%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU594^2 : 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 : 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 08:32:35 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 328 ( 78 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 443 ( 7 ~; 13 |; 12 &; 332 @)
% ( 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 : 25 ( 21 usr; 8 con; 0-4 aty)
% ( 31 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 123 ( 65 ^; 54 !; 4 ?; 123 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
in__Cong: $o ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
subsetI1: $o ).
thf(func_def_6,type,
binintersect: $i > $i > $i ).
thf(func_def_7,type,
binintersectEL: $o ).
thf(func_def_8,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
vIMP: $o > $o > $o ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_13,type,
vIFF: $o > $o > $o ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_22,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,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersect) ).
thf(f4,axiom,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(f5,conjecture,
( in__Cong
=> ( subsetI1
=> ( binintersectEL
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( subset @ X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(f6,negated_conjecture,
~ ( in__Cong
=> ( subsetI1
=> ( binintersectEL
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( subset @ X1 @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f9,plain,
( subsetI1
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
( binintersectEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( in__Cong
=> ( subsetI1
=> ( binintersectEL
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( subset @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
~ ( ( in__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( binintersectEL = $true )
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( binintersect @ X0 @ X1 )
= X1 ) )
& ( binintersectEL = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( binintersect @ X0 @ X1 )
= X1 ) )
& ( binintersectEL = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( $true
!= ( subset @ sK1 @ sK0 ) )
& ( sK1
= ( binintersect @ sK0 @ sK1 ) )
& ( binintersectEL = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f18]) ).
thf(f21,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f22,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f23,plain,
( binintersectEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f25,plain,
subsetI1 = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
binintersectEL = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f27,plain,
( sK1
= ( binintersect @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f28,plain,
( $true
!= ( subset @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f32,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f21,f25]) ).
thf(f33,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(definition_unfolding,[],[f23,f26,f22]) ).
thf(f34,plain,
( sK1
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f27,f22]) ).
thf(f35,plain,
( sK1
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ Y0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( in @ Y2 @ Y0 ) ) )
=> ( in @ X1 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( in @ Y2 @ Y0 ) ) )
=> ( in @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1
@ ( dsetconstr @ Y0
@ ^ [Y1: $i] : ( in @ Y1 @ X2 ) ) )
=> ( in @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1
@ ( dsetconstr @ Y0
@ ^ [Y1: $i] : ( in @ Y1 @ X2 ) ) )
=> ( in @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) )
=> ( in @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) ) )
| ( $true
= ( in @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f41]) ).
thf(f43,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,[],[f32]) ).
thf(f44,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,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,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( subset @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f48,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,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK2 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f49]) ).
thf(f67,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f42,f35]) ).
thf(f124,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK2 @ sK0 @ X0 ) @ sK1 ) )
| ( $true
= ( subset @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f67,f50]) ).
thf(f125,plain,
! [X0: $i] :
( ( $false
= ( in @ ( sK2 @ sK0 @ X0 ) @ sK1 ) )
| ( $true
= ( subset @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f124]) ).
thf(f156,plain,
( ( $true = $false )
| ( $true
= ( subset @ sK1 @ sK0 ) )
| ( $true
= ( subset @ sK1 @ sK0 ) ) ),
inference(constrained_superposition,[],[f51,f125]) ).
thf(f157,plain,
( ( $true = $false )
| ( $true
= ( subset @ sK1 @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f156]) ).
thf(f158,plain,
( $true
= ( subset @ sK1 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f157]) ).
thf(f166,plain,
$false,
inference(forward_subsumption_resolution,[],[f158,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU594^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 % Computer : n026.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 13:58:44 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.21/0.30 % (637690)Will run a generic schedule for satisfiability detection.
% 0.21/0.30 % (637696)% WARNING: option uhcvi not known.
% 0.21/0.30 % (637695)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2915701852_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.30 % (637697)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=178567060:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.30 % (637696)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=60959972:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.30 % (637699)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3737242042:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.30 % (637696)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.30 % (637699)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.30 % Exception at run slice level
% 0.21/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.30 % (637696)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.30 % (637701)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3773797909:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.30 % (637698)dis+10_1_sil=32000:sp=arity:random_seed=1035370353:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.30 % (637696) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-637690-637696"...
% 0.21/0.30 % (637699) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-637690-637699"...
% 0.21/0.30 % (637696)...printing done.
% 0.21/0.30 % (637699)...printing done.
% 0.21/0.30 % (637699)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (637699)------------------------------
% 0.21/0.30 % (637699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (637699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (637699)CaDiCaL version: 2.1.3
% 0.21/0.30 % (637699)Termination reason: Refutation
% 0.21/0.30 % (637699)Time elapsed: 0.008 s
% 0.21/0.30 % (637699)Peak memory usage: 12 MB
% 0.21/0.30 % (637699)Instructions burned: 13 (million)
% 0.21/0.30 % (637690)Success in time 0.046 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------