%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL584^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:14:23 AM UTC 2026
% Result : Theorem 0.24s 0.31s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 17
% Syntax : Number of formulae : 153 ( 46 unt; 0 typ; 9 def)
% Number of atoms : 1240 ( 190 equ; 0 cnn)
% Maximal formula atoms : 14 ( 8 avg)
% Number of connectives : 1341 ( 106 ~; 217 |; 61 &; 788 @)
% ( 9 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 95 ( 95 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 47 usr; 16 con; 0-4 aty)
% ( 64 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 234 ( 0 sgn 33 !; 0 ?; 234 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
a: $i > $o ).
thf(func_def_21,type,
b: $i > $o ).
thf(func_def_22,type,
r: $i > $i > $o ).
thf(func_def_23,type,
s: $i > $i > $o ).
thf(func_def_24,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_27,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_30,type,
vNOT: $o > $o ).
thf(func_def_31,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
vAND: $o > $o > $o ).
thf(func_def_33,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vIMP: $o > $o > $o ).
thf(func_def_36,type,
vOR: $o > $o > $o ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mand) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f7,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimpl @ X0 @ X1 ) @ ( mimpl @ X1 @ X0 ) ) )
= miff ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',miff) ).
thf(f8,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,conjecture,
mvalid @ ( miff @ ( mbox @ r @ ( mand @ a @ b ) ) @ ( mand @ ( mbox @ r @ a ) @ ( mbox @ r @ b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f17,negated_conjecture,
~ ( mvalid @ ( miff @ ( mbox @ r @ ( mand @ a @ b ) ) @ ( mand @ ( mbox @ r @ a ) @ ( mbox @ r @ b ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f18,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f19,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f20,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f22,plain,
~ ( mvalid @ ( miff @ ( mbox @ r @ ( mand @ a @ b ) ) @ ( mand @ ( mbox @ r @ a ) @ ( mbox @ r @ b ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f23,plain,
( ( mvalid @ ( miff @ ( mbox @ r @ ( mand @ a @ b ) ) @ ( mand @ ( mbox @ r @ a ) @ ( mbox @ r @ b ) ) ) )
!= $true ),
inference(fool_elimination,[],[f22]) ).
thf(f24,plain,
( miff
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimpl @ Y0 @ Y1 ) @ ( mimpl @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f26,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f27,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f30,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f5]) ).
thf(f31,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f36,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f37,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f40,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f41,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f46,plain,
( ( mvalid @ ( miff @ ( mbox @ r @ ( mand @ a @ b ) ) @ ( mand @ ( mbox @ r @ a ) @ ( mbox @ r @ b ) ) ) )
!= $true ),
inference(flattening,[],[f23]) ).
thf(f48,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f50,plain,
( ( mvalid @ ( miff @ ( mbox @ r @ ( mand @ a @ b ) ) @ ( mand @ ( mbox @ r @ a ) @ ( mbox @ r @ b ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f52,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f54,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f55,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f57,plain,
( miff
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimpl @ Y0 @ Y1 ) @ ( mimpl @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f58,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f59,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f65,plain,
( mimpl
= ( ^ [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,[],[f55,f52,f54]) ).
thf(f66,plain,
( miff
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f57,f58,f65,f65]) ).
thf(f67,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ r
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ a
@ b ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ r
@ a )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ r
@ b ) ) ) ) ),
inference(definition_unfolding,[],[f50,f59,f66,f48,f58,f58,f48,f48]) ).
thf(f68,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( ( b @ Y1 )
& ( a @ Y1 ) ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( ( b @ Y1 )
& ( a @ Y1 ) ) ) )
| ( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
( ( ^ [Y0: $i] :
( ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( ( b @ Y1 )
& ( a @ Y1 ) ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( ( b @ Y1 )
& ( a @ Y1 ) ) ) )
| ( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) ) )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) ) )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f71]) ).
thf(f74,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) ) )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X1: $i] :
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f74]) ).
thf(f77,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) )
@ X1 ) )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f75]) ).
thf(f78,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) )
@ X1 ) ) ),
inference(not_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) )
@ X1 ) ) ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) )
@ X1 ) ) ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f81,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( r @ sK0 @ X2 )
=> ( b @ X2 ) ) )
| ( $true
= ( ( r @ sK0 @ X1 )
=> ( ( b @ X1 )
& ( a @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( b @ X2 ) )
| ( $false
= ( r @ sK0 @ X2 ) )
| ( $true
= ( ( r @ sK0 @ X1 )
=> ( ( b @ X1 )
& ( a @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( b @ X2 ) )
| ( $false
= ( r @ sK0 @ X2 ) )
| ( ( ( b @ X1 )
& ( a @ X1 ) )
= $true )
| ( ( r @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f83]) ).
thf(f86,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( b @ X1 ) )
| ( $true
= ( b @ X2 ) )
| ( ( r @ sK0 @ X1 )
= $false )
| ( $false
= ( r @ sK0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f84]) ).
thf(f87,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) )
@ X2 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f79]) ).
thf(f88,plain,
! [X2: $i,X1: $i] :
( ( ( ( r @ sK0 @ X2 )
=> ( a @ X2 ) )
= $true )
| ( $true
= ( ( r @ sK0 @ X1 )
=> ( ( b @ X1 )
& ( a @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK0 @ X2 ) )
| ( $true
= ( a @ X2 ) )
| ( $true
= ( ( r @ sK0 @ X1 )
=> ( ( b @ X1 )
& ( a @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X1: $i] :
( ( ( r @ sK0 @ X1 )
= $false )
| ( $true
= ( a @ X2 ) )
| ( $false
= ( r @ sK0 @ X2 ) )
| ( ( ( b @ X1 )
& ( a @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( a @ X2 ) )
| ( ( r @ sK0 @ X1 )
= $false )
| ( $false
= ( r @ sK0 @ X2 ) )
| ( $true
= ( a @ X1 ) ) ),
inference(and_proxy_clausification,[],[f90]) ).
thf(f105,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f72]) ).
thf(f135,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f105]) ).
thf(f136,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) )
@ sK4 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( ( ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) )
@ sK5 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f136]) ).
thf(f138,plain,
( ( ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) )
@ sK4 )
= $false )
| ( ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) )
@ sK5 )
= $false )
| ( ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) )
@ sK6 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( ( $false
= ( ( r @ sK0 @ sK6 )
=> ( ( b @ sK6 )
& ( a @ sK6 ) ) ) )
| ( ( ( r @ sK0 @ sK5 )
=> ( a @ sK5 ) )
= $false )
| ( ( ( r @ sK0 @ sK4 )
=> ( b @ sK4 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( ( ( ( b @ sK6 )
& ( a @ sK6 ) )
= $false )
| ( ( ( r @ sK0 @ sK4 )
=> ( b @ sK4 ) )
= $false )
| ( ( ( r @ sK0 @ sK5 )
=> ( a @ sK5 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ( ( ( r @ sK0 @ sK4 )
=> ( b @ sK4 ) )
= $false )
| ( $true
= ( r @ sK0 @ sK6 ) )
| ( ( ( r @ sK0 @ sK5 )
=> ( a @ sK5 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f142,plain,
( ( ( ( r @ sK0 @ sK5 )
=> ( a @ sK5 ) )
= $false )
| ( $false
= ( b @ sK4 ) )
| ( $true
= ( r @ sK0 @ sK6 ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( ( ( ( r @ sK0 @ sK5 )
=> ( a @ sK5 ) )
= $false )
| ( $true
= ( r @ sK0 @ sK6 ) )
| ( $true
= ( r @ sK0 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f144,plain,
( ( $true
= ( r @ sK0 @ sK4 ) )
| ( $true
= ( r @ sK0 @ sK6 ) )
| ( ( a @ sK5 )
= $false ) ),
inference(imp_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( $true
= ( r @ sK0 @ sK6 ) )
| ( $true
= ( r @ sK0 @ sK4 ) )
| ( $true
= ( r @ sK0 @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f143]) ).
thf(f146,plain,
( ( $false
= ( b @ sK4 ) )
| ( ( a @ sK5 )
= $false )
| ( $true
= ( r @ sK0 @ sK6 ) ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f147,plain,
( ( $true
= ( r @ sK0 @ sK6 ) )
| ( $false
= ( b @ sK4 ) )
| ( $true
= ( r @ sK0 @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f148,plain,
( ( ( ( r @ sK0 @ sK5 )
=> ( a @ sK5 ) )
= $false )
| ( ( a @ sK6 )
= $false )
| ( ( ( r @ sK0 @ sK4 )
=> ( b @ sK4 ) )
= $false )
| ( ( b @ sK6 )
= $false ) ),
inference(and_proxy_clausification,[],[f140]) ).
thf(f149,plain,
( ( ( a @ sK6 )
= $false )
| ( ( b @ sK6 )
= $false )
| ( ( a @ sK5 )
= $false )
| ( ( ( r @ sK0 @ sK4 )
=> ( b @ sK4 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( $true
= ( r @ sK0 @ sK5 ) )
| ( ( a @ sK6 )
= $false )
| ( ( ( r @ sK0 @ sK4 )
=> ( b @ sK4 ) )
= $false )
| ( ( b @ sK6 )
= $false ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( $true
= ( r @ sK0 @ sK5 ) )
| ( $false
= ( b @ sK4 ) )
| ( ( a @ sK6 )
= $false )
| ( ( b @ sK6 )
= $false ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $true
= ( r @ sK0 @ sK4 ) )
| ( ( b @ sK6 )
= $false )
| ( $true
= ( r @ sK0 @ sK5 ) )
| ( ( a @ sK6 )
= $false ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f153,plain,
( ( ( a @ sK6 )
= $false )
| ( $false
= ( b @ sK4 ) )
| ( ( a @ sK5 )
= $false )
| ( ( b @ sK6 )
= $false ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f154,plain,
( ( ( a @ sK5 )
= $false )
| ( ( b @ sK6 )
= $false )
| ( ( a @ sK6 )
= $false )
| ( $true
= ( r @ sK0 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f156,definition,
( spl7_1
<=> ! [X1: $i] :
( ( $true
= ( b @ X1 ) )
| ( ( r @ sK0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f157,plain,
( ! [X1: $i] :
( ( ( r @ sK0 @ X1 )
= $false )
| ( $true
= ( b @ X1 ) ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f156]) ).
thf(f158,plain,
( spl7_1
| spl7_1 ),
inference(avatar_split_clause,[],[f86,f156,f156]) ).
thf(f160,definition,
( spl7_2
<=> ! [X1: $i] :
( ( $true
= ( a @ X1 ) )
| ( ( r @ sK0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f161,plain,
( ! [X1: $i] :
( ( ( r @ sK0 @ X1 )
= $false )
| ( $true
= ( a @ X1 ) ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f160]) ).
thf(f164,plain,
( spl7_2
| spl7_2 ),
inference(avatar_split_clause,[],[f91,f160,f160]) ).
thf(f206,definition,
( spl7_10
<=> ( $true
= ( r @ sK0 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition]) ).
thf(f208,plain,
( ( $true
= ( r @ sK0 @ sK6 ) )
| ~ spl7_10 ),
inference(avatar_component_clause,[],[f206]) ).
thf(f210,definition,
( spl7_11
<=> ( $true
= ( r @ sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_11])],[avatar_definition]) ).
thf(f212,plain,
( ( $true
= ( r @ sK0 @ sK4 ) )
| ~ spl7_11 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f214,definition,
( spl7_12
<=> ( $true
= ( r @ sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_12])],[avatar_definition]) ).
thf(f216,plain,
( ( $true
= ( r @ sK0 @ sK5 ) )
| ~ spl7_12 ),
inference(avatar_component_clause,[],[f214]) ).
thf(f217,plain,
( spl7_10
| spl7_11
| spl7_12 ),
inference(avatar_split_clause,[],[f145,f214,f210,f206]) ).
thf(f219,definition,
( spl7_13
<=> ( ( a @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl7_13])],[avatar_definition]) ).
thf(f221,plain,
( ( ( a @ sK5 )
= $false )
| ~ spl7_13 ),
inference(avatar_component_clause,[],[f219]) ).
thf(f222,plain,
( spl7_10
| spl7_13
| spl7_11 ),
inference(avatar_split_clause,[],[f144,f210,f219,f206]) ).
thf(f224,definition,
( spl7_14
<=> ( $false
= ( b @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_14])],[avatar_definition]) ).
thf(f226,plain,
( ( $false
= ( b @ sK4 ) )
| ~ spl7_14 ),
inference(avatar_component_clause,[],[f224]) ).
thf(f227,plain,
( spl7_10
| spl7_14
| spl7_12 ),
inference(avatar_split_clause,[],[f147,f214,f224,f206]) ).
thf(f228,plain,
( spl7_14
| spl7_10
| spl7_13 ),
inference(avatar_split_clause,[],[f146,f219,f206,f224]) ).
thf(f230,definition,
( spl7_15
<=> ( ( b @ sK6 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl7_15])],[avatar_definition]) ).
thf(f232,plain,
( ( ( b @ sK6 )
= $false )
| ~ spl7_15 ),
inference(avatar_component_clause,[],[f230]) ).
thf(f234,definition,
( spl7_16
<=> ( ( a @ sK6 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl7_16])],[avatar_definition]) ).
thf(f236,plain,
( ( ( a @ sK6 )
= $false )
| ~ spl7_16 ),
inference(avatar_component_clause,[],[f234]) ).
thf(f237,plain,
( spl7_15
| spl7_16
| spl7_12
| spl7_11 ),
inference(avatar_split_clause,[],[f152,f210,f214,f234,f230]) ).
thf(f238,plain,
( spl7_14
| spl7_16
| spl7_15
| spl7_12 ),
inference(avatar_split_clause,[],[f151,f214,f230,f234,f224]) ).
thf(f239,plain,
( spl7_16
| spl7_11
| spl7_13
| spl7_15 ),
inference(avatar_split_clause,[],[f154,f230,f219,f210,f234]) ).
thf(f240,plain,
( spl7_16
| spl7_15
| spl7_14
| spl7_13 ),
inference(avatar_split_clause,[],[f153,f219,f224,f230,f234]) ).
thf(f246,plain,
( ( $true
= ( a @ sK5 ) )
| ( $true = $false )
| ~ spl7_2
| ~ spl7_12 ),
inference(constrained_superposition,[],[f216,f161]) ).
thf(f248,plain,
( ( $true
= ( a @ sK5 ) )
| ~ spl7_2
| ~ spl7_12 ),
inference(trivial_inequality_removal,[],[f246]) ).
thf(f252,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_12
| ~ spl7_13 ),
inference(forward_demodulation,[],[f248,f221]) ).
thf(f253,plain,
( $false
| ~ spl7_2
| ~ spl7_12
| ~ spl7_13 ),
inference(trivial_inequality_removal,[],[f252]) ).
thf(f254,plain,
( ~ spl7_2
| ~ spl7_12
| ~ spl7_13 ),
inference(avatar_contradiction_clause,[],[f253]) ).
thf(f256,plain,
( ( $true
= ( b @ sK4 ) )
| ( $true = $false )
| ~ spl7_1
| ~ spl7_11 ),
inference(constrained_superposition,[],[f212,f157]) ).
thf(f262,plain,
( ( $true
= ( b @ sK4 ) )
| ~ spl7_1
| ~ spl7_11 ),
inference(trivial_inequality_removal,[],[f256]) ).
thf(f266,plain,
( ( $true = $false )
| ~ spl7_1
| ~ spl7_11
| ~ spl7_14 ),
inference(forward_demodulation,[],[f262,f226]) ).
thf(f267,plain,
( $false
| ~ spl7_1
| ~ spl7_11
| ~ spl7_14 ),
inference(trivial_inequality_removal,[],[f266]) ).
thf(f268,plain,
( ~ spl7_1
| ~ spl7_11
| ~ spl7_14 ),
inference(avatar_contradiction_clause,[],[f267]) ).
thf(f270,plain,
( ( $true
= ( b @ sK6 ) )
| ( $true = $false )
| ~ spl7_1
| ~ spl7_10 ),
inference(constrained_superposition,[],[f208,f157]) ).
thf(f271,plain,
( ( $true
= ( a @ sK6 ) )
| ( $true = $false )
| ~ spl7_2
| ~ spl7_10 ),
inference(constrained_superposition,[],[f161,f208]) ).
thf(f274,plain,
( ( $true
= ( b @ sK6 ) )
| ~ spl7_1
| ~ spl7_10 ),
inference(trivial_inequality_removal,[],[f270]) ).
thf(f275,plain,
( ( $true
= ( a @ sK6 ) )
| ~ spl7_2
| ~ spl7_10 ),
inference(trivial_inequality_removal,[],[f271]) ).
thf(f280,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_10
| ~ spl7_16 ),
inference(forward_demodulation,[],[f275,f236]) ).
thf(f281,plain,
( $false
| ~ spl7_2
| ~ spl7_10
| ~ spl7_16 ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f282,plain,
( ~ spl7_2
| ~ spl7_10
| ~ spl7_16 ),
inference(avatar_contradiction_clause,[],[f281]) ).
thf(f283,plain,
( ( $true = $false )
| ~ spl7_1
| ~ spl7_10
| ~ spl7_15 ),
inference(forward_demodulation,[],[f232,f274]) ).
thf(f284,plain,
( $false
| ~ spl7_1
| ~ spl7_10
| ~ spl7_15 ),
inference(trivial_inequality_removal,[],[f283]) ).
thf(f285,plain,
( ~ spl7_1
| ~ spl7_10
| ~ spl7_15 ),
inference(avatar_contradiction_clause,[],[f284]) ).
cnf(s1,plain,
( spl7_1
| spl7_1 ),
inference(sat_conversion,[],[f158]) ).
cnf(s2,plain,
spl7_1,
inference(rat,[],[s1]) ).
cnf(s5,plain,
( spl7_2
| spl7_2 ),
inference(sat_conversion,[],[f164]) ).
cnf(s6,plain,
spl7_2,
inference(rat,[],[s5]) ).
cnf(s19,plain,
( spl7_10
| spl7_11
| spl7_12 ),
inference(sat_conversion,[],[f217]) ).
cnf(s20,plain,
( spl7_10
| spl7_11
| spl7_13 ),
inference(sat_conversion,[],[f222]) ).
cnf(s21,plain,
( spl7_10
| spl7_12
| spl7_14 ),
inference(sat_conversion,[],[f227]) ).
cnf(s22,plain,
( spl7_10
| spl7_13
| spl7_14 ),
inference(sat_conversion,[],[f228]) ).
cnf(s23,plain,
( spl7_11
| spl7_12
| spl7_15
| spl7_16 ),
inference(sat_conversion,[],[f237]) ).
cnf(s24,plain,
( spl7_12
| spl7_14
| spl7_15
| spl7_16 ),
inference(sat_conversion,[],[f238]) ).
cnf(s25,plain,
( spl7_11
| spl7_13
| spl7_15
| spl7_16 ),
inference(sat_conversion,[],[f239]) ).
cnf(s26,plain,
( spl7_13
| spl7_14
| spl7_15
| spl7_16 ),
inference(sat_conversion,[],[f240]) ).
cnf(s28,plain,
( ~ spl7_2
| ~ spl7_12
| ~ spl7_13 ),
inference(sat_conversion,[],[f254]) ).
cnf(s30,plain,
( ~ spl7_1
| ~ spl7_11
| ~ spl7_14 ),
inference(sat_conversion,[],[f268]) ).
cnf(s32,plain,
( ~ spl7_2
| ~ spl7_10
| ~ spl7_16 ),
inference(sat_conversion,[],[f282]) ).
cnf(s33,plain,
( ~ spl7_1
| ~ spl7_10
| ~ spl7_15 ),
inference(sat_conversion,[],[f285]) ).
cnf(s34,plain,
( spl7_11
| spl7_10 ),
inference(rat,[],[s28,s19,s20,s6]) ).
cnf(s35,plain,
( spl7_14
| spl7_10 ),
inference(rat,[],[s28,s21,s22,s6]) ).
cnf(s36,plain,
spl7_10,
inference(rat,[],[s35,s30,s34,s2]) ).
cnf(s37,plain,
~ spl7_15,
inference(rat,[],[s33,s2,s36]) ).
cnf(s38,plain,
~ spl7_16,
inference(rat,[],[s32,s6,s36]) ).
cnf(s39,plain,
spl7_13,
inference(rat,[],[s30,s25,s26,s2,s37,s38]) ).
cnf(s40,plain,
~ spl7_12,
inference(rat,[],[s28,s6,s39]) ).
cnf(s41,plain,
spl7_14,
inference(rat,[],[s24,s38,s37,s40]) ).
cnf(s42,plain,
spl7_11,
inference(rat,[],[s23,s38,s37,s40]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s30,s2,s41,s42]) ).
thf(f286,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL584^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n011.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 08:57:01 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.24/0.31 % (4023192)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.31 % (4023199)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1285769314:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.31 % (4023197)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3637187263:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.31 % (4023198)lrs+10_16_si=on:nwc=1.5:random_seed=2802609991:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.31 % (4023200)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=4081592920: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)
% 0.24/0.31 % (4023199)Refutation not found, incomplete strategy
% 0.24/0.31 % (4023199)------------------------------
% 0.24/0.31 % (4023199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.31 % (4023199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.31 % (4023199)CaDiCaL version: 2.1.3
% 0.24/0.31 % (4023199)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.31 % (4023199)Time elapsed: 0.003 s
% 0.24/0.31 % (4023199)Peak memory usage: 12 MB
% 0.24/0.31 % (4023199)Instructions burned: 4 (million)
% 0.24/0.31 % (4023199)------------------------------
% 0.24/0.31 % (4023199)------------------------------
% 0.24/0.31 % (4023197) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4023192-4023197"...
% 0.24/0.31 % (4023203)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.31 % (4023203)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
% 0.24/0.31 % (4023198) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4023192-4023198"...
% 0.24/0.31 % (4023197)...printing done.
% 0.24/0.31 % (4023202)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2211639921:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.31 % (4023197)Refutation found. Thanks to Tanya!
% 0.24/0.31 % SZS status Theorem for theBenchmark
% 0.24/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.31 % (4023197)------------------------------
% 0.24/0.31 % (4023197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.31 % (4023197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.31 % (4023197)CaDiCaL version: 2.1.3
% 0.24/0.31 % (4023197)Termination reason: Refutation
% 0.24/0.31 % (4023197)Time elapsed: 0.010 s
% 0.24/0.31 % (4023197)Peak memory usage: 13 MB
% 0.24/0.31 % (4023197)Instructions burned: 17 (million)
% 0.24/0.31 % (4023192)Success in time 0.048 s
% 0.24/0.31 % Vampire exiting
%------------------------------------------------------------------------------