%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL715^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 0.19s 0.31s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 11
% Syntax : Number of formulae : 102 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 597 ( 160 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 1205 ( 193 ~; 145 |; 12 &; 760 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 212 ( 212 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 50 usr; 5 con; 0-4 aty)
% ( 72 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 380 ( 270 ^; 107 !; 3 ?; 380 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vIMP: $o > $o > $o ).
thf(func_def_41,type,
vAND: $o > $o > $o ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
vNOT: $o > $o ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_48,type,
sK1: $i > ( $i > $o ) > $i ).
thf(func_def_49,type,
sK2: $i > ( $i > $o ) > $i ).
thf(func_def_51,type,
sK4: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f11,axiom,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f17,axiom,
( mdia
= ( ^ [X0: $i > $i > $o,X1: $i > $o] : ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mdia) ).
thf(f24,axiom,
( mfunctional
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] :
( ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X2 = X3 ) )
& ( X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mfunctional) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mequiv @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ X1 ) ) ) )
=> ( mfunctional @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mequiv @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ X1 ) ) ) )
=> ( mfunctional @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f34,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f35,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f41,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f42,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mequiv @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ X1 ) ) ) )
=> ( mfunctional @ X0 ) ),
inference(rectify,[],[f33]) ).
thf(f44,plain,
~ ! [X0: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mequiv @ ( mdia @ X0 @ Y0 ) @ ( mbox @ X0 @ Y0 ) ) ) ) )
=> ( ( mfunctional @ X0 )
= $true ) ),
inference(fool_elimination,[],[f43]) ).
thf(f50,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f51,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f58,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f59,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f73,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f74,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f80,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f81,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f82,plain,
( mfunctional
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] :
( ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X2 = X3 ) )
& ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f83,plain,
( mfunctional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f86,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( mfunctional @ X0 )
!= $true )
& ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mequiv @ ( mdia @ X0 @ Y0 ) @ ( mbox @ X0 @ Y0 ) ) ) ) ) ),
inference(ennf_transformation,[],[f44]) ).
thf(f88,plain,
( ( ( mfunctional @ sK0 )
!= $true )
& ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mequiv @ ( mdia @ sK0 @ Y0 ) @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f89,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f90,plain,
( mfunctional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f92,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f95,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f97,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f104,plain,
( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mequiv @ ( mdia @ sK0 @ Y0 ) @ ( mbox @ sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f105,plain,
( ( mfunctional @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f108,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f111,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f112,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f114,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f117,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
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,[],[f97,f114,f112,f114,f114]) ).
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,[],[f92,f112,f114]) ).
thf(f127,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [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 ) ) )
@ ( ^ [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 )
@ Y0
@ Y1 )
@ ( ^ [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 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f89,f124,f125,f125]) ).
thf(f132,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f117,f114,f95,f114]) ).
thf(f133,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) )
@ sK0 )
!= $true ),
inference(definition_unfolding,[],[f105,f90]) ).
thf(f134,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y6 @ Y7 )
| ( Y5 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y6 @ Y7 )
| ( Y5 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ Y1
@ Y2 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y6 @ Y7 )
| ( Y5 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ Y2
@ Y1 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f104,f111,f108,f127,f132,f95]) ).
thf(f135,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
! [X2: $i > $o,X1: $i] :
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: $i > $o,X1: $i] :
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f140]) ).
thf(f142,plain,
! [X2: $i > $o,X1: $i] :
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f140]) ).
thf(f143,plain,
! [X2: $i > $o,X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X2: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ ( sK1 @ X1 @ X2 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ ( sK1 @ X1 @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ ( sK2 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ( X2 @ ( sK1 @ X1 @ X2 ) )
| ~ ( sK0 @ X1 @ ( sK1 @ X1 @ X2 ) ) )
= $false )
| ( ( ~ ( X2 @ ( sK2 @ X1 @ X2 ) )
| ~ ( sK0 @ X1 @ ( sK2 @ X1 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f151,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( X2 @ ( sK2 @ X1 @ X2 ) )
| ~ ( sK0 @ X1 @ ( sK2 @ X1 @ X2 ) ) )
= $false )
| ( ( X2 @ ( sK1 @ X1 @ X2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f149]) ).
thf(f152,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( sK0 @ X1 @ ( sK2 @ X1 @ X2 ) ) )
= $false )
| ( ( X2 @ ( sK1 @ X1 @ X2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f155,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ ( sK1 @ X1 @ X2 ) )
= $false )
| ( $true
= ( sK0 @ X1 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f162,plain,
! [X2: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f141]) ).
thf(f163,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X3 ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X3 ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( X2 @ X4 )
| ~ ( sK0 @ X1 @ X4 ) )
= $true )
| ( $true
= ( ( X2 @ X3 )
| ~ ( sK0 @ X1 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( sK0 @ X1 @ X4 ) ) )
| ( ( ~ ( X2 @ X4 ) )
= $true )
| ( $true
= ( ( X2 @ X3 )
| ~ ( sK0 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X4 )
= $false )
| ( $true
= ( ( X2 @ X3 )
| ~ ( sK0 @ X1 @ X3 ) ) )
| ( ( ~ ( X2 @ X4 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X4 )
= $false )
| ( $true
= ( ~ ( sK0 @ X1 @ X3 ) ) )
| ( $true
= ( X2 @ X3 ) )
| ( ( ~ ( X2 @ X4 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( ( ~ ( X2 @ X4 ) )
= $true )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( X2 @ X4 )
= $false )
| ( $true
= ( X2 @ X3 ) )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f175,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ sK3 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ sK3 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( ( sK0 @ sK3 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( X1 = Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( ( sK0 @ sK3 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( X1 = Y0 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK4 @ X1 ) )
= $false )
| ( ( sK0 @ sK3 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( ( sK0 @ sK3 @ X1 )
= $false )
| ( ( ( sK0 @ sK3 @ ( sK4 @ X1 ) )
=> ( X1
= ( sK4 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( ( X1
= ( sK4 @ X1 ) )
= $false )
| ( ( sK0 @ sK3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK3 @ ( sK4 @ X1 ) ) )
| ( ( sK0 @ sK3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f181]) ).
thf(f184,plain,
! [X1: $i] :
( ( ( sK4 @ X1 )
!= X1 )
| ( ( sK0 @ sK3 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f182]) ).
thf(f186,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X2 @ X0 )
= $false ) ),
inference(leibniz_equality_elimination,[],[f173]) ).
thf(f244,plain,
! [X0: $i,X1: $i] :
( ( ( sK0 @ sK3 @ X0 )
= $false )
| ( $true = $false )
| ( ( sK4 @ X0 )
= X1 )
| ( ( sK0 @ sK3 @ X1 )
= $false ) ),
inference(constrained_superposition,[],[f183,f186]) ).
thf(f249,plain,
! [X0: $i,X1: $i] :
( ( ( sK0 @ sK3 @ X0 )
= $false )
| ( ( sK0 @ sK3 @ X1 )
= $false )
| ( ( sK4 @ X0 )
= X1 ) ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f267,plain,
! [X0: $i] :
( ( $false != $false )
| ( ( sK4 @ X0 )
= X0 )
| ( ( sK0 @ sK3 @ X0 )
= $false ) ),
inference(equality_factoring,[],[f249]) ).
thf(f273,plain,
! [X0: $i] :
( ( ( sK4 @ X0 )
= X0 )
| ( ( sK0 @ sK3 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f267]) ).
thf(f282,plain,
! [X0: $i] :
( ( sK0 @ sK3 @ X0 )
= $false ),
inference(forward_subsumption_resolution,[],[f273,f184]) ).
thf(f749,plain,
! [X0: $i > $o] :
( ( ( X0 @ ( sK1 @ sK3 @ X0 ) )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f282,f155]) ).
thf(f771,plain,
! [X0: $i > $o] :
( ( X0 @ ( sK1 @ sK3 @ X0 ) )
= $false ),
inference(trivial_inequality_removal,[],[f749]) ).
thf(f795,plain,
( ( ^ [Y0: $i] : $true
@ ( sK1 @ sK3
@ ^ [Y0: $i] : $true ) )
= $false ),
inference(primitive_instantiation,[],[f771]) ).
thf(f808,plain,
$true = $false,
inference(beta-eta_normalization,[],[f795]) ).
thf(f809,plain,
$false,
inference(trivial_inequality_removal,[],[f808]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL715^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n004.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 09:49:52 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.31 % (1081991)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.31 % (1081997)lrs+10_16_si=on:nwc=1.5:random_seed=2170049168:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.31 % (1081996)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2411671186:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.31 % (1081999)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=543783936: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)
% 0.19/0.31 % (1081998)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2243809440:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.31 % (1081997)Instruction limit reached!
% 0.19/0.31 % (1081997)------------------------------
% 0.19/0.31 % (1081997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (1081997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (1081997)CaDiCaL version: 2.1.3
% 0.19/0.31 % (1081997)Termination reason: Instruction limit
% 0.19/0.31 % (1081997)Termination phase: Saturation
% 0.19/0.31 % (1081997)Time elapsed: 0.009 s
% 0.19/0.31 % (1081997)Peak memory usage: 12 MB
% 0.19/0.31 % (1081997)Instructions burned: 19 (million)
% 0.19/0.31 % (1081998)Instruction limit reached!
% 0.19/0.31 % (1081998)------------------------------
% 0.19/0.31 % (1081998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (1081998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (1081998)CaDiCaL version: 2.1.3
% 0.19/0.31 % (1081998)Termination reason: Instruction limit
% 0.19/0.31 % (1081998)Termination phase: Property scanning
% 0.19/0.31 % (1081998)Time elapsed: 0.002 s
% 0.19/0.31 % (1081998)Peak memory usage: 10 MB
% 0.19/0.31 % (1081998)Instructions burned: 4 (million)
% 0.19/0.31 % (1082000)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3364265492:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.31 % (1082007)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3801532176:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.31 % (1082007)Instruction limit reached!
% 0.19/0.31 % (1082007)------------------------------
% 0.19/0.31 % (1082007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (1082007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (1082007)CaDiCaL version: 2.1.3
% 0.19/0.31 % (1082007)Termination reason: Instruction limit
% 0.19/0.31 % (1082007)Termination phase: Property scanning
% 0.19/0.31 % (1082007)Time elapsed: 0.001 s
% 0.19/0.31 % (1082007)Peak memory usage: 10 MB
% 0.19/0.31 % (1082007)Instructions burned: 3 (million)
% 0.19/0.31 % (1082002)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.31 % (1082002)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
% 0.19/0.31 % (1082001)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2488689699:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.31 % (1082008)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4265927740:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.19/0.31 % (1082000)Instruction limit reached!
% 0.19/0.31 % (1082000)------------------------------
% 0.19/0.31 % (1082000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (1082000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (1082000)CaDiCaL version: 2.1.3
% 0.19/0.31 % (1082000)Termination reason: Instruction limit
% 0.19/0.31 % (1082000)Termination phase: Saturation
% 0.19/0.31 % (1082000)Time elapsed: 0.014 s
% 0.19/0.31 % (1082000)Peak memory usage: 12 MB
% 0.19/0.31 % (1082002)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=479627084:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.31 % (1082000)Instructions burned: 25 (million)
% 0.19/0.31 % (1082011)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.19/0.31 % (1082008)Instruction limit reached!
% 0.19/0.31 % (1082008)------------------------------
% 0.19/0.31 % (1082008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (1082008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (1082008)CaDiCaL version: 2.1.3
% 0.19/0.31 % (1082008)Termination reason: Instruction limit
% 0.19/0.31 % (1082008)Termination phase: Property scanning
% 0.19/0.31 % (1082008)Time elapsed: 0.003 s
% 0.19/0.31 % (1082008)Peak memory usage: 10 MB
% 0.19/0.31 % (1082008)Instructions burned: 5 (million)
% 0.19/0.31 % (1082011)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3354952780:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.19/0.31 % (1081996) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1081991-1081996"...
% 0.19/0.31 % (1082011)Instruction limit reached!
% 0.19/0.31 % (1082011)------------------------------
% 0.19/0.31 % (1082011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (1082011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (1082011)CaDiCaL version: 2.1.3
% 0.19/0.31 % (1082011)Termination reason: Instruction limit
% 0.19/0.31 % (1082011)Termination phase: Saturation
% 0.19/0.31 % (1082011)Time elapsed: 0.002 s
% 0.19/0.31 % (1082011)Peak memory usage: 12 MB
% 0.19/0.31 % (1082011)Instructions burned: 10 (million)
% 0.19/0.31 % (1081996)...printing done.
% 0.19/0.31 % (1081996)Refutation found. Thanks to Tanya!
% 0.19/0.31 % SZS status Theorem for theBenchmark
% 0.19/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.31 % (1081996)------------------------------
% 0.19/0.31 % (1081996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (1081996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (1081996)CaDiCaL version: 2.1.3
% 0.19/0.31 % (1081996)Termination reason: Refutation
% 0.19/0.31 % (1081996)Time elapsed: 0.031 s
% 0.19/0.31 % (1081996)Peak memory usage: 12 MB
% 0.19/0.31 % (1081996)Instructions burned: 64 (million)
% 0.19/0.31 % (1081991)Success in time 0.065 s
% 0.19/0.31 % Vampire exiting
%------------------------------------------------------------------------------