%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU559^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 08:32:26 AM UTC 2026
% Result : Theorem 0.10s 0.27s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 26 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 131 ( 12 ~; 4 |; 2 &; 93 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 6 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 34 ( 15 ^; 17 !; 2 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_3,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vIMP: $o > $o > $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(f1,axiom,
( subset
= ( ^ [X0: $i,X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
thf(f2,conjecture,
! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(f3,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( subset
= ( ^ [X0: $i,X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( subset @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( $true
!= ( subset @ sK0 @ sK1 ) )
& ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK1 ) )
| ( $true
!= ( in @ X2 @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
thf(f10,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK0 ) )
| ( $true
= ( in @ X2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( $true
!= ( subset @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f12,f10]) ).
thf(f16,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( in @ Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( in @ Y0 @ sK1 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( $false
= ( ( in @ sK2 @ sK0 )
=> ( in @ sK2 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
( $false
= ( in @ sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( ( $true != $true )
| ( $true
= ( in @ sK2 @ sK1 ) ) ),
inference(constrained_superposition,[],[f11,f20]) ).
thf(f22,plain,
( $true
= ( in @ sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f21]) ).
thf(f23,plain,
$true = $false,
inference(forward_demodulation,[],[f22,f19]) ).
thf(f24,plain,
$false,
inference(trivial_inequality_removal,[],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU559^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n017.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 13:45:37 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 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
% 0.10/0.27 % (365981)Will run a generic schedule for satisfiability detection.
% 0.10/0.27 % (365986)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1247581576_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.27 % Exception at run slice level
% 0.10/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.27 % (365987)% WARNING: option uhcvi not known.
% 0.10/0.27 % (365987)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1185444860:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.27 % (365988)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3130038867:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.27 % (365989)dis+10_1_sil=32000:sp=arity:random_seed=2162445455:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.27 % (365990)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3851238075:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.27 % (365987)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.27 % (365992)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1503536074:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.27 % (365991)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3980669654:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.27 % (365990)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.27 % (365987)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.10/0.27 % (365989) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-365981-365989"...
% 0.10/0.27 % (365990) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-365981-365990"...
% 0.10/0.27 % (365988) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-365981-365988"...
% 0.10/0.27 % (365987) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-365981-365987"...
% 0.10/0.27 % (365992) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-365981-365992"...
% 0.10/0.27 % (365991) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-365981-365991"...
% 0.10/0.27 % (365994)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1605380541:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.10/0.27 % Exception at run slice level
% 0.10/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.27 % (365989)...printing done.
% 0.10/0.27 % (365990)...printing done.
% 0.10/0.27 % (365988)...printing done.
% 0.10/0.27 % (365987)...printing done.
% 0.10/0.27 % (365992)...printing done.
% 0.10/0.27 % (365991)...printing done.
% 0.10/0.27 % (365989)Refutation found. Thanks to Tanya!
% 0.10/0.27 % SZS status Theorem for theBenchmark
% 0.10/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.27 % (365989)------------------------------
% 0.10/0.27 % (365989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.27 % (365989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.27 % (365989)CaDiCaL version: 2.1.3
% 0.10/0.27 % (365989)Termination reason: Refutation
% 0.10/0.27 % (365989)Time elapsed: 0.002 s
% 0.10/0.27 % (365989)Peak memory usage: 12 MB
% 0.10/0.27 % (365989)Instructions burned: 2 (million)
% 0.10/0.27 % (365981)Success in time 0.046 s
% 0.10/0.27 % Vampire exiting
%------------------------------------------------------------------------------