TSTP Solution File: SEV507^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV507^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n025.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 : Sun May 5 09:43:27 EDT 2024
% Result : Theorem 0.14s 0.37s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 26
% Syntax : Number of formulae : 45 ( 18 unt; 20 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 : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 3 con; 0-5 aty)
% Number of variables : 63 ( 0 ^ 48 !; 4 ?; 63 :)
% ( 11 !>; 0 ?*; 0 @-; 0 @+)
% 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_18,type,
sK1: sK0 > 'type/realax/real' ).
thf(func_def_20,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,f18]) ).
thf(f18,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/sandbox2/tmp/tmp.aQP7chRM87/Vampire---4.8_22214','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'] :
( ( $true != $true )
| ( ( '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(superposition,[],[f16,f21]) ).
thf(f21,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/sandbox2/tmp/tmp.aQP7chRM87/Vampire---4.8_22214','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(f16,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,[],[f12]) ).
thf(f12,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/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 ) ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( ( 'const/iterate/monoidal' @ X2 @ X3 )
= $true )
=> ( ! [X7: X0 > X2] :
( ( 'const/iterate/neutral' @ X2 @ X3 )
= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) )
& ! [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 ) ) ) ) ) ) ),
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/sandbox2/tmp/tmp.aQP7chRM87/Vampire---4.8_22214','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,[],[f19,f20]) ).
thf(f20,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/sandbox2/tmp/tmp.aQP7chRM87/Vampire---4.8_22214','thm/iterate/sum_') ).
thf(f19,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])],[f13,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(f13,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/sandbox2/tmp/tmp.aQP7chRM87/Vampire---4.8_22214','thm/iterate/SUM_CLAUSES_0') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV507^1 : TPTP v8.1.2. Released v7.0.0.
% 0.06/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 12:19:43 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH1_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.aQP7chRM87/Vampire---4.8_22214
% 0.14/0.36 % (22325)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.14/0.36 % (22327)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.14/0.36 % (22328)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.14/0.37 % (22325)Instruction limit reached!
% 0.14/0.37 % (22325)------------------------------
% 0.14/0.37 % (22325)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (22325)Termination reason: Unknown
% 0.14/0.37 % (22325)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (22325)Memory used [KB]: 895
% 0.14/0.37 % (22325)Time elapsed: 0.002 s
% 0.14/0.37 % (22325)Instructions burned: 2 (million)
% 0.14/0.37 % (22325)------------------------------
% 0.14/0.37 % (22325)------------------------------
% 0.14/0.37 % (22327)Refutation not found, incomplete strategy
% 0.14/0.37 % (22327)------------------------------
% 0.14/0.37 % (22327)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (22327)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % (22327)Memory used [KB]: 5500
% 0.14/0.37 % (22327)Time elapsed: 0.002 s
% 0.14/0.37 % (22327)Instructions burned: 2 (million)
% 0.14/0.37 % (22327)------------------------------
% 0.14/0.37 % (22327)------------------------------
% 0.14/0.37 % (22328)First to succeed.
% 0.14/0.37 % (22322)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.14/0.37 % (22326)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.14/0.37 % (22323)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 Vampire---4 for (2999ds/4Mi)
% 0.14/0.37 % (22326)Instruction limit reached!
% 0.14/0.37 % (22326)------------------------------
% 0.14/0.37 % (22326)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (22326)Termination reason: Unknown
% 0.14/0.37 % (22326)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (22326)Memory used [KB]: 895
% 0.14/0.37 % (22326)Time elapsed: 0.003 s
% 0.14/0.37 % (22326)Instructions burned: 2 (million)
% 0.14/0.37 % (22326)------------------------------
% 0.14/0.37 % (22326)------------------------------
% 0.14/0.37 % (22328)Refutation found. Thanks to Tanya!
% 0.14/0.37 % SZS status Theorem for Vampire---4
% 0.14/0.37 % SZS output start Proof for Vampire---4
% See solution above
% 0.14/0.37 % (22328)------------------------------
% 0.14/0.37 % (22328)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (22328)Termination reason: Refutation
% 0.14/0.37
% 0.14/0.37 % (22328)Memory used [KB]: 5500
% 0.14/0.37 % (22328)Time elapsed: 0.005 s
% 0.14/0.37 % (22328)Instructions burned: 3 (million)
% 0.14/0.37 % (22328)------------------------------
% 0.14/0.37 % (22328)------------------------------
% 0.14/0.37 % (22321)Success in time 0.015 s
% 0.14/0.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------