%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET623^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:23:23 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 8
% Syntax : Number of formulae : 170 ( 21 unt; 0 typ; 6 def)
% Number of atoms : 3211 ( 510 equ; 0 cnn)
% Maximal formula atoms : 6 ( 18 avg)
% Number of connectives : 2724 ( 535 ~; 600 |; 424 &;1159 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 9 con; 0-4 aty)
% Number of variables : 44 ( 0 sgn 9 !; 3 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
is_a: $i > ( $i > $o ) > $o ).
thf(func_def_3,type,
emptyset: $i > $o ).
thf(func_def_4,type,
unord_pair: $i > $i > $i > $o ).
thf(func_def_5,type,
singleton: $i > $i > $o ).
thf(func_def_6,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
complement: ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_12,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_13,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_14,type,
misses: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_15,type,
vAND: $o > $o > $o ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_24,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_26,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vIMP: $o > $o > $o ).
thf(func_def_28,type,
sK0: $i > $o ).
thf(func_def_29,type,
sK1: $i > $o ).
thf(func_def_30,type,
sK2: $i > $o ).
thf(f7,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) )
= excl_union ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',excl_union) ).
thf(f15,conjecture,
! [X2: $i > $o,X0: $i > $o,X1: $i > $o] :
( ( excl_union @ ( excl_union @ X0 @ X1 ) @ X2 )
= ( excl_union @ X0 @ ( excl_union @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X2: $i > $o,X0: $i > $o,X1: $i > $o] :
( ( excl_union @ ( excl_union @ X0 @ X1 ) @ X2 )
= ( excl_union @ X0 @ ( excl_union @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f19,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) )
= excl_union ),
inference(rectify,[],[f7]) ).
thf(f20,plain,
( excl_union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ( Y1 @ Y2 )
& ~ ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f39,plain,
~ ! [X2: $i > $o,X0: $i > $o,X1: $i > $o] :
( ( excl_union @ X1 @ ( excl_union @ X2 @ X0 ) )
= ( excl_union @ ( excl_union @ X1 @ X2 ) @ X0 ) ),
inference(rectify,[],[f16]) ).
thf(f40,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( excl_union @ X1 @ ( excl_union @ X2 @ X0 ) )
!= ( excl_union @ ( excl_union @ X1 @ X2 ) @ X0 ) ),
inference(ennf_transformation,[],[f39]) ).
thf(f41,plain,
( ( excl_union @ sK1 @ ( excl_union @ sK2 @ sK0 ) )
!= ( excl_union @ ( excl_union @ sK1 @ sK2 ) @ sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f40]) ).
thf(f45,plain,
( ( excl_union @ sK1 @ ( excl_union @ sK2 @ sK0 ) )
!= ( excl_union @ ( excl_union @ sK1 @ sK2 ) @ sK0 ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f52,plain,
( excl_union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ( Y1 @ Y2 )
& ~ ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f60,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ( Y1 @ Y2 )
& ~ ( Y0 @ Y2 ) ) )
@ sK1
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ( Y1 @ Y2 )
& ~ ( Y0 @ Y2 ) ) )
@ sK2
@ sK0 ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ( Y1 @ Y2 )
& ~ ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ( Y1 @ Y2 )
& ~ ( Y0 @ Y2 ) ) )
@ sK1
@ sK2 )
@ sK0 ) ),
inference(definition_unfolding,[],[f45,f52,f52,f52,f52]) ).
thf(f61,plain,
( ( ^ [Y0: $i] :
( ( ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
& ~ ( ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
| ( ( ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
( ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
& ~ ( ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
| ( ( ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
& ~ ( sK1 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: $i] :
( ( ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f61]) ).
thf(f63,plain,
( ( ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
& ~ ( ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
| ( ( ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
& ~ ( sK1 @ Y0 ) ) )
@ sK3 )
= $true )
| ( ( ^ [Y0: $i] :
( ( ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
@ sK3 )
= $true ) ),
inference(xor_proxy_clausification,[],[f62]) ).
thf(f64,plain,
( ( ( ^ [Y0: $i] :
( ( ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
@ sK3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
& ~ ( ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
| ( ( ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
& ~ ( sK1 @ Y0 ) ) )
@ sK3 )
= $false ) ),
inference(xor_proxy_clausification,[],[f62]) ).
thf(f65,plain,
( ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
( ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( ( ( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $false )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f65]) ).
thf(f68,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f67]) ).
thf(f69,plain,
( ( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $false )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f67]) ).
thf(f70,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f69]) ).
thf(f71,plain,
( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( $false
= ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f70]) ).
thf(f73,plain,
( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $false
= ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f71]) ).
thf(f74,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( $false
= ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ( $false
= ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f75]) ).
thf(f77,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f77]) ).
thf(f80,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f82,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f83,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f82]) ).
thf(f111,plain,
( ( $false
= ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f68]) ).
thf(f112,plain,
( ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f111]) ).
thf(f113,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f112]) ).
thf(f114,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f113]) ).
thf(f115,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f114]) ).
thf(f116,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f115]) ).
thf(f152,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f116]) ).
thf(f153,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f170,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f171,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f171]) ).
thf(f179,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f172]) ).
thf(f183,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f184,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f184]) ).
thf(f186,plain,
( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f66]) ).
thf(f187,plain,
( ( ( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $false )
| ( ( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f189,plain,
( ( ( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f188]) ).
thf(f191,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f192,plain,
( ( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK0 @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f200,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f195]) ).
thf(f201,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f201]) ).
thf(f221,plain,
( ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false )
| ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f237,plain,
( ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $false )
| ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f221]) ).
thf(f238,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f237]) ).
thf(f239,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f238]) ).
thf(f240,plain,
( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f239]) ).
thf(f241,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f240]) ).
thf(f243,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f241]) ).
thf(f245,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f243]) ).
thf(f246,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f247,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f246]) ).
thf(f258,plain,
( ( $true
= ( ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f259,plain,
( ( ( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f258]) ).
thf(f260,plain,
( ( $true
= ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f259]) ).
thf(f261,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f260]) ).
thf(f262,plain,
( ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f260]) ).
thf(f264,plain,
( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f262]) ).
thf(f265,plain,
( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f264]) ).
thf(f266,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f265]) ).
thf(f267,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f265]) ).
thf(f269,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f267]) ).
thf(f271,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f269]) ).
thf(f273,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f271]) ).
thf(f274,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f273]) ).
thf(f276,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f274]) ).
thf(f278,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f276]) ).
thf(f279,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f278]) ).
thf(f408,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f266]) ).
thf(f451,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f408]) ).
thf(f452,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $false )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f451]) ).
thf(f453,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f452]) ).
thf(f538,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $false )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f453]) ).
thf(f550,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f538]) ).
thf(f552,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f550]) ).
thf(f553,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f552]) ).
thf(f554,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f553]) ).
thf(f555,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f554]) ).
thf(f1247,plain,
( ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f261]) ).
thf(f1248,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1247]) ).
thf(f1326,plain,
( ( $true
= ( ~ ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ) )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1248]) ).
thf(f1327,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1248]) ).
thf(f1329,plain,
( ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f1327]) ).
thf(f1330,plain,
( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f1329]) ).
thf(f1331,plain,
( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1330]) ).
thf(f1332,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK2 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1331]) ).
thf(f1354,plain,
( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f1332]) ).
thf(f1366,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ~ ( sK2 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1354]) ).
thf(f1373,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f1366]) ).
thf(f1374,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK2 @ sK3 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f1373]) ).
thf(f1375,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f1374]) ).
thf(f1376,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f1375]) ).
thf(f1377,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f1376]) ).
thf(f1388,plain,
( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
= $false )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f1326]) ).
thf(f1389,plain,
( ( ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f1388]) ).
thf(f1442,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f1389]) ).
thf(f1443,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f1442]) ).
thf(f1444,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f1443]) ).
thf(f1445,plain,
( ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1444]) ).
thf(f1488,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f1445]) ).
thf(f1489,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f1488]) ).
thf(f1490,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f1489]) ).
thf(f1491,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f1490]) ).
thf(f1492,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f1491]) ).
thf(f1498,definition,
( spl4_1
<=> ( ( sK1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f1500,plain,
( ( ( sK1 @ sK3 )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f1498]) ).
thf(f1502,definition,
( spl4_2
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f1504,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f1502]) ).
thf(f1506,definition,
( spl4_3
<=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f1508,plain,
( ( ( sK2 @ sK3 )
= $true )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f1506]) ).
thf(f1509,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f83,f1506,f1502,f1498]) ).
thf(f1511,definition,
( spl4_4
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f1513,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f1511]) ).
thf(f1515,definition,
( spl4_5
<=> ( ( sK2 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f1517,plain,
( ( ( sK2 @ sK3 )
= $false )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f1515]) ).
thf(f1518,plain,
( spl4_4
| spl4_5
| spl4_1 ),
inference(avatar_split_clause,[],[f185,f1498,f1515,f1511]) ).
thf(f1520,definition,
( spl4_6
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f1522,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f1520]) ).
thf(f1523,plain,
( spl4_2
| spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f202,f1520,f1515,f1502]) ).
thf(f1524,plain,
( spl4_6
| spl4_4
| spl4_3 ),
inference(avatar_split_clause,[],[f247,f1506,f1511,f1520]) ).
thf(f1525,plain,
( spl4_2
| spl4_3
| spl4_6 ),
inference(avatar_split_clause,[],[f279,f1520,f1506,f1502]) ).
thf(f1526,plain,
( spl4_2
| spl4_5
| spl4_1 ),
inference(avatar_split_clause,[],[f555,f1498,f1515,f1502]) ).
thf(f1527,plain,
( spl4_5
| spl4_4
| spl4_6 ),
inference(avatar_split_clause,[],[f1377,f1520,f1511,f1515]) ).
thf(f1528,plain,
( spl4_3
| spl4_4
| spl4_1 ),
inference(avatar_split_clause,[],[f1492,f1498,f1511,f1506]) ).
thf(f1529,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_4 ),
inference(forward_demodulation,[],[f1504,f1513]) ).
thf(f1530,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f1529]) ).
thf(f1531,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f1530]) ).
thf(f1532,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_6 ),
inference(forward_demodulation,[],[f1522,f1500]) ).
thf(f1533,plain,
( $false
| ~ spl4_1
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f1532]) ).
thf(f1534,plain,
( ~ spl4_1
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f1533]) ).
thf(f1536,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_5 ),
inference(forward_demodulation,[],[f1508,f1517]) ).
thf(f1537,plain,
( $false
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f1536]) ).
thf(f1538,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f1537]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f1509]) ).
cnf(s2,plain,
( spl4_1
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f1518]) ).
cnf(s3,plain,
( spl4_2
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f1523]) ).
cnf(s4,plain,
( spl4_3
| spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f1524]) ).
cnf(s5,plain,
( spl4_2
| spl4_3
| spl4_6 ),
inference(sat_conversion,[],[f1525]) ).
cnf(s6,plain,
( spl4_1
| spl4_2
| spl4_5 ),
inference(sat_conversion,[],[f1526]) ).
cnf(s7,plain,
( spl4_4
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f1527]) ).
cnf(s8,plain,
( spl4_1
| spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f1528]) ).
cnf(s9,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f1531]) ).
cnf(s10,plain,
( ~ spl4_1
| ~ spl4_6 ),
inference(sat_conversion,[],[f1534]) ).
cnf(s11,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f1538]) ).
cnf(s12,plain,
( spl4_2
| spl4_1 ),
inference(rat,[],[s11,s1,s6]) ).
cnf(s13,plain,
( spl4_4
| spl4_1 ),
inference(rat,[],[s11,s8,s2]) ).
cnf(s14,plain,
spl4_1,
inference(rat,[],[s13,s9,s12]) ).
cnf(s15,plain,
~ spl4_6,
inference(rat,[],[s10,s14]) ).
cnf(s16,plain,
spl4_5,
inference(rat,[],[s9,s3,s7,s15]) ).
cnf(s17,plain,
~ spl4_3,
inference(rat,[],[s11,s16]) ).
cnf(s18,plain,
spl4_4,
inference(rat,[],[s4,s15,s17]) ).
cnf(s19,plain,
spl4_2,
inference(rat,[],[s5,s15,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s9,s18,s19]) ).
thf(f1539,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET623^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:39:06 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.29 % (2123702)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (2123711)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2821559452:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (2123713)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (2123713)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.29 % (2123708)lrs+10_16_si=on:nwc=1.5:random_seed=1994955322:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (2123707)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3114474380:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (2123709)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=888558933:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (2123710)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3504731664:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.29 % (2123712)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=119814924:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (2123713)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2686088656:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (2123711)Instruction limit reached!
% 0.21/0.29 % (2123711)------------------------------
% 0.21/0.29 % (2123711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2123711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2123711)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2123711)Termination reason: Instruction limit
% 0.21/0.29 % (2123711)Termination phase: Saturation
% 0.21/0.29 % (2123711)Time elapsed: 0.008 s
% 0.21/0.29 % (2123711)Peak memory usage: 12 MB
% 0.21/0.29 % (2123711)Instructions burned: 26 (million)
% 0.21/0.29 % (2123709)Instruction limit reached!
% 0.21/0.29 % (2123709)------------------------------
% 0.21/0.29 % (2123709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2123709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2123709)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2123709)Termination reason: Instruction limit
% 0.21/0.29 % (2123709)Termination phase: Saturation
% 0.21/0.29 % (2123709)Time elapsed: 0.002 s
% 0.21/0.29 % (2123709)Peak memory usage: 12 MB
% 0.21/0.29 % (2123709)Instructions burned: 4 (million)
% 0.21/0.29 % (2123707) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2123702-2123707"...
% 0.21/0.29 % (2123708) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2123702-2123708"...
% 0.21/0.29 % (2123712) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2123702-2123712"...
% 0.21/0.29 % (2123713) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2123702-2123713"...
% 0.21/0.29 % (2123707)...printing done.
% 0.21/0.29 % (2123708)...printing done.
% 0.21/0.29 % (2123707)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (2123707)------------------------------
% 0.21/0.29 % (2123707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2123707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2123707)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2123707)Termination reason: Refutation
% 0.21/0.29 % (2123707)Time elapsed: 0.012 s
% 0.21/0.29 % (2123707)Peak memory usage: 13 MB
% 0.21/0.29 % (2123707)Instructions burned: 25 (million)
% 0.21/0.29 % (2123702)Success in time 0.045 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------