%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL877^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:14:39 AM UTC 2026
% Result : Theorem 1.41s 0.50s
% Output : Refutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 27
% Syntax : Number of formulae : 411 ( 39 unt; 0 typ; 19 def)
% Number of atoms : 4167 ( 841 equ; 0 cnn)
% Maximal formula atoms : 14 ( 10 avg)
% Number of connectives : 6069 (1291 ~;1447 |; 0 &;3034 @)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 401 ( 401 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 78 usr; 31 con; 0-4 aty)
% ( 275 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1133 ( 0 sgn 515 !; 1 ?;1133 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_50,type,
sK3: $i > $o ).
thf(func_def_51,type,
sK4: $i > $o ).
thf(func_def_59,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_60,type,
sK13: ( $i > $o ) > $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f17,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o] : ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) )
= mdia ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mdia) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) ) ) )
<=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ ( mnot @ ( mbox @ X0 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) ) ) )
<=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ ( mnot @ ( mbox @ X0 @ X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f41,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f42,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f44,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f55,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f56,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f67,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f68,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f69,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f72,plain,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) ) ) )
<=> ( mvalid
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X0 @ ( mnot @ ( mbox @ X0 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f73,plain,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ X0 @ Y0 ) @ ( mbox @ X0 @ ( mdia @ X0 @ Y0 ) ) ) ) )
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X0 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f76,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f77,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f85,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f86,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ X0 @ Y0 ) @ ( mbox @ X0 @ ( mdia @ X0 @ Y0 ) ) ) ) )
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X0 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f73]) ).
thf(f88,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ sK0 @ Y0 ) @ ( mbox @ sK0 @ ( mdia @ sK0 @ Y0 ) ) ) ) )
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK0 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f89,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f90,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f92,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f94,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ sK0 @ Y0 ) @ ( mbox @ sK0 @ ( mdia @ sK0 @ Y0 ) ) ) ) )
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK0 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f97,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f99,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f100,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f101,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f105,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f100,f89,f99]) ).
thf(f109,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f97,f99,f92,f99]) ).
thf(f110,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 ) ) ) ) )
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f94,f90,f101,f105,f109,f92,f109,f90,f101,f105,f99,f92,f92,f99,f92]) ).
thf(f111,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 ) ) ) ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f110]) ).
thf(f112,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ) ) ),
inference(xor_proxy_clausification,[],[f110]) ).
thf(f113,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f113]) ).
thf(f115,plain,
( ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ sK1 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f114]) ).
thf(f116,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ sK2 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ sK2 @ Y1 ) ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f115]) ).
thf(f117,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ sK2 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ sK2 @ Y1 ) ) ) )
@ sK3 ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f116]) ).
thf(f118,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ sK2 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ sK2 @ Y1 ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f117]) ).
thf(f119,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK2 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK2 @ Y0 ) ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK2 @ Y0 ) ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f119]) ).
thf(f121,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK2 @ Y0 ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f119]) ).
thf(f122,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK2 @ Y0 ) )
@ sK5 ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f121]) ).
thf(f123,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK2 @ Y0 ) )
@ sK5 ) ) ),
inference(or_proxy_clausification,[],[f122]) ).
thf(f124,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK2 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f122]) ).
thf(f125,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK2 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f124]) ).
thf(f126,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) )
| ~ ( sK0 @ sK2 @ sK5 ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) ) )
| ~ ( sK0 @ sK1 @ sK6 ) ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
( ( $false
= ( ~ ( sK0 @ sK2 @ sK5 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) ) )
| ~ ( sK0 @ sK1 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f126]) ).
thf(f128,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) ) )
| ~ ( sK0 @ sK1 @ sK6 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f126]) ).
thf(f129,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f128]) ).
thf(f130,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f128]) ).
thf(f131,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f130]) ).
thf(f132,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f131]) ).
thf(f133,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK4 @ X2 )
| ~ ( sK0 @ sK6 @ X2 ) )
= $true )
| ( ( ~ ( sK3 @ X1 )
| ~ ( sK0 @ sK5 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( sK0 @ sK6 @ X2 ) )
= $true )
| ( ( sK4 @ X2 )
= $true )
| ( ( ~ ( sK3 @ X1 )
| ~ ( sK0 @ sK5 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ sK6 @ X2 ) )
| ( ( ~ ( sK3 @ X1 )
| ~ ( sK0 @ sK5 @ X1 ) )
= $true )
| ( ( sK4 @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( sK0 @ sK5 @ X1 ) )
= $true )
| ( $false
= ( sK0 @ sK6 @ X2 ) )
| ( ( ~ ( sK3 @ X1 ) )
= $true )
| ( ( sK4 @ X2 )
= $true ) ),
inference(or_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( sK3 @ X1 ) )
= $true )
| ( ( sK4 @ X2 )
= $true )
| ( $false
= ( sK0 @ sK6 @ X2 ) )
| ( ( sK0 @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ sK5 @ X1 )
= $false )
| ( $false
= ( sK3 @ X1 ) )
| ( ( sK4 @ X2 )
= $true )
| ( $false
= ( sK0 @ sK6 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ( $false
= ( ~ ( sK0 @ sK1 @ sK6 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f129]) ).
thf(f142,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) )
= $true )
| ( ( sK0 @ sK1 @ sK6 )
= $true ) ),
inference(not_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ sK6 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X1: $i] :
( ( ( ~ ( sK3 @ X1 )
| ~ ( sK0 @ sK5 @ X1 ) )
= $true )
| ( ( sK0 @ sK1 @ sK6 )
= $true ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
! [X1: $i] :
( ( ( ~ ( sK3 @ X1 ) )
= $true )
| ( ( ~ ( sK0 @ sK5 @ X1 ) )
= $true )
| ( ( sK0 @ sK1 @ sK6 )
= $true ) ),
inference(or_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X1: $i] :
( ( ( ~ ( sK0 @ sK5 @ X1 ) )
= $true )
| ( $false
= ( sK3 @ X1 ) )
| ( ( sK0 @ sK1 @ sK6 )
= $true ) ),
inference(not_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ sK6 )
= $true )
| ( ( sK0 @ sK5 @ X1 )
= $false )
| ( $false
= ( sK3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( ( sK0 @ sK2 @ sK5 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) ) )
| ~ ( sK0 @ sK1 @ sK6 ) ) ) ),
inference(not_proxy_clausification,[],[f127]) ).
thf(f149,plain,
( ( $false
= ( ~ ( sK0 @ sK1 @ sK6 ) ) )
| ( ( sK0 @ sK2 @ sK5 )
= $true ) ),
inference(or_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) ) ) ) )
| ( ( sK0 @ sK2 @ sK5 )
= $true ) ),
inference(or_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( ( sK0 @ sK2 @ sK5 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ sK5 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ sK5 )
= $true )
| ( ( ( sK4 @ X1 )
| ~ ( sK0 @ sK6 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( ( sK4 @ X1 )
= $true )
| ( ( sK0 @ sK2 @ sK5 )
= $true )
| ( ( ~ ( sK0 @ sK6 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ sK5 )
= $true )
| ( ( sK4 @ X1 )
= $true )
| ( $false
= ( sK0 @ sK6 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( ( sK0 @ sK1 @ sK6 )
= $true )
| ( ( sK0 @ sK2 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[],[f149]) ).
thf(f157,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK2 @ Y0 ) )
@ sK5 ) ) ),
inference(not_proxy_clausification,[],[f123]) ).
thf(f158,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK2 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK2 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) )
| ~ ( sK0 @ sK2 @ sK5 ) )
= $false )
| ( $false
= ( ( sK4 @ sK7 )
| ~ ( sK0 @ sK1 @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ( sK4 @ sK7 )
| ~ ( sK0 @ sK1 @ sK7 ) ) )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) ) ) )
| ( $false
= ( ( sK4 @ sK7 )
| ~ ( sK0 @ sK1 @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( $false
= ( ( sK4 @ sK7 )
| ~ ( sK0 @ sK1 @ sK7 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) )
= $true )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( sK4 @ sK7 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f166,plain,
! [X1: $i] :
( ( $false
= ( sK4 @ sK7 ) )
| ( ( ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( ( ~ ( sK3 @ X1 )
| ~ ( sK0 @ sK5 @ X1 ) )
= $true )
| ( $false
= ( sK4 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( ( ~ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( sK4 @ sK7 ) )
| ( ( ~ ( sK0 @ sK5 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( ( ~ ( sK0 @ sK5 @ X1 ) )
= $true )
| ( $false
= ( sK4 @ sK7 ) )
| ( $false
= ( sK3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( ( sK0 @ sK5 @ X1 )
= $false )
| ( $false
= ( sK4 @ sK7 ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $false
= ( ~ ( sK0 @ sK1 @ sK7 ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f172,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ sK7 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ sK7 )
= $true )
| ( ( ~ ( sK3 @ X1 )
| ~ ( sK0 @ sK5 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ sK7 )
= $true )
| ( ( ~ ( sK3 @ X1 ) )
= $true )
| ( ( ~ ( sK0 @ sK5 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( ( ~ ( sK0 @ sK5 @ X1 ) )
= $true )
| ( ( sK0 @ sK1 @ sK7 )
= $true )
| ( $false
= ( sK3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( ( sK0 @ sK1 @ sK7 )
= $true )
| ( ( sK0 @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $false
= ( ~ ( sK0 @ sK1 @ sK7 ) ) )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f178,plain,
( ( $false
= ( sK4 @ sK7 ) )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f179,plain,
( ( $false
= ( sK4 @ sK7 ) )
| ( ( sK0 @ sK2 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $false
= ( ~ ( sK0 @ sK2 @ sK5 ) ) )
| ( ( sK0 @ sK1 @ sK7 )
= $true ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f181,plain,
( ( ( sK0 @ sK1 @ sK7 )
= $true )
| ( ( sK0 @ sK2 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK2 @ Y0 ) ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f120]) ).
thf(f183,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK2 @ Y0 ) ) ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f186,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK2 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK2 @ Y0 ) )
@ sK9 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK8 @ Y0 ) ) )
| ~ ( sK0 @ sK1 @ sK8 ) ) )
| ( $false
= ( ~ ( sK3 @ sK9 )
| ~ ( sK0 @ sK2 @ sK9 ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
( ( $false
= ( ~ ( sK0 @ sK1 @ sK8 ) ) )
| ( $false
= ( ~ ( sK3 @ sK9 )
| ~ ( sK0 @ sK2 @ sK9 ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( $false
= ( ~ ( sK3 @ sK9 )
| ~ ( sK0 @ sK2 @ sK9 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK8 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f191,plain,
( ( $false
= ( ~ ( sK0 @ sK2 @ sK9 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK8 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( ( ~ ( sK3 @ sK9 ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK8 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f193,plain,
( ( ( sK3 @ sK9 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK8 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ( ( sK3 @ sK9 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK8 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( ( ( sK3 @ sK9 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK8 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( ( sK4 @ X1 )
| ~ ( sK0 @ sK8 @ X1 ) ) )
| ( ( sK3 @ sK9 )
= $true ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( ( sK4 @ X1 )
= $true )
| ( ( ~ ( sK0 @ sK8 @ X1 ) )
= $true )
| ( ( sK3 @ sK9 )
= $true ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( ( sK4 @ X1 )
= $true )
| ( $false
= ( sK0 @ sK8 @ X1 ) )
| ( ( sK3 @ sK9 )
= $true ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK8 @ Y0 ) ) ) ) )
| ( ( sK0 @ sK2 @ sK9 )
= $true ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f200,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK8 @ Y0 ) ) )
= $true )
| ( ( sK0 @ sK2 @ sK9 )
= $true ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ sK9 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK8 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ sK9 )
= $true )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( sK0 @ sK8 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ sK9 )
= $true )
| ( ( ~ ( sK0 @ sK8 @ X1 ) )
= $true )
| ( ( sK4 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK8 @ X1 ) )
| ( ( sK4 @ X1 )
= $true )
| ( ( sK0 @ sK2 @ sK9 )
= $true ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
( ( ( sK0 @ sK1 @ sK8 )
= $true )
| ( $false
= ( ~ ( sK3 @ sK9 )
| ~ ( sK0 @ sK2 @ sK9 ) ) ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f206,plain,
( ( ( sK0 @ sK1 @ sK8 )
= $true )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK9 ) ) ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f207,plain,
( ( ( sK0 @ sK1 @ sK8 )
= $true )
| ( ( ~ ( sK3 @ sK9 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f208,plain,
( ( ( sK0 @ sK1 @ sK8 )
= $true )
| ( ( sK3 @ sK9 )
= $true ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( ( ( sK0 @ sK2 @ sK9 )
= $true )
| ( ( sK0 @ sK1 @ sK8 )
= $true ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f210,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK2 @ Y0 ) )
@ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f184]) ).
thf(f211,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK2 @ Y0 ) )
@ sK10 ) ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK2 @ Y0 ) )
@ sK10 ) ) ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK11 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK2 @ Y0 ) )
@ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( $false
= ( ( sK4 @ sK11 )
| ~ ( sK0 @ sK1 @ sK11 ) ) )
| ( $false
= ( ~ ( sK3 @ sK10 )
| ~ ( sK0 @ sK2 @ sK10 ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
( ( $false
= ( ~ ( sK3 @ sK10 )
| ~ ( sK0 @ sK2 @ sK10 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK11 ) ) ) ),
inference(or_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( ( $false
= ( sK4 @ sK11 ) )
| ( $false
= ( ~ ( sK3 @ sK10 )
| ~ ( sK0 @ sK2 @ sK10 ) ) ) ),
inference(or_proxy_clausification,[],[f214]) ).
thf(f217,plain,
( ( ( ~ ( sK0 @ sK2 @ sK10 ) )
= $false )
| ( $false
= ( sK4 @ sK11 ) ) ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ( $false
= ( sK4 @ sK11 ) )
| ( $false
= ( ~ ( sK3 @ sK10 ) ) ) ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f219,plain,
( ( $false
= ( sK4 @ sK11 ) )
| ( ( sK3 @ sK10 )
= $true ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f220,plain,
( ( ( sK0 @ sK2 @ sK10 )
= $true )
| ( $false
= ( sK4 @ sK11 ) ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f221,plain,
( ( ( ~ ( sK0 @ sK2 @ sK10 ) )
= $false )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK11 ) ) ) ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f222,plain,
( ( $false
= ( ~ ( sK3 @ sK10 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK11 ) ) ) ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f223,plain,
( ( ( sK3 @ sK10 )
= $true )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK11 ) ) ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( ( ( sK0 @ sK1 @ sK11 )
= $true )
| ( ( sK3 @ sK10 )
= $true ) ),
inference(not_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ( $false
= ( ~ ( sK0 @ sK1 @ sK11 ) ) )
| ( ( sK0 @ sK2 @ sK10 )
= $true ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f226,plain,
( ( ( sK0 @ sK1 @ sK11 )
= $true )
| ( ( sK0 @ sK2 @ sK10 )
= $true ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f228,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X2 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ X2 @ Y1 ) ) ) ) )
= $true )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X2 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ X2 @ Y1 ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X3: $i > $o,X1: $i,X4: $i > $o] :
( ( ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X2 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ X2 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X3: $i > $o,X1: $i,X4: $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X2 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X2 @ Y0 ) ) ) )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X3: $i > $o,X1: $i,X4: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X2 @ Y0 ) ) )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X2 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X3: $i > $o,X1: $i,X4: $i > $o,X5: $i] :
( ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X2 @ Y0 ) ) ) )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X2 @ Y0 ) )
@ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X3: $i > $o,X1: $i,X4: $i > $o,X5: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X2 @ Y0 ) )
@ X5 )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X2 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X3: $i > $o,X1: $i,X4: $i > $o,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) )
= $true )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X2 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X2 @ Y0 ) )
@ X5 )
= $true ) ),
inference(or_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X3: $i > $o,X1: $i,X6: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X2 @ Y0 ) ) ) ) )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X6 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X2 @ Y0 ) )
@ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X3: $i > $o,X1: $i,X6: $i,X4: $i > $o,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X2 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X6 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X2 @ Y0 ) )
@ X5 )
= $true )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X3: $i > $o,X1: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X2 @ Y0 ) )
@ X7 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X6 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X2 @ Y0 ) )
@ X5 )
= $true )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X3: $i > $o,X1: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X6 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X2 @ Y0 ) )
@ X5 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X2 @ Y0 ) )
@ X7 )
= $true ) ),
inference(not_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X3: $i > $o,X1: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X2 @ Y0 ) )
@ X5 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X2 @ Y0 ) )
@ X7 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X6 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X8 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X2 @ Y0 ) )
@ X7 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X6 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X2 @ Y0 ) )
@ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) ) )
| ~ ( sK0 @ X2 @ X5 ) )
= $true )
| ( ( ( X4 @ X8 )
| ~ ( sK0 @ X1 @ X8 ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X6 ) )
= $true )
| ( ( ~ ( X3 @ X7 )
| ~ ( sK0 @ X2 @ X7 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) ) ) )
= $true )
| ( ( ~ ( sK0 @ X2 @ X5 ) )
= $true )
| ( ( ( X4 @ X8 )
| ~ ( sK0 @ X1 @ X8 ) )
= $true )
| ( ( ~ ( X3 @ X7 )
| ~ ( sK0 @ X2 @ X7 ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X6 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( ~ ( sK0 @ X2 @ X5 ) )
= $true )
| ( ( ~ ( X3 @ X7 )
| ~ ( sK0 @ X2 @ X7 ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) ) ) )
| ( ( ( X4 @ X8 )
| ~ ( sK0 @ X1 @ X8 ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X6 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( ( X4 @ X8 )
| ~ ( sK0 @ X1 @ X8 ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X6 ) )
= $true )
| ( ( ~ ( X3 @ X7 )
| ~ ( sK0 @ X2 @ X7 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X6 ) )
= $true )
| ( ( ~ ( sK0 @ X1 @ X8 ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) ) ) )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( ~ ( X3 @ X7 )
| ~ ( sK0 @ X2 @ X7 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f247]) ).
thf(f249,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( X4 @ X8 )
= $true )
| ( ( ~ ( X3 @ X7 )
| ~ ( sK0 @ X2 @ X7 ) )
= $true )
| ( ( ~ ( sK0 @ X1 @ X8 ) )
= $true )
| ( ( ~ ( sK0 @ X1 @ X6 ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( ~ ( sK0 @ X1 @ X8 ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) )
@ ( sK12 @ X3 @ X5 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) ) ) )
= $true )
| ( ( X4 @ X8 )
= $true )
| ( ( ~ ( sK0 @ X1 @ X6 ) )
= $true )
| ( ( ~ ( X3 @ X7 )
| ~ ( sK0 @ X2 @ X7 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( sK0 @ X1 @ X8 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) )
@ ( sK12 @ X3 @ X5 ) ) )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( X4 @ X8 )
= $true )
| ( ( ~ ( sK0 @ X1 @ X6 ) )
= $true )
| ( ( ~ ( X3 @ X7 )
| ~ ( sK0 @ X2 @ X7 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) )
@ ( sK12 @ X3 @ X5 ) ) )
| ( ( ~ ( sK0 @ X1 @ X6 ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( X4 @ X8 )
= $true )
| ( ( ~ ( X3 @ X7 )
| ~ ( sK0 @ X2 @ X7 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X8 )
= $true )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) )
@ ( sK13 @ X4 @ X6 ) )
= $false )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( ( ~ ( sK0 @ X1 @ X6 ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) )
@ ( sK12 @ X3 @ X5 ) ) )
| ( ( ~ ( X3 @ X7 )
| ~ ( sK0 @ X2 @ X7 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) )
@ ( sK12 @ X3 @ X5 ) ) )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( ( ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) )
@ ( sK13 @ X4 @ X6 ) )
= $false )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( ( ~ ( X3 @ X7 )
| ~ ( sK0 @ X2 @ X7 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( ~ ( sK0 @ X2 @ X7 ) )
= $true )
| ( ( ~ ( X3 @ X7 ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) )
@ ( sK12 @ X3 @ X5 ) ) )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( ( ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) )
@ ( sK13 @ X4 @ X6 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) )
@ ( sK13 @ X4 @ X6 ) )
= $false )
| ( ( ~ ( X3 @ X7 ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) )
@ ( sK12 @ X3 @ X5 ) ) ) ),
inference(not_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) )
@ ( sK12 @ X3 @ X5 ) ) )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( X3 @ X7 )
= $false )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( ( X4 @ X8 )
= $true )
| ( ( ^ [Y0: $i] :
( ( X4 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) )
@ ( sK13 @ X4 @ X6 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( sK0 @ X1 @ X6 ) )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( ( X3 @ X7 )
= $false )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( ( X4 @ ( sK13 @ X4 @ X6 ) )
| ~ ( sK0 @ X6 @ ( sK13 @ X4 @ X6 ) ) ) )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( ~ ( X3 @ ( sK12 @ X3 @ X5 ) )
| ~ ( sK0 @ X5 @ ( sK12 @ X3 @ X5 ) ) ) ) ),
inference(beta-eta_normalization,[],[f257]) ).
thf(f259,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( sK0 @ X1 @ X6 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( ~ ( X3 @ ( sK12 @ X3 @ X5 ) )
| ~ ( sK0 @ X5 @ ( sK12 @ X3 @ X5 ) ) ) )
| ( $false
= ( ~ ( sK0 @ X6 @ ( sK13 @ X4 @ X6 ) ) ) )
| ( ( X3 @ X7 )
= $false )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( $false
= ( sK0 @ X1 @ X8 ) ) ),
inference(or_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( sK0 @ X2 @ X7 ) )
| ( $false
= ( ~ ( X3 @ ( sK12 @ X3 @ X5 ) )
| ~ ( sK0 @ X5 @ ( sK12 @ X3 @ X5 ) ) ) )
| ( $false
= ( X4 @ ( sK13 @ X4 @ X6 ) ) )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( X3 @ X7 )
= $false )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( sK0 @ X1 @ X6 ) ) ),
inference(or_proxy_clausification,[],[f258]) ).
thf(f261,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( ~ ( sK0 @ X5 @ ( sK12 @ X3 @ X5 ) ) ) )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( ( X4 @ X8 )
= $true )
| ( ( X3 @ X7 )
= $false )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( X4 @ ( sK13 @ X4 @ X6 ) ) ) ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( X4 @ ( sK13 @ X4 @ X6 ) ) )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( ~ ( X3 @ ( sK12 @ X3 @ X5 ) ) ) )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( ( X3 @ X7 )
= $false )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) ) ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f263,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( X3 @ X7 )
= $false )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( X4 @ ( sK13 @ X4 @ X6 ) ) )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( X3 @ ( sK12 @ X3 @ X5 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X8 )
= $true )
| ( ( sK0 @ X5 @ ( sK12 @ X3 @ X5 ) )
= $true )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( X4 @ ( sK13 @ X4 @ X6 ) ) )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( ( X3 @ X7 )
= $false ) ),
inference(not_proxy_clausification,[],[f261]) ).
thf(f265,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( sK0 @ X1 @ X6 ) )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( ~ ( sK0 @ X5 @ ( sK12 @ X3 @ X5 ) ) ) )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( ( X3 @ X7 )
= $false )
| ( $false
= ( ~ ( sK0 @ X6 @ ( sK13 @ X4 @ X6 ) ) ) ) ),
inference(or_proxy_clausification,[],[f259]) ).
thf(f266,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( ~ ( X3 @ ( sK12 @ X3 @ X5 ) ) ) )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( ( X3 @ X7 )
= $false )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( ~ ( sK0 @ X6 @ ( sK13 @ X4 @ X6 ) ) ) )
| ( $false
= ( sK0 @ X1 @ X6 ) ) ),
inference(or_proxy_clausification,[],[f259]) ).
thf(f267,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( sK0 @ X1 @ X8 ) )
| ( ( X4 @ X8 )
= $true )
| ( ( X3 @ ( sK12 @ X3 @ X5 ) )
= $true )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( ( X3 @ X7 )
= $false )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( $false
= ( ~ ( sK0 @ X6 @ ( sK13 @ X4 @ X6 ) ) ) ) ),
inference(not_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( X3 @ ( sK12 @ X3 @ X5 ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( ( X3 @ X7 )
= $false )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( ( sK0 @ X6 @ ( sK13 @ X4 @ X6 ) )
= $true )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( ( sK0 @ X5 @ ( sK12 @ X3 @ X5 ) )
= $true )
| ( ( X3 @ X7 )
= $false )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( ~ ( sK0 @ X6 @ ( sK13 @ X4 @ X6 ) ) ) )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( $false
= ( sK0 @ X1 @ X8 ) ) ),
inference(not_proxy_clausification,[],[f265]) ).
thf(f270,plain,
! [X2: $i,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( sK0 @ X1 @ X8 ) )
| ( ( X3 @ X7 )
= $false )
| ( ( sK0 @ X5 @ ( sK12 @ X3 @ X5 ) )
= $true )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( X4 @ X8 )
= $true )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( ( sK0 @ X6 @ ( sK13 @ X4 @ X6 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f269]) ).
thf(f272,definition,
( spl14_1
<=> ! [X1: $i] :
( ( ( sK0 @ sK5 @ X1 )
= $false )
| ( $false
= ( sK3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
thf(f273,plain,
( ! [X1: $i] :
( ( ( sK0 @ sK5 @ X1 )
= $false )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f275,definition,
( spl14_2
<=> ! [X2: $i] :
( ( ( sK4 @ X2 )
= $true )
| ( $false
= ( sK0 @ sK6 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
thf(f276,plain,
( ! [X2: $i] :
( ( $false
= ( sK0 @ sK6 @ X2 ) )
| ( ( sK4 @ X2 )
= $true ) )
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f275]) ).
thf(f277,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f140,f275,f272]) ).
thf(f279,definition,
( spl14_3
<=> ( ( sK0 @ sK1 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
thf(f281,plain,
( ( ( sK0 @ sK1 @ sK6 )
= $true )
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f279]) ).
thf(f282,plain,
( spl14_1
| spl14_3 ),
inference(avatar_split_clause,[],[f147,f279,f272]) ).
thf(f284,definition,
( spl14_4
<=> ( ( sK0 @ sK2 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
thf(f286,plain,
( ( ( sK0 @ sK2 @ sK5 )
= $true )
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f287,plain,
( spl14_2
| spl14_4 ),
inference(avatar_split_clause,[],[f155,f284,f275]) ).
thf(f288,plain,
( spl14_4
| spl14_3 ),
inference(avatar_split_clause,[],[f156,f279,f284]) ).
thf(f290,definition,
( spl14_5
<=> ( $false
= ( sK4 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
thf(f292,plain,
( ( $false
= ( sK4 @ sK7 ) )
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f290]) ).
thf(f293,plain,
( spl14_1
| spl14_5 ),
inference(avatar_split_clause,[],[f170,f290,f272]) ).
thf(f295,definition,
( spl14_6
<=> ( ( sK0 @ sK1 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
thf(f297,plain,
( ( ( sK0 @ sK1 @ sK7 )
= $true )
| ~ spl14_6 ),
inference(avatar_component_clause,[],[f295]) ).
thf(f298,plain,
( spl14_6
| spl14_1 ),
inference(avatar_split_clause,[],[f176,f272,f295]) ).
thf(f299,plain,
( spl14_5
| spl14_4 ),
inference(avatar_split_clause,[],[f179,f284,f290]) ).
thf(f300,plain,
( spl14_4
| spl14_6 ),
inference(avatar_split_clause,[],[f181,f295,f284]) ).
thf(f302,definition,
( spl14_7
<=> ! [X1: $i] :
( ( ( sK4 @ X1 )
= $true )
| ( $false
= ( sK0 @ sK8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_7])],[avatar_definition]) ).
thf(f303,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK8 @ X1 ) )
| ( ( sK4 @ X1 )
= $true ) )
| ~ spl14_7 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f305,definition,
( spl14_8
<=> ( ( sK3 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_8])],[avatar_definition]) ).
thf(f307,plain,
( ( ( sK3 @ sK9 )
= $true )
| ~ spl14_8 ),
inference(avatar_component_clause,[],[f305]) ).
thf(f308,plain,
( spl14_7
| spl14_8 ),
inference(avatar_split_clause,[],[f198,f305,f302]) ).
thf(f310,definition,
( spl14_9
<=> ( ( sK0 @ sK2 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_9])],[avatar_definition]) ).
thf(f312,plain,
( ( ( sK0 @ sK2 @ sK9 )
= $true )
| ~ spl14_9 ),
inference(avatar_component_clause,[],[f310]) ).
thf(f313,plain,
( spl14_7
| spl14_9 ),
inference(avatar_split_clause,[],[f204,f310,f302]) ).
thf(f315,definition,
( spl14_10
<=> ( ( sK0 @ sK1 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_10])],[avatar_definition]) ).
thf(f317,plain,
( ( ( sK0 @ sK1 @ sK8 )
= $true )
| ~ spl14_10 ),
inference(avatar_component_clause,[],[f315]) ).
thf(f318,plain,
( spl14_10
| spl14_8 ),
inference(avatar_split_clause,[],[f208,f305,f315]) ).
thf(f319,plain,
( spl14_9
| spl14_10 ),
inference(avatar_split_clause,[],[f209,f315,f310]) ).
thf(f321,definition,
( spl14_11
<=> ( ( sK3 @ sK10 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition]) ).
thf(f323,plain,
( ( ( sK3 @ sK10 )
= $true )
| ~ spl14_11 ),
inference(avatar_component_clause,[],[f321]) ).
thf(f325,definition,
( spl14_12
<=> ( $false
= ( sK4 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_12])],[avatar_definition]) ).
thf(f327,plain,
( ( $false
= ( sK4 @ sK11 ) )
| ~ spl14_12 ),
inference(avatar_component_clause,[],[f325]) ).
thf(f328,plain,
( spl14_11
| spl14_12 ),
inference(avatar_split_clause,[],[f219,f325,f321]) ).
thf(f330,definition,
( spl14_13
<=> ( ( sK0 @ sK2 @ sK10 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_13])],[avatar_definition]) ).
thf(f332,plain,
( ( ( sK0 @ sK2 @ sK10 )
= $true )
| ~ spl14_13 ),
inference(avatar_component_clause,[],[f330]) ).
thf(f333,plain,
( spl14_13
| spl14_12 ),
inference(avatar_split_clause,[],[f220,f325,f330]) ).
thf(f335,definition,
( spl14_14
<=> ( ( sK0 @ sK1 @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_14])],[avatar_definition]) ).
thf(f337,plain,
( ( ( sK0 @ sK1 @ sK11 )
= $true )
| ~ spl14_14 ),
inference(avatar_component_clause,[],[f335]) ).
thf(f338,plain,
( spl14_11
| spl14_14 ),
inference(avatar_split_clause,[],[f224,f335,f321]) ).
thf(f339,plain,
( spl14_13
| spl14_14 ),
inference(avatar_split_clause,[],[f226,f335,f330]) ).
thf(f341,definition,
( spl14_15
<=> ! [X3: $i > $o,X7: $i,X5: $i,X2: $i] :
( ( ( X3 @ X7 )
= $false )
| ( ( X3 @ ( sK12 @ X3 @ X5 ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( sK0 @ X2 @ X7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
thf(f342,plain,
( ! [X2: $i,X3: $i > $o,X7: $i,X5: $i] :
( ( ( X3 @ ( sK12 @ X3 @ X5 ) )
= $true )
| ( ( X3 @ X7 )
= $false )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( sK0 @ X2 @ X7 ) ) )
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f341]) ).
thf(f344,definition,
( spl14_16
<=> ! [X4: $i > $o,X8: $i,X6: $i,X1: $i] :
( ( ( X4 @ X8 )
= $true )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( $false
= ( X4 @ ( sK13 @ X4 @ X6 ) ) )
| ( $false
= ( sK0 @ X1 @ X8 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition]) ).
thf(f345,plain,
( ! [X1: $i,X8: $i,X6: $i,X4: $i > $o] :
( ( $false
= ( X4 @ ( sK13 @ X4 @ X6 ) ) )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( ( X4 @ X8 )
= $true ) )
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f344]) ).
thf(f346,plain,
( spl14_15
| spl14_16 ),
inference(avatar_split_clause,[],[f263,f344,f341]) ).
thf(f348,definition,
( spl14_17
<=> ! [X3: $i > $o,X7: $i,X5: $i,X2: $i] :
( ( ( sK0 @ X5 @ ( sK12 @ X3 @ X5 ) )
= $true )
| ( ( X3 @ X7 )
= $false )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_17])],[avatar_definition]) ).
thf(f349,plain,
( ! [X2: $i,X3: $i > $o,X7: $i,X5: $i] :
( ( ( sK0 @ X5 @ ( sK12 @ X3 @ X5 ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( X3 @ X7 )
= $false )
| ( $false
= ( sK0 @ X2 @ X7 ) ) )
| ~ spl14_17 ),
inference(avatar_component_clause,[],[f348]) ).
thf(f350,plain,
( spl14_17
| spl14_16 ),
inference(avatar_split_clause,[],[f264,f344,f348]) ).
thf(f352,definition,
( spl14_18
<=> ! [X4: $i > $o,X8: $i,X6: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( ( sK0 @ X6 @ ( sK13 @ X4 @ X6 ) )
= $true )
| ( ( X4 @ X8 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition]) ).
thf(f353,plain,
( ! [X1: $i,X8: $i,X6: $i,X4: $i > $o] :
( ( ( sK0 @ X6 @ ( sK13 @ X4 @ X6 ) )
= $true )
| ( $false
= ( sK0 @ X1 @ X8 ) )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( ( X4 @ X8 )
= $true ) )
| ~ spl14_18 ),
inference(avatar_component_clause,[],[f352]) ).
thf(f354,plain,
( spl14_15
| spl14_18 ),
inference(avatar_split_clause,[],[f268,f352,f341]) ).
thf(f355,plain,
( spl14_17
| spl14_18 ),
inference(avatar_split_clause,[],[f270,f352,f348]) ).
thf(f359,plain,
( ! [X2: $i,X8: $i > $o,X7: $i,X5: $i] :
( ( ( ^ [Y0: $i] :
~ ( X8 @ Y0 )
@ ( sK12
@ ^ [Y0: $i] :
~ ( X8 @ Y0 )
@ X5 ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
~ ( X8 @ Y0 )
@ X7 ) )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) ) )
| ~ spl14_15 ),
inference(primitive_instantiation,[],[f342]) ).
thf(f363,plain,
( ! [X2: $i,X8: $i > $o,X7: $i,X5: $i] :
( ( $false
= ( sK0 @ X2 @ X7 ) )
| ( $false
= ( ~ ( X8 @ X7 ) ) )
| ( ( ~ ( X8
@ ( sK12
@ ^ [Y0: $i] :
~ ( X8 @ Y0 )
@ X5 ) ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X5 ) ) )
| ~ spl14_15 ),
inference(beta-eta_normalization,[],[f359]) ).
thf(f364,plain,
( ! [X2: $i,X8: $i > $o,X7: $i,X5: $i] :
( ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( X8 @ X7 )
= $true )
| ( ( ~ ( X8
@ ( sK12
@ ^ [Y0: $i] :
~ ( X8 @ Y0 )
@ X5 ) ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X7 ) ) )
| ~ spl14_15 ),
inference(not_proxy_clausification,[],[f363]) ).
thf(f365,plain,
( ! [X2: $i,X8: $i > $o,X7: $i,X5: $i] :
( ( ( X8
@ ( sK12
@ ^ [Y0: $i] :
~ ( X8 @ Y0 )
@ X5 ) )
= $false )
| ( ( X8 @ X7 )
= $true )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( sK0 @ X2 @ X7 ) ) )
| ~ spl14_15 ),
inference(not_proxy_clausification,[],[f364]) ).
thf(f391,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X0 @ X1 )
= $true )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X3 @ X0 ) )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( $false = $true )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( ^ [Y0: $i] :
~ ( sK0 @ X0 @ Y0 )
@ X4 ) ) )
| ~ spl14_15
| ~ spl14_17 ),
inference(superposition,[],[f365,f349]) ).
thf(f397,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X3 @ X0 ) )
| ( $false
= ( ^ [Y0: $i] :
~ ( sK0 @ X0 @ Y0 )
@ X4 ) )
| ( ( sK0 @ X0 @ X1 )
= $true )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( sK0 @ X3 @ X4 ) ) )
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f391]) ).
thf(f398,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X0 @ X1 )
= $true )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( $false
= ( ~ ( sK0 @ X0 @ X4 ) ) )
| ( $false
= ( sK0 @ X3 @ X0 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( sK0 @ X2 @ X1 ) ) )
| ~ spl14_15
| ~ spl14_17 ),
inference(beta-eta_normalization,[],[f397]) ).
thf(f399,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X0 @ X4 )
= $true )
| ( ( sK0 @ X0 @ X1 )
= $true )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( sK0 @ X3 @ X0 ) ) )
| ~ spl14_15
| ~ spl14_17 ),
inference(not_proxy_clausification,[],[f398]) ).
thf(f411,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( sK4 @ ( sK12 @ X0 @ sK6 ) )
= $true )
| ( $false = $true )
| ( $false
= ( sK0 @ X1 @ sK6 ) )
| ( ( X0 @ X2 )
= $false )
| ( $false
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl14_2
| ~ spl14_17 ),
inference(superposition,[],[f276,f349]) ).
thf(f416,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( sK4 @ ( sK12 @ X0 @ sK6 ) )
= $true )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X1 @ sK6 ) )
| ( ( X0 @ X2 )
= $false ) )
| ~ spl14_2
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f411]) ).
thf(f497,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $true )
| ( $false != $false )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $true )
| ( $false
= ( sK0 @ X0 @ X2 ) ) )
| ~ spl14_15
| ~ spl14_17 ),
inference(equality_factoring,[],[f399]) ).
thf(f511,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( ( sK0 @ X2 @ X1 )
= $true )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( ( sK0 @ X0 @ X1 )
= $false ) )
| ~ spl14_15
| ~ spl14_17 ),
inference(duplicate_literal_removal,[],[f497]) ).
thf(f512,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X2 ) )
| ( ( sK0 @ X2 @ X1 )
= $true )
| ( ( sK0 @ X0 @ X1 )
= $false ) )
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f511]) ).
thf(f560,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X3 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( ( sK0 @ X0 @ X4 )
= $true )
| ( $false = $true )
| ( ( sK0 @ X0 @ X2 )
= $true ) )
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f353,f345]) ).
thf(f561,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( $false = $true )
| ( ( sK4 @ ( sK13 @ X0 @ sK6 ) )
= $true )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( ( X0 @ X2 )
= $true )
| ( $false
= ( sK0 @ X1 @ sK6 ) ) )
| ~ spl14_2
| ~ spl14_18 ),
inference(superposition,[],[f276,f353]) ).
thf(f565,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( sK4 @ ( sK13 @ X0 @ sK6 ) )
= $true )
| ( ( X0 @ X2 )
= $true )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X1 @ sK6 ) ) )
| ~ spl14_2
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f561]) ).
thf(f568,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X3 @ X0 ) )
| ( ( sK0 @ X0 @ X2 )
= $true )
| ( ( sK0 @ X0 @ X4 )
= $true ) )
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f560]) ).
thf(f582,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ sK6 ) )
| ( ( sK4 @ X1 )
= $true )
| ( ( sK4 @ X3 )
= $true )
| ( $false = $true )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( $false
= ( sK0 @ X0 @ sK6 ) )
| ( ( sK0 @ X2 @ X3 )
= $false ) )
| ~ spl14_2
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f345,f565]) ).
thf(f589,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ sK6 ) )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK4 @ X3 )
= $true )
| ( $false
= ( sK0 @ X0 @ sK6 ) )
| ( ( sK0 @ X2 @ X3 )
= $false )
| ( ( sK4 @ X1 )
= $true ) )
| ~ spl14_2
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f582]) ).
thf(f591,definition,
( spl14_24
<=> ! [X2: $i,X3: $i] :
( ( ( sK0 @ X2 @ X3 )
= $false )
| ( $false
= ( sK0 @ X2 @ sK6 ) )
| ( ( sK4 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl14_24])],[avatar_definition]) ).
thf(f592,plain,
( ! [X2: $i,X3: $i] :
( ( $false
= ( sK0 @ X2 @ sK6 ) )
| ( ( sK0 @ X2 @ X3 )
= $false )
| ( ( sK4 @ X3 )
= $true ) )
| ~ spl14_24 ),
inference(avatar_component_clause,[],[f591]) ).
thf(f602,plain,
( spl14_24
| spl14_24
| ~ spl14_2
| ~ spl14_16
| ~ spl14_18 ),
inference(avatar_split_clause,[],[f589,f352,f344,f275,f591,f591]) ).
thf(f632,plain,
( ! [X0: $i] :
( ( ( sK4 @ X0 )
= $true )
| ( $false
= ( sK0 @ sK1 @ X0 ) )
| ( $false = $true ) )
| ~ spl14_3
| ~ spl14_24 ),
inference(superposition,[],[f281,f592]) ).
thf(f634,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK1 @ X0 ) )
| ( ( sK4 @ X0 )
= $true ) )
| ~ spl14_3
| ~ spl14_24 ),
inference(trivial_inequality_removal,[],[f632]) ).
thf(f659,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X2 ) )
| ( ( sK0 @ X2 @ X1 )
= $true )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( $false != $false )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( ( sK0 @ X2 @ X1 )
= $true ) )
| ~ spl14_16
| ~ spl14_18 ),
inference(equality_factoring,[],[f568]) ).
thf(f683,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X2 ) )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $true )
| ( $false != $false ) )
| ~ spl14_16
| ~ spl14_18 ),
inference(duplicate_literal_removal,[],[f659]) ).
thf(f684,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X2 ) )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $true ) )
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f683]) ).
thf(f705,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK6 @ X0 )
= $true )
| ( $false = $true )
| ( $false
= ( sK0 @ sK1 @ X0 ) ) )
| ~ spl14_3
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f684,f281]) ).
thf(f712,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK5 @ X0 )
= $true )
| ( $false
= ( sK0 @ sK2 @ X0 ) )
| ( $false = $true ) )
| ~ spl14_4
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f286,f684]) ).
thf(f724,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK2 @ X0 ) )
| ( ( sK0 @ sK5 @ X0 )
= $true ) )
| ~ spl14_4
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f712]) ).
thf(f733,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK1 @ X0 ) )
| ( ( sK0 @ sK6 @ X0 )
= $true ) )
| ~ spl14_3
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f705]) ).
thf(f851,plain,
( ( $false = $true )
| ( ( sK0 @ sK5 @ sK10 )
= $true )
| ~ spl14_4
| ~ spl14_13
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f724,f332]) ).
thf(f857,plain,
( ( ( sK0 @ sK5 @ sK9 )
= $true )
| ( $false = $true )
| ~ spl14_4
| ~ spl14_9
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f312,f724]) ).
thf(f862,plain,
( ( ( sK0 @ sK5 @ sK10 )
= $true )
| ~ spl14_4
| ~ spl14_13
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f851]) ).
thf(f865,plain,
( ( ( sK0 @ sK5 @ sK9 )
= $true )
| ~ spl14_4
| ~ spl14_9
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f857]) ).
thf(f916,plain,
( ( $false
= ( sK3 @ sK10 ) )
| ( $false = $true )
| ~ spl14_1
| ~ spl14_4
| ~ spl14_13
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f862,f273]) ).
thf(f924,plain,
( ( $false
= ( sK3 @ sK10 ) )
| ~ spl14_1
| ~ spl14_4
| ~ spl14_13
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f916]) ).
thf(f929,plain,
( ( $false = $true )
| ~ spl14_1
| ~ spl14_4
| ~ spl14_11
| ~ spl14_13
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f323,f924]) ).
thf(f932,plain,
( $false
| ~ spl14_1
| ~ spl14_4
| ~ spl14_11
| ~ spl14_13
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f929]) ).
thf(f933,plain,
( ~ spl14_1
| ~ spl14_4
| ~ spl14_11
| ~ spl14_13
| ~ spl14_16
| ~ spl14_18 ),
inference(avatar_contradiction_clause,[],[f932]) ).
thf(f950,plain,
( ( $false = $true )
| ( $false
= ( sK3 @ sK9 ) )
| ~ spl14_1
| ~ spl14_4
| ~ spl14_9
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f865,f273]) ).
thf(f956,plain,
( ( $false
= ( sK3 @ sK9 ) )
| ~ spl14_1
| ~ spl14_4
| ~ spl14_9
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f950]) ).
thf(f962,plain,
( ( $false = $true )
| ~ spl14_1
| ~ spl14_4
| ~ spl14_8
| ~ spl14_9
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f956,f307]) ).
thf(f966,plain,
( $false
| ~ spl14_1
| ~ spl14_4
| ~ spl14_8
| ~ spl14_9
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f962]) ).
thf(f967,plain,
( ~ spl14_1
| ~ spl14_4
| ~ spl14_8
| ~ spl14_9
| ~ spl14_16
| ~ spl14_18 ),
inference(avatar_contradiction_clause,[],[f966]) ).
thf(f975,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK1 @ X0 ) )
| ( $false = $true )
| ( ( sK0 @ sK8 @ X0 )
= $true ) )
| ~ spl14_10
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f684,f317]) ).
thf(f978,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK1 @ X0 ) )
| ( ( sK0 @ sK8 @ X0 )
= $true ) )
| ~ spl14_10
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f975]) ).
thf(f1027,plain,
( ( ( sK0 @ sK6 @ sK7 )
= $true )
| ( $false = $true )
| ~ spl14_3
| ~ spl14_6
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f733,f297]) ).
thf(f1042,plain,
( ( ( sK0 @ sK6 @ sK7 )
= $true )
| ~ spl14_3
| ~ spl14_6
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f1027]) ).
thf(f1137,plain,
( ( $false = $true )
| ( ( sK0 @ sK8 @ sK11 )
= $true )
| ~ spl14_10
| ~ spl14_14
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f337,f978]) ).
thf(f1142,plain,
( ( ( sK0 @ sK8 @ sK11 )
= $true )
| ~ spl14_10
| ~ spl14_14
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f1137]) ).
thf(f1453,plain,
( ( $false = $true )
| ( ( sK4 @ sK11 )
= $true )
| ~ spl14_7
| ~ spl14_10
| ~ spl14_14
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f303,f1142]) ).
thf(f1461,plain,
( ( ( sK4 @ sK11 )
= $true )
| ~ spl14_7
| ~ spl14_10
| ~ spl14_14
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f1453]) ).
thf(f1465,plain,
( ( $false = $true )
| ~ spl14_7
| ~ spl14_10
| ~ spl14_12
| ~ spl14_14
| ~ spl14_16
| ~ spl14_18 ),
inference(forward_demodulation,[],[f1461,f327]) ).
thf(f1466,plain,
( $false
| ~ spl14_7
| ~ spl14_10
| ~ spl14_12
| ~ spl14_14
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f1465]) ).
thf(f1467,plain,
( ~ spl14_7
| ~ spl14_10
| ~ spl14_12
| ~ spl14_14
| ~ spl14_16
| ~ spl14_18 ),
inference(avatar_contradiction_clause,[],[f1466]) ).
thf(f1666,plain,
( ( $false = $true )
| ( ( sK4 @ sK7 )
= $true )
| ~ spl14_2
| ~ spl14_3
| ~ spl14_6
| ~ spl14_16
| ~ spl14_18 ),
inference(superposition,[],[f276,f1042]) ).
thf(f1671,plain,
( ( ( sK4 @ sK7 )
= $true )
| ~ spl14_2
| ~ spl14_3
| ~ spl14_6
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f1666]) ).
thf(f1678,plain,
( ( $false = $true )
| ~ spl14_2
| ~ spl14_3
| ~ spl14_5
| ~ spl14_6
| ~ spl14_16
| ~ spl14_18 ),
inference(forward_demodulation,[],[f1671,f292]) ).
thf(f1679,plain,
( $false
| ~ spl14_2
| ~ spl14_3
| ~ spl14_5
| ~ spl14_6
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f1678]) ).
thf(f1680,plain,
( ~ spl14_2
| ~ spl14_3
| ~ spl14_5
| ~ spl14_6
| ~ spl14_16
| ~ spl14_18 ),
inference(avatar_contradiction_clause,[],[f1679]) ).
thf(f1708,plain,
( ! [X2: $i,X8: $i > $o,X7: $i,X5: $i] :
( ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( ( ^ [Y0: $i] :
~ ( X8 @ Y0 )
@ ( sK12
@ ^ [Y0: $i] :
~ ( X8 @ Y0 )
@ X5 ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
~ ( X8 @ Y0 )
@ X7 ) ) )
| ~ spl14_15 ),
inference(primitive_instantiation,[],[f342]) ).
thf(f1722,plain,
( ! [X2: $i,X8: $i > $o,X7: $i,X5: $i] :
( ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( ~ ( X8
@ ( sK12
@ ^ [Y0: $i] :
~ ( X8 @ Y0 )
@ X5 ) ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( $false
= ( ~ ( X8 @ X7 ) ) ) )
| ~ spl14_15 ),
inference(beta-eta_normalization,[],[f1708]) ).
thf(f1723,plain,
( ! [X2: $i,X8: $i > $o,X7: $i,X5: $i] :
( ( $false
= ( sK0 @ X2 @ X7 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( X8
@ ( sK12
@ ^ [Y0: $i] :
~ ( X8 @ Y0 )
@ X5 ) )
= $false )
| ( $false
= ( ~ ( X8 @ X7 ) ) ) )
| ~ spl14_15 ),
inference(not_proxy_clausification,[],[f1722]) ).
thf(f1724,plain,
( ! [X2: $i,X8: $i > $o,X7: $i,X5: $i] :
( ( ( X8
@ ( sK12
@ ^ [Y0: $i] :
~ ( X8 @ Y0 )
@ X5 ) )
= $false )
| ( $false
= ( sK0 @ X2 @ X7 ) )
| ( $false
= ( sK0 @ X2 @ X5 ) )
| ( ( X8 @ X7 )
= $true ) )
| ~ spl14_15 ),
inference(not_proxy_clausification,[],[f1723]) ).
thf(f1795,plain,
( ( $false = $true )
| ( ( sK4 @ sK7 )
= $true )
| ~ spl14_3
| ~ spl14_6
| ~ spl14_24 ),
inference(superposition,[],[f297,f634]) ).
thf(f1808,plain,
( ( ( sK4 @ sK7 )
= $true )
| ~ spl14_3
| ~ spl14_6
| ~ spl14_24 ),
inference(trivial_inequality_removal,[],[f1795]) ).
thf(f1822,plain,
( ( $false = $true )
| ~ spl14_3
| ~ spl14_5
| ~ spl14_6
| ~ spl14_24 ),
inference(forward_demodulation,[],[f1808,f292]) ).
thf(f1823,plain,
( $false
| ~ spl14_3
| ~ spl14_5
| ~ spl14_6
| ~ spl14_24 ),
inference(trivial_inequality_removal,[],[f1822]) ).
thf(f1824,plain,
( ~ spl14_3
| ~ spl14_5
| ~ spl14_6
| ~ spl14_24 ),
inference(avatar_contradiction_clause,[],[f1823]) ).
thf(f2008,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK1 @ X0 ) )
| ( $false = $true )
| ( ( sK0 @ sK8 @ X0 )
= $true ) )
| ~ spl14_10
| ~ spl14_15
| ~ spl14_17 ),
inference(superposition,[],[f512,f317]) ).
thf(f2021,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK2 @ X0 ) )
| ( ( sK0 @ sK5 @ X0 )
= $true )
| ( $false = $true ) )
| ~ spl14_4
| ~ spl14_15
| ~ spl14_17 ),
inference(superposition,[],[f286,f512]) ).
thf(f2053,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK1 @ X0 ) )
| ( ( sK0 @ sK8 @ X0 )
= $true ) )
| ~ spl14_10
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f2008]) ).
thf(f2056,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK2 @ X0 ) )
| ( ( sK0 @ sK5 @ X0 )
= $true ) )
| ~ spl14_4
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f2021]) ).
thf(f2146,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ X1 )
= $false )
| ( $false = $true )
| ( ( sK0 @ X2 @ X3 )
= $false )
| ( ( sK4 @ X1 )
= $true )
| ( $false
= ( sK0 @ X0 @ sK6 ) )
| ( $false
= ( sK0 @ X2 @ sK6 ) )
| ( ( ^ [Y0: $i] :
~ ( sK4 @ Y0 )
@ X3 )
= $false ) )
| ~ spl14_2
| ~ spl14_15
| ~ spl14_17 ),
inference(superposition,[],[f1724,f416]) ).
thf(f2152,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK4 @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
~ ( sK4 @ Y0 )
@ X3 )
= $false )
| ( ( sK0 @ X2 @ X3 )
= $false )
| ( $false
= ( sK0 @ X2 @ sK6 ) )
| ( $false
= ( sK0 @ X0 @ sK6 ) ) )
| ~ spl14_2
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f2146]) ).
thf(f2153,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ sK6 ) )
| ( $false
= ( ~ ( sK4 @ X3 ) ) )
| ( $false
= ( sK0 @ X0 @ sK6 ) )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK0 @ X2 @ X3 )
= $false )
| ( ( sK4 @ X1 )
= $true ) )
| ~ spl14_2
| ~ spl14_15
| ~ spl14_17 ),
inference(beta-eta_normalization,[],[f2152]) ).
thf(f2154,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ sK6 ) )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK4 @ X3 )
= $true )
| ( ( sK0 @ X2 @ X3 )
= $false )
| ( ( sK4 @ X1 )
= $true )
| ( $false
= ( sK0 @ X0 @ sK6 ) ) )
| ~ spl14_2
| ~ spl14_15
| ~ spl14_17 ),
inference(not_proxy_clausification,[],[f2153]) ).
thf(f2158,plain,
( spl14_24
| spl14_24
| ~ spl14_2
| ~ spl14_15
| ~ spl14_17 ),
inference(avatar_split_clause,[],[f2154,f348,f341,f275,f591,f591]) ).
thf(f2324,plain,
( ( $false = $true )
| ( ( sK0 @ sK8 @ sK11 )
= $true )
| ~ spl14_10
| ~ spl14_14
| ~ spl14_15
| ~ spl14_17 ),
inference(superposition,[],[f2053,f337]) ).
thf(f2337,plain,
( ( ( sK0 @ sK8 @ sK11 )
= $true )
| ~ spl14_10
| ~ spl14_14
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f2324]) ).
thf(f2348,plain,
( ( $false = $true )
| ( ( sK4 @ sK11 )
= $true )
| ~ spl14_7
| ~ spl14_10
| ~ spl14_14
| ~ spl14_15
| ~ spl14_17 ),
inference(superposition,[],[f2337,f303]) ).
thf(f2363,plain,
( ( ( sK4 @ sK11 )
= $true )
| ~ spl14_7
| ~ spl14_10
| ~ spl14_14
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f2348]) ).
thf(f2367,plain,
( ( $false = $true )
| ~ spl14_7
| ~ spl14_10
| ~ spl14_12
| ~ spl14_14
| ~ spl14_15
| ~ spl14_17 ),
inference(forward_demodulation,[],[f2363,f327]) ).
thf(f2368,plain,
( $false
| ~ spl14_7
| ~ spl14_10
| ~ spl14_12
| ~ spl14_14
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f2367]) ).
thf(f2369,plain,
( ~ spl14_7
| ~ spl14_10
| ~ spl14_12
| ~ spl14_14
| ~ spl14_15
| ~ spl14_17 ),
inference(avatar_contradiction_clause,[],[f2368]) ).
thf(f2539,plain,
( ( $false = $true )
| ( ( sK0 @ sK5 @ sK9 )
= $true )
| ~ spl14_4
| ~ spl14_9
| ~ spl14_15
| ~ spl14_17 ),
inference(superposition,[],[f2056,f312]) ).
thf(f2547,plain,
( ( ( sK0 @ sK5 @ sK10 )
= $true )
| ( $false = $true )
| ~ spl14_4
| ~ spl14_13
| ~ spl14_15
| ~ spl14_17 ),
inference(superposition,[],[f332,f2056]) ).
thf(f2552,plain,
( ( ( sK0 @ sK5 @ sK9 )
= $true )
| ~ spl14_4
| ~ spl14_9
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f2539]) ).
thf(f2559,plain,
( ( ( sK0 @ sK5 @ sK10 )
= $true )
| ~ spl14_4
| ~ spl14_13
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f2547]) ).
thf(f2583,plain,
( ( $false
= ( sK3 @ sK9 ) )
| ( $false = $true )
| ~ spl14_1
| ~ spl14_4
| ~ spl14_9
| ~ spl14_15
| ~ spl14_17 ),
inference(superposition,[],[f273,f2552]) ).
thf(f2592,plain,
( ( $false
= ( sK3 @ sK9 ) )
| ~ spl14_1
| ~ spl14_4
| ~ spl14_9
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f2583]) ).
thf(f2595,plain,
( ( $false
= ( sK3 @ sK10 ) )
| ( $false = $true )
| ~ spl14_1
| ~ spl14_4
| ~ spl14_13
| ~ spl14_15
| ~ spl14_17 ),
inference(superposition,[],[f2559,f273]) ).
thf(f2605,plain,
( ( $false
= ( sK3 @ sK10 ) )
| ~ spl14_1
| ~ spl14_4
| ~ spl14_13
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f2595]) ).
thf(f2611,plain,
( ( $false = $true )
| ~ spl14_1
| ~ spl14_4
| ~ spl14_11
| ~ spl14_13
| ~ spl14_15
| ~ spl14_17 ),
inference(superposition,[],[f2605,f323]) ).
thf(f2615,plain,
( $false
| ~ spl14_1
| ~ spl14_4
| ~ spl14_11
| ~ spl14_13
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f2611]) ).
thf(f2616,plain,
( ~ spl14_1
| ~ spl14_4
| ~ spl14_11
| ~ spl14_13
| ~ spl14_15
| ~ spl14_17 ),
inference(avatar_contradiction_clause,[],[f2615]) ).
thf(f2617,plain,
( ( $false = $true )
| ~ spl14_1
| ~ spl14_4
| ~ spl14_8
| ~ spl14_9
| ~ spl14_15
| ~ spl14_17 ),
inference(forward_demodulation,[],[f307,f2592]) ).
thf(f2618,plain,
( $false
| ~ spl14_1
| ~ spl14_4
| ~ spl14_8
| ~ spl14_9
| ~ spl14_15
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f2617]) ).
thf(f2619,plain,
( ~ spl14_1
| ~ spl14_4
| ~ spl14_8
| ~ spl14_9
| ~ spl14_15
| ~ spl14_17 ),
inference(avatar_contradiction_clause,[],[f2618]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f277]) ).
cnf(s2,plain,
( spl14_1
| spl14_3 ),
inference(sat_conversion,[],[f282]) ).
cnf(s3,plain,
( spl14_2
| spl14_4 ),
inference(sat_conversion,[],[f287]) ).
cnf(s4,plain,
( spl14_3
| spl14_4 ),
inference(sat_conversion,[],[f288]) ).
cnf(s5,plain,
( spl14_1
| spl14_5 ),
inference(sat_conversion,[],[f293]) ).
cnf(s6,plain,
( spl14_1
| spl14_6 ),
inference(sat_conversion,[],[f298]) ).
cnf(s7,plain,
( spl14_4
| spl14_5 ),
inference(sat_conversion,[],[f299]) ).
cnf(s8,plain,
( spl14_4
| spl14_6 ),
inference(sat_conversion,[],[f300]) ).
cnf(s9,plain,
( spl14_7
| spl14_8 ),
inference(sat_conversion,[],[f308]) ).
cnf(s10,plain,
( spl14_7
| spl14_9 ),
inference(sat_conversion,[],[f313]) ).
cnf(s11,plain,
( spl14_8
| spl14_10 ),
inference(sat_conversion,[],[f318]) ).
cnf(s12,plain,
( spl14_9
| spl14_10 ),
inference(sat_conversion,[],[f319]) ).
cnf(s13,plain,
( spl14_11
| spl14_12 ),
inference(sat_conversion,[],[f328]) ).
cnf(s14,plain,
( spl14_12
| spl14_13 ),
inference(sat_conversion,[],[f333]) ).
cnf(s15,plain,
( spl14_11
| spl14_14 ),
inference(sat_conversion,[],[f338]) ).
cnf(s16,plain,
( spl14_13
| spl14_14 ),
inference(sat_conversion,[],[f339]) ).
cnf(s17,plain,
( spl14_15
| spl14_16 ),
inference(sat_conversion,[],[f346]) ).
cnf(s18,plain,
( spl14_16
| spl14_17 ),
inference(sat_conversion,[],[f350]) ).
cnf(s19,plain,
( spl14_15
| spl14_18 ),
inference(sat_conversion,[],[f354]) ).
cnf(s20,plain,
( spl14_17
| spl14_18 ),
inference(sat_conversion,[],[f355]) ).
cnf(s28,plain,
( spl14_24
| ~ spl14_16
| ~ spl14_18
| ~ spl14_2
| spl14_24 ),
inference(sat_conversion,[],[f602]) ).
cnf(s29,plain,
( ~ spl14_2
| ~ spl14_16
| ~ spl14_18
| spl14_24 ),
inference(rat,[],[s28]) ).
cnf(s42,plain,
( ~ spl14_1
| ~ spl14_4
| ~ spl14_11
| ~ spl14_13
| ~ spl14_16
| ~ spl14_18 ),
inference(sat_conversion,[],[f933]) ).
cnf(s44,plain,
( ~ spl14_1
| ~ spl14_4
| ~ spl14_8
| ~ spl14_9
| ~ spl14_16
| ~ spl14_18 ),
inference(sat_conversion,[],[f967]) ).
cnf(s72,plain,
( ~ spl14_7
| ~ spl14_10
| ~ spl14_12
| ~ spl14_14
| ~ spl14_16
| ~ spl14_18 ),
inference(sat_conversion,[],[f1467]) ).
cnf(s81,plain,
( ~ spl14_2
| ~ spl14_3
| ~ spl14_5
| ~ spl14_6
| ~ spl14_16
| ~ spl14_18 ),
inference(sat_conversion,[],[f1680]) ).
cnf(s91,plain,
( ~ spl14_3
| ~ spl14_5
| ~ spl14_6
| ~ spl14_24 ),
inference(sat_conversion,[],[f1824]) ).
cnf(s94,plain,
( spl14_24
| ~ spl14_15
| ~ spl14_17
| ~ spl14_2
| spl14_24 ),
inference(sat_conversion,[],[f2158]) ).
cnf(s95,plain,
( ~ spl14_2
| ~ spl14_15
| ~ spl14_17
| spl14_24 ),
inference(rat,[],[s94]) ).
cnf(s101,plain,
( ~ spl14_7
| ~ spl14_10
| ~ spl14_12
| ~ spl14_14
| ~ spl14_15
| ~ spl14_17 ),
inference(sat_conversion,[],[f2369]) ).
cnf(s115,plain,
( ~ spl14_1
| ~ spl14_4
| ~ spl14_11
| ~ spl14_13
| ~ spl14_15
| ~ spl14_17 ),
inference(sat_conversion,[],[f2616]) ).
cnf(s116,plain,
( ~ spl14_1
| ~ spl14_4
| ~ spl14_8
| ~ spl14_9
| ~ spl14_15
| ~ spl14_17 ),
inference(sat_conversion,[],[f2619]) ).
cnf(s117,plain,
( spl14_15
| spl14_1 ),
inference(rat,[],[s29,s17,s19,s1,s91,s5,s2,s6]) ).
cnf(s118,plain,
( ~ spl14_15
| spl14_24
| ~ spl14_2 ),
inference(rat,[],[s29,s18,s20,s95]) ).
cnf(s119,plain,
spl14_1,
inference(rat,[],[s118,s117,s91,s1,s2,s5,s6]) ).
cnf(s120,plain,
( spl14_4
| ~ spl14_3
| spl14_15
| ~ spl14_2 ),
inference(rat,[],[s81,s7,s8,s19,s17]) ).
cnf(s121,plain,
( spl14_7
| ~ spl14_4
| spl14_15 ),
inference(rat,[],[s44,s9,s10,s19,s17,s119]) ).
cnf(s122,plain,
( spl14_11
| ~ spl14_10
| ~ spl14_7
| spl14_15 ),
inference(rat,[],[s72,s13,s15,s19,s17]) ).
cnf(s123,plain,
( ~ spl14_10
| ~ spl14_4
| spl14_15 ),
inference(rat,[],[s72,s14,s16,s42,s122,s19,s17,s121,s119]) ).
cnf(s124,plain,
( ~ spl14_4
| spl14_15 ),
inference(rat,[],[s44,s11,s12,s123,s19,s17,s119]) ).
cnf(s125,plain,
( spl14_15
| ~ spl14_2 ),
inference(rat,[],[s120,s4,s124]) ).
cnf(s126,plain,
( spl14_11
| spl14_9
| ~ spl14_18
| ~ spl14_16 ),
inference(rat,[],[s72,s13,s15,s12,s10]) ).
cnf(s127,plain,
( spl14_9
| ~ spl14_4
| ~ spl14_18
| ~ spl14_16 ),
inference(rat,[],[s72,s14,s16,s42,s126,s10,s12,s119]) ).
cnf(s128,plain,
( spl14_11
| spl14_8
| ~ spl14_18
| ~ spl14_16 ),
inference(rat,[],[s72,s13,s15,s11,s9]) ).
cnf(s129,plain,
( ~ spl14_9
| ~ spl14_4
| ~ spl14_18
| ~ spl14_16 ),
inference(rat,[],[s72,s14,s16,s42,s128,s9,s11,s44,s119]) ).
cnf(s130,plain,
( ~ spl14_4
| ~ spl14_18
| ~ spl14_16 ),
inference(rat,[],[s129,s127]) ).
cnf(s132,plain,
( spl14_11
| spl14_9
| ~ spl14_17
| ~ spl14_15 ),
inference(rat,[],[s101,s13,s15,s12,s10]) ).
cnf(s133,plain,
( spl14_9
| ~ spl14_4
| ~ spl14_17
| ~ spl14_15 ),
inference(rat,[],[s101,s14,s16,s115,s132,s10,s12,s119]) ).
cnf(s134,plain,
( spl14_11
| spl14_8
| ~ spl14_17
| ~ spl14_15 ),
inference(rat,[],[s101,s13,s15,s11,s9]) ).
cnf(s135,plain,
( ~ spl14_9
| ~ spl14_4
| ~ spl14_17
| ~ spl14_15 ),
inference(rat,[],[s101,s14,s16,s115,s134,s9,s11,s116,s119]) ).
cnf(s136,plain,
( ~ spl14_4
| ~ spl14_17
| ~ spl14_15 ),
inference(rat,[],[s135,s133]) ).
cnf(s137,plain,
( spl14_4
| ~ spl14_24 ),
inference(rat,[],[s91,s4,s7,s8]) ).
cnf(s138,plain,
( ~ spl14_4
| ~ spl14_15 ),
inference(rat,[],[s130,s18,s20,s136]) ).
cnf(s139,plain,
( ~ spl14_15
| ~ spl14_2 ),
inference(rat,[],[s138,s137,s118]) ).
cnf(s140,plain,
~ spl14_2,
inference(rat,[],[s139,s125]) ).
cnf(s141,plain,
spl14_4,
inference(rat,[],[s3,s140]) ).
cnf(s142,plain,
spl14_15,
inference(rat,[],[s124,s141]) ).
cnf(s143,plain,
$false,
inference(rat,[],[s138,s142,s141]) ).
thf(f2621,plain,
$false,
inference(avatar_sat_refutation,[],[s143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL877^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n026.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 10:22:27 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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
% 0.68/0.38 % (405519)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.68/0.38 % (405527)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=1344475226: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)
% 0.68/0.38 % (405530)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.68/0.38 % (405530)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
% 0.68/0.38 % (405524)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3753849539:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.68/0.38 % (405526)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=860305030:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.68/0.38 % (405525)lrs+10_16_si=on:nwc=1.5:random_seed=4286427849:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.68/0.38 % (405528)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2756562236:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.68/0.38 % (405529)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=765078703:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.68/0.38 % (405530)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=2197349546:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.68/0.38 % (405526)Instruction limit reached!
% 0.68/0.38 % (405526)------------------------------
% 0.68/0.38 % (405526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (405526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (405526)CaDiCaL version: 2.1.3
% 0.68/0.38 % (405526)Termination reason: Instruction limit
% 0.68/0.38 % (405526)Termination phase: Preprocessing 1
% 0.68/0.38 % (405526)Time elapsed: 0.002 s
% 0.68/0.38 % (405526)Peak memory usage: 10 MB
% 0.68/0.38 % (405526)Instructions burned: 4 (million)
% 0.68/0.38 % (405525)Instruction limit reached!
% 0.68/0.38 % (405525)------------------------------
% 0.68/0.38 % (405525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (405525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (405525)CaDiCaL version: 2.1.3
% 0.68/0.38 % (405525)Termination reason: Instruction limit
% 0.68/0.38 % (405525)Termination phase: Saturation
% 0.68/0.38 % (405525)Time elapsed: 0.010 s
% 0.68/0.38 % (405525)Peak memory usage: 12 MB
% 0.68/0.38 % (405525)Instructions burned: 20 (million)
% 0.68/0.38 % (405528)Instruction limit reached!
% 0.68/0.38 % (405528)------------------------------
% 0.68/0.38 % (405528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (405528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (405528)CaDiCaL version: 2.1.3
% 0.68/0.38 % (405528)Termination reason: Instruction limit
% 0.68/0.38 % (405528)Termination phase: Saturation
% 0.68/0.38 % (405528)Time elapsed: 0.014 s
% 0.68/0.38 % (405528)Peak memory usage: 12 MB
% 0.68/0.38 % (405528)Instructions burned: 26 (million)
% 0.68/0.38 % (405538)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=169901695:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.38 % (405538)Instruction limit reached!
% 0.68/0.38 % (405538)------------------------------
% 0.68/0.38 % (405538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (405538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (405538)CaDiCaL version: 2.1.3
% 0.68/0.38 % (405538)Termination reason: Instruction limit
% 0.68/0.38 % (405538)Termination phase: Function definition elimination
% 0.68/0.38 % (405538)Time elapsed: 0.003 s
% 0.68/0.38 % (405538)Peak memory usage: 10 MB
% 0.68/0.38 % (405538)Instructions burned: 6 (million)
% 0.68/0.38 % (405530)Refutation not found, incomplete strategy
% 0.68/0.38 % (405530)------------------------------
% 0.68/0.38 % (405530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.42 % (405530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.42 % (405530)CaDiCaL version: 2.1.3
% 0.68/0.42 % (405530)Termination reason: Refutation not found, incomplete strategy
% 0.68/0.42 % (405530)Time elapsed: 0.027 s
% 0.68/0.42 % (405530)Peak memory usage: 13 MB
% 0.68/0.42 % (405530)Instructions burned: 48 (million)
% 0.68/0.42 % (405530)------------------------------
% 0.68/0.42 % (405530)------------------------------
% 0.68/0.42 % (405540)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.42 % (405539)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3878322876:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.68/0.42 % (405540)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1004073257:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.68/0.42 % (405539)Instruction limit reached!
% 0.68/0.42 % (405539)------------------------------
% 0.68/0.42 % (405539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.42 % (405539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.42 % (405539)CaDiCaL version: 2.1.3
% 0.68/0.42 % (405539)Termination reason: Instruction limit
% 0.68/0.42 % (405539)Termination phase: Property scanning
% 0.68/0.42 % (405539)Time elapsed: 0.003 s
% 0.68/0.42 % (405539)Peak memory usage: 10 MB
% 0.68/0.42 % (405539)Instructions burned: 6 (million)
% 0.68/0.42 % (405540)Instruction limit reached!
% 0.68/0.42 % (405540)------------------------------
% 0.68/0.42 % (405540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.42 % (405540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.42 % (405540)CaDiCaL version: 2.1.3
% 0.68/0.42 % (405540)Termination reason: Instruction limit
% 0.68/0.42 % (405540)Termination phase: Property scanning
% 0.68/0.42 % (405540)Time elapsed: 0.003 s
% 0.68/0.42 % (405540)Peak memory usage: 10 MB
% 0.68/0.42 % (405540)Instructions burned: 7 (million)
% 0.68/0.42 % (405529)Instruction limit reached!
% 0.68/0.42 % (405529)------------------------------
% 0.68/0.42 % (405529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.42 % (405529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.42 % (405529)CaDiCaL version: 2.1.3
% 0.68/0.42 % (405529)Termination reason: Instruction limit
% 0.68/0.42 % (405529)Termination phase: Saturation
% 0.68/0.42 % (405529)Time elapsed: 0.038 s
% 0.68/0.42 % (405529)Peak memory usage: 12 MB
% 0.68/0.42 % (405529)Instructions burned: 76 (million)
% 0.68/0.42 % (405543)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
% 0.68/0.42 % (405543)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.42 % (405524)Instruction limit reached!
% 0.68/0.42 % (405524)------------------------------
% 0.68/0.42 % (405524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.42 % (405524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.42 % (405524)CaDiCaL version: 2.1.3
% 0.68/0.42 % (405524)Termination reason: Instruction limit
% 0.68/0.42 % (405524)Termination phase: Saturation
% 0.68/0.42 % (405524)Time elapsed: 0.045 s
% 0.68/0.42 % (405524)Peak memory usage: 12 MB
% 0.68/0.42 % (405524)Instructions burned: 87 (million)
% 0.68/0.42 % (405543)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=883975546:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.68/0.42 % (405542)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=851477858:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.68/0.42 % (405548)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.68/0.42 % (405547)lrs+10_1_si=on:cs=on:random_seed=3403881697:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.68/0.42 % (405548)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=908169893:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.46 % (405548)Instruction limit reached!
% 0.68/0.46 % (405548)------------------------------
% 0.68/0.46 % (405548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (405548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (405548)CaDiCaL version: 2.1.3
% 0.68/0.46 % (405548)Termination reason: Instruction limit
% 0.68/0.46 % (405548)Termination phase: Function definition elimination
% 0.68/0.46 % (405548)Time elapsed: 0.003 s
% 0.68/0.46 % (405548)Peak memory usage: 10 MB
% 0.68/0.46 % (405548)Instructions burned: 6 (million)
% 0.68/0.46 % (405547)Instruction limit reached!
% 0.68/0.46 % (405547)------------------------------
% 0.68/0.46 % (405547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (405547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (405547)CaDiCaL version: 2.1.3
% 0.68/0.46 % (405547)Termination reason: Instruction limit
% 0.68/0.46 % (405547)Termination phase: Saturation
% 0.68/0.46 % (405547)Time elapsed: 0.004 s
% 0.68/0.46 % (405547)Peak memory usage: 11 MB
% 0.68/0.46 % (405547)Instructions burned: 9 (million)
% 0.68/0.46 % (405542)Instruction limit reached!
% 0.68/0.46 % (405542)------------------------------
% 0.68/0.46 % (405542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (405542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (405542)CaDiCaL version: 2.1.3
% 0.68/0.46 % (405542)Termination reason: Instruction limit
% 0.68/0.46 % (405542)Termination phase: Saturation
% 0.68/0.46 % (405542)Time elapsed: 0.010 s
% 0.68/0.46 % (405542)Peak memory usage: 11 MB
% 0.68/0.46 % (405542)Instructions burned: 13 (million)
% 0.68/0.46 % (405543)Instruction limit reached!
% 0.68/0.46 % (405543)------------------------------
% 0.68/0.46 % (405543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (405543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (405543)CaDiCaL version: 2.1.3
% 0.68/0.46 % (405543)Termination reason: Instruction limit
% 0.68/0.46 % (405543)Termination phase: Saturation
% 0.68/0.46 % (405543)Time elapsed: 0.014 s
% 0.68/0.46 % (405543)Peak memory usage: 12 MB
% 0.68/0.46 % (405543)Instructions burned: 30 (million)
% 0.68/0.46 % (405549)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=560429028:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.68/0.46 % (405546)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1502760755:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.68/0.46 % (405549)Refutation not found, incomplete strategy
% 0.68/0.46 % (405549)------------------------------
% 0.68/0.46 % (405549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (405549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (405549)CaDiCaL version: 2.1.3
% 0.68/0.46 % (405549)Termination reason: Refutation not found, incomplete strategy
% 0.68/0.46 % (405549)Time elapsed: 0.010 s
% 0.68/0.46 % (405549)Peak memory usage: 12 MB
% 0.68/0.46 % (405549)Instructions burned: 19 (million)
% 0.68/0.46 % (405549)------------------------------
% 0.68/0.46 % (405549)------------------------------
% 0.68/0.46 % (405554)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1634709846:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.68/0.46 % (405555)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1729774194:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.68/0.46 % (405557)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=41234962:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.68/0.46 % (405556)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4131715026:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.68/0.46 % (405554)Refutation not found, incomplete strategy
% 0.68/0.46 % (405554)------------------------------
% 0.68/0.46 % (405554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (405554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.49 % (405554)CaDiCaL version: 2.1.3
% 1.41/0.49 % (405554)Termination reason: Refutation not found, incomplete strategy
% 1.41/0.49 % (405554)Time elapsed: 0.006 s
% 1.41/0.49 % (405554)Peak memory usage: 12 MB
% 1.41/0.49 % (405554)Instructions burned: 12 (million)
% 1.41/0.49 % (405554)------------------------------
% 1.41/0.49 % (405554)------------------------------
% 1.41/0.49 % (405556)Instruction limit reached!
% 1.41/0.49 % (405556)------------------------------
% 1.41/0.49 % (405556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.49 % (405556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.49 % (405556)CaDiCaL version: 2.1.3
% 1.41/0.49 % (405556)Termination reason: Instruction limit
% 1.41/0.49 % (405556)Termination phase: Saturation
% 1.41/0.49 % (405556)Time elapsed: 0.006 s
% 1.41/0.49 % (405556)Peak memory usage: 11 MB
% 1.41/0.49 % (405556)Instructions burned: 14 (million)
% 1.41/0.49 % (405560)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=337047446:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.41/0.49 % (405555)Instruction limit reached!
% 1.41/0.49 % (405555)------------------------------
% 1.41/0.49 % (405555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.49 % (405555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.49 % (405555)CaDiCaL version: 2.1.3
% 1.41/0.49 % (405555)Termination reason: Instruction limit
% 1.41/0.49 % (405555)Termination phase: Saturation
% 1.41/0.49 % (405555)Time elapsed: 0.015 s
% 1.41/0.49 % (405555)Peak memory usage: 12 MB
% 1.41/0.49 % (405555)Instructions burned: 25 (million)
% 1.41/0.49 % (405560)Instruction limit reached!
% 1.41/0.49 % (405560)------------------------------
% 1.41/0.49 % (405560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.49 % (405560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.49 % (405560)CaDiCaL version: 2.1.3
% 1.41/0.49 % (405560)Termination reason: Instruction limit
% 1.41/0.49 % (405560)Termination phase: Saturation
% 1.41/0.49 % (405560)Time elapsed: 0.007 s
% 1.41/0.49 % (405560)Peak memory usage: 11 MB
% 1.41/0.49 % (405560)Instructions burned: 15 (million)
% 1.41/0.49 % (405565)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=184918301:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.41/0.49 % (405565)Instruction limit reached!
% 1.41/0.49 % (405565)------------------------------
% 1.41/0.49 % (405565)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.49 % (405565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.49 % (405565)CaDiCaL version: 2.1.3
% 1.41/0.49 % (405565)Termination reason: Instruction limit
% 1.41/0.49 % (405565)Termination phase: Property scanning
% 1.41/0.49 % (405565)Time elapsed: 0.003 s
% 1.41/0.49 % (405565)Peak memory usage: 10 MB
% 1.41/0.49 % (405565)Instructions burned: 6 (million)
% 1.41/0.49 % (405568)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1667415819:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.41/0.49 % (405546)Instruction limit reached!
% 1.41/0.49 % (405546)------------------------------
% 1.41/0.49 % (405546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.49 % (405546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.49 % (405546)CaDiCaL version: 2.1.3
% 1.41/0.49 % (405546)Termination reason: Instruction limit
% 1.41/0.49 % (405546)Termination phase: Saturation
% 1.41/0.49 % (405546)Time elapsed: 0.047 s
% 1.41/0.49 % (405546)Peak memory usage: 12 MB
% 1.41/0.49 % (405546)Instructions burned: 87 (million)
% 1.41/0.49 % (405569)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2664782133:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.41/0.49 % (405566)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2264669513:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.41/0.49 % (405571)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 1.41/0.49 % (405571)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.41/0.50 % (405568)Instruction limit reached!
% 1.41/0.50 % (405568)------------------------------
% 1.41/0.50 % (405568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (405568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (405568)CaDiCaL version: 2.1.3
% 1.41/0.50 % (405568)Termination reason: Instruction limit
% 1.41/0.50 % (405568)Termination phase: Saturation
% 1.41/0.50 % (405568)Time elapsed: 0.011 s
% 1.41/0.50 % (405568)Peak memory usage: 11 MB
% 1.41/0.50 % (405568)Instructions burned: 23 (million)
% 1.41/0.50 % (405571)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=1979479418:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.41/0.50 % (405573)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.41/0.50 % (405573)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=2364316455:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.41/0.50 % (405571)Instruction limit reached!
% 1.41/0.50 % (405571)------------------------------
% 1.41/0.50 % (405571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (405571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (405571)CaDiCaL version: 2.1.3
% 1.41/0.50 % (405571)Termination reason: Instruction limit
% 1.41/0.50 % (405571)Termination phase: Saturation
% 1.41/0.50 % (405571)Time elapsed: 0.007 s
% 1.41/0.50 % (405571)Peak memory usage: 12 MB
% 1.41/0.50 % (405571)Instructions burned: 15 (million)
% 1.41/0.50 % (405573)Instruction limit reached!
% 1.41/0.50 % (405573)------------------------------
% 1.41/0.50 % (405573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (405573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (405573)CaDiCaL version: 2.1.3
% 1.41/0.50 % (405573)Termination reason: Instruction limit
% 1.41/0.50 % (405573)Termination phase: Property scanning
% 1.41/0.50 % (405573)Time elapsed: 0.004 s
% 1.41/0.50 % (405573)Peak memory usage: 11 MB
% 1.41/0.50 % (405573)Instructions burned: 8 (million)
% 1.41/0.50 % (405576)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=364690862:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.41/0.50 % (405566)Instruction limit reached!
% 1.41/0.50 % (405566)------------------------------
% 1.41/0.50 % (405566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (405566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (405566)CaDiCaL version: 2.1.3
% 1.41/0.50 % (405566)Termination reason: Instruction limit
% 1.41/0.50 % (405566)Termination phase: Saturation
% 1.41/0.50 % (405566)Time elapsed: 0.026 s
% 1.41/0.50 % (405566)Peak memory usage: 12 MB
% 1.41/0.50 % (405566)Instructions burned: 26 (million)
% 1.41/0.50 % (405569)Instruction limit reached!
% 1.41/0.50 % (405569)------------------------------
% 1.41/0.50 % (405569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (405569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (405569)CaDiCaL version: 2.1.3
% 1.41/0.50 % (405569)Termination reason: Instruction limit
% 1.41/0.50 % (405569)Termination phase: Saturation
% 1.41/0.50 % (405569)Time elapsed: 0.033 s
% 1.41/0.50 % (405569)Peak memory usage: 12 MB
% 1.41/0.50 % (405569)Instructions burned: 60 (million)
% 1.41/0.50 % (405579)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=767050064:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.41/0.50 % (405580)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2922543203:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.41/0.50 % (405527)Instruction limit reached!
% 1.41/0.50 % (405527)------------------------------
% 1.41/0.50 % (405527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (405527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (405527)CaDiCaL version: 2.1.3
% 1.41/0.50 % (405527)Termination reason: Instruction limit
% 1.41/0.50 % (405527)Termination phase: Saturation
% 1.41/0.50 % (405527)Time elapsed: 0.169 s
% 1.41/0.50 % (405527)Peak memory usage: 15 MB
% 1.41/0.50 % (405527)Instructions burned: 638 (million)
% 1.41/0.50 % (405576)Instruction limit reached!
% 1.41/0.50 % (405576)------------------------------
% 1.41/0.50 % (405576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (405576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (405576)CaDiCaL version: 2.1.3
% 1.41/0.50 % (405576)Termination reason: Instruction limit
% 1.41/0.50 % (405576)Termination phase: Saturation
% 1.41/0.50 % (405576)Time elapsed: 0.016 s
% 1.41/0.50 % (405576)Peak memory usage: 12 MB
% 1.41/0.50 % (405576)Instructions burned: 32 (million)
% 1.41/0.50 % (405579)Instruction limit reached!
% 1.41/0.50 % (405579)------------------------------
% 1.41/0.50 % (405579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (405579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (405579)CaDiCaL version: 2.1.3
% 1.41/0.50 % (405579)Termination reason: Instruction limit
% 1.41/0.50 % (405579)Termination phase: Saturation
% 1.41/0.50 % (405579)Time elapsed: 0.008 s
% 1.41/0.50 % (405579)Peak memory usage: 11 MB
% 1.41/0.50 % (405579)Instructions burned: 8 (million)
% 1.41/0.50 % (405580)Instruction limit reached!
% 1.41/0.50 % (405580)------------------------------
% 1.41/0.50 % (405580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (405580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (405580)CaDiCaL version: 2.1.3
% 1.41/0.50 % (405580)Termination reason: Instruction limit
% 1.41/0.50 % (405580)Termination phase: Saturation
% 1.41/0.50 % (405580)Time elapsed: 0.010 s
% 1.41/0.50 % (405580)Peak memory usage: 11 MB
% 1.41/0.50 % (405580)Instructions burned: 24 (million)
% 1.41/0.50 % (405586)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3819240526:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.41/0.50 % (405583)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=469311042:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.41/0.50 % (405582)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=589056266:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.41/0.50 % (405587)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=813687067:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.41/0.50 % (405590)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.41/0.50 % (405583)Refutation not found, incomplete strategy
% 1.41/0.50 % (405583)------------------------------
% 1.41/0.50 % (405583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (405583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (405583)CaDiCaL version: 2.1.3
% 1.41/0.50 % (405583)Termination reason: Refutation not found, incomplete strategy
% 1.41/0.50 % (405583)Time elapsed: 0.009 s
% 1.41/0.50 % (405583)Peak memory usage: 12 MB
% 1.41/0.50 % (405583)Instructions burned: 18 (million)
% 1.41/0.50 % (405583)------------------------------
% 1.41/0.50 % (405583)------------------------------
% 1.41/0.50 % (405557) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-405519-405557"...
% 1.41/0.50 % (405587)Refutation not found, incomplete strategy
% 1.41/0.50 % (405587)------------------------------
% 1.41/0.50 % (405587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (405587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (405587)CaDiCaL version: 2.1.3
% 1.41/0.50 % (405587)Termination reason: Refutation not found, incomplete strategy
% 1.41/0.50 % (405587)Time elapsed: 0.007 s
% 1.41/0.50 % (405587)Peak memory usage: 12 MB
% 1.41/0.50 % (405587)Instructions burned: 14 (million)
% 1.41/0.50 % (405590)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2841792695:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.41/0.50 % (405588)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2042361365:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.41/0.50 % (405587)------------------------------
% 1.41/0.50 % (405587)------------------------------
% 1.41/0.50 % (405582)Instruction limit reached!
% 1.41/0.50 % (405582)------------------------------
% 1.41/0.50 % (405582)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (405582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (405582)CaDiCaL version: 2.1.3
% 1.41/0.50 % (405582)Termination reason: Instruction limit
% 1.41/0.50 % (405582)Termination phase: Saturation
% 1.41/0.50 % (405582)Time elapsed: 0.012 s
% 1.41/0.50 % (405582)Peak memory usage: 12 MB
% 1.41/0.50 % (405582)Instructions burned: 20 (million)
% 1.41/0.50 % (405590)Instruction limit reached!
% 1.41/0.50 % (405590)------------------------------
% 1.41/0.50 % (405590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (405590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (405590)CaDiCaL version: 2.1.3
% 1.41/0.50 % (405590)Termination reason: Instruction limit
% 1.41/0.50 % (405590)Termination phase: Saturation
% 1.41/0.50 % (405590)Time elapsed: 0.003 s
% 1.41/0.50 % (405590)Peak memory usage: 10 MB
% 1.41/0.50 % (405590)Instructions burned: 7 (million)
% 1.41/0.50 % (405557)...printing done.
% 1.41/0.50 % (405557)Refutation found. Thanks to Tanya!
% 1.41/0.50 % SZS status Theorem for theBenchmark
% 1.41/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 1.41/0.51 % (405557)------------------------------
% 1.41/0.51 % (405557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.51 % (405557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.51 % (405557)CaDiCaL version: 2.1.3
% 1.41/0.51 % (405557)Termination reason: Refutation
% 1.41/0.51 % (405557)Time elapsed: 0.120 s
% 1.41/0.51 % (405557)Peak memory usage: 13 MB
% 1.41/0.51 % (405557)Instructions burned: 234 (million)
% 1.41/0.51 % (405519)Success in time 0.249 s
% 1.41/0.51 % Vampire exiting
%------------------------------------------------------------------------------