%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET623^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:23:44 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 8
% Syntax : Number of formulae : 177 ( 20 unt; 0 typ; 6 def)
% Number of atoms : 3530 ( 544 equ; 0 cnn)
% Maximal formula atoms : 6 ( 19 avg)
% Number of connectives : 3027 ( 600 ~; 655 |; 493 &;1273 @)
% ( 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 : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 9 con; 0-4 aty)
% Number of variables : 41 ( 0 sgn 6 !; 3 ?; 41 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
vAND: $o > $o > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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,
( excl_union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',excl_union) ).
thf(f15,conjecture,
! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( excl_union @ ( excl_union @ X0 @ X1 ) @ X2 )
= ( excl_union @ X0 @ ( excl_union @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( excl_union @ ( excl_union @ X0 @ X1 ) @ X2 )
= ( excl_union @ X0 @ ( excl_union @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f24,plain,
( excl_union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f25,plain,
( excl_union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ~ ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f39,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( excl_union @ ( excl_union @ X0 @ X1 ) @ X2 )
!= ( excl_union @ X0 @ ( excl_union @ X1 @ X2 ) ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f40,plain,
( ( excl_union @ ( excl_union @ sK0 @ sK1 ) @ sK2 )
!= ( excl_union @ sK0 @ ( excl_union @ sK1 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f39]) ).
thf(f47,plain,
( excl_union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ~ ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f55,plain,
( ( excl_union @ ( excl_union @ sK0 @ sK1 ) @ sK2 )
!= ( excl_union @ sK0 @ ( excl_union @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f59,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ~ ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ~ ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
@ sK0
@ sK1 )
@ sK2 )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ~ ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
@ sK0
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ~ ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
@ sK1
@ sK2 ) ) ),
inference(definition_unfolding,[],[f55,f47,f47,f47,f47]) ).
thf(f60,plain,
( ( ^ [Y0: $i] :
( ( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( ~ ( sK0 @ Y0 )
& ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f68,plain,
( ( ^ [Y0: $i] :
( ( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ( sK2 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( ~ ( sK0 @ Y0 )
& ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f60]) ).
thf(f69,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ( sK2 @ Y0 ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( ~ ( sK0 @ Y0 )
& ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
& ( sK2 @ Y0 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( ~ ( sK0 @ Y0 )
& ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f68]) ).
thf(f71,plain,
( ( $false
= ( ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
( ( $false
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( ( $false
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f71]) ).
thf(f74,plain,
( ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f75]) ).
thf(f77,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f75]) ).
thf(f78,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f78]) ).
thf(f80,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f79]) ).
thf(f81,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f102,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f81]) ).
thf(f103,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f102]) ).
thf(f104,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f103]) ).
thf(f106,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f104]) ).
thf(f107,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f106]) ).
thf(f118,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f76]) ).
thf(f120,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f118]) ).
thf(f121,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f120]) ).
thf(f122,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f121]) ).
thf(f123,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f122]) ).
thf(f129,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f123]) ).
thf(f130,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f129]) ).
thf(f131,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f130]) ).
thf(f143,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) )
| ( $false
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f144,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $false
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $false
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f146,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $false
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f150,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f153]) ).
thf(f156,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f156]) ).
thf(f164,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f165,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f164]) ).
thf(f168,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f169,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f168]) ).
thf(f214,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f144]) ).
thf(f215,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f214]) ).
thf(f236,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f215]) ).
thf(f237,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f238,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f237]) ).
thf(f239,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f238]) ).
thf(f249,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f250,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f249]) ).
thf(f252,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f250]) ).
thf(f253,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f252]) ).
thf(f256,plain,
( ( $true
= ( ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f257,plain,
( ( $true
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f256]) ).
thf(f258,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f257]) ).
thf(f259,plain,
( ( $true
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f257]) ).
thf(f260,plain,
( ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f259]) ).
thf(f261,plain,
( ( $false
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f262,plain,
( ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f263,plain,
( ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f262]) ).
thf(f264,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f263]) ).
thf(f265,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f264]) ).
thf(f267,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f265]) ).
thf(f268,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f267]) ).
thf(f269,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f268]) ).
thf(f325,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f269]) ).
thf(f326,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f325]) ).
thf(f329,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f326]) ).
thf(f330,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f329]) ).
thf(f335,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f330]) ).
thf(f336,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f335]) ).
thf(f337,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f336]) ).
thf(f610,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f261]) ).
thf(f611,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f610]) ).
thf(f612,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f611]) ).
thf(f687,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f612]) ).
thf(f689,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f687]) ).
thf(f690,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f689]) ).
thf(f691,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f690]) ).
thf(f801,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f691]) ).
thf(f802,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f801]) ).
thf(f804,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f802]) ).
thf(f805,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f804]) ).
thf(f808,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f805]) ).
thf(f809,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f808]) ).
thf(f965,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f258]) ).
thf(f966,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f965]) ).
thf(f967,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f965]) ).
thf(f968,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f967]) ).
thf(f970,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f968]) ).
thf(f971,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f970]) ).
thf(f973,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f971]) ).
thf(f974,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f973]) ).
thf(f975,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f974]) ).
thf(f982,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f975]) ).
thf(f984,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f982]) ).
thf(f985,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f984]) ).
thf(f986,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f985]) ).
thf(f987,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f986]) ).
thf(f990,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f987]) ).
thf(f991,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f990]) ).
thf(f1036,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f966]) ).
thf(f1037,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f1036]) ).
thf(f1174,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f1037]) ).
thf(f1175,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f1174]) ).
thf(f1176,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ~ ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f1175]) ).
thf(f1231,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f1176]) ).
thf(f1233,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f1231]) ).
thf(f1235,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f1233]) ).
thf(f1236,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f1235]) ).
thf(f1308,definition,
( spl4_1
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f1310,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f1308]) ).
thf(f1312,definition,
( spl4_2
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f1314,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f1312]) ).
thf(f1316,definition,
( spl4_3
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f1318,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f1316]) ).
thf(f1319,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f107,f1316,f1312,f1308]) ).
thf(f1321,definition,
( spl4_4
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f1323,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f1321]) ).
thf(f1325,definition,
( spl4_5
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f1327,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f1325]) ).
thf(f1328,plain,
( spl4_4
| spl4_5
| spl4_3 ),
inference(avatar_split_clause,[],[f131,f1316,f1325,f1321]) ).
thf(f1330,definition,
( spl4_6
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f1332,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f1330]) ).
thf(f1333,plain,
( spl4_1
| spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f169,f1330,f1325,f1308]) ).
thf(f1334,plain,
( spl4_4
| spl4_2
| spl4_6 ),
inference(avatar_split_clause,[],[f253,f1330,f1312,f1321]) ).
thf(f1335,plain,
( spl4_6
| spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f337,f1312,f1308,f1330]) ).
thf(f1336,plain,
( spl4_4
| spl4_6
| spl4_5 ),
inference(avatar_split_clause,[],[f809,f1325,f1330,f1321]) ).
thf(f1337,plain,
( spl4_5
| spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f991,f1316,f1308,f1325]) ).
thf(f1338,plain,
( spl4_4
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f1236,f1316,f1312,f1321]) ).
thf(f1341,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_5 ),
inference(forward_demodulation,[],[f1314,f1327]) ).
thf(f1342,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f1341]) ).
thf(f1343,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f1342]) ).
thf(f1346,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_4 ),
inference(constrained_superposition,[],[f1310,f1323]) ).
thf(f1350,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f1346]) ).
thf(f1351,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f1350]) ).
thf(f1356,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_6 ),
inference(constrained_superposition,[],[f1332,f1318]) ).
thf(f1357,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_6 ),
inference(constrained_superposition,[],[f1318,f1332]) ).
thf(f1358,plain,
( $false
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f1357]) ).
thf(f1359,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f1358]) ).
thf(f1360,plain,
( $false
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f1356]) ).
thf(f1361,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f1360]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f1319]) ).
cnf(s2,plain,
( spl4_3
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f1328]) ).
cnf(s3,plain,
( spl4_1
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f1333]) ).
cnf(s4,plain,
( spl4_2
| spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f1334]) ).
cnf(s5,plain,
( spl4_1
| spl4_2
| spl4_6 ),
inference(sat_conversion,[],[f1335]) ).
cnf(s6,plain,
( spl4_4
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f1336]) ).
cnf(s7,plain,
( spl4_1
| spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f1337]) ).
cnf(s8,plain,
( spl4_2
| spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f1338]) ).
cnf(s9,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f1343]) ).
cnf(s11,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f1351]) ).
cnf(s12,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f1359]) ).
cnf(s13,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f1361]) ).
cnf(s14,plain,
( spl4_2
| spl4_1 ),
inference(rat,[],[s12,s1,s5]) ).
cnf(s15,plain,
( spl4_5
| spl4_1 ),
inference(rat,[],[s12,s7,s3]) ).
cnf(s16,plain,
spl4_1,
inference(rat,[],[s15,s9,s14]) ).
cnf(s17,plain,
~ spl4_4,
inference(rat,[],[s11,s16]) ).
cnf(s18,plain,
spl4_6,
inference(rat,[],[s9,s4,s6,s17]) ).
cnf(s19,plain,
~ spl4_3,
inference(rat,[],[s13,s18]) ).
cnf(s20,plain,
spl4_5,
inference(rat,[],[s2,s17,s19]) ).
cnf(s21,plain,
spl4_2,
inference(rat,[],[s8,s17,s19]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s9,s20,s21]) ).
thf(f1363,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET623^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n015.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:43:03 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.08/0.25 % (3539739)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (3539745)% WARNING: option uhcvi not known.
% 0.08/0.25 % (3539745)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1372458659:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.25 % (3539745)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (3539745)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.25 % (3539745) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3539739-3539745"...
% 0.08/0.25 % (3539744)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=955228948_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.25 % (3539746)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4243227145:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.25 % (3539747)dis+10_1_sil=32000:sp=arity:random_seed=493880671:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.25 % (3539748)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1880018617:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.25 % Exception at run slice level
% 0.08/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.25 % (3539748)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (3539745)...printing done.
% 0.08/0.25 % (3539745)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (3539745)------------------------------
% 0.08/0.25 % (3539745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (3539745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (3539745)CaDiCaL version: 2.1.3
% 0.08/0.25 % (3539745)Termination reason: Refutation
% 0.08/0.25 % (3539745)Time elapsed: 0.010 s
% 0.08/0.25 % (3539745)Peak memory usage: 13 MB
% 0.08/0.25 % (3539745)Instructions burned: 39 (million)
% 0.08/0.25 % (3539739)Success in time 0.038 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------