TSTP Solution File: SEV486^1 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV486^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n019.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 16:04:04 EDT 2024
% Result : Theorem 0.20s 0.39s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 187 ( 45 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 316 ( 10 ~; 13 |; 6 &; 274 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 4 con; 0-4 aty)
% ( 0 !!; 12 ??; 0 @@+; 0 @@-)
% Number of variables : 79 ( 29 ^ 43 !; 7 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/sets/SETSPEC':
!>[X0: $tType] : ( X0 > $o > X0 > $o ) ).
thf(func_def_2,type,
'const/sets/HAS_SIZE':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' > $o ) ).
thf(func_def_3,type,
'const/sets/GSPEC':
!>[X0: $tType] : ( ( X0 > $o ) > X0 > $o ) ).
thf(func_def_4,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
'const/sets/CARD':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' ) ).
thf(func_def_6,type,
'const/arith/<': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_8,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK0: 'type/nums/num' ).
thf(func_def_19,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f51,plain,
$false,
inference(trivial_inequality_removal,[],[f49]) ).
thf(f49,plain,
$true = $false,
inference(superposition,[],[f30,f42]) ).
thf(f42,plain,
( $false
= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ sK0 ) @ Y1 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f40]) ).
thf(f40,plain,
( ( $true != $true )
| ( $false
= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ sK0 ) @ Y1 ) ) ) ) ) ),
inference(superposition,[],[f17,f38]) ).
thf(f38,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f35,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false )
| ( $true = $false )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(superposition,[],[f33,f21]) ).
thf(f21,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $false )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[],[f19]) ).
thf(f19,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) ) ) ),
inference(binary_proxy_clausification,[],[f16]) ).
thf(f16,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) )
& ( 'const/sets/FINITE' @ X0 @ X1 ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) )
& ( 'const/sets/FINITE' @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_') ).
thf(f33,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true
= ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ ( 'const/sets/CARD' @ X0 @ X1 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false ) ),
inference(equality_resolution,[],[f24]) ).
thf(f24,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/CARD' @ X0 @ X1 )
!= X2 )
| ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f23]) ).
thf(f23,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false )
| ( $false
= ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) ) ),
inference(binary_proxy_clausification,[],[f18]) ).
thf(f18,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $true )
| ( $false
= ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) ) ) ),
inference(binary_proxy_clausification,[],[f16]) ).
thf(f17,plain,
( $true
!= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ sK0 ) @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
( $true
!= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ sK0 ) @ Y1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: 'type/nums/num'] :
( $true
!= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) ) )
=> ( $true
!= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ sK0 ) @ Y1 ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
? [X0: 'type/nums/num'] :
( $true
!= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
~ ! [X0: 'type/nums/num'] :
( $true
= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f6,plain,
~ ! [X0: 'type/nums/num'] :
( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [X1: 'type/nums/num'] :
? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num'] :
( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [X1: 'type/nums/num'] :
? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) ) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
! [X0: 'type/nums/num'] :
( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [X1: 'type/nums/num'] :
? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_NUMSEG_LT_') ).
thf(f30,plain,
! [X0: 'type/nums/num'] :
( $true
= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f28,plain,
! [X0: 'type/nums/num'] :
( ( $true
= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) ) )
| ( $true = $false ) ),
inference(superposition,[],[f21,f15]) ).
thf(f15,plain,
! [X0: 'type/nums/num'] :
( $true
= ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) )
@ X0 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: 'type/nums/num'] :
( $true
= ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) )
@ X0 ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
! [X0: 'type/nums/num'] :
( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [X1: 'type/nums/num'] :
? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) )
@ X0 ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: 'type/nums/num'] :
( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [X1: 'type/nums/num'] :
? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) )
@ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_NUMSEG_LT_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEV486^1 : TPTP v8.2.0. Released v7.0.0.
% 0.04/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n019.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 21 18:50:09 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.20/0.36 This is a TH1_THM_EQU_NAR problem
% 0.20/0.36 Running higher-order theorem proving
% 0.20/0.36 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.20/0.38 % (8129)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.38 % (8130)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)
% 0.20/0.38 % (8132)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.38 % (8131)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)
% 0.20/0.38 % (8133)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 % (8134)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)
% 0.20/0.38 % (8135)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.38 % (8132)Instruction limit reached!
% 0.20/0.38 % (8132)------------------------------
% 0.20/0.38 % (8132)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (8134)Refutation not found, incomplete strategy
% 0.20/0.38 % (8134)------------------------------
% 0.20/0.38 % (8134)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (8133)Instruction limit reached!
% 0.20/0.38 % (8133)------------------------------
% 0.20/0.38 % (8133)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (8132)Termination reason: Unknown
% 0.20/0.38 % (8133)Termination reason: Unknown
% 0.20/0.38 % (8132)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (8133)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (8132)Memory used [KB]: 5500
% 0.20/0.38 % (8133)Memory used [KB]: 5500
% 0.20/0.38 % (8132)Time elapsed: 0.004 s
% 0.20/0.38 % (8132)Instructions burned: 2 (million)
% 0.20/0.38 % (8133)Time elapsed: 0.004 s
% 0.20/0.38 % (8133)Instructions burned: 2 (million)
% 0.20/0.38 % (8132)------------------------------
% 0.20/0.38 % (8132)------------------------------
% 0.20/0.38 % (8133)------------------------------
% 0.20/0.38 % (8133)------------------------------
% 0.20/0.38 % (8134)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.38
% 0.20/0.38
% 0.20/0.38 % (8134)Memory used [KB]: 5500
% 0.20/0.38 % (8134)Time elapsed: 0.004 s
% 0.20/0.38 % (8134)Instructions burned: 1 (million)
% 0.20/0.38 % (8134)------------------------------
% 0.20/0.38 % (8134)------------------------------
% 0.20/0.38 % (8130)Instruction limit reached!
% 0.20/0.38 % (8130)------------------------------
% 0.20/0.38 % (8130)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (8130)Termination reason: Unknown
% 0.20/0.38 % (8130)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (8130)Memory used [KB]: 5500
% 0.20/0.38 % (8130)Time elapsed: 0.005 s
% 0.20/0.38 % (8130)Instructions burned: 4 (million)
% 0.20/0.38 % (8130)------------------------------
% 0.20/0.38 % (8130)------------------------------
% 0.20/0.38 % (8131)First to succeed.
% 0.20/0.39 % (8131)Refutation found. Thanks to Tanya!
% 0.20/0.39 % SZS status Theorem for theBenchmark
% 0.20/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.39 % (8131)------------------------------
% 0.20/0.39 % (8131)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (8131)Termination reason: Refutation
% 0.20/0.39
% 0.20/0.39 % (8131)Memory used [KB]: 5500
% 0.20/0.39 % (8131)Time elapsed: 0.009 s
% 0.20/0.39 % (8131)Instructions burned: 8 (million)
% 0.20/0.39 % (8131)------------------------------
% 0.20/0.39 % (8131)------------------------------
% 0.20/0.39 % (8128)Success in time 0.012 s
%------------------------------------------------------------------------------