TSTP Solution File: SEV450^1 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV450^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n020.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 0.12s 0.40s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 276 ( 69 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 318 ( 34 ~; 55 |; 0 &; 224 @)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 70 ( 0 ^ 66 !; 4 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/UNION':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_11,type,
sK1: sK0 > $o ).
thf(func_def_13,type,
sK3:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_14,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK5: sK0 ).
thf(f185,plain,
$false,
inference(avatar_sat_refutation,[],[f52,f61,f122,f128,f184]) ).
thf(f184,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f183]) ).
thf(f183,plain,
( $false
| ~ spl2_1
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f182]) ).
thf(f182,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_4 ),
inference(forward_demodulation,[],[f176,f60]) ).
thf(f60,plain,
( ( ( sK1 @ sK5 )
= $false )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f58,plain,
( spl2_4
<=> ( ( sK1 @ sK5 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
thf(f176,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f172,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK5 ) )
| ~ spl2_1 ),
inference(superposition,[],[f164,f40]) ).
thf(f40,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[],[f15]) ).
thf(f15,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(f164,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f163]) ).
thf(f163,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ( $true = $false )
| ~ spl2_1 ),
inference(duplicate_literal_removal,[],[f159]) ).
thf(f159,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ( $true = $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ~ spl2_1 ),
inference(superposition,[],[f47,f64]) ).
thf(f64,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
= $true )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f62,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
= $false )
| ( $true = $false )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
= $true ) ),
inference(superposition,[],[f39,f36]) ).
thf(f36,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $false )
| ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[],[f35]) ).
thf(f35,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $false )
| ( $true
= ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
| ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,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 @ X2 )
| ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f8,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(fool_elimination,[],[f7]) ).
thf(f7,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(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) )
= ( 'const/sets/IN' @ X0 @ X4 @ X2 ) )
| ( 'const/sets/IN' @ X0 @ X4 @ X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_UNION_') ).
thf(f39,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( ( X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f15]) ).
thf(f47,plain,
( ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f45,plain,
( spl2_1
<=> ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
thf(f128,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f127]) ).
thf(f127,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f123]) ).
thf(f123,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(backward_demodulation,[],[f51,f60]) ).
thf(f51,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f49,plain,
( spl2_2
<=> ( $true
= ( sK1 @ sK5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
thf(f122,plain,
( spl2_4
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f117,f54,f58]) ).
thf(f54,plain,
( spl2_3
<=> ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
thf(f117,plain,
( ( ( sK1 @ sK5 )
= $false )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f114]) ).
thf(f114,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $true = $false )
| ~ spl2_3 ),
inference(superposition,[],[f39,f108]) ).
thf(f108,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 )
= $false )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f107]) ).
thf(f107,plain,
( ( $true = $false )
| ( ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 )
= $false )
| ~ spl2_3 ),
inference(superposition,[],[f56,f94]) ).
thf(f94,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f91]) ).
thf(f91,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
= $false )
| ( $true = $false ) ),
inference(superposition,[],[f37,f40]) ).
thf(f37,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f34]) ).
thf(f34,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( $false
= ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
| ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f56,plain,
( ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
= $false )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f61,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f43,f58,f54]) ).
thf(f43,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[],[f41]) ).
thf(f41,plain,
( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
!= ( sK1 @ sK5 ) ),
inference(negative_extensionality,[],[f16]) ).
thf(f16,plain,
( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 )
!= sK1 ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 )
!= sK1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
!= X1 )
=> ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 )
!= sK1 ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
? [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
!= X1 ),
inference(ennf_transformation,[],[f11]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
= X1 ),
inference(rectify,[],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X2: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X2 @ X2 )
= X2 ),
inference(negated_conjecture,[],[f4]) ).
thf(f4,conjecture,
! [X0: $tType,X2: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X2 @ X2 )
= X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/UNION_IDEMPOT_') ).
thf(f52,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f42,f49,f45]) ).
thf(f42,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[],[f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEV450^1 : TPTP v8.2.0. Released v7.0.0.
% 0.12/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n020.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:32:39 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 This is a TH1_THM_EQU_NAR problem
% 0.12/0.36 Running higher-order theorem proving
% 0.12/0.36 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
% 0.12/0.38 % (29628)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.38 % (29631)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.38 % (29629)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)
% 0.12/0.38 % (29630)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)
% 0.12/0.38 % (29632)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)
% 0.12/0.38 % (29633)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)
% 0.12/0.38 % (29634)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.38 % Exception at run slice level
% 0.12/0.38 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.12/0.38 % (29631)Instruction limit reached!
% 0.12/0.38 % (29631)------------------------------
% 0.12/0.38 % (29631)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (29631)Termination reason: Unknown
% 0.12/0.38 % (29631)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (29631)Memory used [KB]: 5373
% 0.12/0.38 % (29631)Time elapsed: 0.004 s
% 0.12/0.38 % (29631)Instructions burned: 2 (million)
% 0.12/0.38 % (29631)------------------------------
% 0.12/0.38 % (29631)------------------------------
% 0.12/0.38 % (29633)Refutation not found, incomplete strategy
% 0.12/0.38 % (29633)------------------------------
% 0.12/0.38 % (29633)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (29633)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.38
% 0.12/0.38
% 0.12/0.38 % (29633)Memory used [KB]: 5500
% 0.12/0.38 % (29633)Time elapsed: 0.005 s
% 0.12/0.38 % (29633)Instructions burned: 3 (million)
% 0.12/0.38 % (29633)------------------------------
% 0.12/0.38 % (29633)------------------------------
% 0.12/0.38 % (29629)Instruction limit reached!
% 0.12/0.38 % (29629)------------------------------
% 0.12/0.38 % (29629)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (29629)Termination reason: Unknown
% 0.12/0.38 % (29629)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (29629)Memory used [KB]: 5500
% 0.12/0.38 % (29629)Time elapsed: 0.005 s
% 0.12/0.38 % (29629)Instructions burned: 5 (million)
% 0.12/0.38 % (29629)------------------------------
% 0.12/0.38 % (29629)------------------------------
% 0.12/0.39 % (29634)Instruction limit reached!
% 0.12/0.39 % (29634)------------------------------
% 0.12/0.39 % (29634)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (29634)Termination reason: Unknown
% 0.12/0.39 % (29634)Termination phase: Saturation
% 0.12/0.39
% 0.12/0.39 % (29634)Memory used [KB]: 5628
% 0.12/0.39 % (29634)Time elapsed: 0.016 s
% 0.12/0.39 % (29634)Instructions burned: 18 (million)
% 0.12/0.39 % (29634)------------------------------
% 0.12/0.39 % (29634)------------------------------
% 0.12/0.39 % (29630)First to succeed.
% 0.12/0.40 % (29630)Refutation found. Thanks to Tanya!
% 0.12/0.40 % SZS status Theorem for theBenchmark
% 0.12/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.40 % (29630)------------------------------
% 0.12/0.40 % (29630)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.40 % (29630)Termination reason: Refutation
% 0.12/0.40
% 0.12/0.40 % (29630)Memory used [KB]: 5628
% 0.12/0.40 % (29630)Time elapsed: 0.017 s
% 0.12/0.40 % (29630)Instructions burned: 20 (million)
% 0.12/0.40 % (29630)------------------------------
% 0.12/0.40 % (29630)------------------------------
% 0.12/0.40 % (29627)Success in time 0.031 s
%------------------------------------------------------------------------------