TSTP Solution File: SEV502^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV502^1 : TPTP v8.2.0. 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 : n002.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 : Tue May 21 04:14:01 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 43 ( 12 unt; 14 typ; 0 def)
% Number of atoms : 185 ( 57 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 442 ( 29 ~; 15 |; 17 &; 370 @)
% ( 0 <=>; 11 =>; 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 : 14 ( 11 usr; 3 con; 0-5 aty)
% Number of variables : 74 ( 0 ^ 54 !; 12 ?; 74 :)
% ( 8 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/DELETE':
!>[X0: $tType] : ( ( X0 > $o ) > X0 > X0 > $o ) ).
thf(func_def_4,type,
'const/iterate/nsum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > 'type/nums/num' ) ).
thf(func_def_5,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_6,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_7,type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_11,type,
sK1: sK0 > 'type/nums/num' ).
thf(func_def_12,type,
sK2: sK0 > $o ).
thf(func_def_13,type,
sK3: sK0 ).
thf(func_def_15,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f36,plain,
$false,
inference(subsumption_resolution,[],[f35,f23]) ).
thf(f23,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f18]) ).
thf(f18,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true )
& ( ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK1 )
!= ( 'const/arith/+' @ ( sK1 @ sK3 ) @ ( 'const/iterate/nsum' @ sK0 @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK3 ) @ sK1 ) ) )
& ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0] :
( ( $true
= ( 'const/sets/FINITE' @ X0 @ X2 ) )
& ( ( 'const/arith/+' @ ( X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X3 ) @ X1 ) )
!= ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) )
=> ( ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true )
& ( ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK1 )
!= ( 'const/arith/+' @ ( sK1 @ sK3 ) @ ( 'const/iterate/nsum' @ sK0 @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK3 ) @ sK1 ) ) )
& ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f16,plain,
? [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0] :
( ( $true
= ( 'const/sets/FINITE' @ X0 @ X2 ) )
& ( ( 'const/arith/+' @ ( X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X3 ) @ X1 ) )
!= ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) ),
inference(flattening,[],[f15]) ).
thf(f15,plain,
? [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0] :
( ( ( 'const/arith/+' @ ( X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X3 ) @ X1 ) )
!= ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
& ( $true
= ( 'const/sets/FINITE' @ X0 @ X2 ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f8,plain,
~ ! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
& ( $true
= ( 'const/sets/FINITE' @ X0 @ X2 ) ) )
=> ( ( 'const/arith/+' @ ( X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X3 ) @ X1 ) )
= ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
=> ( ( 'const/arith/+' @ ( X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X3 ) @ X1 ) )
= ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/nums/num',X3: X0 > $o,X4: X0] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
& ( 'const/sets/IN' @ X0 @ X4 @ X3 ) )
=> ( ( 'const/arith/+' @ ( X1 @ X4 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X3 @ X4 ) @ X1 ) )
= ( 'const/iterate/nsum' @ X0 @ X3 @ X1 ) ) ),
inference(negated_conjecture,[],[f4]) ).
thf(f4,conjecture,
! [X0: $tType,X1: X0 > 'type/nums/num',X3: X0 > $o,X4: X0] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
& ( 'const/sets/IN' @ X0 @ X4 @ X3 ) )
=> ( ( 'const/arith/+' @ ( X1 @ X4 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X3 @ X4 ) @ X1 ) )
= ( 'const/iterate/nsum' @ X0 @ X3 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NSUM_DELETE_') ).
thf(f35,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true ),
inference(subsumption_resolution,[],[f34,f19]) ).
thf(f19,plain,
( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f12,plain,
( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ),
inference(fool_elimination,[],[f11]) ).
thf(f11,plain,
'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+',
inference(rectify,[],[f3]) ).
thf(f3,axiom,
'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+',
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_ADD_') ).
thf(f34,plain,
( ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
!= $true )
| ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true ) ),
inference(subsumption_resolution,[],[f33,f21]) ).
thf(f21,plain,
( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f33,plain,
( ( $true
!= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) )
| ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
!= $true )
| ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f32,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true )
| ( ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK2 @ sK1 )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK2 @ sK1 ) )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) )
| ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
!= $true ) ),
inference(superposition,[],[f25,f24]) ).
thf(f24,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0 > $o,X5: X0] :
( ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 )
= ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
!= $true )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ! [X3: X0 > X1,X4: X0 > $o,X5: X0] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
!= $true )
| ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 )
= ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) ) ) ) ),
inference(flattening,[],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ! [X3: X0 > X1,X4: X0 > $o,X5: X0] :
( ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 )
= ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
!= $true ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true )
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true )
& ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
= $true ) )
=> ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 )
= ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( 'const/sets/IN' @ X0 @ X5 @ X4 ) )
=> ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 )
= ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X2: $tType,X1: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X1 )
=> ! [X3: X0 > X2,X4: X0 > $o,X5: X0] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( 'const/sets/IN' @ X0 @ X5 @ X4 ) )
=> ( ( X1 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X2 @ X1 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) )
= ( 'const/iterate/iterate' @ X0 @ X2 @ X1 @ X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_DELETE_') ).
thf(f25,plain,
( ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK2 @ sK1 )
!= ( 'const/arith/+' @ ( sK1 @ sK3 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK3 ) @ sK1 ) ) ),
inference(definition_unfolding,[],[f22,f20,f20]) ).
thf(f20,plain,
! [X0: $tType] :
( 'const/iterate/nsum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' ) ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType] :
( 'const/iterate/nsum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/nsum_') ).
thf(f22,plain,
( ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK1 )
!= ( 'const/arith/+' @ ( sK1 @ sK3 ) @ ( 'const/iterate/nsum' @ sK0 @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK3 ) @ sK1 ) ) ),
inference(cnf_transformation,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV502^1 : TPTP v8.2.0. Released v7.0.0.
% 0.11/0.14 % 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
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 : Sun May 19 19:04:53 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/sandbox/benchmark/theBenchmark.p
% 0.14/0.37 % (28868)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (28870)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)
% 0.14/0.37 % (28869)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)
% 0.14/0.37 % (28871)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (28873)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)
% 0.14/0.37 % (28874)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (28871)Instruction limit reached!
% 0.14/0.37 % (28871)------------------------------
% 0.14/0.37 % (28871)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (28871)Termination reason: Unknown
% 0.14/0.37 % (28871)Termination phase: Preprocessing 3
% 0.14/0.37
% 0.14/0.37 % (28871)Memory used [KB]: 895
% 0.14/0.37 % (28871)Time elapsed: 0.003 s
% 0.14/0.37 % (28871)Instructions burned: 2 (million)
% 0.14/0.37 % (28871)------------------------------
% 0.14/0.37 % (28871)------------------------------
% 0.14/0.37 % (28869)Instruction limit reached!
% 0.14/0.37 % (28869)------------------------------
% 0.14/0.37 % (28869)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (28869)Termination reason: Unknown
% 0.14/0.37 % (28869)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (28869)Memory used [KB]: 5500
% 0.14/0.37 % (28869)Time elapsed: 0.005 s
% 0.14/0.37 % (28869)Instructions burned: 5 (million)
% 0.14/0.37 % (28869)------------------------------
% 0.14/0.37 % (28869)------------------------------
% 0.14/0.37 % (28873)First to succeed.
% 0.14/0.38 % (28870)Also succeeded, but the first one will report.
% 0.14/0.38 % (28872)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)
% 0.14/0.38 % (28874)Also succeeded, but the first one will report.
% 0.14/0.38 % (28873)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (28873)------------------------------
% 0.14/0.38 % (28873)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (28873)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (28873)Memory used [KB]: 5500
% 0.14/0.38 % (28873)Time elapsed: 0.007 s
% 0.14/0.38 % (28873)Instructions burned: 6 (million)
% 0.14/0.38 % (28873)------------------------------
% 0.14/0.38 % (28873)------------------------------
% 0.14/0.38 % (28867)Success in time 0.009 s
% 0.14/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------