%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL872^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:14:38 AM UTC 2026
% Result : Theorem 0.20s 0.34s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 34
% Syntax : Number of formulae : 281 ( 57 unt; 0 typ; 25 def)
% Number of atoms : 2364 ( 492 equ; 0 cnn)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 3265 ( 446 ~; 622 |; 53 &;1914 @)
% ( 26 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 331 ( 331 >; 0 *; 0 +; 0 <<)
% Number of symbols : 91 ( 86 usr; 35 con; 0-4 aty)
% ( 159 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 722 ( 0 sgn 262 !; 2 ?; 722 :)
% 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,
i: $i > $i > $o ).
thf(func_def_33,type,
j: $i > $i > $o ).
thf(func_def_34,type,
k: $i > $i > $o ).
thf(func_def_35,type,
l: $i > $i > $o ).
thf(func_def_36,type,
confluence: ( $i > $i > $o ) > ( $i > $i > $o ) > ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vIMP: $o > $o > $o ).
thf(func_def_46,type,
vAND: $o > $o > $o ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_49,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
sF0: $o ).
thf(func_def_54,type,
sF1: $o ).
thf(func_def_55,type,
sK2: $i > $i > $i ).
thf(func_def_59,type,
sK6: $i > ( $i > $o ) > $i ).
thf(func_def_60,type,
sK7: $i > ( $i > $o ) > $i ).
thf(func_def_62,type,
sK9: $i > $o ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
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,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
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,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i > $i > $o,X3: $i > $i > $o] :
! [X4: $i,X6: $i,X5: $i] :
( ( ( X2 @ X4 @ X6 )
& ( X0 @ X4 @ X5 ) )
=> ? [X7: $i] :
( ( X1 @ X5 @ X7 )
& ( X3 @ X6 @ X7 ) ) ) )
= confluence ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',confluence) ).
thf(f33,conjecture,
( ( confluence @ i @ j @ k @ l )
<=> ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mdia @ i @ ( mbox @ j @ X0 ) ) @ ( mbox @ k @ ( mdia @ l @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f34,negated_conjecture,
~ ( ( confluence @ i @ j @ k @ l )
<=> ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mdia @ i @ ( mbox @ j @ X0 ) ) @ ( mbox @ k @ ( mdia @ l @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
thf(f38,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f39,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f49,plain,
~ ( ( confluence @ i @ j @ k @ l )
<=> ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mdia @ i @ ( mbox @ j @ X0 ) ) @ ( mbox @ k @ ( mdia @ l @ X0 ) ) ) ) ) ),
inference(rectify,[],[f34]) ).
thf(f50,plain,
( ( confluence @ i @ j @ k @ l )
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ i @ ( mbox @ j @ Y0 ) ) @ ( mbox @ k @ ( mdia @ l @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f52,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f63,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i > $i > $o,X3: $i > $i > $o] :
! [X4: $i,X5: $i,X6: $i] :
( ( ( X2 @ X4 @ X5 )
& ( X0 @ X4 @ X6 ) )
=> ? [X7: $i] :
( ( X1 @ X6 @ X7 )
& ( X3 @ X5 @ X7 ) ) ) )
= confluence ),
inference(rectify,[],[f32]) ).
thf(f64,plain,
( confluence
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i > $i > $o,Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y0 @ Y6 @ Y4 )
& ( Y2 @ Y6 @ Y5 ) )
=> ( ?? @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y5 @ Y7 )
& ( Y1 @ Y4 @ Y7 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f65,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f66,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f70,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f77,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f80,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f81,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f83,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f84,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f90,plain,
( ( confluence @ i @ j @ k @ l )
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ i @ ( mbox @ j @ Y0 ) ) @ ( mbox @ k @ ( mdia @ l @ Y0 ) ) ) ) ) ),
inference(flattening,[],[f50]) ).
thf(f91,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f94,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f95,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f99,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f104,plain,
( ( confluence @ i @ j @ k @ l )
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ i @ ( mbox @ j @ Y0 ) ) @ ( mbox @ k @ ( mdia @ l @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f110,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f112,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f114,plain,
( confluence
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i > $i > $o,Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y0 @ Y6 @ Y4 )
& ( Y2 @ Y6 @ Y5 ) )
=> ( ?? @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y5 @ Y7 )
& ( Y1 @ Y4 @ Y7 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f121,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f127,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,[],[f99,f94,f112]) ).
thf(f134,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,[],[f121,f112,f95,f112]) ).
thf(f135,plain,
( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i > $i > $o,Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y0 @ Y6 @ Y4 )
& ( Y2 @ Y6 @ Y5 ) )
=> ( ?? @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y5 @ Y7 )
& ( Y1 @ Y4 @ Y7 ) ) ) ) ) ) )
@ i
@ j
@ k
@ l )
!= ( ^ [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 ) ) )
@ i
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ j
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ k
@ ( ^ [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 ) ) )
@ l
@ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f104,f114,f91,f110,f127,f134,f95,f95,f134]) ).
thf(f136,definition,
( sF0
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i > $i > $o,Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y0 @ Y6 @ Y4 )
& ( Y2 @ Y6 @ Y5 ) )
=> ( ?? @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y5 @ Y7 )
& ( Y1 @ Y4 @ Y7 ) ) ) ) ) ) )
@ i
@ j
@ k
@ l ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f137,definition,
( sF1
= ( ^ [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 ) ) )
@ i
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ j
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ k
@ ( ^ [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 ) ) )
@ l
@ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f138,plain,
sF1 != sF0,
inference(definition_folding,[],[f135,f137,f136]) ).
thf(f139,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i > $i > $o,Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y0 @ Y6 @ Y4 )
& ( Y2 @ Y6 @ Y5 ) )
=> ( ?? @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y5 @ Y7 )
& ( Y1 @ Y4 @ Y7 ) ) ) ) ) ) )
@ i
@ j
@ k
@ l ) ) ),
inference(iff_proxy_clausification,[],[f136]) ).
thf(f140,plain,
( ( $false = sF0 )
| ( $true
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i > $i > $o,Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y0 @ Y6 @ Y4 )
& ( Y2 @ Y6 @ Y5 ) )
=> ( ?? @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y5 @ Y7 )
& ( Y1 @ Y4 @ Y7 ) ) ) ) ) ) )
@ i
@ j
@ k
@ l ) ) ),
inference(iff_proxy_clausification,[],[f136]) ).
thf(f141,plain,
( ( $false = sF0 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( i @ Y2 @ Y0 )
& ( k @ Y2 @ Y1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( l @ Y1 @ Y3 )
& ( j @ Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X1: $i] :
( ( $false = sF0 )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( i @ Y2 @ Y0 )
& ( k @ Y2 @ Y1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( l @ Y1 @ Y3 )
& ( j @ Y0 @ Y3 ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X1: $i] :
( ( $false = sF0 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( i @ Y1 @ X1 )
& ( k @ Y1 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( l @ Y0 @ Y2 )
& ( j @ X1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
! [X2: $i,X1: $i] :
( ( $false = sF0 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( i @ Y1 @ X1 )
& ( k @ Y1 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( l @ Y0 @ Y2 )
& ( j @ X1 @ Y2 ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( i @ Y0 @ X1 )
& ( k @ Y0 @ X2 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( l @ X2 @ Y1 )
& ( j @ X1 @ Y1 ) ) ) ) ) )
| ( $false = sF0 ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( i @ Y0 @ X1 )
& ( k @ Y0 @ X2 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( l @ X2 @ Y1 )
& ( j @ X1 @ Y1 ) ) ) )
@ X3 ) )
| ( $false = sF0 ) ),
inference(pi_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF0 )
| ( ( ( ( i @ X3 @ X1 )
& ( k @ X3 @ X2 ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( l @ X2 @ Y0 )
& ( j @ X1 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( i @ X3 @ X1 )
& ( k @ X3 @ X2 ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( l @ X2 @ Y0 )
& ( j @ X1 @ Y0 ) ) ) )
| ( $false = sF0 ) ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( k @ X3 @ X2 ) )
| ( $false = sF0 )
| ( $false
= ( i @ X3 @ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( l @ X2 @ Y0 )
& ( j @ X1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( l @ X2 @ Y0 )
& ( j @ X1 @ Y0 ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( $false = sF0 )
| ( $false
= ( k @ X3 @ X2 ) )
| ( $false
= ( i @ X3 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( i @ X3 @ X1 ) )
| ( $false
= ( k @ X3 @ X2 ) )
| ( $false = sF0 )
| ( $true
= ( ( l @ X2 @ ( sK2 @ X1 @ X2 ) )
& ( j @ X1 @ ( sK2 @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF0 )
| ( $false
= ( i @ X3 @ X1 ) )
| ( $false
= ( k @ X3 @ X2 ) )
| ( $true
= ( j @ X1 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF0 )
| ( $true
= ( l @ X2 @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( i @ X3 @ X1 ) )
| ( $false
= ( k @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f151]) ).
thf(f154,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( i @ Y2 @ Y0 )
& ( k @ Y2 @ Y1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( l @ Y1 @ Y3 )
& ( j @ Y0 @ Y3 ) ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f155,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( i @ Y2 @ Y0 )
& ( k @ Y2 @ Y1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( l @ Y1 @ Y3 )
& ( j @ Y0 @ Y3 ) ) ) ) ) )
@ sK3 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( $true = sF0 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( i @ Y1 @ sK3 )
& ( k @ Y1 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( l @ Y0 @ Y2 )
& ( j @ sK3 @ Y2 ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( i @ Y1 @ sK3 )
& ( k @ Y1 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( l @ Y0 @ Y2 )
& ( j @ sK3 @ Y2 ) ) ) ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( i @ Y0 @ sK3 )
& ( k @ Y0 @ sK4 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( l @ sK4 @ Y1 )
& ( j @ sK3 @ Y1 ) ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( i @ Y0 @ sK3 )
& ( k @ Y0 @ sK4 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( l @ sK4 @ Y1 )
& ( j @ sK3 @ Y1 ) ) ) )
@ sK5 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( ( ( ( i @ sK5 @ sK3 )
& ( k @ sK5 @ sK4 ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( l @ sK4 @ Y0 )
& ( j @ sK3 @ Y0 ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( ( $true = sF0 )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( l @ sK4 @ Y0 )
& ( j @ sK3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $true = sF0 )
| ( $true
= ( ( i @ sK5 @ sK3 )
& ( k @ sK5 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( $true
= ( k @ sK5 @ sK4 ) )
| ( $true = sF0 ) ),
inference(and_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $true = sF0 )
| ( $true
= ( i @ sK5 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f162]) ).
thf(f165,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ( l @ sK4 @ Y0 )
& ( j @ sK3 @ Y0 ) )
@ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f166,plain,
! [X1: $i] :
( ( $false
= ( ( l @ sK4 @ X1 )
& ( j @ sK3 @ X1 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $false
= ( j @ sK3 @ X1 ) )
| ( $true = sF0 )
| ( $false
= ( l @ sK4 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $true = sF0 )
| ( sF1 = $true ) ),
inference(xor_proxy_clausification,[],[f138]) ).
thf(f169,plain,
( ( sF1 = $false )
| ( $false = sF0 ) ),
inference(xor_proxy_clausification,[],[f138]) ).
thf(f170,plain,
( ( $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 > $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 ) ) )
@ i
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ j
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ k
@ ( ^ [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 ) ) )
@ l
@ Y0 ) ) ) ) ) )
| ( sF1 = $true ) ),
inference(iff_proxy_clausification,[],[f137]) ).
thf(f171,plain,
( ( sF1 = $false )
| ( $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 ) ) )
@ i
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ j
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ k
@ ( ^ [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 ) ) )
@ l
@ Y0 ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f137]) ).
thf(f172,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( l @ Y2 @ Y3 ) ) )
| ~ ( k @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( j @ Y2 @ Y3 ) ) )
| ~ ( i @ Y0 @ Y2 ) ) ) ) ) ) )
| ( sF1 = $false ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( sF1 = $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( l @ Y2 @ Y3 ) ) )
| ~ ( k @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( j @ Y2 @ Y3 ) ) )
| ~ ( i @ Y0 @ Y2 ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( l @ Y1 @ Y2 ) ) )
| ~ ( k @ X1 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( j @ Y1 @ Y2 ) ) )
| ~ ( i @ X1 @ Y1 ) ) ) ) ) )
| ( sF1 = $false ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( l @ Y1 @ Y2 ) ) )
| ~ ( k @ X1 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( j @ Y1 @ Y2 ) ) )
| ~ ( i @ X1 @ Y1 ) ) ) )
@ X2 ) )
| ( sF1 = $false ) ),
inference(pi_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i > $o,X1: $i] :
( ( sF1 = $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( l @ Y0 @ Y1 ) ) )
| ~ ( k @ X1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( j @ Y0 @ Y1 ) ) )
| ~ ( i @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
! [X2: $i > $o,X1: $i] :
( ( sF1 = $false )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( j @ Y0 @ Y1 ) ) )
| ~ ( i @ X1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( l @ Y0 @ Y1 ) ) )
| ~ ( k @ X1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( l @ Y0 @ Y1 ) ) )
| ~ ( k @ X1 @ Y0 ) ) ) )
| ( sF1 = $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( j @ Y0 @ Y1 ) ) )
| ~ ( i @ X1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( l @ Y0 @ Y1 ) ) )
| ~ ( k @ X1 @ Y0 ) )
@ X3 ) )
| ( sF1 = $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( j @ Y0 @ Y1 ) ) )
| ~ ( i @ X1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( j @ Y0 @ Y1 ) ) )
| ~ ( i @ X1 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( l @ Y0 @ Y1 ) ) )
| ~ ( k @ X1 @ Y0 ) )
@ X3 ) )
| ( sF1 = $false ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( j @ Y0 @ Y1 ) ) )
| ~ ( i @ X1 @ Y0 ) )
@ X4 ) )
| ( sF1 = $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( l @ Y0 @ Y1 ) ) )
| ~ ( k @ X1 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( l @ X3 @ Y0 ) ) )
| ~ ( k @ X1 @ X3 ) ) )
| ( sF1 = $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( j @ X4 @ Y0 ) ) )
| ~ ( i @ X1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( l @ X3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( j @ X4 @ Y0 ) ) )
| ~ ( i @ X1 @ X4 ) ) )
| ( $true
= ( ~ ( k @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( j @ X4 @ Y0 ) ) )
| ~ ( i @ X1 @ X4 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( l @ X3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( k @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( i @ X1 @ X4 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( j @ X4 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( l @ X3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( k @ X1 @ X3 ) ) )
| ( sF1 = $false ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( i @ X1 @ X4 ) )
| ( sF1 = $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( l @ X3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( k @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( j @ X4 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( l @ X3 @ Y0 ) )
@ ( sK6 @ X3 @ X2 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( j @ X4 @ Y0 ) ) ) ) )
| ( sF1 = $false )
| ( $false
= ( i @ X1 @ X4 ) )
| ( $true
= ( ~ ( k @ X1 @ X3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( j @ X4 @ Y0 ) ) )
= $false )
| ( $false
= ( i @ X1 @ X4 ) )
| ( $true
= ( ~ ( k @ X1 @ X3 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( l @ X3 @ Y0 ) )
@ ( sK6 @ X3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( l @ X3 @ Y0 ) )
@ ( sK6 @ X3 @ X2 ) ) )
| ( sF1 = $false )
| ( $false
= ( i @ X1 @ X4 ) )
| ( $true
= ( ~ ( k @ X1 @ X3 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( j @ X4 @ Y0 ) )
@ ( sK7 @ X4 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( $false
= ( i @ X1 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( j @ X4 @ Y0 ) )
@ ( sK7 @ X4 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( l @ X3 @ Y0 ) )
@ ( sK6 @ X3 @ X2 ) ) )
| ( $false
= ( k @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ~ ( X2 @ ( sK6 @ X3 @ X2 ) )
| ~ ( l @ X3 @ ( sK6 @ X3 @ X2 ) ) ) )
| ( sF1 = $false )
| ( $false
= ( k @ X1 @ X3 ) )
| ( $false
= ( ( X2 @ ( sK7 @ X4 @ X2 ) )
| ~ ( j @ X4 @ ( sK7 @ X4 @ X2 ) ) ) )
| ( $false
= ( i @ X1 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ~ ( l @ X3 @ ( sK6 @ X3 @ X2 ) ) ) )
| ( sF1 = $false )
| ( $false
= ( k @ X1 @ X3 ) )
| ( $false
= ( ( X2 @ ( sK7 @ X4 @ X2 ) )
| ~ ( j @ X4 @ ( sK7 @ X4 @ X2 ) ) ) )
| ( $false
= ( i @ X1 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( k @ X1 @ X3 ) )
| ( $false
= ( ~ ( X2 @ ( sK6 @ X3 @ X2 ) ) ) )
| ( sF1 = $false )
| ( $false
= ( ( X2 @ ( sK7 @ X4 @ X2 ) )
| ~ ( j @ X4 @ ( sK7 @ X4 @ X2 ) ) ) )
| ( $false
= ( i @ X1 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f194,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( X2 @ ( sK6 @ X3 @ X2 ) ) )
| ( $false
= ( ( X2 @ ( sK7 @ X4 @ X2 ) )
| ~ ( j @ X4 @ ( sK7 @ X4 @ X2 ) ) ) )
| ( $false
= ( k @ X1 @ X3 ) )
| ( $false
= ( i @ X1 @ X4 ) )
| ( sF1 = $false ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( X2 @ ( sK6 @ X3 @ X2 ) ) )
| ( sF1 = $false )
| ( $false
= ( k @ X1 @ X3 ) )
| ( $false
= ( i @ X1 @ X4 ) )
| ( $false
= ( ~ ( j @ X4 @ ( sK7 @ X4 @ X2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( X2 @ ( sK6 @ X3 @ X2 ) ) )
| ( $false
= ( k @ X1 @ X3 ) )
| ( sF1 = $false )
| ( ( X2 @ ( sK7 @ X4 @ X2 ) )
= $false )
| ( $false
= ( i @ X1 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f197,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( k @ X1 @ X3 ) )
| ( $false
= ( i @ X1 @ X4 ) )
| ( sF1 = $false )
| ( $true
= ( j @ X4 @ ( sK7 @ X4 @ X2 ) ) )
| ( $true
= ( X2 @ ( sK6 @ X3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f198,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( l @ X3 @ ( sK6 @ X3 @ X2 ) )
= $true )
| ( sF1 = $false )
| ( $false
= ( ( X2 @ ( sK7 @ X4 @ X2 ) )
| ~ ( j @ X4 @ ( sK7 @ X4 @ X2 ) ) ) )
| ( $false
= ( k @ X1 @ X3 ) )
| ( $false
= ( i @ X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f192]) ).
thf(f199,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( l @ X3 @ ( sK6 @ X3 @ X2 ) )
= $true )
| ( sF1 = $false )
| ( $false
= ( k @ X1 @ X3 ) )
| ( $false
= ( ~ ( j @ X4 @ ( sK7 @ X4 @ X2 ) ) ) )
| ( $false
= ( i @ X1 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( X2 @ ( sK7 @ X4 @ X2 ) )
= $false )
| ( $false
= ( i @ X1 @ X4 ) )
| ( sF1 = $false )
| ( ( l @ X3 @ ( sK6 @ X3 @ X2 ) )
= $true )
| ( $false
= ( k @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f201,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( l @ X3 @ ( sK6 @ X3 @ X2 ) )
= $true )
| ( $false
= ( i @ X1 @ X4 ) )
| ( sF1 = $false )
| ( $false
= ( k @ X1 @ X3 ) )
| ( $true
= ( j @ X4 @ ( sK7 @ X4 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f202,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( l @ Y2 @ Y3 ) ) )
| ~ ( k @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( j @ Y2 @ Y3 ) ) )
| ~ ( i @ Y0 @ Y2 ) ) ) ) ) ) )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f203,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( l @ Y2 @ Y3 ) ) )
| ~ ( k @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( j @ Y2 @ Y3 ) ) )
| ~ ( i @ Y0 @ Y2 ) ) ) ) )
@ sK8 ) )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( l @ Y1 @ Y2 ) ) )
| ~ ( k @ sK8 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( j @ Y1 @ Y2 ) ) )
| ~ ( i @ sK8 @ Y1 ) ) ) ) ) )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
( ( sF1 = $true )
| ( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( l @ Y1 @ Y2 ) ) )
| ~ ( k @ sK8 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( j @ Y1 @ Y2 ) ) )
| ~ ( i @ sK8 @ Y1 ) ) ) )
@ sK9 ) ) ),
inference(sigma_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( ( sF1 = $true )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK9 @ Y1 )
| ~ ( l @ Y0 @ Y1 ) ) )
| ~ ( k @ sK8 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK9 @ Y1 )
| ~ ( j @ Y0 @ Y1 ) ) )
| ~ ( i @ sK8 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK9 @ Y1 )
| ~ ( j @ Y0 @ Y1 ) ) )
| ~ ( i @ sK8 @ Y0 ) ) ) ) )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( sF1 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK9 @ Y1 )
| ~ ( l @ Y0 @ Y1 ) ) )
| ~ ( k @ sK8 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f209,plain,
( ( sF1 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK9 @ Y1 )
| ~ ( l @ Y0 @ Y1 ) ) )
| ~ ( k @ sK8 @ Y0 ) )
@ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK9 @ Y0 )
| ~ ( l @ sK10 @ Y0 ) ) )
| ~ ( k @ sK8 @ sK10 ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
( ( $false
= ( ~ ( k @ sK8 @ sK10 ) ) )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK9 @ Y0 )
| ~ ( l @ sK10 @ Y0 ) ) ) ) )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f213,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK9 @ Y0 )
| ~ ( l @ sK10 @ Y0 ) ) )
= $true )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK9 @ Y0 )
| ~ ( l @ sK10 @ Y0 ) )
@ X1 ) )
| ( sF1 = $true ) ),
inference(pi_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( ( sF1 = $true )
| ( $true
= ( ~ ( sK9 @ X1 )
| ~ ( l @ sK10 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
! [X1: $i] :
( ( $true
= ( ~ ( l @ sK10 @ X1 ) ) )
| ( $true
= ( ~ ( sK9 @ X1 ) ) )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( sF1 = $true )
| ( ( l @ sK10 @ X1 )
= $false )
| ( $true
= ( ~ ( sK9 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( ( sK9 @ X1 )
= $false )
| ( sF1 = $true )
| ( ( l @ sK10 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f219,plain,
( ( $true
= ( k @ sK8 @ sK10 ) )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f220,plain,
( ( sF1 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK9 @ Y1 )
| ~ ( j @ Y0 @ Y1 ) ) )
| ~ ( i @ sK8 @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f221,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK9 @ Y1 )
| ~ ( j @ Y0 @ Y1 ) ) )
| ~ ( i @ sK8 @ Y0 ) ) )
= $false )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK9 @ Y1 )
| ~ ( j @ Y0 @ Y1 ) ) )
| ~ ( i @ sK8 @ Y0 ) )
@ sK11 )
= $false )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f221]) ).
thf(f223,plain,
( ( sF1 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK9 @ Y0 )
| ~ ( j @ sK11 @ Y0 ) ) )
| ~ ( i @ sK8 @ sK11 ) ) ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
( ( sF1 = $true )
| ( $false
= ( ~ ( i @ sK8 @ sK11 ) ) ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK9 @ Y0 )
| ~ ( j @ sK11 @ Y0 ) ) ) ) )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f226,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK9 @ Y0 )
| ~ ( j @ sK11 @ Y0 ) ) )
= $true )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK9 @ Y0 )
| ~ ( j @ sK11 @ Y0 ) )
@ X1 ) )
| ( sF1 = $true ) ),
inference(pi_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X1: $i] :
( ( sF1 = $true )
| ( $true
= ( ( sK9 @ X1 )
| ~ ( j @ sK11 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f227]) ).
thf(f229,plain,
! [X1: $i] :
( ( sF1 = $true )
| ( $true
= ( ~ ( j @ sK11 @ X1 ) ) )
| ( $true
= ( sK9 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X1: $i] :
( ( sF1 = $true )
| ( $false
= ( j @ sK11 @ X1 ) )
| ( $true
= ( sK9 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( ( sF1 = $true )
| ( ( i @ sK8 @ sK11 )
= $true ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f233,definition,
( spl12_1
<=> ( $false = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
thf(f235,plain,
( ( $false = sF0 )
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f237,definition,
( spl12_2
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $true
= ( l @ X2 @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( k @ X3 @ X2 ) )
| ( $false
= ( i @ X3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
thf(f238,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( l @ X2 @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( k @ X3 @ X2 ) )
| ( $false
= ( i @ X3 @ X1 ) ) )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f239,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f153,f237,f233]) ).
thf(f241,definition,
( spl12_3
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( i @ X3 @ X1 ) )
| ( $true
= ( j @ X1 @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( k @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
thf(f242,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( j @ X1 @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( i @ X3 @ X1 ) )
| ( $false
= ( k @ X3 @ X2 ) ) )
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f243,plain,
( spl12_1
| spl12_3 ),
inference(avatar_split_clause,[],[f152,f241,f233]) ).
thf(f245,definition,
( spl12_4
<=> ( $true
= ( i @ sK5 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
thf(f247,plain,
( ( $true
= ( i @ sK5 @ sK3 ) )
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f249,definition,
( spl12_5
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
thf(f251,plain,
( ( $true = sF0 )
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f252,plain,
( spl12_4
| spl12_5 ),
inference(avatar_split_clause,[],[f164,f249,f245]) ).
thf(f254,definition,
( spl12_6
<=> ( $true
= ( k @ sK5 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
thf(f256,plain,
( ( $true
= ( k @ sK5 @ sK4 ) )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f254]) ).
thf(f257,plain,
( spl12_5
| spl12_6 ),
inference(avatar_split_clause,[],[f163,f254,f249]) ).
thf(f259,definition,
( spl12_7
<=> ! [X1: $i] :
( ( $false
= ( j @ sK3 @ X1 ) )
| ( $false
= ( l @ sK4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
thf(f260,plain,
( ! [X1: $i] :
( ( $false
= ( l @ sK4 @ X1 ) )
| ( $false
= ( j @ sK3 @ X1 ) ) )
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f261,plain,
( spl12_7
| spl12_5 ),
inference(avatar_split_clause,[],[f167,f249,f259]) ).
thf(f263,definition,
( spl12_8
<=> ( sF1 = $false ) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
thf(f265,plain,
( ( sF1 = $false )
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f263]) ).
thf(f266,plain,
( spl12_1
| spl12_8 ),
inference(avatar_split_clause,[],[f169,f263,f233]) ).
thf(f268,definition,
( spl12_9
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
thf(f270,plain,
( ( sF1 = $true )
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f268]) ).
thf(f271,plain,
( spl12_5
| spl12_9 ),
inference(avatar_split_clause,[],[f168,f268,f249]) ).
thf(f273,definition,
( spl12_10
<=> ! [X4: $i,X3: $i,X2: $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( sK6 @ X3 @ X2 ) ) )
| ( $false
= ( i @ X1 @ X4 ) )
| ( ( X2 @ ( sK7 @ X4 @ X2 ) )
= $false )
| ( $false
= ( k @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
thf(f274,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( X2 @ ( sK6 @ X3 @ X2 ) ) )
| ( $false
= ( k @ X1 @ X3 ) )
| ( $false
= ( i @ X1 @ X4 ) )
| ( ( X2 @ ( sK7 @ X4 @ X2 ) )
= $false ) )
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f273]) ).
thf(f275,plain,
( spl12_10
| spl12_8 ),
inference(avatar_split_clause,[],[f196,f263,f273]) ).
thf(f277,definition,
( spl12_11
<=> ! [X4: $i,X3: $i,X2: $i > $o,X1: $i] :
( ( $false
= ( k @ X1 @ X3 ) )
| ( $true
= ( X2 @ ( sK6 @ X3 @ X2 ) ) )
| ( $true
= ( j @ X4 @ ( sK7 @ X4 @ X2 ) ) )
| ( $false
= ( i @ X1 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
thf(f278,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( j @ X4 @ ( sK7 @ X4 @ X2 ) ) )
| ( $false
= ( i @ X1 @ X4 ) )
| ( $false
= ( k @ X1 @ X3 ) )
| ( $true
= ( X2 @ ( sK6 @ X3 @ X2 ) ) ) )
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f277]) ).
thf(f279,plain,
( spl12_11
| spl12_8 ),
inference(avatar_split_clause,[],[f197,f263,f277]) ).
thf(f281,definition,
( spl12_12
<=> ! [X4: $i,X3: $i,X2: $i > $o,X1: $i] :
( ( ( X2 @ ( sK7 @ X4 @ X2 ) )
= $false )
| ( $false
= ( k @ X1 @ X3 ) )
| ( ( l @ X3 @ ( sK6 @ X3 @ X2 ) )
= $true )
| ( $false
= ( i @ X1 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
thf(f282,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( l @ X3 @ ( sK6 @ X3 @ X2 ) )
= $true )
| ( ( X2 @ ( sK7 @ X4 @ X2 ) )
= $false )
| ( $false
= ( i @ X1 @ X4 ) )
| ( $false
= ( k @ X1 @ X3 ) ) )
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f281]) ).
thf(f283,plain,
( spl12_8
| spl12_12 ),
inference(avatar_split_clause,[],[f200,f281,f263]) ).
thf(f285,definition,
( spl12_13
<=> ! [X4: $i,X3: $i,X2: $i > $o,X1: $i] :
( ( ( l @ X3 @ ( sK6 @ X3 @ X2 ) )
= $true )
| ( $true
= ( j @ X4 @ ( sK7 @ X4 @ X2 ) ) )
| ( $false
= ( i @ X1 @ X4 ) )
| ( $false
= ( k @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
thf(f286,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( j @ X4 @ ( sK7 @ X4 @ X2 ) ) )
| ( ( l @ X3 @ ( sK6 @ X3 @ X2 ) )
= $true )
| ( $false
= ( i @ X1 @ X4 ) )
| ( $false
= ( k @ X1 @ X3 ) ) )
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f285]) ).
thf(f287,plain,
( spl12_13
| spl12_8 ),
inference(avatar_split_clause,[],[f201,f263,f285]) ).
thf(f289,definition,
( spl12_14
<=> ! [X1: $i] :
( ( ( sK9 @ X1 )
= $false )
| ( ( l @ sK10 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition]) ).
thf(f290,plain,
( ! [X1: $i] :
( ( ( l @ sK10 @ X1 )
= $false )
| ( ( sK9 @ X1 )
= $false ) )
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f289]) ).
thf(f291,plain,
( spl12_14
| spl12_9 ),
inference(avatar_split_clause,[],[f218,f268,f289]) ).
thf(f293,definition,
( spl12_15
<=> ( $true
= ( k @ sK8 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
thf(f295,plain,
( ( $true
= ( k @ sK8 @ sK10 ) )
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f293]) ).
thf(f296,plain,
( spl12_15
| spl12_9 ),
inference(avatar_split_clause,[],[f219,f268,f293]) ).
thf(f298,definition,
( spl12_16
<=> ! [X1: $i] :
( ( $false
= ( j @ sK11 @ X1 ) )
| ( $true
= ( sK9 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_16])],[avatar_definition]) ).
thf(f299,plain,
( ! [X1: $i] :
( ( $false
= ( j @ sK11 @ X1 ) )
| ( $true
= ( sK9 @ X1 ) ) )
| ~ spl12_16 ),
inference(avatar_component_clause,[],[f298]) ).
thf(f300,plain,
( spl12_9
| spl12_16 ),
inference(avatar_split_clause,[],[f230,f298,f268]) ).
thf(f302,definition,
( spl12_17
<=> ( ( i @ sK8 @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_17])],[avatar_definition]) ).
thf(f304,plain,
( ( ( i @ sK8 @ sK11 )
= $true )
| ~ spl12_17 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f305,plain,
( spl12_9
| spl12_17 ),
inference(avatar_split_clause,[],[f231,f302,f268]) ).
thf(f306,plain,
( ( $true = $false )
| ~ spl12_8
| ~ spl12_9 ),
inference(forward_demodulation,[],[f270,f265]) ).
thf(f307,plain,
( $false
| ~ spl12_8
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f306]) ).
thf(f308,plain,
( ~ spl12_8
| ~ spl12_9 ),
inference(avatar_contradiction_clause,[],[f307]) ).
thf(f324,plain,
( ! [X0: $i,X1: $i] :
( ( ( k @ X1 @ sK10 )
= $false )
| ( $true = $false )
| ( ( i @ X1 @ X0 )
= $false )
| ( $false
= ( sK9 @ ( sK2 @ X0 @ sK10 ) ) ) )
| ~ spl12_2
| ~ spl12_14 ),
inference(constrained_superposition,[],[f290,f238]) ).
thf(f325,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK9 @ ( sK2 @ X0 @ sK10 ) ) )
| ( ( i @ X1 @ X0 )
= $false )
| ( ( k @ X1 @ sK10 )
= $false ) )
| ~ spl12_2
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f324]) ).
thf(f327,plain,
( ! [X0: $i,X1: $i] :
( ( ( i @ X1 @ sK11 )
= $false )
| ( $false
= ( k @ X1 @ X0 ) )
| ( $true = $false )
| ( $true
= ( sK9 @ ( sK2 @ sK11 @ X0 ) ) ) )
| ~ spl12_3
| ~ spl12_16 ),
inference(constrained_superposition,[],[f242,f299]) ).
thf(f329,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK9 @ ( sK2 @ sK11 @ X0 ) ) )
| ( ( i @ X1 @ sK11 )
= $false )
| ( $false
= ( k @ X1 @ X0 ) ) )
| ~ spl12_3
| ~ spl12_16 ),
inference(trivial_inequality_removal,[],[f327]) ).
thf(f333,plain,
( ! [X0: $i,X1: $i] :
( ( ( i @ X1 @ sK11 )
= $false )
| ( ( i @ X0 @ sK11 )
= $false )
| ( $true = $false )
| ( ( k @ X1 @ sK10 )
= $false )
| ( ( k @ X0 @ sK10 )
= $false ) )
| ~ spl12_2
| ~ spl12_3
| ~ spl12_14
| ~ spl12_16 ),
inference(constrained_superposition,[],[f329,f325]) ).
thf(f336,plain,
( ! [X0: $i,X1: $i] :
( ( ( k @ X1 @ sK10 )
= $false )
| ( ( k @ X0 @ sK10 )
= $false )
| ( ( i @ X0 @ sK11 )
= $false )
| ( ( i @ X1 @ sK11 )
= $false ) )
| ~ spl12_2
| ~ spl12_3
| ~ spl12_14
| ~ spl12_16 ),
inference(trivial_inequality_removal,[],[f333]) ).
thf(f338,definition,
( spl12_18
<=> ! [X0: $i] :
( ( ( k @ X0 @ sK10 )
= $false )
| ( ( i @ X0 @ sK11 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl12_18])],[avatar_definition]) ).
thf(f339,plain,
( ! [X0: $i] :
( ( ( k @ X0 @ sK10 )
= $false )
| ( ( i @ X0 @ sK11 )
= $false ) )
| ~ spl12_18 ),
inference(avatar_component_clause,[],[f338]) ).
thf(f341,plain,
( spl12_18
| spl12_18
| ~ spl12_2
| ~ spl12_3
| ~ spl12_14
| ~ spl12_16 ),
inference(avatar_split_clause,[],[f336,f298,f289,f241,f237,f338,f338]) ).
thf(f342,plain,
( ( $true = $false )
| ~ spl12_1
| ~ spl12_5 ),
inference(forward_demodulation,[],[f235,f251]) ).
thf(f343,plain,
( $false
| ~ spl12_1
| ~ spl12_5 ),
inference(trivial_inequality_removal,[],[f342]) ).
thf(f344,plain,
( ~ spl12_1
| ~ spl12_5 ),
inference(avatar_contradiction_clause,[],[f343]) ).
thf(f377,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( i @ X2 @ X1 )
= $false )
| ( $false
= ( X0 @ ( sK7 @ X1 @ X0 ) ) )
| ( $true = $false )
| ( $false
= ( k @ X2 @ sK4 ) )
| ( $false
= ( j @ sK3 @ ( sK6 @ sK4 @ X0 ) ) ) )
| ~ spl12_7
| ~ spl12_12 ),
inference(constrained_superposition,[],[f260,f282]) ).
thf(f379,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( j @ sK3 @ ( sK6 @ sK4 @ X0 ) ) )
| ( ( i @ X2 @ X1 )
= $false )
| ( $false
= ( k @ X2 @ sK4 ) )
| ( $false
= ( X0 @ ( sK7 @ X1 @ X0 ) ) ) )
| ~ spl12_7
| ~ spl12_12 ),
inference(trivial_inequality_removal,[],[f377]) ).
thf(f415,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( j @ sK3 @ ( sK7 @ X1 @ ( j @ sK3 ) ) ) )
| ( ( i @ X2 @ X3 )
= $false )
| ( $false
= ( k @ X2 @ sK4 ) )
| ( $false
= ( j @ sK3 @ ( sK7 @ X3 @ ( j @ sK3 ) ) ) )
| ( $false
= ( i @ X0 @ X1 ) )
| ( ( k @ X0 @ sK4 )
= $false ) )
| ~ spl12_7
| ~ spl12_10
| ~ spl12_12 ),
inference(constrained_superposition,[],[f274,f379]) ).
thf(f417,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( i @ X2 @ X3 )
= $false )
| ( $false
= ( j @ sK3 @ ( sK7 @ X1 @ ( j @ sK3 ) ) ) )
| ( ( k @ X0 @ sK4 )
= $false )
| ( $false
= ( j @ sK3 @ ( sK7 @ X3 @ ( j @ sK3 ) ) ) )
| ( $false
= ( i @ X0 @ X1 ) )
| ( $false
= ( k @ X2 @ sK4 ) ) )
| ~ spl12_7
| ~ spl12_10
| ~ spl12_12 ),
inference(trivial_inequality_removal,[],[f415]) ).
thf(f420,definition,
( spl12_21
<=> ! [X2: $i,X3: $i] :
( ( $false
= ( j @ sK3 @ ( sK7 @ X3 @ ( j @ sK3 ) ) ) )
| ( $false
= ( k @ X2 @ sK4 ) )
| ( ( i @ X2 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl12_21])],[avatar_definition]) ).
thf(f421,plain,
( ! [X2: $i,X3: $i] :
( ( $false
= ( j @ sK3 @ ( sK7 @ X3 @ ( j @ sK3 ) ) ) )
| ( ( i @ X2 @ X3 )
= $false )
| ( $false
= ( k @ X2 @ sK4 ) ) )
| ~ spl12_21 ),
inference(avatar_component_clause,[],[f420]) ).
thf(f423,plain,
( spl12_21
| spl12_21
| ~ spl12_7
| ~ spl12_10
| ~ spl12_12 ),
inference(avatar_split_clause,[],[f417,f281,f273,f259,f420,f420]) ).
thf(f425,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( i @ X1 @ sK3 ) )
| ( ( k @ X0 @ sK4 )
= $false )
| ( $false
= ( k @ X1 @ X2 ) )
| ( ( i @ X0 @ sK3 )
= $false )
| ( $true
= ( j @ sK3 @ ( sK6 @ X2 @ ( j @ sK3 ) ) ) )
| ( $true = $false ) )
| ~ spl12_11
| ~ spl12_21 ),
inference(constrained_superposition,[],[f421,f278]) ).
thf(f427,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( k @ X1 @ X0 ) )
| ( $false
= ( i @ X1 @ sK3 ) )
| ( $false
= ( i @ X2 @ sK3 ) )
| ( $true
= ( l @ X0 @ ( sK6 @ X0 @ ( j @ sK3 ) ) ) )
| ( $true = $false )
| ( $false
= ( k @ X2 @ sK4 ) ) )
| ~ spl12_13
| ~ spl12_21 ),
inference(constrained_superposition,[],[f286,f421]) ).
thf(f432,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( i @ X1 @ sK3 ) )
| ( $false
= ( k @ X1 @ X0 ) )
| ( $false
= ( i @ X2 @ sK3 ) )
| ( $true
= ( l @ X0 @ ( sK6 @ X0 @ ( j @ sK3 ) ) ) )
| ( $false
= ( k @ X2 @ sK4 ) ) )
| ~ spl12_13
| ~ spl12_21 ),
inference(trivial_inequality_removal,[],[f427]) ).
thf(f433,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( j @ sK3 @ ( sK6 @ X2 @ ( j @ sK3 ) ) ) )
| ( ( i @ X0 @ sK3 )
= $false )
| ( $false
= ( k @ X1 @ X2 ) )
| ( $false
= ( i @ X1 @ sK3 ) )
| ( ( k @ X0 @ sK4 )
= $false ) )
| ~ spl12_11
| ~ spl12_21 ),
inference(trivial_inequality_removal,[],[f425]) ).
thf(f435,definition,
( spl12_22
<=> ! [X0: $i,X1: $i] :
( ( ( i @ X0 @ sK3 )
= $false )
| ( $false
= ( k @ X0 @ X1 ) )
| ( ( j @ sK3 @ ( sK6 @ X1 @ ( j @ sK3 ) ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl12_22])],[avatar_definition]) ).
thf(f436,plain,
( ! [X0: $i,X1: $i] :
( ( ( j @ sK3 @ ( sK6 @ X1 @ ( j @ sK3 ) ) )
= $true )
| ( $false
= ( k @ X0 @ X1 ) )
| ( ( i @ X0 @ sK3 )
= $false ) )
| ~ spl12_22 ),
inference(avatar_component_clause,[],[f435]) ).
thf(f438,definition,
( spl12_23
<=> ! [X2: $i] :
( ( $false
= ( i @ X2 @ sK3 ) )
| ( $false
= ( k @ X2 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_23])],[avatar_definition]) ).
thf(f439,plain,
( ! [X2: $i] :
( ( $false
= ( k @ X2 @ sK4 ) )
| ( $false
= ( i @ X2 @ sK3 ) ) )
| ~ spl12_23 ),
inference(avatar_component_clause,[],[f438]) ).
thf(f442,definition,
( spl12_24
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( i @ X2 @ sK3 ) )
| ( ( l @ X1 @ ( sK6 @ X1 @ ( j @ sK3 ) ) )
= $true )
| ( ( k @ X2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl12_24])],[avatar_definition]) ).
thf(f443,plain,
( ! [X2: $i,X1: $i] :
( ( ( l @ X1 @ ( sK6 @ X1 @ ( j @ sK3 ) ) )
= $true )
| ( ( k @ X2 @ X1 )
= $false )
| ( $false
= ( i @ X2 @ sK3 ) ) )
| ~ spl12_24 ),
inference(avatar_component_clause,[],[f442]) ).
thf(f445,plain,
( spl12_23
| spl12_24
| ~ spl12_13
| ~ spl12_21 ),
inference(avatar_split_clause,[],[f432,f420,f285,f442,f438]) ).
thf(f446,plain,
( spl12_22
| spl12_23
| ~ spl12_11
| ~ spl12_21 ),
inference(avatar_split_clause,[],[f433,f420,f277,f438,f435]) ).
thf(f451,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( i @ X0 @ sK3 )
= $false )
| ( ( k @ X0 @ sK4 )
= $false )
| ( $false
= ( j @ sK3 @ ( sK6 @ sK4 @ ( j @ sK3 ) ) ) ) )
| ~ spl12_7
| ~ spl12_24 ),
inference(constrained_superposition,[],[f443,f260]) ).
thf(f458,plain,
( ! [X0: $i] :
( ( $false
= ( j @ sK3 @ ( sK6 @ sK4 @ ( j @ sK3 ) ) ) )
| ( ( i @ X0 @ sK3 )
= $false )
| ( ( k @ X0 @ sK4 )
= $false ) )
| ~ spl12_7
| ~ spl12_24 ),
inference(trivial_inequality_removal,[],[f451]) ).
thf(f468,definition,
( spl12_27
<=> ( $false
= ( j @ sK3 @ ( sK6 @ sK4 @ ( j @ sK3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_27])],[avatar_definition]) ).
thf(f470,plain,
( ( $false
= ( j @ sK3 @ ( sK6 @ sK4 @ ( j @ sK3 ) ) ) )
| ~ spl12_27 ),
inference(avatar_component_clause,[],[f468]) ).
thf(f473,plain,
( spl12_27
| spl12_23
| ~ spl12_7
| ~ spl12_24 ),
inference(avatar_split_clause,[],[f458,f442,f259,f438,f468]) ).
thf(f476,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( k @ X0 @ sK4 )
= $false )
| ( ( i @ X0 @ sK3 )
= $false ) )
| ~ spl12_22
| ~ spl12_27 ),
inference(constrained_superposition,[],[f470,f436]) ).
thf(f481,plain,
( ! [X0: $i] :
( ( ( k @ X0 @ sK4 )
= $false )
| ( ( i @ X0 @ sK3 )
= $false ) )
| ~ spl12_22
| ~ spl12_27 ),
inference(trivial_inequality_removal,[],[f476]) ).
thf(f486,plain,
( spl12_23
| ~ spl12_22
| ~ spl12_27 ),
inference(avatar_split_clause,[],[f481,f468,f435,f438]) ).
thf(f489,plain,
( ( $true = $false )
| ( $false
= ( i @ sK5 @ sK3 ) )
| ~ spl12_6
| ~ spl12_23 ),
inference(constrained_superposition,[],[f256,f439]) ).
thf(f492,plain,
( ( $false
= ( i @ sK5 @ sK3 ) )
| ~ spl12_6
| ~ spl12_23 ),
inference(trivial_inequality_removal,[],[f489]) ).
thf(f496,plain,
( ( $true = $false )
| ~ spl12_4
| ~ spl12_6
| ~ spl12_23 ),
inference(forward_demodulation,[],[f492,f247]) ).
thf(f497,plain,
( $false
| ~ spl12_4
| ~ spl12_6
| ~ spl12_23 ),
inference(trivial_inequality_removal,[],[f496]) ).
thf(f498,plain,
( ~ spl12_4
| ~ spl12_6
| ~ spl12_23 ),
inference(avatar_contradiction_clause,[],[f497]) ).
thf(f507,plain,
( ( ( i @ sK8 @ sK11 )
= $false )
| ( $true = $false )
| ~ spl12_15
| ~ spl12_18 ),
inference(constrained_superposition,[],[f295,f339]) ).
thf(f510,plain,
( ( ( i @ sK8 @ sK11 )
= $false )
| ~ spl12_15
| ~ spl12_18 ),
inference(trivial_inequality_removal,[],[f507]) ).
thf(f514,plain,
( ( $true = $false )
| ~ spl12_15
| ~ spl12_17
| ~ spl12_18 ),
inference(forward_demodulation,[],[f510,f304]) ).
thf(f515,plain,
( $false
| ~ spl12_15
| ~ spl12_17
| ~ spl12_18 ),
inference(trivial_inequality_removal,[],[f514]) ).
thf(f516,plain,
( ~ spl12_15
| ~ spl12_17
| ~ spl12_18 ),
inference(avatar_contradiction_clause,[],[f515]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f239]) ).
cnf(s2,plain,
( spl12_1
| spl12_3 ),
inference(sat_conversion,[],[f243]) ).
cnf(s3,plain,
( spl12_4
| spl12_5 ),
inference(sat_conversion,[],[f252]) ).
cnf(s4,plain,
( spl12_5
| spl12_6 ),
inference(sat_conversion,[],[f257]) ).
cnf(s5,plain,
( spl12_5
| spl12_7 ),
inference(sat_conversion,[],[f261]) ).
cnf(s6,plain,
( spl12_1
| spl12_8 ),
inference(sat_conversion,[],[f266]) ).
cnf(s7,plain,
( spl12_5
| spl12_9 ),
inference(sat_conversion,[],[f271]) ).
cnf(s8,plain,
( spl12_8
| spl12_10 ),
inference(sat_conversion,[],[f275]) ).
cnf(s9,plain,
( spl12_8
| spl12_11 ),
inference(sat_conversion,[],[f279]) ).
cnf(s10,plain,
( spl12_8
| spl12_12 ),
inference(sat_conversion,[],[f283]) ).
cnf(s11,plain,
( spl12_8
| spl12_13 ),
inference(sat_conversion,[],[f287]) ).
cnf(s12,plain,
( spl12_9
| spl12_14 ),
inference(sat_conversion,[],[f291]) ).
cnf(s13,plain,
( spl12_9
| spl12_15 ),
inference(sat_conversion,[],[f296]) ).
cnf(s14,plain,
( spl12_9
| spl12_16 ),
inference(sat_conversion,[],[f300]) ).
cnf(s15,plain,
( spl12_9
| spl12_17 ),
inference(sat_conversion,[],[f305]) ).
cnf(s16,plain,
( ~ spl12_8
| ~ spl12_9 ),
inference(sat_conversion,[],[f308]) ).
cnf(s19,plain,
( spl12_18
| ~ spl12_3
| ~ spl12_14
| ~ spl12_16
| ~ spl12_2
| spl12_18 ),
inference(sat_conversion,[],[f341]) ).
cnf(s20,plain,
( ~ spl12_2
| ~ spl12_3
| ~ spl12_14
| ~ spl12_16
| spl12_18 ),
inference(rat,[],[s19]) ).
cnf(s21,plain,
( ~ spl12_1
| ~ spl12_5 ),
inference(sat_conversion,[],[f344]) ).
cnf(s30,plain,
( spl12_21
| ~ spl12_10
| ~ spl12_12
| ~ spl12_7
| spl12_21 ),
inference(sat_conversion,[],[f423]) ).
cnf(s31,plain,
( ~ spl12_7
| ~ spl12_10
| ~ spl12_12
| spl12_21 ),
inference(rat,[],[s30]) ).
cnf(s34,plain,
( ~ spl12_13
| ~ spl12_21
| spl12_23
| spl12_24 ),
inference(sat_conversion,[],[f445]) ).
cnf(s35,plain,
( ~ spl12_11
| ~ spl12_21
| spl12_22
| spl12_23 ),
inference(sat_conversion,[],[f446]) ).
cnf(s39,plain,
( ~ spl12_7
| spl12_23
| ~ spl12_24
| spl12_27 ),
inference(sat_conversion,[],[f473]) ).
cnf(s40,plain,
( ~ spl12_22
| spl12_23
| ~ spl12_27 ),
inference(sat_conversion,[],[f486]) ).
cnf(s43,plain,
( ~ spl12_4
| ~ spl12_6
| ~ spl12_23 ),
inference(sat_conversion,[],[f498]) ).
cnf(s47,plain,
( ~ spl12_15
| ~ spl12_17
| ~ spl12_18 ),
inference(sat_conversion,[],[f516]) ).
cnf(s48,plain,
spl12_1,
inference(rat,[],[s20,s47,s12,s13,s14,s15,s16,s1,s2,s6]) ).
cnf(s49,plain,
~ spl12_5,
inference(rat,[],[s21,s48]) ).
cnf(s50,plain,
spl12_9,
inference(rat,[],[s7,s49]) ).
cnf(s51,plain,
spl12_7,
inference(rat,[],[s5,s49]) ).
cnf(s52,plain,
spl12_6,
inference(rat,[],[s4,s49]) ).
cnf(s53,plain,
spl12_4,
inference(rat,[],[s3,s49]) ).
cnf(s54,plain,
~ spl12_8,
inference(rat,[],[s16,s50]) ).
cnf(s55,plain,
~ spl12_23,
inference(rat,[],[s43,s52,s53]) ).
cnf(s56,plain,
spl12_13,
inference(rat,[],[s11,s54]) ).
cnf(s57,plain,
spl12_12,
inference(rat,[],[s10,s54]) ).
cnf(s58,plain,
spl12_11,
inference(rat,[],[s9,s54]) ).
cnf(s59,plain,
spl12_10,
inference(rat,[],[s8,s54]) ).
cnf(s60,plain,
spl12_21,
inference(rat,[],[s31,s51,s57,s59]) ).
cnf(s61,plain,
spl12_22,
inference(rat,[],[s35,s55,s58,s60]) ).
cnf(s62,plain,
spl12_24,
inference(rat,[],[s34,s56,s55,s60]) ).
cnf(s63,plain,
~ spl12_27,
inference(rat,[],[s40,s55,s61]) ).
cnf(s64,plain,
$false,
inference(rat,[],[s39,s55,s51,s63,s62]) ).
thf(f517,plain,
$false,
inference(avatar_sat_refutation,[],[s64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL872^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n001.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 10:23:20 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.34 % (1060068)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.34 % (1060078)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2401167855:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.34 % (1060074)lrs+10_16_si=on:nwc=1.5:random_seed=925774377:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.34 % (1060073)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2263859620:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.34 % (1060075)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2824478964:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.34 % (1060076)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=831937041: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)
% 0.20/0.34 % (1060077)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3315500120:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.34 % (1060075)Instruction limit reached!
% 0.20/0.34 % (1060075)------------------------------
% 0.20/0.34 % (1060075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1060075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1060075)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1060075)Termination reason: Instruction limit
% 0.20/0.34 % (1060075)Termination phase: Property scanning
% 0.20/0.34 % (1060075)Time elapsed: 0.002 s
% 0.20/0.34 % (1060075)Peak memory usage: 10 MB
% 0.20/0.34 % (1060075)Instructions burned: 4 (million)
% 0.20/0.34 % (1060079)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.34 % (1060079)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
% 0.20/0.34 % (1060074)Instruction limit reached!
% 0.20/0.34 % (1060074)------------------------------
% 0.20/0.34 % (1060074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1060074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1060074)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1060074)Termination reason: Instruction limit
% 0.20/0.34 % (1060074)Termination phase: Saturation
% 0.20/0.34 % (1060074)Time elapsed: 0.009 s
% 0.20/0.34 % (1060074)Peak memory usage: 12 MB
% 0.20/0.34 % (1060074)Instructions burned: 18 (million)
% 0.20/0.34 % (1060079)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=2108466759:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.34 % (1060077)Instruction limit reached!
% 0.20/0.34 % (1060077)------------------------------
% 0.20/0.34 % (1060077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1060077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1060077)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1060077)Termination reason: Instruction limit
% 0.20/0.34 % (1060077)Termination phase: Saturation
% 0.20/0.34 % (1060077)Time elapsed: 0.014 s
% 0.20/0.34 % (1060077)Peak memory usage: 11 MB
% 0.20/0.34 % (1060077)Instructions burned: 25 (million)
% 0.20/0.34 % (1060078)Instruction limit reached!
% 0.20/0.34 % (1060078)------------------------------
% 0.20/0.34 % (1060078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1060078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1060078)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1060078)Termination reason: Instruction limit
% 0.20/0.34 % (1060078)Termination phase: Saturation
% 0.20/0.34 % (1060078)Time elapsed: 0.021 s
% 0.20/0.34 % (1060078)Peak memory usage: 13 MB
% 0.20/0.34 % (1060078)Instructions burned: 77 (million)
% 0.20/0.34 % (1060086)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2321486629:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.34 % (1060086)Instruction limit reached!
% 0.20/0.34 % (1060086)------------------------------
% 0.20/0.34 % (1060086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1060086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1060086)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1060086)Termination reason: Instruction limit
% 0.20/0.34 % (1060086)Termination phase: Property scanning
% 0.20/0.34 % (1060086)Time elapsed: 0.002 s
% 0.20/0.34 % (1060086)Peak memory usage: 10 MB
% 0.20/0.34 % (1060086)Instructions burned: 4 (million)
% 0.20/0.34 % (1060087)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2770926600:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.34 % (1060090)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3229052357:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.34 % (1060089)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.34 % (1060087)Instruction limit reached!
% 0.20/0.34 % (1060087)------------------------------
% 0.20/0.34 % (1060087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1060087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1060087)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1060087)Termination reason: Instruction limit
% 0.20/0.34 % (1060087)Termination phase: Function definition elimination
% 0.20/0.34 % (1060087)Time elapsed: 0.003 s
% 0.20/0.34 % (1060087)Peak memory usage: 10 MB
% 0.20/0.34 % (1060087)Instructions burned: 6 (million)
% 0.20/0.34 % (1060090)Instruction limit reached!
% 0.20/0.34 % (1060090)------------------------------
% 0.20/0.34 % (1060090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1060090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1060090)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1060090)Termination reason: Instruction limit
% 0.20/0.34 % (1060090)Termination phase: Saturation
% 0.20/0.34 % (1060090)Time elapsed: 0.003 s
% 0.20/0.34 % (1060090)Peak memory usage: 11 MB
% 0.20/0.34 % (1060090)Instructions burned: 12 (million)
% 0.20/0.34 % (1060089)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1684887014:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.34 % (1060089)Instruction limit reached!
% 0.20/0.34 % (1060089)------------------------------
% 0.20/0.34 % (1060089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1060089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1060089)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1060089)Termination reason: Instruction limit
% 0.20/0.34 % (1060089)Termination phase: Saturation
% 0.20/0.34 % (1060089)Time elapsed: 0.004 s
% 0.20/0.34 % (1060089)Peak memory usage: 11 MB
% 0.20/0.34 % (1060089)Instructions burned: 9 (million)
% 0.20/0.34 % (1060092)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
% 0.20/0.34 % (1060092)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.34 % (1060079) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1060068-1060079"...
% 0.20/0.34 % (1060092)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3791579428:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.34 % (1060096)lrs+10_1_si=on:cs=on:random_seed=2746128030:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.20/0.34 % (1060073)Instruction limit reached!
% 0.20/0.34 % (1060073)------------------------------
% 0.20/0.34 % (1060073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1060073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1060073)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1060073)Termination reason: Instruction limit
% 0.20/0.34 % (1060073)Termination phase: Saturation
% 0.20/0.34 % (1060073)Time elapsed: 0.046 s
% 0.20/0.34 % (1060073)Peak memory usage: 12 MB
% 0.20/0.34 % (1060073)Instructions burned: 87 (million)
% 0.20/0.34 % (1060096)Instruction limit reached!
% 0.20/0.34 % (1060096)------------------------------
% 0.20/0.34 % (1060096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1060096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1060096)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1060096)Termination reason: Instruction limit
% 0.20/0.34 % (1060096)Termination phase: Saturation
% 0.20/0.34 % (1060096)Time elapsed: 0.002 s
% 0.20/0.34 % (1060096)Peak memory usage: 11 MB
% 0.20/0.34 % (1060096)Instructions burned: 8 (million)
% 0.20/0.34 % (1060095)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=2899434160:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.34 % (1060098)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.20/0.34 % (1060102)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1778498766:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.20/0.34 % (1060098)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=3232367957:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.34 % (1060098)Instruction limit reached!
% 0.20/0.34 % (1060098)------------------------------
% 0.20/0.34 % (1060098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1060098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1060098)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1060098)Termination reason: Instruction limit
% 0.20/0.34 % (1060098)Termination phase: shuffling
% 0.20/0.34 % (1060098)Time elapsed: 0.002 s
% 0.20/0.34 % (1060098)Peak memory usage: 10 MB
% 0.20/0.34 % (1060098)Instructions burned: 4 (million)
% 0.20/0.34 % (1060079)...printing done.
% 0.20/0.34 % (1060102)Refutation not found, incomplete strategy
% 0.20/0.34 % (1060102)------------------------------
% 0.20/0.34 % (1060102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1060102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1060102)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1060102)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.34 % (1060102)Time elapsed: 0.003 s
% 0.20/0.34 % (1060102)Peak memory usage: 12 MB
% 0.20/0.34 % (1060102)Instructions burned: 13 (million)
% 0.20/0.34 % (1060102)------------------------------
% 0.20/0.34 % (1060102)------------------------------
% 0.20/0.34 % (1060079)Refutation found. Thanks to Tanya!
% 0.20/0.34 % SZS status Theorem for theBenchmark
% 0.20/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.34 % (1060079)------------------------------
% 0.20/0.34 % (1060079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1060079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1060079)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1060079)Termination reason: Refutation
% 0.20/0.34 % (1060079)Time elapsed: 0.050 s
% 0.20/0.34 % (1060079)Peak memory usage: 13 MB
% 0.20/0.34 % (1060079)Instructions burned: 52 (million)
% 0.20/0.34 % (1060068)Success in time 0.101 s
% 0.20/0.34 % Vampire exiting
%------------------------------------------------------------------------------