%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU596^2 : 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 : n005.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 08:32:36 AM UTC 2026
% Result : Theorem 0.06s 0.24s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 58 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 385 ( 106 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 515 ( 35 ~; 23 |; 16 &; 357 @)
% ( 0 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 18 usr; 9 con; 0-4 aty)
% ( 39 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 131 ( 48 ^; 75 !; 8 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
emptyI: $o ).
thf(func_def_4,type,
binintersect: $i > $i > $i ).
thf(func_def_5,type,
binintersectEL: $o ).
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,
vNOT: $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,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
sK2: $i > $i ).
thf(f1,axiom,
( emptyI
= ( ! [X0: $i] :
( ! [X1: $i] :
~ ( in @ X1 @ X0 )
=> ( X0 = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(f2,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(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,
( emptyI
=> ( binintersectEL
=> ( binintersectER
=> ! [X0: $i,X1: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( in @ X2 @ X0 ) )
=> ( ( binintersect @ X0 @ X1 )
= emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(f5,negated_conjecture,
~ ( emptyI
=> ( binintersectEL
=> ( binintersectER
=> ! [X0: $i,X1: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( in @ X2 @ X0 ) )
=> ( ( binintersect @ X0 @ X1 )
= emptyset ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( emptyI
= ( ! [X0: $i] :
( ! [X1: $i] :
~ ( in @ X1 @ X0 )
=> ( X0 = emptyset ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( emptyI
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
~ ( in @ Y1 @ Y0 ) )
=> ( emptyset = Y0 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( binintersectEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
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,
~ ( emptyI
=> ( binintersectEL
=> ( binintersectER
=> ! [X0: $i,X1: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( in @ X2 @ X0 ) )
=> ( ( binintersect @ X0 @ X1 )
= emptyset ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
~ ( ( emptyI = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectER = $true )
=> ! [X0: $i,X1: $i] :
( ~ ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( emptyset
= ( binintersect @ X0 @ X1 ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( emptyset
!= ( binintersect @ X0 @ X1 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( binintersectER = $true )
& ( binintersectEL = $true )
& ( emptyI = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( emptyset
!= ( binintersect @ X0 @ X1 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( binintersectER = $true )
& ( binintersectEL = $true )
& ( emptyI = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( emptyset
!= ( binintersect @ sK0 @ sK1 ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK1 ) )
| ( $true
!= ( in @ X2 @ sK0 ) ) )
& ( binintersectER = $true )
& ( binintersectEL = $true )
& ( emptyI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
thf(f17,plain,
( emptyI
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
~ ( in @ Y1 @ Y0 ) )
=> ( emptyset = Y0 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f18,plain,
( binintersectEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
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(f20,plain,
emptyI = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f21,plain,
binintersectEL = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
binintersectER = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK1 ) )
| ( $true
!= ( in @ X2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f24,plain,
( emptyset
!= ( binintersect @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
~ ( in @ Y1 @ Y0 ) )
=> ( emptyset = Y0 ) ) )
= $true ),
inference(definition_unfolding,[],[f17,f20]) ).
thf(f28,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) )
= $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 @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( binintersect @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( binintersect @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( binintersect @ X3 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binintersect @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
~ ( in @ Y1 @ Y0 ) )
=> ( emptyset = Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f45,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ X1 ) )
=> ( emptyset = X1 ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ X1 ) ) )
| ( $true
= ( emptyset = X1 ) ) ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
~ ( in @ Y0 @ X1 )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( emptyset = X1 ) ) ),
inference(sigma_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
~ ( in @ Y0 @ X1 )
@ ( sK2 @ X1 ) ) )
| ( emptyset = X1 ) ),
inference(equality_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X1: $i] :
( ( $false
= ( ~ ( in @ ( sK2 @ X1 ) @ X1 ) ) )
| ( emptyset = X1 ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X1: $i] :
( ( $true
= ( in @ ( sK2 @ X1 ) @ X1 ) )
| ( emptyset = X1 ) ),
inference(not_proxy_clausification,[],[f49]) ).
thf(f63,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( emptyset
= ( binintersect @ X0 @ X1 ) )
| ( $true
= ( in @ ( sK2 @ ( binintersect @ X0 @ X1 ) ) @ X1 ) ) ),
inference(constrained_superposition,[],[f50,f36]) ).
thf(f64,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ ( binintersect @ X0 @ X1 ) ) @ X1 ) )
| ( emptyset
= ( binintersect @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f67,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( emptyset
= ( binintersect @ X0 @ X1 ) )
| ( $true
= ( in @ ( sK2 @ ( binintersect @ X0 @ X1 ) ) @ X0 ) ) ),
inference(constrained_superposition,[],[f50,f43]) ).
thf(f68,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ ( binintersect @ X0 @ X1 ) ) @ X0 ) )
| ( emptyset
= ( binintersect @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f103,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( sK2 @ ( binintersect @ X0 @ sK1 ) ) @ sK0 ) )
| ( emptyset
= ( binintersect @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f23,f64]) ).
thf(f110,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( sK2 @ ( binintersect @ X0 @ sK1 ) ) @ sK0 ) )
| ( emptyset
= ( binintersect @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f190,plain,
( ( $true != $true )
| ( emptyset
= ( binintersect @ sK0 @ sK1 ) )
| ( emptyset
= ( binintersect @ sK0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f110,f68]) ).
thf(f193,plain,
( ( $true != $true )
| ( emptyset
= ( binintersect @ sK0 @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f190]) ).
thf(f194,plain,
( emptyset
= ( binintersect @ sK0 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f193]) ).
thf(f195,plain,
$false,
inference(forward_subsumption_resolution,[],[f194,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU596^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.17 % Computer : n005.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 13:56:01 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.20 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
% 0.06/0.24 % (1703912)Will run a generic schedule for satisfiability detection.
% 0.06/0.24 % (1703918)% WARNING: option uhcvi not known.
% 0.06/0.24 % (1703918)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3018225381:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.24 % (1703918)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.06/0.24 % (1703918)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.06/0.24 % (1703918) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1703912-1703918"...
% 0.06/0.24 % (1703918)...printing done.
% 0.06/0.24 % (1703918)Refutation found. Thanks to Tanya!
% 0.06/0.24 % SZS status Theorem for theBenchmark
% 0.06/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.25 % (1703918)------------------------------
% 0.06/0.25 % (1703918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.25 % (1703918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.25 % (1703918)CaDiCaL version: 2.1.3
% 0.06/0.25 % (1703918)Termination reason: Refutation
% 0.06/0.25 % (1703918)Time elapsed: 0.005 s
% 0.06/0.25 % (1703918)Peak memory usage: 12 MB
% 0.06/0.25 % (1703918)Instructions burned: 13 (million)
% 0.06/0.25 % (1703912)Success in time 0.034 s
% 0.06/0.25 % Vampire exiting
%------------------------------------------------------------------------------