TSTP Solution File: SEV451^1 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV451^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n029.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 16:03:55 EDT 2024
% Result : Theorem 0.13s 0.40s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 42 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 233 ( 17 ~; 23 |; 0 &; 190 @)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 64 ( 0 ^ 60 !; 4 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/UNIV':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_1,type,
'const/sets/UNION':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_12,type,
sK1: sK0 > $o ).
thf(func_def_14,type,
sK3:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK5: sK0 ).
thf(f164,plain,
$false,
inference(avatar_sat_refutation,[],[f69,f79,f161]) ).
thf(f161,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[],[f160]) ).
thf(f160,plain,
( $false
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f149]) ).
thf(f149,plain,
( ( $false = $true )
| ~ spl2_4 ),
inference(superposition,[],[f145,f19]) ).
thf(f19,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNIV_') ).
thf(f145,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ 'const/sets/UNIV' @ sK0 ) )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f144]) ).
thf(f144,plain,
( ( $false = $true )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ 'const/sets/UNIV' @ sK0 ) )
| ~ spl2_4 ),
inference(superposition,[],[f68,f119]) ).
thf(f119,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
= $true )
| ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f118,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
= $true )
| ( $false = $true )
| ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
inference(superposition,[],[f43,f41]) ).
thf(f41,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true )
| ( $false
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[],[f38]) ).
thf(f38,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true )
| ( $false
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[],[f22]) ).
thf(f22,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
| ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X1: X0 > $o,X3: X0 > $o,X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
= ( 'const/sets/IN' @ X0 @ X4 @ X3 ) )
| ( 'const/sets/IN' @ X0 @ X4 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNION_') ).
thf(f43,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[],[f20]) ).
thf(f20,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( X1 @ X2 )
= ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( X1 @ X2 )
= ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
= ( X2 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(f68,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f66,plain,
( spl2_4
<=> ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
thf(f79,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f78]) ).
thf(f78,plain,
( $false
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f75,plain,
( ( $false = $true )
| ~ spl2_3 ),
inference(superposition,[],[f64,f47]) ).
thf(f47,plain,
! [X0: $tType,X1: X0] :
( $true
= ( 'const/sets/UNIV' @ X0 @ X1 ) ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f45,plain,
! [X0: $tType,X1: X0] :
( ( $true
= ( 'const/sets/UNIV' @ X0 @ X1 ) )
| ( $false = $true ) ),
inference(superposition,[],[f43,f19]) ).
thf(f64,plain,
( ( ( 'const/sets/UNIV' @ sK0 @ sK5 )
= $false )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f62,plain,
( spl2_3
<=> ( ( 'const/sets/UNIV' @ sK0 @ sK5 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
thf(f69,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f51,f66,f62]) ).
thf(f51,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5 ) )
| ( ( 'const/sets/UNIV' @ sK0 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[],[f49]) ).
thf(f49,plain,
( ( 'const/sets/UNIV' @ sK0 @ sK5 )
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5 ) ),
inference(negative_extensionality,[],[f21]) ).
thf(f21,plain,
( 'const/sets/UNIV'
@ ( sK0
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f17,plain,
( 'const/sets/UNIV'
@ ( sK0
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16]) ).
thf(f16,plain,
( ? [X0: $tType,X1: X0 > $o] :
( 'const/sets/UNIV'
@ ( X0
!= ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ) ) )
=> ( 'const/sets/UNIV'
@ ( sK0
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f15,plain,
? [X0: $tType,X1: X0 > $o] :
( 'const/sets/UNIV'
@ ( X0
!= ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o] :
( 'const/sets/UNIV'
@ ( X0
= ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ) ) ),
inference(negated_conjecture,[],[f5]) ).
thf(f5,conjecture,
! [X0: $tType,X1: X0 > $o] :
( 'const/sets/UNIV'
@ ( X0
= ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/UNION_UNIV_1') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEV451^1 : TPTP v8.2.0. Released v7.0.0.
% 0.12/0.13 % Command : run_vampire %s %d THM
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 21 18:47:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.36 This is a TH1_THM_EQU_NAR problem
% 0.13/0.36 Running higher-order theorem proving
% 0.13/0.36 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
% 0.13/0.38 % (13227)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.38 % (13224)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.38 % (13226)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)
% 0.13/0.38 % (13229)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)
% 0.13/0.38 % (13230)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.38 % (13228)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)
% 0.13/0.38 % (13227)Instruction limit reached!
% 0.13/0.38 % (13227)------------------------------
% 0.13/0.38 % (13227)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.38 % Exception at run slice level% (13227)Termination reason: Unknown
% 0.13/0.38
% 0.13/0.38 % (13227)Termination phase: Saturation
% 0.13/0.38 User error:
% 0.13/0.38 Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.13/0.38 % (13227)Memory used [KB]: 5373
% 0.13/0.38 % (13227)Time elapsed: 0.004 s
% 0.13/0.38 % (13227)Instructions burned: 2 (million)
% 0.13/0.38 % (13227)------------------------------
% 0.13/0.38 % (13227)------------------------------
% 0.13/0.38 % (13225)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)
% 0.13/0.38 % (13229)Refutation not found, incomplete strategy
% 0.13/0.38 % (13229)------------------------------
% 0.13/0.38 % (13229)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.38 % (13229)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.38
% 0.13/0.38
% 0.13/0.38 % (13229)Memory used [KB]: 5500
% 0.13/0.38 % (13229)Time elapsed: 0.005 s
% 0.13/0.38 % (13229)Instructions burned: 3 (million)
% 0.13/0.38 % (13229)------------------------------
% 0.13/0.38 % (13229)------------------------------
% 0.13/0.39 % (13225)Instruction limit reached!
% 0.13/0.39 % (13225)------------------------------
% 0.13/0.39 % (13225)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (13225)Termination reason: Unknown
% 0.13/0.39 % (13225)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (13225)Memory used [KB]: 5500
% 0.13/0.39 % (13225)Time elapsed: 0.005 s
% 0.13/0.39 % (13225)Instructions burned: 4 (million)
% 0.13/0.39 % (13225)------------------------------
% 0.13/0.39 % (13225)------------------------------
% 0.13/0.39 % (13226)First to succeed.
% 0.13/0.39 % (13230)Instruction limit reached!
% 0.13/0.39 % (13230)------------------------------
% 0.13/0.39 % (13230)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (13230)Termination reason: Unknown
% 0.13/0.39 % (13230)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (13230)Memory used [KB]: 5628
% 0.13/0.39 % (13230)Time elapsed: 0.016 s
% 0.13/0.39 % (13230)Instructions burned: 18 (million)
% 0.13/0.39 % (13230)------------------------------
% 0.13/0.39 % (13230)------------------------------
% 0.13/0.40 % (13226)Refutation found. Thanks to Tanya!
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.40 % (13226)------------------------------
% 0.13/0.40 % (13226)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.40 % (13226)Termination reason: Refutation
% 0.13/0.40
% 0.13/0.40 % (13226)Memory used [KB]: 5628
% 0.13/0.40 % (13226)Time elapsed: 0.016 s
% 0.13/0.40 % (13226)Instructions burned: 17 (million)
% 0.13/0.40 % (13226)------------------------------
% 0.13/0.40 % (13226)------------------------------
% 0.13/0.40 % (13223)Success in time 0.029 s
%------------------------------------------------------------------------------