%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL717^1 : 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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:14:33 AM UTC 2026
% Result : Theorem 3.24s 0.84s
% Output : Refutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 12
% Syntax : Number of formulae : 152 ( 70 unt; 0 typ; 3 def)
% Number of atoms : 1588 ( 436 equ; 0 cnn)
% Maximal formula atoms : 13 ( 10 avg)
% Number of connectives : 2837 ( 315 ~; 577 |; 19 &;1697 @)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 268 ( 268 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 57 usr; 9 con; 0-4 aty)
% ( 196 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 573 ( 0 sgn 213 !; 0 ?; 573 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_35,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
vIMP: $o > $o > $o ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_42,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
sK0: $i > $i > $o ).
thf(func_def_54,type,
sK4: ( $i > $o ) > $i > $i ).
thf(func_def_55,type,
sK5: $i > $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ 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,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( ( ^ [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(f26,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X3: $i,X1: $i,X2: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( ( X2 = X3 )
| ( X0 @ X2 @ X3 )
| ( X0 @ X3 @ X2 ) ) ) )
= mweakly_connected ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mweakly_connected) ).
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] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mor @ ( mbox @ X0 @ ( mimplies @ ( mand @ X1 @ ( mbox @ X0 @ X1 ) ) @ X2 ) ) @ ( mbox @ X0 @ ( mimplies @ ( mand @ X2 @ ( mbox @ X0 @ X2 ) ) @ X1 ) ) ) ) ) )
=> ( mweakly_connected @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( 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 ) ) ) ) ) )
=> ( mweakly_connected @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f34,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f52,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f53,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f57,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X2 @ X3 ) )
=> ( ( X1 = X3 )
| ( X0 @ X3 @ X1 )
| ( X0 @ X1 @ X3 ) ) ) )
= mweakly_connected ),
inference(rectify,[],[f26]) ).
thf(f58,plain,
( mweakly_connected
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y1 @ Y3 )
| ( Y3 = Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f61,plain,
~ ! [X0: $i > $i > $o] :
( ( 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 ) ) ) ) ) )
=> ( mweakly_connected @ X0 ) ),
inference(rectify,[],[f33]) ).
thf(f62,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [Y1: $i > $o] :
( mforall_prop
@ ^ [Y2: $i > $o] : ( mor @ ( mbox @ Y0 @ ( mimplies @ ( mand @ Y1 @ ( mbox @ Y0 @ Y1 ) ) @ Y2 ) ) @ ( mbox @ Y0 @ ( mimplies @ ( mand @ Y2 @ ( mbox @ Y0 @ Y2 ) ) @ Y1 ) ) ) ) ) )
=> ( mweakly_connected @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f65,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
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(f71,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f72,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f74,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f77,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
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(f90,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [Y1: $i > $o] :
( mforall_prop
@ ^ [Y2: $i > $o] : ( mor @ ( mbox @ Y0 @ ( mimplies @ ( mand @ Y1 @ ( mbox @ Y0 @ Y1 ) ) @ Y2 ) ) @ ( mbox @ Y0 @ ( mimplies @ ( mand @ Y2 @ ( mbox @ Y0 @ Y2 ) ) @ Y1 ) ) ) ) ) )
=> ( mweakly_connected @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f92,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f94,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f100,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f103,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f104,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f110,plain,
( mweakly_connected
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y1 @ Y3 )
| ( Y3 = Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f113,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f115,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f122,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f113,f100,f104,f100,f100]) ).
thf(f123,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,[],[f115,f104,f100]) ).
thf(f131,plain,
( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ ( ^ [Y1: ( $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [Y2: ( $i > $o ) > $i > $o,Y3: $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y0
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ Y1
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y0
@ Y1 ) )
@ Y2 ) )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y0
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ Y2
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y0
@ Y2 ) )
@ Y1 ) ) ) ) ) )
=> ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( ( Y1 @ Y4 @ Y2 )
| ( Y1 @ Y2 @ Y4 )
| ( Y4 = Y2 ) ) ) ) ) )
@ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f90,f92,f94,f94,f104,f103,f123,f122,f103,f103,f123,f122,f103,f110]) ).
thf(f132,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ~ ~ ( ~ ( Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y4 )
| ~ ( Y0 @ Y1 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ~ ( ~ ( Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y2 @ Y4 )
| ~ ( Y0 @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y1 @ Y3 )
| ( Y3 = Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f133,plain,
( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ~ ~ ( ~ ( Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y4 )
| ~ ( Y0 @ Y1 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) )
| ( Y2 @ Y4 )
| ~ ( Y0 @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y1 @ Y3 )
| ( Y3 = Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f132]) ).
thf(f134,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) )
| ( Y3 @ Y4 )
| ~ ( Y0 @ Y1 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) )
| ( Y2 @ Y4 )
| ~ ( Y0 @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y1 @ Y3 )
| ( Y3 = Y1 ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f133]) ).
thf(f135,plain,
( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) )
| ( Y3 @ Y4 )
| ~ ( Y0 @ Y1 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) )
| ( Y2 @ Y4 )
| ~ ( Y0 @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y1 @ Y3 )
| ( Y3 = Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f134]) ).
thf(f136,plain,
( $false
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) )
| ( Y3 @ Y4 )
| ~ ( Y0 @ Y1 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) )
| ( Y2 @ Y4 )
| ~ ( Y0 @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y1 @ Y3 )
| ( Y3 = Y1 ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( sK0 @ Y3 @ Y4 ) ) )
| ( Y2 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( sK0 @ Y3 @ Y4 ) ) )
| ( Y1 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( ( sK0 @ Y2 @ Y0 )
| ( sK0 @ Y0 @ Y2 )
| ( Y2 = Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( ( sK0 @ Y2 @ Y0 )
| ( sK0 @ Y0 @ Y2 )
| ( Y2 = Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( sK0 @ Y3 @ Y4 ) ) )
| ( Y2 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( sK0 @ Y3 @ Y4 ) ) )
| ( Y1 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f140,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( ( sK0 @ Y2 @ Y0 )
| ( sK0 @ Y0 @ Y2 )
| ( Y2 = Y0 ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f138]) ).
thf(f141,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK1 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( ( sK0 @ Y1 @ sK1 )
| ( sK0 @ sK1 @ Y1 )
| ( Y1 = sK1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f153,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK1 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( ( sK0 @ Y1 @ sK1 )
| ( sK0 @ sK1 @ Y1 )
| ( Y1 = sK1 ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f141]) ).
thf(f155,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK2 @ sK1 )
& ( sK0 @ sK2 @ Y0 ) )
=> ( ( sK0 @ Y0 @ sK1 )
| ( sK0 @ sK1 @ Y0 )
| ( Y0 = sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f157,plain,
( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK2 @ sK1 )
& ( sK0 @ sK2 @ Y0 ) )
=> ( ( sK0 @ Y0 @ sK1 )
| ( sK0 @ sK1 @ Y0 )
| ( Y0 = sK1 ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f159,plain,
( $false
= ( ( ( sK0 @ sK2 @ sK1 )
& ( sK0 @ sK2 @ sK3 ) )
=> ( ( sK0 @ sK3 @ sK1 )
| ( sK0 @ sK1 @ sK3 )
| ( sK3 = sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f161,plain,
( $false
= ( ( sK0 @ sK3 @ sK1 )
| ( sK0 @ sK1 @ sK3 )
| ( sK3 = sK1 ) ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f162,plain,
( $true
= ( ( sK0 @ sK2 @ sK1 )
& ( sK0 @ sK2 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f163,plain,
( $true
= ( sK0 @ sK2 @ sK3 ) ),
inference(and_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( $true
= ( sK0 @ sK2 @ sK1 ) ),
inference(and_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( ( sK3 = sK1 )
= $false ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f166,plain,
( $false
= ( ( sK0 @ sK3 @ sK1 )
| ( sK0 @ sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f167,plain,
sK1 != sK3,
inference(equality_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( $false
= ( sK0 @ sK1 @ sK3 ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( $false
= ( sK0 @ sK3 @ sK1 ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f170,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( sK0 @ Y3 @ Y4 ) ) )
| ( Y2 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( sK0 @ Y3 @ Y4 ) ) )
| ( Y1 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f139]) ).
thf(f171,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ( Y1 @ Y2 )
| ~ ( sK0 @ X1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ( Y0 @ Y2 )
| ~ ( sK0 @ X1 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ( Y1 @ Y2 )
| ~ ( sK0 @ X1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ( Y0 @ Y2 )
| ~ ( sK0 @ X1 @ Y2 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( X2 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ( X2 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( X2 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ( X2 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X3 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X3 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X4 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X3 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( $true
= ( ~ ( X3 @ X4 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) )
| ( X2 @ X4 )
| ~ ( sK0 @ X1 @ X4 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X3 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( $true
= ( ~ ( X3 @ X4 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) )
| ( X2 @ X4 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X3 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( sK0 @ X1 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( ( X2 @ X4 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X3 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( X3 @ X4 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( sK0 @ X1 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( $true
= ( ~ ( sK0 @ X1 @ X4 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X3 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( ( X2 @ X4 )
= $true )
| ( $true
= ( ~ ( X3 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ~ ( X3 @ X4 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X3 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK0 @ X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( ( X2 @ X4 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X3 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( X3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X3 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( ( X3 @ X4 )
= $false )
| ( ( X2 @ X4 )
= $true ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( ( X3 @ X4 )
= $false )
| ( ( X2 @ X4 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ( X3 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) )
| ( ( X3 @ X4 )
= $false )
| ( ( X2 @ X4 )
= $true )
| ( $true
= ( ~ ( X2 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) ) )
| ( X3 @ X5 )
| ~ ( sK0 @ X1 @ X5 ) ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( X2 @ X4 )
= $true )
| ( $true
= ( ~ ( sK0 @ X1 @ X5 ) ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) )
| ( ( ~ ( X2 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) ) )
| ( X3 @ X5 ) )
= $true )
| ( ( X3 @ X4 )
= $false ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( ~ ( X2 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) ) )
| ( X3 @ X5 ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X4 )
= $false )
| ( $false
= ( sK0 @ X1 @ X5 ) )
| ( $false
= ( sK0 @ X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( X2 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) ) ) ) )
| ( ( X3 @ X4 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X1 @ X5 ) )
| ( $true
= ( X3 @ X5 ) )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK0 @ X1 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( X3 @ X4 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( X2 @ X5 ) ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $true
= ( X3 @ X5 ) )
| ( $false
= ( sK0 @ X1 @ X5 ) )
| ( ( X2 @ X4 )
= $true ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( X3 @ X4 )
= $false )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) )
| ( $true
= ( X3 @ X5 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) ) )
= $false )
| ( $true
= ( ~ ( X2 @ X5 ) ) )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK0 @ X1 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X5 @ Y0 ) ) )
= $false )
| ( $false
= ( sK0 @ X1 @ X5 ) )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X4 )
= $false )
| ( $false
= ( X2 @ X5 ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $true
= ( X3 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f195,plain,
! [X2: $i > $o,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] : ( Y1 != X0 )
@ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X0 @ Y0 ) ) ) )
| ( $false
= ( X2 @ X0 ) )
| ( ( sK0 @ X3 @ X1 )
= $false )
| ( $false
= ( sK0 @ X3 @ X0 ) )
| ( X0 = X1 )
| ( $true
= ( X2 @ X1 ) ) ),
inference(leibniz_equality_elimination,[],[f192]) ).
thf(f197,plain,
! [X2: $i > $o,X3: $i,X0: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 != X0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
= $false )
| ( ( sK0 @ X3 @ X1 )
= $false )
| ( $true
= ( X2 @ X1 ) )
| ( $false
= ( X2 @ X0 ) )
| ( X0 = X1 )
| ( $false
= ( sK0 @ X3 @ X0 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f238,plain,
! [X2: $i > $o,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( Y0 != X0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ ( sK5 @ X1 @ X0 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X0 @ Y0 ) ) ) )
| ( $true
= ( X2 @ X1 ) )
| ( X0 = X1 )
| ( $false
= ( X2 @ X0 ) )
| ( ( sK0 @ X3 @ X1 )
= $false )
| ( $false
= ( sK0 @ X3 @ X0 ) ) ),
inference(sigma_proxy_clausification,[],[f197]) ).
thf(f243,plain,
! [X2: $i > $o,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( X2 @ X1 ) )
| ( $false
= ( X2 @ X0 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X0 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X3 @ X0 ) )
| ( ( sK0 @ X3 @ X1 )
= $false )
| ( $false
= ( ( ( sK5 @ X1 @ X0 )
!= X0 )
| ~ ( sK0 @ X1 @ ( sK5 @ X1 @ X0 ) ) ) )
| ( X0 = X1 ) ),
inference(beta-eta_normalization,[],[f238]) ).
thf(f247,plain,
! [X2: $i > $o,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X0 ) )
| ( $true
= ( X2 @ X1 ) )
| ( ( sK0 @ X3 @ X1 )
= $false )
| ( $false
= ( ~ ( sK0 @ X1 @ ( sK5 @ X1 @ X0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X0 @ Y0 ) ) ) )
| ( $false
= ( X2 @ X0 ) )
| ( X0 = X1 ) ),
inference(or_proxy_clausification,[],[f243]) ).
thf(f248,plain,
! [X2: $i > $o,X3: $i,X0: $i,X1: $i] :
( ( ( ( sK5 @ X1 @ X0 )
!= X0 )
= $false )
| ( $true
= ( X2 @ X1 ) )
| ( $false
= ( sK0 @ X3 @ X0 ) )
| ( X0 = X1 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X0 @ Y0 ) ) ) )
| ( $false
= ( X2 @ X0 ) )
| ( ( sK0 @ X3 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f243]) ).
thf(f249,plain,
! [X2: $i > $o,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( X2 @ X0 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X0 @ Y0 ) ) ) )
| ( $true
= ( ( sK5 @ X1 @ X0 )
= X0 ) )
| ( ( sK0 @ X3 @ X1 )
= $false )
| ( X0 = X1 )
| ( $true
= ( X2 @ X1 ) )
| ( $false
= ( sK0 @ X3 @ X0 ) ) ),
inference(not_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X2: $i > $o,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X0 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X3 @ X0 ) )
| ( $false
= ( X2 @ X0 ) )
| ( $true
= ( X2 @ X1 ) )
| ( ( sK0 @ X3 @ X1 )
= $false )
| ( X0 = X1 )
| ( $true
= ( sK0 @ X1 @ ( sK5 @ X1 @ X0 ) ) ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f251,plain,
! [X2: $i > $o,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X0 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X3 @ X0 ) )
| ( ( sK0 @ X3 @ X1 )
= $false )
| ( $false
= ( X2 @ X0 ) )
| ( $true
= ( X2 @ X1 ) )
| ( X0 = X1 )
| ( ( sK5 @ X1 @ X0 )
= X0 ) ),
inference(equality_proxy_clausification,[],[f249]) ).
thf(f296,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] : ( Y1 != X1 )
@ Y0 )
| ~ ( sK0 @ X0 @ Y0 ) ) )
= $false )
| ( X0 = X1 )
| ( ( sK5 @ X1 @ X0 )
= X0 )
| ( X0 = X1 ) ),
inference(leibniz_equality_elimination,[],[f251]) ).
thf(f301,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] : ( Y1 != X1 )
@ Y0 )
| ~ ( sK0 @ X0 @ Y0 ) ) )
= $false )
| ( ( sK5 @ X1 @ X0 )
= X0 )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f296]) ).
thf(f302,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 != X1 )
| ~ ( sK0 @ X0 @ Y0 ) ) )
= $false )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( X0 = X1 )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( ( sK5 @ X1 @ X0 )
= X0 ) ),
inference(beta-eta_normalization,[],[f301]) ).
thf(f390,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] : ( Y1 != X1 )
@ Y0 )
| ~ ( sK0 @ X0 @ Y0 ) ) )
= $false )
| ( X0 = X1 )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( X0 = X1 )
| ( $true
= ( sK0 @ X1 @ ( sK5 @ X1 @ X0 ) ) ) ),
inference(leibniz_equality_elimination,[],[f250]) ).
thf(f394,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] : ( Y1 != X1 )
@ Y0 )
| ~ ( sK0 @ X0 @ Y0 ) ) )
= $false )
| ( X0 = X1 )
| ( $true
= ( sK0 @ X1 @ ( sK5 @ X1 @ X0 ) ) )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f390]) ).
thf(f395,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 != X1 )
| ~ ( sK0 @ X0 @ Y0 ) ) )
= $false )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( X0 = X1 )
| ( $true
= ( sK0 @ X1 @ ( sK5 @ X1 @ X0 ) ) )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f394]) ).
thf(f596,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X0 ) )
| ( ( sK5 @ X1 @ X0 )
= X0 )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( Y0 != X1 )
| ~ ( sK0 @ X0 @ Y0 ) )
@ ( sK5 @ X0 @ X1 ) ) )
| ( X0 = X1 ) ),
inference(sigma_proxy_clausification,[],[f302]) ).
thf(f599,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK5 @ X1 @ X0 )
= X0 )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( ( ( sK5 @ X0 @ X1 )
!= X1 )
| ~ ( sK0 @ X0 @ ( sK5 @ X0 @ X1 ) ) ) )
| ( X0 = X1 ) ),
inference(beta-eta_normalization,[],[f596]) ).
thf(f600,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK5 @ X1 @ X0 )
= X0 )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( ( ~ ( sK0 @ X0 @ ( sK5 @ X0 @ X1 ) ) )
= $false )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( X0 = X1 ) ),
inference(or_proxy_clausification,[],[f599]) ).
thf(f601,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( ( sK5 @ X0 @ X1 )
!= X1 ) )
| ( ( sK5 @ X1 @ X0 )
= X0 )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f599]) ).
thf(f602,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ ( sK5 @ X0 @ X1 ) )
= $true )
| ( X0 = X1 )
| ( ( sK5 @ X1 @ X0 )
= X0 )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f600]) ).
thf(f603,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( X0 = X1 )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( ( sK5 @ X1 @ X0 )
= X0 )
| ( $true
= ( ( sK5 @ X0 @ X1 )
= X1 ) ) ),
inference(not_proxy_clausification,[],[f601]) ).
thf(f604,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( X0 = X1 )
| ( ( sK5 @ X0 @ X1 )
= X1 )
| ( ( sK5 @ X1 @ X0 )
= X0 ) ),
inference(equality_proxy_clausification,[],[f603]) ).
thf(f626,plain,
! [X0: $i] :
( ( sK3
= ( sK5 @ X0 @ sK3 ) )
| ( ( sK5 @ sK3 @ X0 )
= X0 )
| ( sK3 = X0 )
| ( ( sK0 @ sK2 @ X0 )
= $false )
| ( $true = $false ) ),
inference(superposition,[],[f163,f604]) ).
thf(f634,plain,
! [X0: $i] :
( ( sK3
= ( sK5 @ X0 @ sK3 ) )
| ( ( sK5 @ sK3 @ X0 )
= X0 )
| ( sK3 = X0 )
| ( ( sK0 @ sK2 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f626]) ).
thf(f726,plain,
! [X0: $i,X1: $i] :
( ( ( sK5 @ sK3 @ X0 )
= X0 )
| ( ( sK0 @ sK2 @ X0 )
= $false )
| ( sK3 = X0 )
| ( $true
= ( sK0 @ X0 @ sK3 ) )
| ( ( sK5 @ sK3 @ X0 )
= X0 )
| ( $false
= ( sK0 @ X1 @ sK3 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( sK3 = X0 ) ),
inference(superposition,[],[f602,f634]) ).
thf(f730,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X0 @ sK3 ) )
| ( ( sK5 @ sK3 @ X0 )
= X0 )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( sK3 = X0 )
| ( ( sK0 @ sK2 @ X0 )
= $false )
| ( $false
= ( sK0 @ X1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f726]) ).
thf(f782,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ ( sK5 @ X1 @ X0 ) ) )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( Y0 != X1 )
| ~ ( sK0 @ X0 @ Y0 ) )
@ ( sK5 @ X0 @ X1 ) ) )
| ( X0 = X1 )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f395]) ).
thf(f785,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true
= ( sK0 @ X1 @ ( sK5 @ X1 @ X0 ) ) )
| ( $false
= ( ( ( sK5 @ X0 @ X1 )
!= X1 )
| ~ ( sK0 @ X0 @ ( sK5 @ X0 @ X1 ) ) ) )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) ) ),
inference(beta-eta_normalization,[],[f782]) ).
thf(f786,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( ( ~ ( sK0 @ X0 @ ( sK5 @ X0 @ X1 ) ) )
= $false )
| ( $true
= ( sK0 @ X1 @ ( sK5 @ X1 @ X0 ) ) )
| ( X0 = X1 ) ),
inference(or_proxy_clausification,[],[f785]) ).
thf(f789,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ ( sK5 @ X1 @ X0 ) ) )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( X0 = X1 )
| ( ( sK0 @ X0 @ ( sK5 @ X0 @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f786]) ).
thf(f792,plain,
! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( sK1
= ( sK5 @ sK3 @ sK1 ) )
| ( $true = $false )
| ( sK1 = sK3 )
| ( ( sK0 @ X0 @ sK1 )
= $false )
| ( $false
= ( sK0 @ sK2 @ sK1 ) ) ),
inference(superposition,[],[f730,f168]) ).
thf(f799,plain,
! [X0: $i] :
( ( sK1
= ( sK5 @ sK3 @ sK1 ) )
| ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( sK1 = sK3 )
| ( $false
= ( sK0 @ sK2 @ sK1 ) )
| ( ( sK0 @ X0 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f792]) ).
thf(f803,plain,
! [X0: $i] :
( ( sK1
= ( sK5 @ sK3 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK1 ) )
| ( ( sK0 @ X0 @ sK1 )
= $false )
| ( $false
= ( sK0 @ X0 @ sK3 ) ) ),
inference(forward_subsumption_resolution,[],[f799,f167]) ).
thf(f806,plain,
! [X0: $i] :
( ( $true = $false )
| ( sK1
= ( sK5 @ sK3 @ sK1 ) )
| ( ( sK0 @ X0 @ sK1 )
= $false )
| ( $false
= ( sK0 @ X0 @ sK3 ) ) ),
inference(forward_demodulation,[],[f803,f164]) ).
thf(f807,plain,
! [X0: $i] :
( ( ( sK0 @ X0 @ sK1 )
= $false )
| ( sK1
= ( sK5 @ sK3 @ sK1 ) )
| ( $false
= ( sK0 @ X0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f806]) ).
thf(f809,definition,
( spl6_1
<=> ( sK1
= ( sK5 @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f811,plain,
( ( sK1
= ( sK5 @ sK3 @ sK1 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f809]) ).
thf(f813,definition,
( spl6_2
<=> ! [X0: $i] :
( ( ( sK0 @ X0 @ sK1 )
= $false )
| ( $false
= ( sK0 @ X0 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f814,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( ( sK0 @ X0 @ sK1 )
= $false ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f813]) ).
thf(f816,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f807,f813,f809]) ).
thf(f821,plain,
( ( $false
= ( sK0 @ sK2 @ sK1 ) )
| ( $true = $false )
| ~ spl6_2 ),
inference(superposition,[],[f163,f814]) ).
thf(f824,plain,
( ( $false
= ( sK0 @ sK2 @ sK1 ) )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f821]) ).
thf(f837,plain,
( ( $true = $false )
| ~ spl6_2 ),
inference(superposition,[],[f164,f824]) ).
thf(f841,plain,
( $false
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f837]) ).
thf(f842,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f841]) ).
thf(f843,plain,
( ! [X0: $i] :
( ( sK3
= ( sK5 @ sK1 @ sK3 ) )
| ( ( sK0 @ X0 @ sK1 )
= $false )
| ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( sK1 = sK3 )
| ( $true
= ( sK0 @ sK3 @ sK1 ) ) )
| ~ spl6_1 ),
inference(superposition,[],[f602,f811]) ).
thf(f846,plain,
( ! [X0: $i] :
( ( sK3
= ( sK5 @ sK1 @ sK3 ) )
| ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( ( sK0 @ X0 @ sK1 )
= $false )
| ( $true
= ( sK0 @ sK3 @ sK1 ) ) )
| ~ spl6_1 ),
inference(forward_subsumption_resolution,[],[f843,f167]) ).
thf(f849,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK1 )
= $false )
| ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( sK3
= ( sK5 @ sK1 @ sK3 ) ) )
| ~ spl6_1 ),
inference(forward_demodulation,[],[f846,f169]) ).
thf(f850,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( sK3
= ( sK5 @ sK1 @ sK3 ) )
| ( ( sK0 @ X0 @ sK1 )
= $false ) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f849]) ).
thf(f856,definition,
( spl6_4
<=> ( sK3
= ( sK5 @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f858,plain,
( ( sK3
= ( sK5 @ sK1 @ sK3 ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f856]) ).
thf(f859,plain,
( spl6_2
| spl6_4
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f850,f809,f856,f813]) ).
thf(f1447,plain,
( ! [X0: $i] :
( ( sK1 = sK3 )
| ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( ( sK0 @ sK3 @ ( sK5 @ sK3 @ sK1 ) )
= $true )
| ( $true
= ( sK0 @ sK1 @ sK3 ) )
| ( ( sK0 @ X0 @ sK1 )
= $false ) )
| ~ spl6_4 ),
inference(superposition,[],[f789,f858]) ).
thf(f1456,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK3 @ ( sK5 @ sK3 @ sK1 ) )
= $true )
| ( $true
= ( sK0 @ sK1 @ sK3 ) )
| ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( ( sK0 @ X0 @ sK1 )
= $false ) )
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f1447,f167]) ).
thf(f1458,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 @ sK1 ) )
| ( ( sK0 @ X0 @ sK1 )
= $false )
| ( $false
= ( sK0 @ X0 @ sK3 ) ) )
| ~ spl6_1
| ~ spl6_4 ),
inference(forward_demodulation,[],[f1456,f811]) ).
thf(f1461,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( sK0 @ X0 @ sK1 )
= $false )
| ( $true
= ( sK0 @ sK3 @ sK1 ) )
| ( $false
= ( sK0 @ X0 @ sK3 ) ) )
| ~ spl6_1
| ~ spl6_4 ),
inference(forward_demodulation,[],[f1458,f168]) ).
thf(f1462,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 @ sK1 ) )
| ( ( sK0 @ X0 @ sK1 )
= $false ) )
| ~ spl6_1
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f1461]) ).
thf(f1464,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( sK0 @ X0 @ sK1 )
= $false )
| ( $false
= ( sK0 @ X0 @ sK3 ) ) )
| ~ spl6_1
| ~ spl6_4 ),
inference(forward_demodulation,[],[f1462,f169]) ).
thf(f1465,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( ( sK0 @ X0 @ sK1 )
= $false ) )
| ~ spl6_1
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f1464]) ).
thf(f1468,plain,
( spl6_2
| ~ spl6_1
| ~ spl6_4 ),
inference(avatar_split_clause,[],[f1465,f856,f809,f813]) ).
cnf(s2,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f816]) ).
cnf(s4,plain,
~ spl6_2,
inference(sat_conversion,[],[f842]) ).
cnf(s6,plain,
( ~ spl6_1
| spl6_2
| spl6_4 ),
inference(sat_conversion,[],[f859]) ).
cnf(s26,plain,
( ~ spl6_1
| spl6_2
| ~ spl6_4 ),
inference(sat_conversion,[],[f1468]) ).
cnf(s28,plain,
spl6_1,
inference(rat,[],[s2,s4]) ).
cnf(s29,plain,
~ spl6_4,
inference(rat,[],[s26,s4,s28]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s6,s4,s29,s28]) ).
thf(f1469,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL717^1 : TPTP v9.3.1. Bugfixed v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n026.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 09:55:57 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.28 Running higher-order theorem proving
% 0.25/0.31 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
% 0.62/0.48 % (380209)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.62/0.48 % (380218)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=681541110:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.62/0.48 % (380220)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.62/0.48 % (380220)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
% 0.62/0.48 % (380218)Instruction limit reached!
% 0.62/0.48 % (380218)------------------------------
% 0.62/0.48 % (380218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.48 % (380218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.48 % (380215)lrs+10_16_si=on:nwc=1.5:random_seed=2144670506:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.62/0.48 % (380218)CaDiCaL version: 2.1.3
% 0.62/0.48 % (380218)Termination reason: Instruction limit
% 0.62/0.48 % (380218)Termination phase: Saturation
% 0.62/0.48 % (380218)Time elapsed: 0.012 s
% 0.62/0.48 % (380218)Peak memory usage: 12 MB
% 0.62/0.48 % (380218)Instructions burned: 24 (million)
% 0.62/0.48 % (380217)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=715078344: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)
% 0.62/0.48 % (380216)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=895392932:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.62/0.48 % (380214)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4203212210:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.62/0.48 % (380219)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2086354520:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.62/0.48 % (380220)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=4008499031:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.62/0.48 % (380216)Instruction limit reached!
% 0.62/0.48 % (380216)------------------------------
% 0.62/0.48 % (380216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.48 % (380216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.48 % (380216)CaDiCaL version: 2.1.3
% 0.62/0.48 % (380216)Termination reason: Instruction limit
% 0.62/0.48 % (380216)Termination phase: Property scanning
% 0.62/0.48 % (380216)Time elapsed: 0.003 s
% 0.62/0.48 % (380216)Peak memory usage: 10 MB
% 0.62/0.48 % (380216)Instructions burned: 3 (million)
% 0.62/0.48 % (380215)Instruction limit reached!
% 0.62/0.48 % (380215)------------------------------
% 0.62/0.48 % (380215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.48 % (380215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.48 % (380215)CaDiCaL version: 2.1.3
% 0.62/0.48 % (380215)Termination reason: Instruction limit
% 0.62/0.48 % (380215)Termination phase: Saturation
% 0.62/0.48 % (380215)Time elapsed: 0.014 s
% 0.62/0.48 % (380215)Peak memory usage: 12 MB
% 0.62/0.48 % (380215)Instructions burned: 18 (million)
% 0.62/0.48 % (380224)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=876303514:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.62/0.48 % (380224)Instruction limit reached!
% 0.62/0.48 % (380224)------------------------------
% 0.62/0.48 % (380224)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.48 % (380224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.48 % (380224)CaDiCaL version: 2.1.3
% 0.62/0.48 % (380224)Termination reason: Instruction limit
% 0.62/0.48 % (380224)Termination phase: Property scanning
% 0.62/0.48 % (380224)Time elapsed: 0.001 s
% 0.62/0.48 % (380224)Peak memory usage: 10 MB
% 0.62/0.48 % (380224)Instructions burned: 2 (million)
% 0.62/0.48 % (380229)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2351610966:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.62/0.48 % (380230)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.27/0.55 % (380232)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=863481630:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.27/0.55 % (380229)Instruction limit reached!
% 1.27/0.55 % (380229)------------------------------
% 1.27/0.55 % (380229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.27/0.55 % (380229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.27/0.55 % (380229)CaDiCaL version: 2.1.3
% 1.27/0.55 % (380229)Termination reason: Instruction limit
% 1.27/0.55 % (380229)Termination phase: Property scanning
% 1.27/0.55 % (380229)Time elapsed: 0.005 s
% 1.27/0.55 % (380229)Peak memory usage: 10 MB
% 1.27/0.55 % (380229)Instructions burned: 6 (million)
% 1.27/0.55 % (380230)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2528879936:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.27/0.55 % (380232)Instruction limit reached!
% 1.27/0.55 % (380232)------------------------------
% 1.27/0.55 % (380232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.27/0.55 % (380232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.27/0.55 % (380232)CaDiCaL version: 2.1.3
% 1.27/0.55 % (380232)Termination reason: Instruction limit
% 1.27/0.55 % (380232)Termination phase: Saturation
% 1.27/0.55 % (380232)Time elapsed: 0.006 s
% 1.27/0.55 % (380232)Peak memory usage: 12 MB
% 1.27/0.55 % (380232)Instructions burned: 13 (million)
% 1.27/0.55 % (380230)Instruction limit reached!
% 1.27/0.55 % (380230)------------------------------
% 1.27/0.55 % (380230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.27/0.55 % (380230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.27/0.55 % (380230)CaDiCaL version: 2.1.3
% 1.27/0.55 % (380230)Termination reason: Instruction limit
% 1.27/0.55 % (380230)Termination phase: Property scanning
% 1.27/0.55 % (380230)Time elapsed: 0.006 s
% 1.27/0.55 % (380230)Peak memory usage: 10 MB
% 1.27/0.55 % (380230)Instructions burned: 7 (million)
% 1.27/0.55 % (380235)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
% 1.27/0.55 % (380235)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.27/0.55 % (380219)Instruction limit reached!
% 1.27/0.55 % (380219)------------------------------
% 1.27/0.55 % (380219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.27/0.55 % (380219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.27/0.55 % (380219)CaDiCaL version: 2.1.3
% 1.27/0.55 % (380219)Termination reason: Instruction limit
% 1.27/0.55 % (380219)Termination phase: Saturation
% 1.27/0.55 % (380219)Time elapsed: 0.063 s
% 1.27/0.55 % (380219)Peak memory usage: 12 MB
% 1.27/0.55 % (380219)Instructions burned: 75 (million)
% 1.27/0.55 % (380235)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3782093438:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.27/0.55 % (380214)Instruction limit reached!
% 1.27/0.55 % (380214)------------------------------
% 1.27/0.55 % (380214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.27/0.55 % (380214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.27/0.55 % (380214)CaDiCaL version: 2.1.3
% 1.27/0.55 % (380214)Termination reason: Instruction limit
% 1.27/0.55 % (380214)Termination phase: Saturation
% 1.27/0.55 % (380214)Time elapsed: 0.072 s
% 1.27/0.55 % (380214)Peak memory usage: 12 MB
% 1.27/0.55 % (380214)Instructions burned: 87 (million)
% 1.27/0.55 % (380240)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.27/0.55 % (380237)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=1456395770:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.27/0.55 % (380235)Instruction limit reached!
% 1.27/0.55 % (380235)------------------------------
% 1.97/0.60 % (380235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.60 % (380235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.60 % (380235)CaDiCaL version: 2.1.3
% 1.97/0.60 % (380235)Termination reason: Instruction limit
% 1.97/0.60 % (380235)Termination phase: Saturation
% 1.97/0.60 % (380235)Time elapsed: 0.015 s
% 1.97/0.60 % (380235)Peak memory usage: 12 MB
% 1.97/0.60 % (380235)Instructions burned: 28 (million)
% 1.97/0.60 % (380240)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=2229432440:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.97/0.60 % (380240)Instruction limit reached!
% 1.97/0.60 % (380240)------------------------------
% 1.97/0.60 % (380240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.60 % (380240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.60 % (380240)CaDiCaL version: 2.1.3
% 1.97/0.60 % (380240)Termination reason: Instruction limit
% 1.97/0.60 % (380240)Termination phase: Property scanning
% 1.97/0.60 % (380240)Time elapsed: 0.001 s
% 1.97/0.60 % (380240)Peak memory usage: 9 MB
% 1.97/0.60 % (380240)Instructions burned: 2 (million)
% 1.97/0.60 % (380238)lrs+10_1_si=on:cs=on:random_seed=4275105881:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.97/0.60 % (380238)Instruction limit reached!
% 1.97/0.60 % (380238)------------------------------
% 1.97/0.60 % (380238)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.60 % (380238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.60 % (380238)CaDiCaL version: 2.1.3
% 1.97/0.60 % (380238)Termination reason: Instruction limit
% 1.97/0.60 % (380238)Termination phase: Property scanning
% 1.97/0.60 % (380238)Time elapsed: 0.006 s
% 1.97/0.60 % (380238)Peak memory usage: 10 MB
% 1.97/0.60 % (380238)Instructions burned: 8 (million)
% 1.97/0.60 % (380241)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3577094001:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.97/0.60 % (380247)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2087733838:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.97/0.60 % (380243)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=357199369:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.97/0.60 % (380246)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3219085264:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.97/0.60 % (380247)Instruction limit reached!
% 1.97/0.60 % (380247)------------------------------
% 1.97/0.60 % (380247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.60 % (380247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.60 % (380247)CaDiCaL version: 2.1.3
% 1.97/0.60 % (380247)Termination reason: Instruction limit
% 1.97/0.60 % (380247)Termination phase: Saturation
% 1.97/0.60 % (380247)Time elapsed: 0.006 s
% 1.97/0.60 % (380247)Peak memory usage: 12 MB
% 1.97/0.60 % (380247)Instructions burned: 14 (million)
% 1.97/0.60 % (380220)Instruction limit reached!
% 1.97/0.60 % (380220)------------------------------
% 1.97/0.60 % (380220)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.60 % (380220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.60 % (380220)CaDiCaL version: 2.1.3
% 1.97/0.60 % (380220)Termination reason: Instruction limit
% 1.97/0.60 % (380220)Termination phase: Saturation
% 1.97/0.60 % (380220)Time elapsed: 0.124 s
% 1.97/0.60 % (380220)Peak memory usage: 12 MB
% 1.97/0.60 % (380220)Instructions burned: 158 (million)
% 1.97/0.60 % (380243)Refutation not found, incomplete strategy
% 1.97/0.60 % (380243)------------------------------
% 1.97/0.60 % (380243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.60 % (380243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.60 % (380243)CaDiCaL version: 2.1.3
% 1.97/0.60 % (380243)Termination reason: Refutation not found, incomplete strategy
% 1.97/0.60 % (380243)Time elapsed: 0.013 s
% 1.97/0.60 % (380243)Peak memory usage: 12 MB
% 1.97/0.60 % (380243)Instructions burned: 13 (million)
% 1.97/0.60 % (380243)------------------------------
% 2.35/0.65 % (380243)------------------------------
% 2.35/0.65 % (380253)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2665363359:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.35/0.65 % (380246)Instruction limit reached!
% 2.35/0.65 % (380246)------------------------------
% 2.35/0.65 % (380246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.65 % (380246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.65 % (380246)CaDiCaL version: 2.1.3
% 2.35/0.65 % (380246)Termination reason: Instruction limit
% 2.35/0.65 % (380246)Termination phase: Saturation
% 2.35/0.65 % (380246)Time elapsed: 0.023 s
% 2.35/0.65 % (380246)Peak memory usage: 12 MB
% 2.35/0.65 % (380246)Instructions burned: 25 (million)
% 2.35/0.65 % (380241)Refutation not found, incomplete strategy
% 2.35/0.65 % (380241)------------------------------
% 2.35/0.65 % (380241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.65 % (380241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.65 % (380241)CaDiCaL version: 2.1.3
% 2.35/0.65 % (380241)Termination reason: Refutation not found, incomplete strategy
% 2.35/0.65 % (380241)Time elapsed: 0.036 s
% 2.35/0.65 % (380241)Peak memory usage: 13 MB
% 2.35/0.65 % (380241)Instructions burned: 38 (million)
% 2.35/0.65 % (380241)------------------------------
% 2.35/0.65 % (380241)------------------------------
% 2.35/0.65 % (380237)Instruction limit reached!
% 2.35/0.65 % (380237)------------------------------
% 2.35/0.65 % (380237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.65 % (380237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.65 % (380237)CaDiCaL version: 2.1.3
% 2.35/0.65 % (380237)Termination reason: Instruction limit
% 2.35/0.65 % (380237)Termination phase: Saturation
% 2.35/0.65 % (380237)Time elapsed: 0.076 s
% 2.35/0.65 % (380237)Peak memory usage: 13 MB
% 2.35/0.65 % (380237)Instructions burned: 86 (million)
% 2.35/0.65 % (380254)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=687391992:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.35/0.65 % (380255)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=4243587838:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.35/0.65 % (380255)Instruction limit reached!
% 2.35/0.65 % (380255)------------------------------
% 2.35/0.65 % (380255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.65 % (380255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.65 % (380255)CaDiCaL version: 2.1.3
% 2.35/0.65 % (380255)Termination reason: Instruction limit
% 2.35/0.65 % (380255)Termination phase: shuffling
% 2.35/0.65 % (380255)Time elapsed: 0.002 s
% 2.35/0.65 % (380255)Peak memory usage: 9 MB
% 2.35/0.65 % (380255)Instructions burned: 2 (million)
% 2.35/0.65 % (380257)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1011232383:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.35/0.65 % (380254)Instruction limit reached!
% 2.35/0.65 % (380254)------------------------------
% 2.35/0.65 % (380254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.65 % (380254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.65 % (380254)CaDiCaL version: 2.1.3
% 2.35/0.65 % (380254)Termination reason: Instruction limit
% 2.35/0.65 % (380254)Termination phase: Saturation
% 2.35/0.65 % (380254)Time elapsed: 0.013 s
% 2.35/0.65 % (380254)Peak memory usage: 12 MB
% 2.35/0.65 % (380254)Instructions burned: 14 (million)
% 2.35/0.65 % (380258)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2298607746:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.35/0.65 % (380259)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=487760697:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.35/0.65 % (380262)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.35/0.65 % (380262)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.35/0.65 % (380257)Instruction limit reached!
% 2.55/0.74 % (380257)------------------------------
% 2.55/0.74 % (380257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.74 % (380257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.74 % (380257)CaDiCaL version: 2.1.3
% 2.55/0.74 % (380257)Termination reason: Instruction limit
% 2.55/0.74 % (380257)Termination phase: Saturation
% 2.55/0.74 % (380257)Time elapsed: 0.023 s
% 2.55/0.74 % (380257)Peak memory usage: 12 MB
% 2.55/0.74 % (380257)Instructions burned: 27 (million)
% 2.55/0.74 % (380262)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=1377338335:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.55/0.74 % (380258)Instruction limit reached!
% 2.55/0.74 % (380258)------------------------------
% 2.55/0.74 % (380258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.74 % (380258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.74 % (380258)CaDiCaL version: 2.1.3
% 2.55/0.74 % (380258)Termination reason: Instruction limit
% 2.55/0.74 % (380258)Termination phase: Saturation
% 2.55/0.74 % (380258)Time elapsed: 0.020 s
% 2.55/0.74 % (380258)Peak memory usage: 11 MB
% 2.55/0.74 % (380264)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.55/0.74 % (380258)Instructions burned: 23 (million)
% 2.55/0.74 % (380264)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=1874790522:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.55/0.74 % (380262)Instruction limit reached!
% 2.55/0.74 % (380262)------------------------------
% 2.55/0.74 % (380262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.74 % (380262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.74 % (380262)CaDiCaL version: 2.1.3
% 2.55/0.74 % (380262)Termination reason: Instruction limit
% 2.55/0.74 % (380262)Termination phase: Saturation
% 2.55/0.74 % (380262)Time elapsed: 0.014 s
% 2.55/0.74 % (380262)Peak memory usage: 12 MB
% 2.55/0.74 % (380262)Instructions burned: 16 (million)
% 2.55/0.74 % (380264)Instruction limit reached!
% 2.55/0.74 % (380264)------------------------------
% 2.55/0.74 % (380264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.74 % (380264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.74 % (380264)CaDiCaL version: 2.1.3
% 2.55/0.74 % (380264)Termination reason: Instruction limit
% 2.55/0.74 % (380264)Termination phase: Property scanning
% 2.55/0.74 % (380264)Time elapsed: 0.007 s
% 2.55/0.74 % (380264)Peak memory usage: 11 MB
% 2.55/0.74 % (380264)Instructions burned: 8 (million)
% 2.55/0.74 % (380268)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1530685075:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.55/0.74 % (380270)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=416899256:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.55/0.74 % (380270)Instruction limit reached!
% 2.55/0.74 % (380270)------------------------------
% 2.55/0.74 % (380270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.74 % (380270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.74 % (380270)CaDiCaL version: 2.1.3
% 2.55/0.74 % (380270)Termination reason: Instruction limit
% 2.55/0.74 % (380270)Termination phase: Property scanning
% 2.55/0.74 % (380270)Time elapsed: 0.006 s
% 2.55/0.74 % (380270)Peak memory usage: 10 MB
% 2.55/0.74 % (380270)Instructions burned: 7 (million)
% 2.55/0.74 % (380273)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3531554591:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.55/0.74 % (380272)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3801758486:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.55/0.74 % (380259)Instruction limit reached!
% 2.55/0.74 % (380259)------------------------------
% 2.55/0.74 % (380259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.74 % (380259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.83 % (380259)CaDiCaL version: 2.1.3
% 3.24/0.83 % (380259)Termination reason: Instruction limit
% 3.24/0.83 % (380259)Termination phase: Saturation
% 3.24/0.83 % (380259)Time elapsed: 0.056 s
% 3.24/0.83 % (380259)Peak memory usage: 12 MB
% 3.24/0.83 % (380259)Instructions burned: 60 (million)
% 3.24/0.83 % (380268)Instruction limit reached!
% 3.24/0.83 % (380268)------------------------------
% 3.24/0.83 % (380268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.83 % (380268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.83 % (380268)CaDiCaL version: 2.1.3
% 3.24/0.83 % (380268)Termination reason: Instruction limit
% 3.24/0.83 % (380268)Termination phase: Saturation
% 3.24/0.83 % (380268)Time elapsed: 0.028 s
% 3.24/0.83 % (380268)Peak memory usage: 12 MB
% 3.24/0.83 % (380268)Instructions burned: 31 (million)
% 3.24/0.83 % (380272)Instruction limit reached!
% 3.24/0.83 % (380272)------------------------------
% 3.24/0.83 % (380272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.83 % (380272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.83 % (380272)CaDiCaL version: 2.1.3
% 3.24/0.83 % (380272)Termination reason: Instruction limit
% 3.24/0.83 % (380272)Termination phase: Saturation
% 3.24/0.83 % (380272)Time elapsed: 0.019 s
% 3.24/0.83 % (380272)Peak memory usage: 11 MB
% 3.24/0.83 % (380272)Instructions burned: 24 (million)
% 3.24/0.83 % (380273)Instruction limit reached!
% 3.24/0.83 % (380273)------------------------------
% 3.24/0.83 % (380273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.83 % (380273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.83 % (380273)CaDiCaL version: 2.1.3
% 3.24/0.83 % (380273)Termination reason: Instruction limit
% 3.24/0.83 % (380273)Termination phase: Saturation
% 3.24/0.83 % (380273)Time elapsed: 0.020 s
% 3.24/0.83 % (380273)Peak memory usage: 12 MB
% 3.24/0.83 % (380273)Instructions burned: 21 (million)
% 3.24/0.83 % (380253)Instruction limit reached!
% 3.24/0.83 % (380253)------------------------------
% 3.24/0.83 % (380253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.83 % (380253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.83 % (380253)CaDiCaL version: 2.1.3
% 3.24/0.83 % (380253)Termination reason: Instruction limit
% 3.24/0.83 % (380253)Termination phase: Saturation
% 3.24/0.83 % (380253)Time elapsed: 0.133 s
% 3.24/0.83 % (380253)Peak memory usage: 13 MB
% 3.24/0.83 % (380253)Instructions burned: 327 (million)
% 3.24/0.83 % (380276)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=360999269:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 3.24/0.83 % (380279)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3224450255:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 3.24/0.83 % (380280)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2493290426:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 3.24/0.83 % (380280)Refutation not found, incomplete strategy
% 3.24/0.83 % (380280)------------------------------
% 3.24/0.83 % (380280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.83 % (380280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.83 % (380280)CaDiCaL version: 2.1.3
% 3.24/0.83 % (380280)Termination reason: Refutation not found, incomplete strategy
% 3.24/0.83 % (380280)Time elapsed: 0.008 s
% 3.24/0.83 % (380280)Peak memory usage: 12 MB
% 3.24/0.83 % (380280)Instructions burned: 15 (million)
% 3.24/0.83 % (380280)------------------------------
% 3.24/0.83 % (380280)------------------------------
% 3.24/0.83 % (380284)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1417443682:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 3.24/0.83 % (380282)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 3.24/0.83 % (380282)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4153477864:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 3.24/0.83 % (380281)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1187517642:i=42:hud=10:rtra=on_2996 on theBenchmark for (2996ds/42Mi)
% 3.24/0.84 % (380282)Instruction limit reached!
% 3.24/0.84 % (380282)------------------------------
% 3.24/0.84 % (380282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.84 % (380282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.84 % (380282)CaDiCaL version: 2.1.3
% 3.24/0.84 % (380282)Termination reason: Instruction limit
% 3.24/0.84 % (380282)Termination phase: Saturation
% 3.24/0.84 % (380282)Time elapsed: 0.006 s
% 3.24/0.84 % (380282)Peak memory usage: 11 MB
% 3.24/0.84 % (380282)Instructions burned: 8 (million)
% 3.24/0.84 % (380288)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3486468823:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 3.24/0.84 % (380291)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 3.24/0.84 % (380291)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2739209652:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 3.24/0.84 % (380281)Instruction limit reached!
% 3.24/0.84 % (380281)------------------------------
% 3.24/0.84 % (380281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.84 % (380281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.84 % (380281)CaDiCaL version: 2.1.3
% 3.24/0.84 % (380281)Termination reason: Instruction limit
% 3.24/0.84 % (380281)Termination phase: Saturation
% 3.24/0.84 % (380281)Time elapsed: 0.036 s
% 3.24/0.84 % (380281)Peak memory usage: 12 MB
% 3.24/0.84 % (380281)Instructions burned: 43 (million)
% 3.24/0.84 % (380291)Instruction limit reached!
% 3.24/0.84 % (380291)------------------------------
% 3.24/0.84 % (380291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.84 % (380291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.84 % (380291)CaDiCaL version: 2.1.3
% 3.24/0.84 % (380291)Termination reason: Instruction limit
% 3.24/0.84 % (380291)Termination phase: Function definition elimination
% 3.24/0.84 % (380291)Time elapsed: 0.005 s
% 3.24/0.84 % (380291)Peak memory usage: 10 MB
% 3.24/0.84 % (380291)Instructions burned: 6 (million)
% 3.24/0.84 % (380294)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=596914973:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 3.24/0.84 % (380284)Instruction limit reached!
% 3.24/0.84 % (380284)------------------------------
% 3.24/0.84 % (380284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.84 % (380284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.84 % (380284)CaDiCaL version: 2.1.3
% 3.24/0.84 % (380284)Termination reason: Instruction limit
% 3.24/0.84 % (380284)Termination phase: Saturation
% 3.24/0.84 % (380284)Time elapsed: 0.077 s
% 3.24/0.84 % (380284)Peak memory usage: 13 MB
% 3.24/0.84 % (380284)Instructions burned: 182 (million)
% 3.24/0.84 % (380295)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3240254937:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 3.24/0.84 % (380297)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2615110579:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/316Mi)
% 3.24/0.84 % (380294)Instruction limit reached!
% 3.24/0.84 % (380294)------------------------------
% 3.24/0.84 % (380294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.84 % (380294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.84 % (380294)CaDiCaL version: 2.1.3
% 3.24/0.84 % (380294)Termination reason: Instruction limit
% 3.24/0.84 % (380294)Termination phase: Saturation
% 3.24/0.84 % (380294)Time elapsed: 0.021 s
% 3.24/0.84 % (380294)Peak memory usage: 12 MB
% 3.24/0.84 % (380294)Instructions burned: 23 (million)
% 3.24/0.84 % (380295)Instruction limit reached!
% 3.24/0.84 % (380295)------------------------------
% 3.24/0.84 % (380295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.84 % (380295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.84 % (380295)CaDiCaL version: 2.1.3
% 3.24/0.84 % (380295)Termination reason: Instruction limit
% 3.24/0.84 % (380295)Termination phase: Saturation
% 3.24/0.84 % (380295)Time elapsed: 0.017 s
% 3.24/0.84 % (380295)Peak memory usage: 12 MB
% 3.24/0.84 % (380295)Instructions burned: 20 (million)
% 3.24/0.84 % (380279)Instruction limit reached!
% 3.24/0.84 % (380279)------------------------------
% 3.24/0.84 % (380279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.84 % (380279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.84 % (380279)CaDiCaL version: 2.1.3
% 3.24/0.84 % (380279)Termination reason: Instruction limit
% 3.24/0.84 % (380279)Termination phase: Saturation
% 3.24/0.84 % (380279)Time elapsed: 0.123 s
% 3.24/0.84 % (380279)Peak memory usage: 13 MB
% 3.24/0.84 % (380279)Instructions burned: 143 (million)
% 3.24/0.84 % (380301)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3742496755:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2995 on theBenchmark for (2995ds/45Mi)
% 3.24/0.84 % (380300)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=2157708132:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2995 on theBenchmark for (2995ds/853Mi)
% 3.24/0.84 % (380302)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2751428310:i=480:rtra=on_2995 on theBenchmark for (2995ds/480Mi)
% 3.24/0.84 % (380302)Refutation not found, incomplete strategy
% 3.24/0.84 % (380302)------------------------------
% 3.24/0.84 % (380302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.84 % (380302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.84 % (380302)CaDiCaL version: 2.1.3
% 3.24/0.84 % (380302)Termination reason: Refutation not found, incomplete strategy
% 3.24/0.84 % (380302)Time elapsed: 0.007 s
% 3.24/0.84 % (380302)Peak memory usage: 12 MB
% 3.24/0.84 % (380302)Instructions burned: 8 (million)
% 3.24/0.84 % (380302)------------------------------
% 3.24/0.84 % (380302)------------------------------
% 3.24/0.84 % (380301)Instruction limit reached!
% 3.24/0.84 % (380301)------------------------------
% 3.24/0.84 % (380301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.84 % (380301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.84 % (380301)CaDiCaL version: 2.1.3
% 3.24/0.84 % (380301)Termination reason: Instruction limit
% 3.24/0.84 % (380301)Termination phase: Saturation
% 3.24/0.84 % (380301)Time elapsed: 0.026 s
% 3.24/0.84 % (380301)Peak memory usage: 12 MB
% 3.24/0.84 % (380301)Instructions burned: 45 (million)
% 3.24/0.84 % (380288)Instruction limit reached!
% 3.24/0.84 % (380288)------------------------------
% 3.24/0.84 % (380288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.84 % (380288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.84 % (380288)CaDiCaL version: 2.1.3
% 3.24/0.84 % (380288)Termination reason: Instruction limit
% 3.24/0.84 % (380288)Termination phase: Saturation
% 3.24/0.84 % (380288)Time elapsed: 0.127 s
% 3.24/0.84 % (380288)Peak memory usage: 12 MB
% 3.24/0.84 % (380288)Instructions burned: 169 (million)
% 3.24/0.84 % (380276) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-380209-380276"...
% 3.24/0.84 % (380308)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1213058462:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 3.24/0.84 % (380276)...printing done.
% 3.24/0.84 % (380306)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=1104201020:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2995 on theBenchmark for (2995ds/21Mi)
% 3.24/0.84 % (380307)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.24/0.84 % (380308)Instruction limit reached!
% 3.24/0.84 % (380308)------------------------------
% 3.24/0.84 % (380308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.84 % (380308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.84 % (380308)CaDiCaL version: 2.1.3
% 3.24/0.84 % (380308)Termination reason: Instruction limit
% 3.24/0.84 % (380308)Termination phase: Saturation
% 3.24/0.84 % (380308)Time elapsed: 0.012 s
% 3.24/0.84 % (380308)Peak memory usage: 12 MB
% 3.24/0.84 % (380308)Instructions burned: 13 (million)
% 3.24/0.84 % (380276)Refutation found. Thanks to Tanya!
% 3.24/0.84 % SZS status Theorem for theBenchmark
% 3.24/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 3.24/0.84 % (380276)------------------------------
% 3.24/0.84 % (380276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/0.84 % (380276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/0.84 % (380276)CaDiCaL version: 2.1.3
% 3.24/0.84 % (380276)Termination reason: Refutation
% 3.24/0.84 % (380276)Time elapsed: 0.207 s
% 3.24/0.84 % (380276)Peak memory usage: 13 MB
% 3.24/0.84 % (380276)Instructions burned: 241 (million)
% 3.24/0.84 % (380209)Success in time 0.521 s
% 3.24/0.84 % Vampire exiting
%------------------------------------------------------------------------------