%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL877^2 : 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 : n005.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 0.21s 0.34s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 24
% Syntax : Number of formulae : 208 ( 49 unt; 0 typ; 16 def)
% Number of atoms : 1484 ( 316 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 2059 ( 291 ~; 395 |; 25 &;1176 @)
% ( 17 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 243 ( 243 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 70 usr; 25 con; 0-4 aty)
% ( 132 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 497 ( 0 sgn 151 !; 1 ?; 497 :)
% 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,
vIMP: $o > $o > $o ).
thf(func_def_34,type,
vAND: $o > $o > $o ).
thf(func_def_35,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_48,type,
sF1: $o ).
thf(func_def_49,type,
sF2: $o ).
thf(func_def_51,type,
sK4: $i > $o ).
thf(func_def_54,type,
sK7: $i > ( $i > $o ) > $i ).
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] :
( ( X1 @ X2 )
| ( X0 @ 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,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f22,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $i,X2: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) )
= meuclidean ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
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 @ ( mnot @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ ( mnot @ ( mbox @ X0 @ X1 ) ) ) ) ) )
<=> ( meuclidean @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ ( mnot @ ( mbox @ X0 @ X1 ) ) ) ) ) )
<=> ( meuclidean @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f34,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X3 @ X2 ) ) )
= meuclidean ),
inference(rectify,[],[f22]) ).
thf(f35,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f37,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f38,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f40,plain,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ ( mnot @ ( mbox @ X0 @ X1 ) ) ) ) ) )
<=> ( meuclidean @ X0 ) ),
inference(rectify,[],[f33]) ).
thf(f41,plain,
~ ! [X0: $i > $i > $o] :
( ( meuclidean @ X0 )
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X0 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f43,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f52,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f53,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f75,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f76,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f80,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f81,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( meuclidean @ X0 )
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X0 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f41]) ).
thf(f88,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK0 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) )
!= ( meuclidean @ sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f94,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f96,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f98,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f99,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK0 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) )
!= ( meuclidean @ sK0 ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f105,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f106,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f107,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f114,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f124,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f96,f105,f114]) ).
thf(f132,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] :
( ( Y3 @ Y5 )
| ( Y4 @ 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 ) ) ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f99,f106,f107,f124,f114,f98,f98,f114,f98,f94]) ).
thf(f133,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] :
( ( Y3 @ Y5 )
| ( Y4 @ 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 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f134,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] :
( ( Y3 @ Y5 )
| ( Y4 @ 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 ) ) ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f133]) ).
thf(f135,definition,
( sF2
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f136,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 )
= sF2 ),
inference(reorient_equations,[],[f135]) ).
thf(f137,plain,
sF2 != sF1,
inference(definition_folding,[],[f132,f136,f134]) ).
thf(f138,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] :
( ( Y3 @ Y5 )
| ( Y4 @ 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 )
| ( $false = sF1 ) ),
inference(iff_proxy_clausification,[],[f134]) ).
thf(f139,plain,
( ( sF1 = $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] :
( ( Y3 @ Y5 )
| ( Y4 @ 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 ) ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f134]) ).
thf(f140,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ sK3 ) )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ sK3 @ Y1 ) ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( ( ( ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ sK3 @ Y1 ) ) ) )
@ sK4 )
= $false )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( sF1 = $true )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK3 @ Y0 ) ) ) )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK3 @ Y0 ) ) ) ) )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f144]) ).
thf(f147,plain,
( ( sF1 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK3 @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( sF1 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( ( sF1 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK3 @ Y0 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( sF1 = $true )
| ( $false
= ( ( sK4 @ sK5 )
| ~ ( sK0 @ sK3 @ sK5 ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( ( sF1 = $true )
| ( $false
= ( ~ ( sK0 @ sK3 @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( sF1 = $true )
| ( ( sK4 @ sK5 )
= $false ) ),
inference(or_proxy_clausification,[],[f150]) ).
thf(f153,plain,
( ( ( sK0 @ sK3 @ sK5 )
= $true )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f154,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK3 @ Y0 ) )
@ sK6 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f155,plain,
( ( sF1 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) ) )
| ~ ( sK0 @ sK3 @ sK6 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( ( sF1 = $true )
| ( ( ~ ( sK0 @ sK3 @ sK6 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) ) ) ) )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) ) )
= $true )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( sK0 @ sK6 @ Y0 ) )
@ X1 )
= $true )
| ( sF1 = $true ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( sF1 = $true )
| ( ( ( sK4 @ X1 )
| ~ ( sK0 @ sK6 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( ( ~ ( sK0 @ sK6 @ X1 ) )
= $true )
| ( ( sK4 @ X1 )
= $true )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( sF1 = $true )
| ( ( sK0 @ sK6 @ X1 )
= $false )
| ( ( sK4 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( sF1 = $true )
| ( ( sK0 @ sK3 @ sK6 )
= $true ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f164,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
= $true )
| ( $false = sF1 ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f165,plain,
! [X1: $i] :
( ( $false = sF1 )
| ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $false = sF1 )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X1 @ Y1 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X2: $i > $o,X1: $i] :
( ( $false = sF1 )
| ( ( ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X1 @ Y1 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i > $o,X1: $i] :
( ( $false = sF1 )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true )
| ( $false = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $false )
| ( $false = sF1 ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X3 )
= $true )
| ( $false = sF1 )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X3 )
= $true ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false = sF1 )
| ( ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X4 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X3 ) )
= $true )
| ( ( ( X2 @ X4 )
| ~ ( sK0 @ X1 @ X4 ) )
= $true )
| ( $false = sF1 ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) ) ) )
| ( ( ~ ( sK0 @ X1 @ X3 ) )
= $true )
| ( ( ( X2 @ X4 )
| ~ ( sK0 @ X1 @ X4 ) )
= $true )
| ( $false = sF1 ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false = sF1 )
| ( ( ( X2 @ X4 )
| ~ ( sK0 @ X1 @ X4 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) )
= $false )
| ( ( ~ ( sK0 @ X1 @ X3 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) )
= $false )
| ( ( ~ ( sK0 @ X1 @ X4 ) )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( $false = sF1 )
| ( ( ~ ( sK0 @ X1 @ X3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( ~ ( sK0 @ X1 @ X3 ) )
= $true )
| ( $false = sF1 )
| ( $false
= ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) )
@ ( sK7 @ X3 @ X2 ) ) )
| ( ( ~ ( sK0 @ X1 @ X4 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X1 @ X3 ) )
| ( $false = sF1 )
| ( $false
= ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) )
@ ( sK7 @ X3 @ X2 ) ) )
| ( ( X2 @ X4 )
= $true )
| ( ( ~ ( sK0 @ X1 @ X4 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false = sF1 )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) )
@ ( sK7 @ X3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( X2 @ X4 )
= $true )
| ( $false = sF1 )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( $false
= ( ( X2 @ ( sK7 @ X3 @ X2 ) )
| ~ ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false = sF1 )
| ( ( ~ ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK0 @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( X2 @ X4 )
= $true )
| ( $false = sF1 )
| ( ( X2 @ ( sK7 @ X3 @ X2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f184,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( $false = sF1 )
| ( ( sK0 @ X1 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f185,plain,
( ( $false = sF2 )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f136]) ).
thf(f186,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 )
= $false )
| ( sF2 = $true ) ),
inference(iff_proxy_clausification,[],[f136]) ).
thf(f187,plain,
( ( sF2 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK8 )
= $false )
| ( sF2 = $true ) ),
inference(sigma_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( sF2 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK8 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ sK8 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f190,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK8 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ sK8 @ Y0 ) ) )
@ sK9 ) )
| ( sF2 = $true ) ),
inference(sigma_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( sF2 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK8 )
& ( sK0 @ Y0 @ sK9 ) )
=> ( sK0 @ sK8 @ sK9 ) ) ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
( ( ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK8 )
& ( sK0 @ Y0 @ sK9 ) )
=> ( sK0 @ sK8 @ sK9 ) )
@ sK10 )
= $false )
| ( sF2 = $true ) ),
inference(sigma_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( sF2 = $true )
| ( ( ( ( sK0 @ sK10 @ sK8 )
& ( sK0 @ sK10 @ sK9 ) )
=> ( sK0 @ sK8 @ sK9 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
( ( sF2 = $true )
| ( $false
= ( sK0 @ sK8 @ sK9 ) ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( ( sF2 = $true )
| ( ( ( sK0 @ sK10 @ sK8 )
& ( sK0 @ sK10 @ sK9 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f196,plain,
( ( $true
= ( sK0 @ sK10 @ sK9 ) )
| ( sF2 = $true ) ),
inference(and_proxy_clausification,[],[f195]) ).
thf(f197,plain,
( ( ( sK0 @ sK10 @ sK8 )
= $true )
| ( sF2 = $true ) ),
inference(and_proxy_clausification,[],[f195]) ).
thf(f198,plain,
( ( $false = sF2 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f199,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $false = sF2 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X1: $i] :
( ( $false = sF2 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ X1 @ Y0 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X1: $i] :
( ( $false = sF2 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ X1 @ X2 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ X1 @ X2 ) )
@ X3 )
= $true )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( ( sK0 @ X3 @ X1 )
& ( sK0 @ X3 @ X2 ) )
=> ( sK0 @ X1 @ X2 ) )
= $true )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X3 @ X1 )
& ( sK0 @ X3 @ X2 ) ) )
| ( $false = sF2 )
| ( ( sK0 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF2 )
| ( ( sK0 @ X1 @ X2 )
= $true )
| ( ( sK0 @ X3 @ X2 )
= $false )
| ( $false
= ( sK0 @ X3 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f205]) ).
thf(f207,plain,
( ( sF1 = $true )
| ( sF2 = $true ) ),
inference(xor_proxy_clausification,[],[f137]) ).
thf(f208,plain,
( ( $false = sF1 )
| ( $false = sF2 ) ),
inference(xor_proxy_clausification,[],[f137]) ).
thf(f210,definition,
( spl11_1
<=> ( ( sK4 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
thf(f212,plain,
( ( ( sK4 @ sK5 )
= $false )
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f214,definition,
( spl11_2
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f216,plain,
( ( sF1 = $true )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f214]) ).
thf(f217,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f152,f214,f210]) ).
thf(f219,definition,
( spl11_3
<=> ( ( sK0 @ sK3 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
thf(f221,plain,
( ( ( sK0 @ sK3 @ sK5 )
= $true )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f219]) ).
thf(f222,plain,
( spl11_2
| spl11_3 ),
inference(avatar_split_clause,[],[f153,f219,f214]) ).
thf(f224,definition,
( spl11_4
<=> ! [X1: $i] :
( ( ( sK0 @ sK6 @ X1 )
= $false )
| ( ( sK4 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f225,plain,
( ! [X1: $i] :
( ( ( sK0 @ sK6 @ X1 )
= $false )
| ( ( sK4 @ X1 )
= $true ) )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f224]) ).
thf(f226,plain,
( spl11_4
| spl11_2 ),
inference(avatar_split_clause,[],[f162,f214,f224]) ).
thf(f228,definition,
( spl11_5
<=> ( ( sK0 @ sK3 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
thf(f230,plain,
( ( ( sK0 @ sK3 @ sK6 )
= $true )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f231,plain,
( spl11_5
| spl11_2 ),
inference(avatar_split_clause,[],[f163,f214,f228]) ).
thf(f233,definition,
( spl11_6
<=> ! [X4: $i,X3: $i,X2: $i > $o,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( X2 @ ( sK7 @ X3 @ X2 ) )
= $false )
| ( ( X2 @ X4 )
= $true )
| ( ( sK0 @ X1 @ X4 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
thf(f234,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( X2 @ ( sK7 @ X3 @ X2 ) )
= $false )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( X2 @ X4 )
= $true )
| ( ( sK0 @ X1 @ X4 )
= $false ) )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f236,definition,
( spl11_7
<=> ( $false = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
thf(f238,plain,
( ( $false = sF1 )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f236]) ).
thf(f239,plain,
( spl11_6
| spl11_7 ),
inference(avatar_split_clause,[],[f183,f236,f233]) ).
thf(f241,definition,
( spl11_8
<=> ! [X4: $i,X3: $i,X2: $i > $o,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( X2 @ X4 )
= $true )
| ( ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
thf(f242,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) )
= $true )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK0 @ X1 @ X3 ) ) )
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f243,plain,
( spl11_8
| spl11_7 ),
inference(avatar_split_clause,[],[f184,f236,f241]) ).
thf(f245,definition,
( spl11_9
<=> ( ( sK0 @ sK10 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
thf(f247,plain,
( ( ( sK0 @ sK10 @ sK8 )
= $true )
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f249,definition,
( spl11_10
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
thf(f251,plain,
( ( sF2 = $true )
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f252,plain,
( spl11_9
| spl11_10 ),
inference(avatar_split_clause,[],[f197,f249,f245]) ).
thf(f254,definition,
( spl11_11
<=> ( $true
= ( sK0 @ sK10 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
thf(f256,plain,
( ( $true
= ( sK0 @ sK10 @ sK9 ) )
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f254]) ).
thf(f257,plain,
( spl11_11
| spl11_10 ),
inference(avatar_split_clause,[],[f196,f249,f254]) ).
thf(f259,definition,
( spl11_12
<=> ( $false
= ( sK0 @ sK8 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
thf(f261,plain,
( ( $false
= ( sK0 @ sK8 @ sK9 ) )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f262,plain,
( spl11_10
| spl11_12 ),
inference(avatar_split_clause,[],[f194,f259,f249]) ).
thf(f264,definition,
( spl11_13
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( sK0 @ X1 @ X2 )
= $true )
| ( $false
= ( sK0 @ X3 @ X1 ) )
| ( ( sK0 @ X3 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition]) ).
thf(f265,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( ( sK0 @ X1 @ X2 )
= $true )
| ( ( sK0 @ X3 @ X2 )
= $false ) )
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f267,definition,
( spl11_14
<=> ( $false = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
thf(f269,plain,
( ( $false = sF2 )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f267]) ).
thf(f270,plain,
( spl11_13
| spl11_14 ),
inference(avatar_split_clause,[],[f206,f267,f264]) ).
thf(f271,plain,
( spl11_7
| spl11_14 ),
inference(avatar_split_clause,[],[f208,f267,f236]) ).
thf(f272,plain,
( spl11_2
| spl11_10 ),
inference(avatar_split_clause,[],[f207,f249,f214]) ).
thf(f282,plain,
( ( $false = $true )
| ~ spl11_2
| ~ spl11_7 ),
inference(forward_demodulation,[],[f216,f238]) ).
thf(f283,plain,
( $false
| ~ spl11_2
| ~ spl11_7 ),
inference(trivial_inequality_removal,[],[f282]) ).
thf(f284,plain,
( ~ spl11_2
| ~ spl11_7 ),
inference(avatar_contradiction_clause,[],[f283]) ).
thf(f289,plain,
( ( $false = $true )
| ~ spl11_10
| ~ spl11_14 ),
inference(forward_demodulation,[],[f251,f269]) ).
thf(f290,plain,
( $false
| ~ spl11_10
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f289]) ).
thf(f291,plain,
( ~ spl11_10
| ~ spl11_14 ),
inference(avatar_contradiction_clause,[],[f290]) ).
thf(f297,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ sK10 @ X0 ) )
| ( ( sK0 @ sK8 @ X0 )
= $true ) )
| ~ spl11_9
| ~ spl11_13 ),
inference(constrained_superposition,[],[f247,f265]) ).
thf(f302,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK10 @ X0 ) )
| ( ( sK0 @ sK8 @ X0 )
= $true ) )
| ~ spl11_9
| ~ spl11_13 ),
inference(trivial_inequality_removal,[],[f297]) ).
thf(f318,plain,
( ( ( sK0 @ sK8 @ sK9 )
= $true )
| ( $false = $true )
| ~ spl11_9
| ~ spl11_11
| ~ spl11_13 ),
inference(constrained_superposition,[],[f256,f302]) ).
thf(f321,plain,
( ( ( sK0 @ sK8 @ sK9 )
= $true )
| ~ spl11_9
| ~ spl11_11
| ~ spl11_13 ),
inference(trivial_inequality_removal,[],[f318]) ).
thf(f330,plain,
( ( $false = $true )
| ~ spl11_9
| ~ spl11_11
| ~ spl11_12
| ~ spl11_13 ),
inference(forward_demodulation,[],[f321,f261]) ).
thf(f331,plain,
( $false
| ~ spl11_9
| ~ spl11_11
| ~ spl11_12
| ~ spl11_13 ),
inference(trivial_inequality_removal,[],[f330]) ).
thf(f332,plain,
( ~ spl11_9
| ~ spl11_11
| ~ spl11_12
| ~ spl11_13 ),
inference(avatar_contradiction_clause,[],[f331]) ).
thf(f348,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X0 )
= $false )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( $false = $true )
| ( ( sK0 @ X3 @ X0 )
= $false )
| ( ( sK0 @ X0 @ X4 )
= $true )
| ( ( sK0 @ X0 @ X2 )
= $true )
| ( ( sK0 @ X1 @ X2 )
= $false ) )
| ~ spl11_6
| ~ spl11_8 ),
inference(constrained_superposition,[],[f234,f242]) ).
thf(f351,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X3 @ X4 )
= $false )
| ( ( sK0 @ X0 @ X4 )
= $true )
| ( ( sK0 @ X1 @ X0 )
= $false )
| ( ( sK0 @ X3 @ X0 )
= $false )
| ( ( sK0 @ X0 @ X2 )
= $true )
| ( ( sK0 @ X1 @ X2 )
= $false ) )
| ~ spl11_6
| ~ spl11_8 ),
inference(trivial_inequality_removal,[],[f348]) ).
thf(f365,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK0 @ X0 @ X2 )
= $false )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false != $false )
| ( ( sK0 @ X0 @ X2 )
= $false ) )
| ~ spl11_6
| ~ spl11_8 ),
inference(equality_factoring,[],[f351]) ).
thf(f370,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ X1 )
= $false )
| ( $false != $false )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X0 @ X2 )
= $false ) )
| ~ spl11_6
| ~ spl11_8 ),
inference(duplicate_literal_removal,[],[f365]) ).
thf(f371,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ X1 )
= $false )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X0 @ X2 )
= $false ) )
| ~ spl11_6
| ~ spl11_8 ),
inference(trivial_inequality_removal,[],[f370]) ).
thf(f379,plain,
( spl11_13
| ~ spl11_6
| ~ spl11_8 ),
inference(avatar_split_clause,[],[f371,f241,f233,f264]) ).
thf(f408,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( sK0 @ sK6 @ X0 )
= $true )
| ( ( sK0 @ sK3 @ X0 )
= $false ) )
| ~ spl11_5
| ~ spl11_13 ),
inference(constrained_superposition,[],[f230,f265]) ).
thf(f414,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK6 @ X0 )
= $true )
| ( ( sK0 @ sK3 @ X0 )
= $false ) )
| ~ spl11_5
| ~ spl11_13 ),
inference(trivial_inequality_removal,[],[f408]) ).
thf(f525,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( sK4 @ X0 )
= $true )
| ( ( sK0 @ sK3 @ X0 )
= $false ) )
| ~ spl11_4
| ~ spl11_5
| ~ spl11_13 ),
inference(constrained_superposition,[],[f225,f414]) ).
thf(f533,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK3 @ X0 )
= $false )
| ( ( sK4 @ X0 )
= $true ) )
| ~ spl11_4
| ~ spl11_5
| ~ spl11_13 ),
inference(trivial_inequality_removal,[],[f525]) ).
thf(f540,plain,
( ( $false = $true )
| ( ( sK4 @ sK5 )
= $true )
| ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_13 ),
inference(constrained_superposition,[],[f533,f221]) ).
thf(f552,plain,
( ( ( sK4 @ sK5 )
= $true )
| ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_13 ),
inference(trivial_inequality_removal,[],[f540]) ).
thf(f569,plain,
( ( $false = $true )
| ~ spl11_1
| ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_13 ),
inference(forward_demodulation,[],[f552,f212]) ).
thf(f570,plain,
( $false
| ~ spl11_1
| ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_13 ),
inference(trivial_inequality_removal,[],[f569]) ).
thf(f571,plain,
( ~ spl11_1
| ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_13 ),
inference(avatar_contradiction_clause,[],[f570]) ).
cnf(s1,plain,
( spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f217]) ).
cnf(s2,plain,
( spl11_2
| spl11_3 ),
inference(sat_conversion,[],[f222]) ).
cnf(s3,plain,
( spl11_2
| spl11_4 ),
inference(sat_conversion,[],[f226]) ).
cnf(s4,plain,
( spl11_2
| spl11_5 ),
inference(sat_conversion,[],[f231]) ).
cnf(s5,plain,
( spl11_6
| spl11_7 ),
inference(sat_conversion,[],[f239]) ).
cnf(s6,plain,
( spl11_7
| spl11_8 ),
inference(sat_conversion,[],[f243]) ).
cnf(s7,plain,
( spl11_9
| spl11_10 ),
inference(sat_conversion,[],[f252]) ).
cnf(s8,plain,
( spl11_10
| spl11_11 ),
inference(sat_conversion,[],[f257]) ).
cnf(s9,plain,
( spl11_10
| spl11_12 ),
inference(sat_conversion,[],[f262]) ).
cnf(s10,plain,
( spl11_13
| spl11_14 ),
inference(sat_conversion,[],[f270]) ).
cnf(s11,plain,
( spl11_7
| spl11_14 ),
inference(sat_conversion,[],[f271]) ).
cnf(s12,plain,
( spl11_2
| spl11_10 ),
inference(sat_conversion,[],[f272]) ).
cnf(s13,plain,
( ~ spl11_2
| ~ spl11_7 ),
inference(sat_conversion,[],[f284]) ).
cnf(s14,plain,
( ~ spl11_10
| ~ spl11_14 ),
inference(sat_conversion,[],[f291]) ).
cnf(s16,plain,
( ~ spl11_9
| ~ spl11_11
| ~ spl11_12
| ~ spl11_13 ),
inference(sat_conversion,[],[f332]) ).
cnf(s19,plain,
( ~ spl11_6
| ~ spl11_8
| spl11_13 ),
inference(sat_conversion,[],[f379]) ).
cnf(s26,plain,
( ~ spl11_1
| ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_13 ),
inference(sat_conversion,[],[f571]) ).
cnf(s28,plain,
spl11_7,
inference(rat,[],[s16,s7,s8,s9,s19,s14,s5,s6,s11]) ).
cnf(s29,plain,
~ spl11_2,
inference(rat,[],[s13,s28]) ).
cnf(s30,plain,
spl11_10,
inference(rat,[],[s12,s29]) ).
cnf(s31,plain,
spl11_5,
inference(rat,[],[s4,s29]) ).
cnf(s32,plain,
spl11_4,
inference(rat,[],[s3,s29]) ).
cnf(s33,plain,
spl11_3,
inference(rat,[],[s2,s29]) ).
cnf(s34,plain,
spl11_1,
inference(rat,[],[s1,s29]) ).
cnf(s35,plain,
~ spl11_14,
inference(rat,[],[s14,s30]) ).
cnf(s36,plain,
~ spl11_13,
inference(rat,[],[s26,s32,s31,s34,s33]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s10,s35,s36]) ).
thf(f573,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL877^2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n005.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 10:20:01 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.21/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.34 % (1482202)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.34 % (1482212)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=319957727:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.34 % (1482213)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.34 % (1482213)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.34 % (1482211)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=455262171:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.34 % (1482209)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3598528811:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.34 % (1482207)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2736463707:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.34 % (1482208)lrs+10_16_si=on:nwc=1.5:random_seed=4072954439:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.34 % (1482210)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=2631663319:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.34 % (1482213)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=1804426231:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.34 % (1482209)Instruction limit reached!
% 0.21/0.34 % (1482209)------------------------------
% 0.21/0.34 % (1482209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (1482209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (1482209)CaDiCaL version: 2.1.3
% 0.21/0.34 % (1482209)Termination reason: Instruction limit
% 0.21/0.34 % (1482209)Termination phase: Property scanning
% 0.21/0.34 % (1482209)Time elapsed: 0.001 s
% 0.21/0.34 % (1482209)Peak memory usage: 10 MB
% 0.21/0.34 % (1482209)Instructions burned: 3 (million)
% 0.21/0.34 % (1482208)Instruction limit reached!
% 0.21/0.34 % (1482208)------------------------------
% 0.21/0.34 % (1482208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (1482208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (1482208)CaDiCaL version: 2.1.3
% 0.21/0.34 % (1482208)Termination reason: Instruction limit
% 0.21/0.34 % (1482208)Termination phase: Saturation
% 0.21/0.34 % (1482208)Time elapsed: 0.010 s
% 0.21/0.34 % (1482208)Peak memory usage: 12 MB
% 0.21/0.34 % (1482208)Instructions burned: 19 (million)
% 0.21/0.34 % (1482212)Instruction limit reached!
% 0.21/0.34 % (1482212)------------------------------
% 0.21/0.34 % (1482212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (1482212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (1482212)CaDiCaL version: 2.1.3
% 0.21/0.34 % (1482212)Termination reason: Instruction limit
% 0.21/0.34 % (1482212)Termination phase: Saturation
% 0.21/0.34 % (1482212)Time elapsed: 0.020 s
% 0.21/0.34 % (1482212)Peak memory usage: 12 MB
% 0.21/0.34 % (1482212)Instructions burned: 76 (million)
% 0.21/0.34 % (1482211)Instruction limit reached!
% 0.21/0.34 % (1482211)------------------------------
% 0.21/0.34 % (1482211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (1482211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (1482211)CaDiCaL version: 2.1.3
% 0.21/0.34 % (1482211)Termination reason: Instruction limit
% 0.21/0.34 % (1482211)Termination phase: Saturation
% 0.21/0.34 % (1482211)Time elapsed: 0.016 s
% 0.21/0.34 % (1482211)Peak memory usage: 12 MB
% 0.21/0.34 % (1482211)Instructions burned: 29 (million)
% 0.21/0.34 % (1482213) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1482202-1482213"...
% 0.21/0.34 % (1482221)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2387079861:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.34 % (1482223)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.34 % (1482221)Instruction limit reached!
% 0.21/0.34 % (1482221)------------------------------
% 0.21/0.34 % (1482221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (1482221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (1482221)CaDiCaL version: 2.1.3
% 0.21/0.34 % (1482221)Termination reason: Instruction limit
% 0.21/0.34 % (1482221)Termination phase: Saturation
% 0.21/0.34 % (1482221)Time elapsed: 0.003 s
% 0.21/0.34 % (1482221)Peak memory usage: 11 MB
% 0.21/0.34 % (1482221)Instructions burned: 7 (million)
% 0.21/0.34 % (1482223)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=452149258:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.34 % (1482213)...printing done.
% 0.21/0.34 % (1482213)Refutation found. Thanks to Tanya!
% 0.21/0.34 % SZS status Theorem for theBenchmark
% 0.21/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.34 % (1482213)------------------------------
% 0.21/0.34 % (1482213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (1482213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (1482213)CaDiCaL version: 2.1.3
% 0.21/0.34 % (1482213)Termination reason: Refutation
% 0.21/0.34 % (1482213)Time elapsed: 0.024 s
% 0.21/0.34 % (1482213)Peak memory usage: 13 MB
% 0.21/0.34 % (1482213)Instructions burned: 44 (million)
% 0.21/0.34 % (1482202)Success in time 0.069 s
% 0.21/0.34 % Vampire exiting
%------------------------------------------------------------------------------