%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV487^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:39:35 AM UTC 2026
% Result : Theorem 0.18s 0.28s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 146 ( 43 equ; 0 cnn)
% Maximal formula atoms : 2 ( 5 avg)
% Number of connectives : 325 ( 22 ~; 9 |; 21 &; 256 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 3 con; 0-4 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 72 ( 10 ^; 60 !; 2 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
vAND: $o > $o > $o ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
sK1: sK0 > sK0 > $o ).
thf(func_def_15,type,
sK2:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_16,type,
sK3:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > X0 > $o ) > X0 ) ).
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(f2,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= ( ! [X3: X0,X4: X0] :
( ( ( X3 != X4 )
& ( 'const/sets/IN' @ X0 @ X4 @ X1 )
& ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/pairwise_') ).
thf(f3,conjecture,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/PAIRWISE_EMPTY_') ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
= $true ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= ( ! [X3: X0,X4: X0] :
( ( ( X3 != X4 )
& ( 'const/sets/IN' @ X0 @ X4 @ X1 )
& ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
=> ( X2 @ X3 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= ( !! @ X0
@ ^ [Y0: X0] :
( !! @ X0
@ ^ [Y1: X0] :
( ( ( 'const/sets/IN' @ X0 @ Y1 @ X1 )
& ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
& ( Y1 != Y0 ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f10,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(flattening,[],[f6]) ).
thf(f11,plain,
? [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(ennf_transformation,[],[f9]) ).
thf(f12,plain,
( $true
!= ( 'const/sets/pairwise' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11]) ).
thf(f13,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f14,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= ( !! @ X0
@ ^ [Y0: X0] :
( !! @ X0
@ ^ [Y1: X0] :
( ( ( 'const/sets/IN' @ X0 @ Y1 @ X1 )
& ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
& ( Y1 != Y0 ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( $true
!= ( 'const/sets/pairwise' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f18,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( ( !! @ X0
@ ^ [Y0: X0] :
( !! @ X0
@ ^ [Y1: X0] :
( ( ( 'const/sets/IN' @ X0 @ Y1 @ X1 )
& ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
& ( Y1 != Y0 ) )
=> ( X2 @ Y1 @ Y0 ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f14]) ).
thf(f29,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( $false
= ( ^ [Y0: X0] :
( !! @ X0
@ ^ [Y1: X0] :
( ( ( 'const/sets/IN' @ X0 @ Y1 @ X1 )
& ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
& ( Y1 != Y0 ) )
=> ( X2 @ Y1 @ Y0 ) ) )
@ ( sK2 @ X0 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f18]) ).
thf(f30,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( $false
= ( !! @ X0
@ ^ [Y0: X0] :
( ( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
& ( 'const/sets/IN' @ X0 @ ( sK2 @ X0 @ X1 @ X2 ) @ X1 )
& ( Y0
!= ( sK2 @ X0 @ X1 @ X2 ) ) )
=> ( X2 @ Y0 @ ( sK2 @ X0 @ X1 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( $false
= ( ^ [Y0: X0] :
( ( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
& ( 'const/sets/IN' @ X0 @ ( sK2 @ X0 @ X1 @ X2 ) @ X1 )
& ( Y0
!= ( sK2 @ X0 @ X1 @ X2 ) ) )
=> ( X2 @ Y0 @ ( sK2 @ X0 @ X1 @ X2 ) ) )
@ ( sK3 @ X0 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( $false
= ( ( ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 @ X2 ) @ X1 )
& ( 'const/sets/IN' @ X0 @ ( sK2 @ X0 @ X1 @ X2 ) @ X1 )
& ( ( sK3 @ X0 @ X1 @ X2 )
!= ( sK2 @ X0 @ X1 @ X2 ) ) )
=> ( X2 @ ( sK3 @ X0 @ X1 @ X2 ) @ ( sK2 @ X0 @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f34,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( $true
= ( ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 @ X2 ) @ X1 )
& ( 'const/sets/IN' @ X0 @ ( sK2 @ X0 @ X1 @ X2 ) @ X1 )
& ( ( sK3 @ X0 @ X1 @ X2 )
!= ( sK2 @ X0 @ X1 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f32]) ).
thf(f36,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( $true
= ( ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 @ X2 ) @ X1 )
& ( 'const/sets/IN' @ X0 @ ( sK2 @ X0 @ X1 @ X2 ) @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f37,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( $true
= ( 'const/sets/IN' @ X0 @ ( sK2 @ X0 @ X1 @ X2 ) @ X1 ) ) ),
inference(and_proxy_clausification,[],[f36]) ).
thf(f61,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( $true != $true )
| ( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
= $true ) ),
inference(constrained_superposition,[],[f13,f37]) ).
thf(f62,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f67,plain,
$true != $true,
inference(constrained_superposition,[],[f15,f62]) ).
thf(f68,plain,
$false,
inference(trivial_inequality_removal,[],[f67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV487^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n026.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:55:42 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.28 % (773813)Will run a generic schedule for satisfiability detection.
% 0.18/0.28 % (773830)% WARNING: option uhcvi not known.
% 0.18/0.28 % (773830)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2207212524:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.28 % (773830)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.28 % (773830)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.28 % (773829)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2399319011_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.28 % (773831)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=764857228:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.28 % (773833)dis+10_1_sil=32000:sp=arity:random_seed=644019520:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.28 % (773834)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3584629976:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.28 % (773835)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2653897837:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.28 % Exception at run slice level
% 0.18/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.28 % (773836)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=587295305:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.28 % (773834)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.28 % (773836) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-773813-773836"...
% 0.18/0.28 % (773831) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-773813-773831"...
% 0.18/0.28 % (773836)...printing done.
% 0.18/0.28 % (773831)...printing done.
% 0.18/0.28 % (773836)Refutation found. Thanks to Tanya!
% 0.18/0.28 % SZS status Theorem for theBenchmark
% 0.18/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.29 % (773836)------------------------------
% 0.18/0.29 % (773836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.29 % (773836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.29 % (773836)CaDiCaL version: 2.1.3
% 0.18/0.29 % (773836)Termination reason: Refutation
% 0.18/0.29 % (773836)Time elapsed: 0.004 s
% 0.18/0.29 % (773836)Peak memory usage: 12 MB
% 0.18/0.29 % (773836)Instructions burned: 5 (million)
% 0.18/0.29 % (773813)Success in time 0.045 s
% 0.18/0.29 % Vampire exiting
%------------------------------------------------------------------------------