%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL707^1 : TPTP v9.3.1. Bugfixed v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:14:31 AM UTC 2026
% Result : Theorem 0.13s 0.29s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 11
% Syntax : Number of formulae : 122 ( 86 unt; 0 typ; 2 def)
% Number of atoms : 902 ( 179 equ; 0 cnn)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 1462 ( 214 ~; 223 |; 15 &; 904 @)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 173 ( 173 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 53 usr; 8 con; 0-4 aty)
% ( 88 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 313 ( 0 sgn 63 !; 1 ?; 313 :)
% 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_34,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_43,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_49,type,
sK2: $i > $o ).
thf(func_def_50,type,
sK3: $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(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
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(f26,axiom,
( mweakly_connected
= ( ^ [X0: $i > $i > $o] :
! [X3: $i,X2: $i,X1: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( ( X2 = X3 )
| ( X0 @ X3 @ X2 )
| ( X0 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mweakly_connected) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( mweakly_connected @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mor @ ( mbox @ X0 @ ( mimplies @ ( mand @ X1 @ ( mbox @ X0 @ X1 ) ) @ X2 ) ) @ ( mbox @ X0 @ ( mimplies @ ( mand @ X2 @ ( mbox @ X0 @ X2 ) ) @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( mweakly_connected @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mor @ ( mbox @ X0 @ ( mimplies @ ( mand @ X1 @ ( mbox @ X0 @ X1 ) ) @ X2 ) ) @ ( mbox @ X0 @ ( mimplies @ ( mand @ X2 @ ( mbox @ X0 @ X2 ) ) @ X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f34,plain,
~ ! [X0: $i > $i > $o] :
( ( mweakly_connected @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mor @ ( mbox @ X0 @ ( mimplies @ ( mand @ X1 @ ( mbox @ X0 @ X1 ) ) @ X2 ) ) @ ( mbox @ X0 @ ( mimplies @ ( mand @ X2 @ ( mbox @ X0 @ X2 ) ) @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f35,plain,
~ ! [X0: $i > $i > $o] :
( ( ( mweakly_connected @ X0 )
= $true )
=> ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mor @ ( mbox @ X0 @ ( mimplies @ ( mand @ Y0 @ ( mbox @ X0 @ Y0 ) ) @ Y1 ) ) @ ( mbox @ X0 @ ( mimplies @ ( mand @ Y1 @ ( mbox @ X0 @ Y1 ) ) @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f44,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f47,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f48,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f50,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f65,plain,
( mweakly_connected
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X3 @ X1 ) )
=> ( ( X1 = X2 )
| ( X0 @ X1 @ X2 )
| ( X0 @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f66,plain,
( mweakly_connected
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y3 @ Y2 )
| ( Y3 = Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f68,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f69,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f71,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f72,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f79,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f80,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( mweakly_connected @ X0 )
= $true )
& ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mor @ ( mbox @ X0 @ ( mimplies @ ( mand @ Y0 @ ( mbox @ X0 @ Y0 ) ) @ Y1 ) ) @ ( mbox @ X0 @ ( mimplies @ ( mand @ Y1 @ ( mbox @ X0 @ Y1 ) ) @ Y0 ) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f35]) ).
thf(f88,plain,
( ( $true
= ( mweakly_connected @ sK0 ) )
& ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mor @ ( mbox @ sK0 @ ( mimplies @ ( mand @ Y0 @ ( mbox @ sK0 @ Y0 ) ) @ Y1 ) ) @ ( mbox @ sK0 @ ( mimplies @ ( mand @ Y1 @ ( mbox @ sK0 @ Y1 ) ) @ Y0 ) ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f94,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f95,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f96,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f100,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f101,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f111,plain,
( mweakly_connected
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y3 @ Y2 )
| ( Y3 = Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f114,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f115,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f119,plain,
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mor @ ( mbox @ sK0 @ ( mimplies @ ( mand @ Y0 @ ( mbox @ sK0 @ Y0 ) ) @ Y1 ) ) @ ( mbox @ sK0 @ ( mimplies @ ( mand @ Y1 @ ( mbox @ sK0 @ Y1 ) ) @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f120,plain,
( $true
= ( mweakly_connected @ sK0 ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f124,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f96,f101,f94,f101,f101]) ).
thf(f125,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,[],[f114,f94,f101]) ).
thf(f133,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y3 @ Y2 )
| ( Y3 = Y2 ) ) ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f120,f111]) ).
thf(f134,plain,
( $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 ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ sK0
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ Y0
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ sK0
@ Y0 ) )
@ Y1 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ sK0
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ Y1
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ sK0
@ Y1 ) )
@ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f119,f95,f115,f115,f94,f100,f125,f124,f100,f100,f125,f124,f100]) ).
thf(f135,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( sK0 @ Y3 @ Y4 ) ) )
| ~ ( Y2 @ Y3 ) )
| ~ ( sK0 @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( sK0 @ Y3 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) )
| ~ ( sK0 @ Y0 @ Y3 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( sK0 @ Y3 @ Y4 ) ) )
| ~ ( Y2 @ Y3 ) )
| ~ ( sK0 @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( sK0 @ Y3 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) )
| ~ ( sK0 @ Y0 @ Y3 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( Y1 @ Y2 ) )
| ~ ( sK0 @ sK1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( Y0 @ Y2 ) )
| ~ ( sK0 @ sK1 @ Y2 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( Y1 @ Y2 ) )
| ~ ( sK0 @ sK1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( Y0 @ Y2 ) )
| ~ ( sK0 @ sK1 @ Y2 ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( Y0 @ Y1 ) )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK2 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK2 @ Y1 ) )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( Y0 @ Y1 ) )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK2 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK2 @ Y1 ) )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK2 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK2 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f141]) ).
thf(f144,plain,
( $false
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( $false
= ( ( sK2 @ sK4 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) ) )
| ~ ( sK3 @ sK4 ) )
| ~ ( sK0 @ sK1 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
( ( ~ ( sK0 @ sK1 @ sK4 ) )
= $false ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( $false
= ( ( sK2 @ sK4 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) ) )
| ~ ( sK3 @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) ) )
| ~ ( sK3 @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( $false
= ( sK2 @ sK4 ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f150,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) ) )
| ~ ( sK3 @ sK4 ) ) ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) ) )
| ~ ( sK3 @ sK4 ) )
= $false ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( $false
= ( ~ ( sK3 @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f154,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( $true
= ( ( sK3 @ X1 )
| ~ ( sK0 @ sK4 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK4 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( $true
= ( sK3 @ sK4 ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f160,plain,
( $true
= ( sK0 @ sK1 @ sK4 ) ),
inference(not_proxy_clausification,[],[f146]) ).
thf(f161,plain,
( $false
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK2 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f142]) ).
thf(f162,plain,
( $false
= ( ( sK3 @ sK5 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) )
| ~ ( sK2 @ sK5 ) )
| ~ ( sK0 @ sK1 @ sK5 ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( $false
= ( ~ ( sK0 @ sK1 @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( $false
= ( ( sK3 @ sK5 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) )
| ~ ( sK2 @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) )
| ~ ( sK2 @ sK5 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( $false
= ( sK3 @ sK5 ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) )
| ~ ( sK2 @ sK5 ) ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) )
| ~ ( sK2 @ sK5 ) )
= $false ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f170,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f171,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK5 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( $true
= ( ( sK2 @ X1 )
| ~ ( sK0 @ sK5 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( ~ ( sK0 @ sK5 @ X1 ) ) )
| ( $true
= ( sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f177,plain,
( $true
= ( sK0 @ sK1 @ sK5 ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f178,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( ( sK0 @ Y1 @ Y2 )
| ( sK0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f179,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( ( sK0 @ Y1 @ Y2 )
| ( sK0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( ( sK0 @ Y0 @ Y1 )
| ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( ( sK0 @ Y0 @ Y1 )
| ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ X1 @ X2 ) )
=> ( ( sK0 @ X2 @ Y0 )
| ( sK0 @ Y0 @ X2 )
| ( Y0 = X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ X1 @ X2 ) )
=> ( ( sK0 @ X2 @ Y0 )
| ( sK0 @ Y0 @ X2 )
| ( Y0 = X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X1 @ X3 )
& ( sK0 @ X1 @ X2 ) )
=> ( ( sK0 @ X2 @ X3 )
| ( sK0 @ X3 @ X2 )
| ( X3 = X2 ) ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X1 @ X3 )
& ( sK0 @ X1 @ X2 ) ) )
| ( $true
= ( ( sK0 @ X2 @ X3 )
| ( sK0 @ X3 @ X2 )
| ( X3 = X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( ( sK0 @ X2 @ X3 )
| ( sK0 @ X3 @ X2 )
| ( X3 = X2 ) ) ) ),
inference(and_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( sK0 @ X2 @ X3 )
| ( sK0 @ X3 @ X2 ) ) )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( X3 = X2 ) ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ X3 ) )
| ( $true
= ( sK0 @ X3 @ X2 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( X3 = X2 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK0 @ X3 @ X2 ) )
| ( $true
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( X2 = X3 ) ),
inference(equality_proxy_clausification,[],[f188]) ).
thf(f223,plain,
! [X0: $i,X1: $i] :
( ( sK4 = X0 )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ sK4 ) )
| ( $true
= ( sK3 @ X0 ) )
| ( $true = $false )
| ( $true
= ( sK0 @ X0 @ sK4 ) ) ),
inference(constrained_superposition,[],[f189,f158]) ).
thf(f224,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X0 @ sK4 ) )
| ( $false
= ( sK0 @ X1 @ sK4 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $true
= ( sK3 @ X0 ) )
| ( sK4 = X0 ) ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f246,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( sK0 @ X0 @ sK5 )
= $false )
| ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( sK4 = sK5 )
| ( $true
= ( sK2 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) ) ),
inference(constrained_superposition,[],[f175,f224]) ).
thf(f266,plain,
! [X0: $i] :
( ( ( sK0 @ X0 @ sK5 )
= $false )
| ( $true
= ( sK2 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( sK4 = sK5 ) ),
inference(trivial_inequality_removal,[],[f246]) ).
thf(f279,plain,
! [X0: $i] :
( ( $true = $false )
| ( sK4 = sK5 )
| ( ( sK0 @ X0 @ sK5 )
= $false )
| ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) ) ),
inference(forward_demodulation,[],[f266,f149]) ).
thf(f280,plain,
! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( sK4 = sK5 )
| ( $true
= ( sK3 @ sK5 ) )
| ( ( sK0 @ X0 @ sK5 )
= $false ) ),
inference(trivial_inequality_removal,[],[f279]) ).
thf(f283,plain,
! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $true = $false )
| ( sK4 = sK5 )
| ( ( sK0 @ X0 @ sK5 )
= $false ) ),
inference(forward_demodulation,[],[f280,f166]) ).
thf(f284,plain,
! [X0: $i] :
( ( ( sK0 @ X0 @ sK5 )
= $false )
| ( sK4 = sK5 )
| ( $false
= ( sK0 @ X0 @ sK4 ) ) ),
inference(trivial_inequality_removal,[],[f283]) ).
thf(f286,definition,
( spl6_1
<=> ( sK4 = sK5 ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f288,plain,
( ( sK4 = sK5 )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f286]) ).
thf(f290,definition,
( spl6_2
<=> ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( ( sK0 @ X0 @ sK5 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f291,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK5 )
= $false )
| ( $false
= ( sK0 @ X0 @ sK4 ) ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f290]) ).
thf(f293,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f284,f290,f286]) ).
thf(f299,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f177,f291]) ).
thf(f302,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f299]) ).
thf(f309,plain,
( ( $true = $false )
| ~ spl6_2 ),
inference(forward_demodulation,[],[f302,f160]) ).
thf(f310,plain,
( $false
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f311,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f310]) ).
thf(f315,plain,
( ( $false
= ( sK3 @ sK4 ) )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f166,f288]) ).
thf(f319,plain,
( ( $true = $false )
| ~ spl6_1 ),
inference(forward_demodulation,[],[f315,f159]) ).
thf(f320,plain,
( $false
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f319]) ).
thf(f321,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f320]) ).
cnf(s2,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f293]) ).
cnf(s4,plain,
~ spl6_2,
inference(sat_conversion,[],[f311]) ).
cnf(s6,plain,
~ spl6_1,
inference(sat_conversion,[],[f321]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s4,s6]) ).
thf(f322,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL707^1 : TPTP v9.3.1. Bugfixed v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.18 % Computer : n009.cluster.edu
% 0.13/0.18 % Model : x86_64 x86_64
% 0.13/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.18 % Memory : 8046.5625MB
% 0.13/0.18 % OS : Linux 6.8.0-71-generic
% 0.13/0.18 % CPULimit : 300
% 0.13/0.18 % WCLimit : 300
% 0.13/0.18 % DateTime : Tue Sep 29 09:45:30 UTC 2026
% 0.13/0.18 % CPUTime :
% 0.13/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.21 Running higher-order theorem proving
% 0.13/0.23 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
% 0.13/0.29 % (3775241)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.13/0.29 % (3775249)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=3833709748: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)
% 0.13/0.29 % (3775246)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=362317422:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.13/0.29 % (3775248)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=857946786:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.13/0.29 % (3775248)Instruction limit reached!
% 0.13/0.29 % (3775248)------------------------------
% 0.13/0.29 % (3775248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.29 % (3775248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.29 % (3775248)CaDiCaL version: 2.1.3
% 0.13/0.29 % (3775248)Termination reason: Instruction limit
% 0.13/0.29 % (3775248)Termination phase: Property scanning
% 0.13/0.29 % (3775248)Time elapsed: 0.002 s
% 0.13/0.29 % (3775248)Peak memory usage: 9 MB
% 0.13/0.29 % (3775248)Instructions burned: 3 (million)
% 0.13/0.29 % (3775250)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2389155637:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.13/0.29 % (3775246) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3775241-3775246"...
% 0.13/0.29 % (3775252)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.13/0.29 % (3775252)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
% 0.13/0.29 % (3775247)lrs+10_16_si=on:nwc=1.5:random_seed=4184000757:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.13/0.29 % (3775246)...printing done.
% 0.13/0.29 % (3775246)Refutation found. Thanks to Tanya!
% 0.13/0.29 % SZS status Theorem for theBenchmark
% 0.13/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.29 % (3775246)------------------------------
% 0.13/0.29 % (3775246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.29 % (3775246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.29 % (3775246)CaDiCaL version: 2.1.3
% 0.13/0.29 % (3775246)Termination reason: Refutation
% 0.13/0.29 % (3775246)Time elapsed: 0.017 s
% 0.13/0.29 % (3775246)Peak memory usage: 13 MB
% 0.13/0.29 % (3775246)Instructions burned: 33 (million)
% 0.13/0.29 % (3775241)Success in time 0.053 s
% 0.13/0.29 % Vampire exiting
%------------------------------------------------------------------------------