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 21 19:40:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.36 This is a TH1_THM_EQU_NAR problem
% 0.13/0.36 Running higher-order theorem proving
% 0.13/0.36 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.13/0.38 % (9836)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.38 % (9838)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.13/0.38 % (9839)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.38 % (9837)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.13/0.39 % (9840)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.39 % (9841)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.13/0.39 % (9842)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.39 % Exception at run slice level
% 0.13/0.39 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.13/0.39 % (9839)Instruction limit reached!
% 0.13/0.39 % (9839)------------------------------
% 0.13/0.39 % (9839)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (9839)Termination reason: Unknown
% 0.13/0.39 % (9839)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (9839)Memory used [KB]: 1023
% 0.13/0.39 % (9839)Time elapsed: 0.004 s
% 0.13/0.39 % (9839)Instructions burned: 2 (million)
% 0.13/0.39 % (9839)------------------------------
% 0.13/0.39 % (9839)------------------------------
% 0.13/0.39 % (9837)Instruction limit reached!
% 0.13/0.39 % (9837)------------------------------
% 0.13/0.39 % (9837)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (9837)Termination reason: Unknown
% 0.13/0.39 % (9837)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (9837)Memory used [KB]: 5500
% 0.13/0.39 % (9837)Time elapsed: 0.005 s
% 0.13/0.39 % (9837)Instructions burned: 4 (million)
% 0.13/0.39 % (9837)------------------------------
% 0.13/0.39 % (9837)------------------------------
% 0.13/0.39 % (9841)Refutation not found, incomplete strategy
% 0.13/0.39 % (9841)------------------------------
% 0.13/0.39 % (9841)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (9841)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.39
% 0.13/0.39
% 0.13/0.39 % (9841)Memory used [KB]: 5500
% 0.13/0.39 % (9841)Time elapsed: 0.006 s
% 0.13/0.39 % (9841)Instructions burned: 3 (million)
% 0.13/0.39 % (9841)------------------------------
% 0.13/0.39 % (9841)------------------------------
% 0.13/0.39 % (9838)Refutation not found, incomplete strategy
% 0.13/0.39 % (9838)------------------------------
% 0.13/0.39 % (9838)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (9838)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.39
% 0.13/0.39
% 0.13/0.39 % (9838)Memory used [KB]: 5628
% 0.13/0.39 % (9838)Time elapsed: 0.011 s
% 0.13/0.39 % (9838)Instructions burned: 11 (million)
% 0.13/0.39 % (9838)------------------------------
% 0.13/0.39 % (9838)------------------------------
% 0.13/0.40 % (9842)First to succeed.
% 0.13/0.40 % (9842)Refutation found. Thanks to Tanya!
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.40 % (9842)------------------------------
% 0.13/0.40 % (9842)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.40 % (9842)Termination reason: Refutation
% 0.13/0.40
% 0.13/0.40 % (9842)Memory used [KB]: 5628
% 0.13/0.40 % (9842)Time elapsed: 0.015 s
% 0.13/0.40 % (9842)Instructions burned: 13 (million)
% 0.13/0.40 % (9842)------------------------------
% 0.13/0.40 % (9842)------------------------------
% 0.13/0.40 % (9835)Success in time 0.028 s
%------------------------------------------------------------------------------