%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU599^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 08:32:37 AM UTC 2026
% Result : Theorem 0.24s 0.28s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 302 ( 72 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 397 ( 7 ~; 13 |; 12 &; 286 @)
% ( 0 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 8 con; 0-4 aty)
% ( 31 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 95 ( 37 ^; 54 !; 4 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
in__Cong: $o ).
thf(func_def_3,type,
subset: $i > $i > $o ).
thf(func_def_4,type,
subsetI1: $o ).
thf(func_def_5,type,
binintersect: $i > $i > $i ).
thf(func_def_6,type,
binintersectER: $o ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIMP: $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,
vIFF: $o > $o > $o ).
thf(func_def_13,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(func_def_21,type,
sK2: $i > $i > $i ).
thf(f2,axiom,
( subsetI1
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(f3,axiom,
( binintersectER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).
thf(f4,conjecture,
( in__Cong
=> ( subsetI1
=> ( binintersectER
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
=> ( subset @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(f5,negated_conjecture,
~ ( in__Cong
=> ( subsetI1
=> ( binintersectER
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
=> ( subset @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f8,plain,
( subsetI1
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( binintersectER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
( binintersectER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ( in__Cong
=> ( subsetI1
=> ( binintersectER
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
=> ( subset @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
~ ( ( in__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( binintersectER = $true )
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
=> ( ( subset @ X0 @ X1 )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ( ( binintersect @ X0 @ X1 )
= X0 ) )
& ( binintersectER = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ( ( binintersect @ X0 @ X1 )
= X0 ) )
& ( binintersectER = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( $true
!= ( subset @ sK0 @ sK1 ) )
& ( sK0
= ( binintersect @ sK0 @ sK1 ) )
& ( binintersectER = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
thf(f18,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
( binintersectER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f21,plain,
subsetI1 = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
binintersectER = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
( sK0
= ( binintersect @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f24,plain,
( $true
!= ( subset @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f28,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f18,f21]) ).
thf(f29,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f19,f22]) ).
thf(f30,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( binintersect @ Y0 @ X2 ) )
=> ( in @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( binintersect @ Y0 @ X2 ) )
=> ( in @ X1 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( binintersect @ X3 @ X2 ) )
=> ( in @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binintersect @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( subset @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK2 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f43]) ).
thf(f61,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f36,f23]) ).
thf(f95,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK2 @ sK1 @ X0 ) @ sK0 ) )
| ( $true
= ( subset @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f61,f44]) ).
thf(f98,plain,
! [X0: $i] :
( ( $false
= ( in @ ( sK2 @ sK1 @ X0 ) @ sK0 ) )
| ( $true
= ( subset @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f140,plain,
( ( $true = $false )
| ( $true
= ( subset @ sK0 @ sK1 ) )
| ( $true
= ( subset @ sK0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f45,f98]) ).
thf(f141,plain,
( ( $true = $false )
| ( $true
= ( subset @ sK0 @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f140]) ).
thf(f142,plain,
( $true
= ( subset @ sK0 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f141]) ).
thf(f148,plain,
$false,
inference(forward_subsumption_resolution,[],[f142,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU599^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n004.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 13:56:23 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.24/0.28 % (1326329)Will run a generic schedule for satisfiability detection.
% 0.24/0.28 % (1326337)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2075723897_3000 on theBenchmark for (3000ds/0Mi)
% 0.24/0.28 % Exception at run slice level
% 0.24/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.28 % (1326338)% WARNING: option uhcvi not known.
% 0.24/0.28 % (1326338)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=456820836:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.24/0.28 % (1326339)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2125114304:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.24/0.28 % (1326342)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=355259506:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.24/0.28 % (1326340)dis+10_1_sil=32000:sp=arity:random_seed=1383701681:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.24/0.28 % (1326343)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1660447676:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.24/0.28 % (1326338)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.24/0.28 % (1326341)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1427574016:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.24/0.28 % (1326338)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.24/0.28 % (1326341)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.24/0.28 % (1326350)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3744009848:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.24/0.28 % Exception at run slice level
% 0.24/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.28 % (1326340) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1326329-1326340"...
% 0.24/0.28 % (1326338) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1326329-1326338"...
% 0.24/0.28 % (1326342) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1326329-1326342"...
% 0.24/0.28 % (1326343) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1326329-1326343"...
% 0.24/0.28 % (1326341) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1326329-1326341"...
% 0.24/0.28 % (1326340)...printing done.
% 0.24/0.28 % (1326338)...printing done.
% 0.24/0.28 % (1326342)...printing done.
% 0.24/0.28 % (1326341)...printing done.
% 0.24/0.28 % (1326343)...printing done.
% 0.24/0.28 % (1326340)Refutation found. Thanks to Tanya!
% 0.24/0.28 % SZS status Theorem for theBenchmark
% 0.24/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.28 % (1326340)------------------------------
% 0.24/0.28 % (1326340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.28 % (1326340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.28 % (1326340)CaDiCaL version: 2.1.3
% 0.24/0.28 % (1326340)Termination reason: Refutation
% 0.24/0.28 % (1326340)Time elapsed: 0.008 s
% 0.24/0.28 % (1326340)Peak memory usage: 12 MB
% 0.24/0.28 % (1326340)Instructions burned: 12 (million)
% 0.24/0.28 % (1326329)Success in time 0.031 s
% 0.24/0.28 % Vampire exiting
%------------------------------------------------------------------------------