%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU805^2 : 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 : n008.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 08:33:29 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 7
% Syntax : Number of formulae : 89 ( 39 unt; 0 typ; 2 def)
% Number of atoms : 594 ( 162 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 753 ( 56 ~; 54 |; 56 &; 491 @)
% ( 2 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 24 usr; 11 con; 0-4 aty)
% ( 14 !!; 41 ??; 0 @@+; 0 @@-)
% Number of variables : 173 ( 0 sgn 85 !; 16 ?; 173 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
foundationAx: $o ).
thf(func_def_4,type,
nonempty: $i > $o ).
thf(func_def_5,type,
nonemptyE1: $o ).
thf(func_def_6,type,
binintersect: $i > $i > $i ).
thf(func_def_7,type,
disjointsetsI1: $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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
vAND: $o > $o > $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_21,type,
sK1: $i > $i > $i ).
thf(func_def_22,type,
sK2: $i > $i ).
thf(func_def_23,type,
sK3: $i > $i ).
thf(f1,axiom,
( foundationAx
= ( ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ? [X2: $i] :
( ~ ? [X1: $i] :
( ( in @ X1 @ X0 )
& ( in @ X1 @ X2 ) )
& ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(f2,axiom,
( nonempty
= ( ^ [X0: $i] : ( X0 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(f3,axiom,
( nonemptyE1
= ( ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] : ( in @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(f4,axiom,
( disjointsetsI1
= ( ! [X0: $i,X1: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( in @ X2 @ X0 ) )
=> ( ( binintersect @ X0 @ X1 )
= emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(f5,conjecture,
( foundationAx
=> ( nonemptyE1
=> ( disjointsetsI1
=> ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= emptyset )
& ( in @ X1 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundation2) ).
thf(f6,negated_conjecture,
~ ( foundationAx
=> ( nonemptyE1
=> ( disjointsetsI1
=> ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= emptyset )
& ( in @ X1 @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( foundationAx
= ( ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ? [X2: $i] :
( ~ ? [X3: $i] :
( ( in @ X3 @ X0 )
& ( in @ X3 @ X2 ) )
& ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( foundationAx
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f10,plain,
( nonemptyE1
= ( ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] : ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
( nonemptyE1
= ( !! @ $i
@ ^ [Y0: $i] :
( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( disjointsetsI1
= ( ! [X0: $i,X1: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( in @ X2 @ X0 ) )
=> ( ( binintersect @ X0 @ X1 )
= emptyset ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f13,plain,
( disjointsetsI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) )
=> ( emptyset
= ( binintersect @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
~ ( foundationAx
=> ( nonemptyE1
=> ( disjointsetsI1
=> ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= emptyset )
& ( in @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f15,plain,
~ ( ( foundationAx = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( disjointsetsI1 = $true )
=> ! [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
=> ? [X1: $i] :
( ( emptyset
= ( binintersect @ X1 @ X0 ) )
& ( ( in @ X1 @ X0 )
= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( ? [X0: $i] :
( ! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
& ( ( nonempty @ X0 )
= $true ) )
& ( disjointsetsI1 = $true )
& ( nonemptyE1 = $true )
& ( foundationAx = $true ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f17,plain,
( ? [X0: $i] :
( ! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
& ( ( nonempty @ X0 )
= $true ) )
& ( disjointsetsI1 = $true )
& ( nonemptyE1 = $true )
& ( foundationAx = $true ) ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
( ! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ sK0 ) )
| ( $true
!= ( in @ X1 @ sK0 ) ) )
& ( $true
= ( nonempty @ sK0 ) )
& ( disjointsetsI1 = $true )
& ( nonemptyE1 = $true )
& ( foundationAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f17]) ).
thf(f19,plain,
( foundationAx
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f20,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f21,plain,
( nonemptyE1
= ( !! @ $i
@ ^ [Y0: $i] :
( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f22,plain,
( disjointsetsI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) )
=> ( emptyset
= ( binintersect @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f23,plain,
foundationAx = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f24,plain,
nonemptyE1 = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f25,plain,
disjointsetsI1 = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f26,plain,
( $true
= ( nonempty @ sK0 ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f27,plain,
! [X1: $i] :
( ( $true
!= ( in @ X1 @ sK0 ) )
| ( emptyset
!= ( binintersect @ X1 @ sK0 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f30,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f19,f23]) ).
thf(f31,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] : ( emptyset != Y1 )
@ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f21,f24,f20]) ).
thf(f32,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) )
=> ( emptyset
= ( binintersect @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f22,f25]) ).
thf(f33,plain,
( $true
= ( ^ [Y0: $i] : ( emptyset != Y0 )
@ sK0 ) ),
inference(definition_unfolding,[],[f26,f20]) ).
thf(f34,plain,
( $true
= ( emptyset != sK0 ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
( $false
= ( emptyset = sK0 ) ),
inference(not_proxy_clausification,[],[f34]) ).
thf(f36,plain,
emptyset != sK0,
inference(equality_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) )
=> ( emptyset
= ( binintersect @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ X1 ) ) )
=> ( emptyset
= ( binintersect @ 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 ) ) )
=> ( emptyset
= ( binintersect @ 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 ) ) )
=> ( emptyset
= ( binintersect @ 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
= ( emptyset
= ( binintersect @ X2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( in @ Y0 @ X1 ) ) ) )
| ( $true
= ( emptyset
= ( binintersect @ X2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( in @ Y0 @ X1 ) )
@ ( sK1 @ X1 @ X2 ) ) )
| ( $true
= ( emptyset
= ( binintersect @ X2 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( in @ Y0 @ X1 ) )
@ ( sK1 @ X1 @ X2 ) ) )
| ( emptyset
= ( binintersect @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ ( sK1 @ X1 @ X2 ) @ X2 )
& ( in @ ( sK1 @ X1 @ X2 ) @ X1 ) ) )
| ( emptyset
= ( binintersect @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK1 @ X1 @ X2 ) @ X1 ) )
| ( emptyset
= ( binintersect @ X2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK1 @ X1 @ X2 ) @ X2 ) )
| ( emptyset
= ( binintersect @ X2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f48,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] : ( emptyset != Y1 )
@ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f49,plain,
! [X1: $i] :
( $true
= ( ( emptyset != X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X1: $i] :
( ( $false
= ( emptyset != X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X1: $i] :
( ( $true
= ( emptyset = X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X1: $i] :
( ( emptyset = X1 )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X1: $i] :
( ( emptyset = X1 )
| ( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ X1 )
@ ( sK2 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X1: $i] :
( ( $true
= ( in @ ( sK2 @ X1 ) @ X1 ) )
| ( emptyset = X1 ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( in @ Y2 @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f30]) ).
thf(f56,plain,
! [X1: $i] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] : ( in @ Y0 @ X1 )
@ X2 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ X1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] : ( in @ Y0 @ X1 )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( in @ Y1 @ X1 ) ) ) )
@ ( sK3 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $true
= ( ( in @ ( sK3 @ X1 ) @ X1 )
& ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( sK3 @ X1 ) )
& ( in @ Y0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $true
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( sK3 @ X1 ) )
& ( in @ Y0 @ X1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $true
= ( in @ ( sK3 @ X1 ) @ X1 ) ) ),
inference(and_proxy_clausification,[],[f60]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( sK3 @ X1 ) )
& ( in @ Y0 @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f61]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( sK3 @ X1 ) )
& ( in @ Y0 @ X1 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( ( in @ X3 @ ( sK3 @ X1 ) )
& ( in @ X3 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( sK3 @ X1 ) ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( in @ X3 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f81,plain,
! [X0: $i] :
( ( $true != $true )
| ( emptyset
!= ( binintersect @ ( sK3 @ sK0 ) @ sK0 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f27,f62]) ).
thf(f83,plain,
! [X0: $i] :
( ( emptyset
!= ( binintersect @ ( sK3 @ sK0 ) @ sK0 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f81]) ).
thf(f86,definition,
( spl4_1
<=> ! [X0: $i] :
( $false
= ( in @ X0 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f87,plain,
( ! [X0: $i] :
( $false
= ( in @ X0 @ sK0 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f86]) ).
thf(f89,definition,
( spl4_2
<=> ( emptyset
= ( binintersect @ ( sK3 @ sK0 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f91,plain,
( ( emptyset
!= ( binintersect @ ( sK3 @ sK0 ) @ sK0 ) )
| spl4_2 ),
inference(avatar_component_clause,[],[f89]) ).
thf(f92,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f83,f89,f86]) ).
thf(f118,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( emptyset
= ( binintersect @ ( sK3 @ X1 ) @ X0 ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( in @ ( sK1 @ X0 @ ( sK3 @ X1 ) ) @ X1 ) ) ),
inference(constrained_superposition,[],[f47,f66]) ).
thf(f128,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK1 @ X0 @ ( sK3 @ X1 ) ) @ X1 ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( emptyset
= ( binintersect @ ( sK3 @ X1 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f357,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( emptyset
= ( binintersect @ ( sK3 @ X0 ) @ X0 ) )
| ( ( in @ X1 @ X0 )
= $false )
| ( emptyset
= ( binintersect @ ( sK3 @ X0 ) @ X0 ) ) ),
inference(constrained_superposition,[],[f46,f128]) ).
thf(f368,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( emptyset
= ( binintersect @ ( sK3 @ X0 ) @ X0 ) )
| ( ( in @ X1 @ X0 )
= $false ) ),
inference(duplicate_literal_removal,[],[f357]) ).
thf(f369,plain,
! [X0: $i,X1: $i] :
( ( emptyset
= ( binintersect @ ( sK3 @ X0 ) @ X0 ) )
| ( ( in @ X1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f368]) ).
thf(f407,plain,
( ! [X0: $i] :
( ( emptyset != emptyset )
| ( $false
= ( in @ X0 @ sK0 ) ) )
| spl4_2 ),
inference(constrained_superposition,[],[f91,f369]) ).
thf(f423,plain,
( ! [X0: $i] :
( $false
= ( in @ X0 @ sK0 ) )
| spl4_2 ),
inference(trivial_inequality_removal,[],[f407]) ).
thf(f436,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f423,f89,f86]) ).
thf(f437,plain,
( ( $true = $false )
| ( emptyset = sK0 )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f87,f54]) ).
thf(f463,plain,
( ( emptyset = sK0 )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f437]) ).
thf(f466,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f463,f36]) ).
thf(f467,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f466]) ).
cnf(s1,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f92]) ).
cnf(s3,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f436]) ).
cnf(s5,plain,
~ spl4_1,
inference(sat_conversion,[],[f467]) ).
cnf(s6,plain,
spl4_2,
inference(rat,[],[s3,s5]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s6,s5]) ).
thf(f468,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU805^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n008.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:33:09 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.19/0.28 % (3243841)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (3243857)% WARNING: option uhcvi not known.
% 0.19/0.28 % (3243857)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4208895078:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (3243857)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (3243857)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.28 % (3243856)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=769344237_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % (3243858)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=213858677:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (3243860)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1460239300:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (3243859)dis+10_1_sil=32000:sp=arity:random_seed=2060136699:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (3243861)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1354214849:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (3243862)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1086078370:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % (3243860)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (3243857) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3243841-3243857"...
% 0.19/0.28 % (3243857)...printing done.
% 0.19/0.28 % (3243857)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (3243857)------------------------------
% 0.19/0.28 % (3243857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3243857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3243857)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3243857)Termination reason: Refutation
% 0.19/0.28 % (3243857)Time elapsed: 0.012 s
% 0.19/0.28 % (3243857)Peak memory usage: 13 MB
% 0.19/0.28 % (3243857)Instructions burned: 39 (million)
% 0.19/0.28 % (3243841)Success in time 0.043 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------