TSTP Solution File: SEV507^1 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV507^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n018.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 16:04:10 EDT 2024
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 33 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 299 ( 12 ~; 4 |; 4 &; 272 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 3 con; 0-5 aty)
% Number of variables : 52 ( 0 ^ 48 !; 4 ?; 52 :)
% 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/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_3,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_6,type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_7,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_8,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_9,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_10,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_11,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_12,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_13,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_14,type,
'const/class/COND':
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_16,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_19,type,
sK1: sK0 > 'type/realax/real' ).
thf(func_def_21,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f27,plain,
$false,
inference(trivial_inequality_removal,[],[f26]) ).
thf(f26,plain,
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(superposition,[],[f22,f25]) ).
thf(f25,plain,
! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ X0 @ X1 ) ),
inference(forward_demodulation,[],[f24,f20]) ).
thf(f20,plain,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f4,axiom,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NEUTRAL_REAL_ADD_') ).
thf(f24,plain,
! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ X0 @ X1 ) ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f23,plain,
! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ X0 @ X1 ) )
| ( $true != $true ) ),
inference(superposition,[],[f18,f17]) ).
thf(f17,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f9,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
inference(rectify,[],[f2]) ).
thf(f2,axiom,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(f18,plain,
! [X0: $tType,X2: $tType,X3: X2 > X2 > X2,X7: X0 > X2] :
( ( ( 'const/iterate/monoidal' @ X2 @ X3 )
!= $true )
| ( ( 'const/iterate/neutral' @ X2 @ X3 )
= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( ! [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X5 @ X6 ) @ X4 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) @ ( X3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) ) ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true ) )
& ! [X7: X0 > X2] :
( ( 'const/iterate/neutral' @ X2 @ X3 )
= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) ) )
| ( ( 'const/iterate/monoidal' @ X2 @ X3 )
!= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( ( 'const/iterate/monoidal' @ X2 @ X3 )
= $true )
=> ( ! [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X6 )
= $true )
=> ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X5 @ X6 ) @ X4 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) @ ( X3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) ) ) ) )
& ! [X7: X0 > X2] :
( ( 'const/iterate/neutral' @ X2 @ X3 )
= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ( ! [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( 'const/sets/FINITE' @ X1 @ X6 )
=> ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X5 @ X6 ) @ X4 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) @ ( X3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) ) ) ) )
& ! [X7: X0 > X2] :
( ( 'const/iterate/neutral' @ X2 @ X3 )
= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ( ! [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( 'const/sets/FINITE' @ X1 @ X6 )
=> ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X5 @ X6 ) @ X4 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) @ ( X3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) ) ) ) )
& ! [X4: X0 > X2] :
( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
= ( 'const/iterate/neutral' @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_') ).
thf(f22,plain,
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ sK0 @ sK1 ) ),
inference(definition_unfolding,[],[f16,f21]) ).
thf(f21,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(cnf_transformation,[],[f3]) ).
thf(f3,axiom,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/sum_') ).
thf(f16,plain,
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/sum' @ sK0 @ 'const/sets/EMPTY' @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/sum' @ sK0 @ 'const/sets/EMPTY' @ sK0 @ sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f14]) ).
thf(f14,plain,
( ? [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1 ) )
=> ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/sum' @ sK0 @ 'const/sets/EMPTY' @ sK0 @ sK1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
? [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1 ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1 ) ),
inference(negated_conjecture,[],[f5]) ).
thf(f5,conjecture,
! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_CLAUSES_0') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV507^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:28:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TH1_THM_EQU_NAR problem
% 0.12/0.35 Running higher-order theorem proving
% 0.12/0.35 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
% 0.20/0.37 % (24389)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (24389)Instruction limit reached!
% 0.20/0.37 % (24389)------------------------------
% 0.20/0.37 % (24389)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (24389)Termination reason: Unknown
% 0.20/0.37 % (24389)Termination phase: Saturation
% 0.20/0.37
% 0.20/0.37 % (24389)Memory used [KB]: 5500
% 0.20/0.37 % (24389)Time elapsed: 0.003 s
% 0.20/0.37 % (24389)Instructions burned: 2 (million)
% 0.20/0.37 % (24389)------------------------------
% 0.20/0.37 % (24389)------------------------------
% 0.20/0.37 % (24386)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.37 % (24388)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)
% 0.20/0.37 % (24391)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)
% 0.20/0.37 % (24387)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)
% 0.20/0.37 % (24392)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.37 % (24390)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)
% 0.20/0.38 % Exception at run slice level
% 0.20/0.38 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
% 0.20/0.38 % (24391)Refutation not found, incomplete strategy
% 0.20/0.38 % (24391)------------------------------
% 0.20/0.38 % (24391)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (24391)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.38
% 0.20/0.38
% 0.20/0.38 % (24391)Memory used [KB]: 5500
% 0.20/0.38 % (24391)Time elapsed: 0.004 s
% 0.20/0.38 % (24391)Instructions burned: 2 (million)
% 0.20/0.38 % (24391)------------------------------
% 0.20/0.38 % (24391)------------------------------
% 0.20/0.38 % (24387)Instruction limit reached!
% 0.20/0.38 % (24387)------------------------------
% 0.20/0.38 % (24387)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (24387)Termination reason: Unknown
% 0.20/0.38 % (24387)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (24387)Memory used [KB]: 5500
% 0.20/0.38 % (24387)Time elapsed: 0.005 s
% 0.20/0.38 % (24387)Instructions burned: 4 (million)
% 0.20/0.38 % (24387)------------------------------
% 0.20/0.38 % (24387)------------------------------
% 0.20/0.38 % (24388)First to succeed.
% 0.20/0.38 % (24386)Also succeeded, but the first one will report.
% 0.20/0.38 % (24388)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.38 % (24388)------------------------------
% 0.20/0.38 % (24388)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (24388)Termination reason: Refutation
% 0.20/0.38
% 0.20/0.38 % (24388)Memory used [KB]: 5500
% 0.20/0.38 % (24388)Time elapsed: 0.007 s
% 0.20/0.38 % (24388)Instructions burned: 4 (million)
% 0.20/0.38 % (24388)------------------------------
% 0.20/0.38 % (24388)------------------------------
% 0.20/0.38 % (24385)Success in time 0.02 s
%------------------------------------------------------------------------------