TSTP Solution File: ANA105^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ANA105^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n022.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 04:31:11 EDT 2024
% Result : Theorem 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 32 ( 10 unt; 13 typ; 0 def)
% Number of atoms : 72 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 314 ( 12 ~; 3 |; 0 &; 295 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 66 ( 15 ^ 40 !; 8 ?; 66 :)
% ( 3 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/realax/real': $tType ).
thf(type_def_7,type,
'type/nums/num': $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/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_4,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_5,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_11,type,
sK0: 'type/nums/num' > 'type/realax/real' ).
thf(func_def_12,type,
sK1: 'type/nums/num' > 'type/realax/real' ).
thf(func_def_13,type,
sK2: 'type/nums/num' ).
thf(func_def_14,type,
sK3: 'type/nums/num' ).
thf(func_def_16,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f20,plain,
$false,
inference(subsumption_resolution,[],[f19,f17]) ).
thf(f17,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f9,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) )
= $true ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.EUmOFuT4m9/Vampire---4.8_19887','thm/iterate/FINITE_NUMSEG_') ).
thf(f19,plain,
( $true
!= ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f18]) ).
thf(f18,plain,
( ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_add' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_add' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) ) ) ),
inference(superposition,[],[f15,f16]) ).
thf(f16,plain,
! [X0: $tType,X2: X0 > 'type/realax/real',X3: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X2 @ Y0 ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f12,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_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X2 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,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_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X2 @ Y0 ) ) ) ) ),
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 )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_add' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) ) ) ),
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 )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_add' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EUmOFuT4m9/Vampire---4.8_19887','thm/iterate/SUM_ADD_') ).
thf(f15,plain,
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) @ sK0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) @ sK1 ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_add' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) @ sK0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) @ sK1 ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_add' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f13]) ).
thf(f13,plain,
( ? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X1 ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_add' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) @ sK0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 ) @ sK1 ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_add' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X1 ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_add' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f10,plain,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X1 ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_add' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X1 ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_add' @ ( X0 @ X4 ) @ ( X1 @ X4 ) ) ) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X1 ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_add' @ ( X0 @ X4 ) @ ( X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EUmOFuT4m9/Vampire---4.8_19887','thm/iterate/SUM_ADD_NUMSEG_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ANA105^1 : TPTP v8.1.2. Released v7.0.0.
% 0.15/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 15:32:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH1_THM_EQU_NAR problem
% 0.15/0.36 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/sandbox/tmp/tmp.EUmOFuT4m9/Vampire---4.8_19887
% 0.22/0.38 % (19998)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.22/0.38 % (19995)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)
% 0.22/0.38 % (19997)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 Vampire---4 for (2999ds/27Mi)
% 0.22/0.38 % (19996)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)
% 0.22/0.38 % (20000)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)
% 0.22/0.38 % (20001)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.22/0.38 % (19999)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)
% 0.22/0.38 % (20002)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.38 % (19998)Instruction limit reached!
% 0.22/0.38 % (19998)------------------------------
% 0.22/0.38 % (19998)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (19998)Termination reason: Unknown
% 0.22/0.38 % (19999)Instruction limit reached!
% 0.22/0.38 % (19999)------------------------------
% 0.22/0.38 % (19999)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (19998)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (19998)Memory used [KB]: 5373
% 0.22/0.38 % (19998)Time elapsed: 0.004 s
% 0.22/0.38 % (19998)Instructions burned: 2 (million)
% 0.22/0.38 % (19998)------------------------------
% 0.22/0.38 % (19998)------------------------------
% 0.22/0.38 % (19999)Termination reason: Unknown
% 0.22/0.38 % (19999)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (19999)Memory used [KB]: 895
% 0.22/0.38 % (19999)Time elapsed: 0.003 s
% 0.22/0.38 % (19999)Instructions burned: 2 (million)
% 0.22/0.38 % (19999)------------------------------
% 0.22/0.38 % (19999)------------------------------
% 0.22/0.38 % (19996)Instruction limit reached!
% 0.22/0.38 % (19996)------------------------------
% 0.22/0.38 % (19996)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (19996)Termination reason: Unknown
% 0.22/0.38 % (19996)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (19996)Memory used [KB]: 5500
% 0.22/0.38 % (19996)Time elapsed: 0.004 s
% 0.22/0.38 % (19996)Instructions burned: 4 (million)
% 0.22/0.38 % (19996)------------------------------
% 0.22/0.38 % (19996)------------------------------
% 0.22/0.38 % (20000)First to succeed.
% 0.22/0.38 % (20002)Instruction limit reached!
% 0.22/0.38 % (20002)------------------------------
% 0.22/0.38 % (20002)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (20002)Termination reason: Unknown
% 0.22/0.38 % (20002)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (20002)Memory used [KB]: 5500
% 0.22/0.38 % (20002)Time elapsed: 0.005 s
% 0.22/0.38 % (20002)Instructions burned: 4 (million)
% 0.22/0.38 % (20002)------------------------------
% 0.22/0.38 % (20002)------------------------------
% 0.22/0.38 % (19997)Also succeeded, but the first one will report.
% 0.22/0.39 % (20000)Refutation found. Thanks to Tanya!
% 0.22/0.39 % SZS status Theorem for Vampire---4
% 0.22/0.39 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.39 % (20000)------------------------------
% 0.22/0.39 % (20000)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (20000)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (20000)Memory used [KB]: 5500
% 0.22/0.39 % (20000)Time elapsed: 0.006 s
% 0.22/0.39 % (20000)Instructions burned: 2 (million)
% 0.22/0.39 % (20000)------------------------------
% 0.22/0.39 % (20000)------------------------------
% 0.22/0.39 % (19994)Success in time 0.005 s
% 0.22/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------