TSTP Solution File: SEV487^1 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV487^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n032.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 16:04:05 EDT 2024
% Result : Theorem 0.08s 0.31s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 214 ( 74 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 350 ( 40 ~; 23 |; 24 &; 254 @)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 74 ( 0 ^ 64 !; 10 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK2: $tType ).
thf(func_def_0,type,
'const/sets/pairwise':
!>[X0: $tType] : ( ( X0 > X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_6,type,
sK0:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_7,type,
sK1:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_8,type,
sK3: sK2 > sK2 > $o ).
thf(func_def_11,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f31,plain,
$false,
inference(subsumption_resolution,[],[f30,f22]) ).
thf(f22,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(fool_elimination,[],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/NOT_IN_EMPTY_') ).
thf(f30,plain,
( $true
= ( 'const/sets/IN' @ sK2 @ ( sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK2 ) @ 'const/sets/EMPTY' @ sK2 ) ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f29,plain,
( ( $true != $true )
| ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK2 ) @ 'const/sets/EMPTY' @ sK2 ) ) ),
inference(superposition,[],[f28,f24]) ).
thf(f24,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( $true
= ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X1 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f19,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o] :
( ( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( ( ( sK0 @ X0 @ X2 @ X1 )
!= ( sK1 @ X0 @ X2 @ X1 ) )
& ( ( X2 @ ( sK0 @ X0 @ X2 @ X1 ) @ ( sK1 @ X0 @ X2 @ X1 ) )
!= $true )
& ( $true
= ( 'const/sets/IN' @ X0 @ ( sK1 @ X0 @ X2 @ X1 ) @ X1 ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X1 ) ) ) )
& ( ! [X5: X0,X6: X0] :
( ( X5 = X6 )
| ( $true
= ( X2 @ X5 @ X6 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X6 @ X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X5 @ X1 )
!= $true ) )
| ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18]) ).
thf(f18,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o] :
( ? [X3: X0,X4: X0] :
( ( X3 != X4 )
& ( ( X2 @ X3 @ X4 )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true ) )
=> ( ( ( sK0 @ X0 @ X2 @ X1 )
!= ( sK1 @ X0 @ X2 @ X1 ) )
& ( ( X2 @ ( sK0 @ X0 @ X2 @ X1 ) @ ( sK1 @ X0 @ X2 @ X1 ) )
!= $true )
& ( $true
= ( 'const/sets/IN' @ X0 @ ( sK1 @ X0 @ X2 @ X1 ) @ X1 ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X1 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f17,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o] :
( ( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ? [X3: X0,X4: X0] :
( ( X3 != X4 )
& ( ( X2 @ X3 @ X4 )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true ) ) )
& ( ! [X5: X0,X6: X0] :
( ( X5 = X6 )
| ( $true
= ( X2 @ X5 @ X6 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X6 @ X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X5 @ X1 )
!= $true ) )
| ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
!= $true ) ) ),
inference(rectify,[],[f16]) ).
thf(f16,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o] :
( ( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ? [X3: X0,X4: X0] :
( ( X3 != X4 )
& ( ( X2 @ X3 @ X4 )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true ) ) )
& ( ! [X3: X0,X4: X0] :
( ( X3 = X4 )
| ( ( X2 @ X3 @ X4 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true ) )
| ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
<=> ! [X3: X0,X4: X0] :
( ( X3 = X4 )
| ( ( X2 @ X3 @ X4 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
<=> ! [X3: X0,X4: X0] :
( ( ( X2 @ X3 @ X4 )
= $true )
| ( X3 = X4 )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
<=> ! [X3: X0,X4: X0] :
( ( ( X3 != X4 )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true )
& ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true ) )
=> ( ( X2 @ X3 @ X4 )
= $true ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= ( ! [X3: X0,X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
& ( X3 != X4 )
& ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
=> ( X2 @ X3 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= ( ! [X3: X0,X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
& ( X3 != X4 )
& ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/pairwise_') ).
thf(f28,plain,
( $true
!= ( 'const/sets/pairwise' @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK2 ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f21,plain,
( $true
!= ( 'const/sets/pairwise' @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f15,f20]) ).
thf(f20,plain,
( ? [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true )
=> ( $true
!= ( 'const/sets/pairwise' @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f15,plain,
? [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(ennf_transformation,[],[f12]) ).
thf(f12,plain,
~ ! [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
= $true ),
inference(true_and_false_elimination,[],[f8]) ).
thf(f8,plain,
~ ! [X0: $tType,X1: X0 > X0 > $o] :
( $true
<=> ( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
= $true ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0 > X0 > $o] :
( $true
= ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: X0 > X0 > $o] :
( $true
= ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/PAIRWISE_EMPTY_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV487^1 : TPTP v8.2.0. Released v7.0.0.
% 0.00/0.09 % Command : run_vampire %s %d THM
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Fri Jun 21 19:41:53 EDT 2024
% 0.08/0.28 % CPUTime :
% 0.08/0.29 This is a TH1_THM_EQU_NAR problem
% 0.08/0.29 Running higher-order theorem proving
% 0.08/0.29 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
% 0.08/0.30 % (19653)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)
% 0.08/0.30 % (19654)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)
% 0.08/0.30 % (19650)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)
% 0.08/0.30 % Exception at run slice level
% 0.08/0.30 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
% 0.08/0.30 % (19652)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.08/0.30 % (19654)Refutation not found, incomplete strategy
% 0.08/0.30 % (19654)------------------------------
% 0.08/0.30 % (19654)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.08/0.30 % (19654)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.30
% 0.08/0.30
% 0.08/0.30 % (19654)Memory used [KB]: 5500
% 0.08/0.30 % (19654)Time elapsed: 0.002 s
% 0.08/0.30 % (19654)Instructions burned: 2 (million)
% 0.08/0.30 % (19654)------------------------------
% 0.08/0.30 % (19654)------------------------------
% 0.08/0.30 % (19652)Instruction limit reached!
% 0.08/0.30 % (19652)------------------------------
% 0.08/0.30 % (19652)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.08/0.30 % (19652)Termination reason: Unknown
% 0.08/0.30 % (19655)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.08/0.30 % (19652)Termination phase: Saturation
% 0.08/0.30
% 0.08/0.30 % (19652)Memory used [KB]: 5373
% 0.08/0.30 % (19652)Time elapsed: 0.003 s
% 0.08/0.30 % (19652)Instructions burned: 2 (million)
% 0.08/0.30 % (19652)------------------------------
% 0.08/0.30 % (19652)------------------------------
% 0.08/0.30 % (19650)Instruction limit reached!
% 0.08/0.30 % (19650)------------------------------
% 0.08/0.30 % (19650)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.08/0.30 % (19650)Termination reason: Unknown
% 0.08/0.30 % (19650)Termination phase: Saturation
% 0.08/0.30
% 0.08/0.30 % (19650)Memory used [KB]: 5500
% 0.08/0.30 % (19650)Time elapsed: 0.004 s
% 0.08/0.30 % (19650)Instructions burned: 5 (million)
% 0.08/0.30 % (19650)------------------------------
% 0.08/0.30 % (19650)------------------------------
% 0.08/0.31 % (19651)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)
% 0.08/0.31 % (19649)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.08/0.31 % (19655)First to succeed.
% 0.08/0.31 % (19655)Refutation found. Thanks to Tanya!
% 0.08/0.31 % SZS status Theorem for theBenchmark
% 0.08/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.31 % (19655)------------------------------
% 0.08/0.31 % (19655)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.08/0.31 % (19655)Termination reason: Refutation
% 0.08/0.31
% 0.08/0.31 % (19655)Memory used [KB]: 5500
% 0.08/0.31 % (19655)Time elapsed: 0.005 s
% 0.08/0.31 % (19655)Instructions burned: 2 (million)
% 0.08/0.31 % (19655)------------------------------
% 0.08/0.31 % (19655)------------------------------
% 0.08/0.31 % (19648)Success in time 0.013 s
%------------------------------------------------------------------------------