%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA068^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:46:00 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 171 ( 41 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 232 ( 26 ~; 15 |; 3 &; 182 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 3 con; 0-4 aty)
% ( 0 !!; 3 ??; 0 @@+; 0 @@-)
% Number of variables : 61 ( 8 ^; 51 !; 2 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'const/sets/UNIV':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_1,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/SETSPEC':
!>[X0: $tType] : ( X0 > $o > X0 > $o ) ).
thf(func_def_3,type,
'const/sets/INFINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/GSPEC':
!>[X0: $tType] : ( ( X0 > $o ) > X0 > $o ) ).
thf(func_def_5,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_8,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: 'type/realax/real'] :
~ ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ X1 @ ( 'const/realax/real_le' @ X0 @ X2 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_REAL_INTERVAL_1') ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_UNIV_') ).
thf(f3,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( 'const/sets/FINITE' @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_') ).
thf(f4,axiom,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/INFINITE' @ X0 @ X1 )
= ( ~ ( 'const/sets/FINITE' @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INFINITE_') ).
thf(f5,conjecture,
'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/real_INFINITE_') ).
thf(f6,negated_conjecture,
~ ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
! [X0: 'type/realax/real'] :
~ ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ X1 @ ( 'const/realax/real_le' @ X0 @ X2 ) @ X2 ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
! [X0: 'type/realax/real'] :
( ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ Y0 @ ( 'const/realax/real_le' @ X0 @ Y1 ) @ Y1 ) ) ) )
!= $true ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( 'const/sets/FINITE' @ X0 @ X1 ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) )
=> ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/INFINITE' @ X0 @ X1 )
= ( ~ ( 'const/sets/FINITE' @ X0 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/INFINITE' @ X0 @ X1 )
= ( ~ ( 'const/sets/FINITE' @ X0 @ X1 ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
( ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' )
!= $true ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
! [X0: 'type/realax/real'] :
( ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ Y0 @ ( 'const/realax/real_le' @ X0 @ Y1 ) @ Y1 ) ) ) )
!= $true ),
inference(flattening,[],[f8]) ).
thf(f18,plain,
( ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' )
!= $true ),
inference(flattening,[],[f16]) ).
thf(f19,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f20,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true ) ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
! [X0: 'type/realax/real'] :
( ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ Y0 @ ( 'const/realax/real_le' @ X0 @ Y1 ) @ Y1 ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f22,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f23,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/INFINITE' @ X0 @ X1 )
= ( ~ ( 'const/sets/FINITE' @ X0 @ X1 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f25,plain,
( ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' )
!= $true ),
inference(cnf_transformation,[],[f18]) ).
thf(f28,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/INFINITE' @ X0 @ X1 )
= $true )
| ( ( ~ ( 'const/sets/FINITE' @ X0 @ X1 ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f24]) ).
thf(f31,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/INFINITE' @ X0 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f28]) ).
thf(f45,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true != $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( $true
!= ( 'const/sets/FINITE' @ X0 @ 'const/sets/UNIV' @ X0 ) ) ),
inference(constrained_superposition,[],[f23,f22]) ).
thf(f46,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true
!= ( 'const/sets/FINITE' @ X0 @ 'const/sets/UNIV' @ X0 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f60,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true != $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( $true
= ( 'const/sets/INFINITE' @ X0 @ 'const/sets/UNIV' @ X0 ) ) ),
inference(constrained_superposition,[],[f46,f31]) ).
thf(f62,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( $true
= ( 'const/sets/INFINITE' @ X0 @ 'const/sets/UNIV' @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f60]) ).
thf(f68,plain,
( ( $true != $true )
| ( ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' )
= $true ) ),
inference(constrained_superposition,[],[f21,f62]) ).
thf(f73,plain,
( ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' )
= $true ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f78,plain,
$false,
inference(forward_subsumption_resolution,[],[f73,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA068^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n026.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 17:41:57 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.24 Running first-order model finding
% 0.10/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.30 % (930998)Will run a generic schedule for satisfiability detection.
% 0.22/0.30 % (931006)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2879872_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.30 % Exception at run slice level
% 0.22/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.30 % (931007)% WARNING: option uhcvi not known.
% 0.22/0.30 % (931009)dis+10_1_sil=32000:sp=arity:random_seed=4088798115:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.30 % (931008)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2762918499:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.30 % (931007)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3482851296:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.30 % (931010)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=721832209:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.30 % (931011)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3073691222:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.30 % (931007)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.30 % (931012)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4088096644:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.30 % (931007)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.30 % (931010)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.30 % (931009) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-930998-931009"...
% 0.22/0.30 % (931010) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-930998-931010"...
% 0.22/0.30 % (931007) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-930998-931007"...
% 0.22/0.30 % (931011) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-930998-931011"...
% 0.22/0.30 % (931014)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=453074429:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.30 % Exception at run slice level
% 0.22/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.30 % (931009)...printing done.
% 0.22/0.30 % (931010)...printing done.
% 0.22/0.30 % (931007)...printing done.
% 0.22/0.30 % (931011)...printing done.
% 0.22/0.30 % (931008) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-930998-931008"...
% 0.22/0.30 % (931009)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (931009)------------------------------
% 0.22/0.30 % (931009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (931009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (931009)CaDiCaL version: 2.1.3
% 0.22/0.30 % (931009)Termination reason: Refutation
% 0.22/0.30 % (931009)Time elapsed: 0.004 s
% 0.22/0.30 % (931009)Peak memory usage: 12 MB
% 0.22/0.30 % (931009)Instructions burned: 5 (million)
% 0.22/0.30 % (930998)Success in time 0.05 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------