%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n017.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 08:14:59 AM UTC 2026
% Result : Theorem 0.46s 0.38s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 17
% Syntax : Number of formulae : 156 ( 46 unt; 0 typ; 9 def)
% Number of atoms : 1299 ( 195 equ; 0 cnn)
% Maximal formula atoms : 14 ( 8 avg)
% Number of connectives : 1437 ( 111 ~; 223 |; 66 &; 847 @)
% ( 9 <=>; 108 =>; 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)
% ( 73 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 247 ( 0 sgn 34 !; 0 ?; 247 :)
% 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_26,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(func_def_28,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
vOR: $o > $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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
vIMP: $o > $o > $o ).
thf(func_def_35,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
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,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
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,
( miff
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimpl @ X0 @ X1 ) @ ( mimpl @ X1 @ X0 ) ) ) ),
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(f20,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f21,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f23,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f24,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f25,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f27,plain,
( miff
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimpl @ Y0 @ Y1 ) @ ( mimpl @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f28,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f29,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f36,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f37,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f44,plain,
~ ( mvalid @ ( miff @ ( mbox @ r @ ( mand @ a @ b ) ) @ ( mand @ ( mbox @ r @ a ) @ ( mbox @ r @ b ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f45,plain,
( ( mvalid @ ( miff @ ( mbox @ r @ ( mand @ a @ b ) ) @ ( mand @ ( mbox @ r @ a ) @ ( mbox @ r @ b ) ) ) )
!= $true ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( ( mvalid @ ( miff @ ( mbox @ r @ ( mand @ a @ b ) ) @ ( mand @ ( mbox @ r @ a ) @ ( mbox @ r @ b ) ) ) )
!= $true ),
inference(flattening,[],[f45]) ).
thf(f49,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f50,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f51,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f52,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f53,plain,
( miff
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimpl @ Y0 @ Y1 ) @ ( mimpl @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f54,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f58,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f62,plain,
( ( mvalid @ ( miff @ ( mbox @ r @ ( mand @ a @ b ) ) @ ( mand @ ( mbox @ r @ a ) @ ( mbox @ r @ b ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f46]) ).
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,[],[f52,f50,f49]) ).
thf(f66,plain,
( miff
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ 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,[],[f53,f51,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] :
( ( Y2 @ Y4 )
& ( Y3 @ 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] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ a
@ b ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ 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,[],[f62,f58,f66,f54,f51,f51,f54,f54]) ).
thf(f68,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( ( a @ Y1 )
& ( b @ Y1 ) ) ) )
| ( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) )
& ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( ( a @ Y1 )
& ( b @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
( $false
= ( ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( ( a @ Y1 )
& ( b @ Y1 ) ) ) )
| ( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) )
& ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( ( a @ Y1 )
& ( b @ Y1 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( $false
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ 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 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
( ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f71]) ).
thf(f74,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f74]) ).
thf(f77,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f76]) ).
thf(f79,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f77]) ).
thf(f80,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( r @ sK0 @ X1 )
=> ( a @ X1 ) ) )
| ( $true
= ( ( r @ sK0 @ X2 )
=> ( ( a @ X2 )
& ( b @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK0 @ X1 ) )
| ( $true
= ( ( r @ sK0 @ X2 )
=> ( ( a @ X2 )
& ( b @ X2 ) ) ) )
| ( $true
= ( a @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK0 @ X1 ) )
| ( $false
= ( r @ sK0 @ X2 ) )
| ( $true
= ( a @ X1 ) )
| ( $true
= ( ( a @ X2 )
& ( b @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f83]) ).
thf(f86,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK0 @ X1 ) )
| ( $false
= ( r @ sK0 @ X2 ) )
| ( $true
= ( a @ X1 ) )
| ( $true
= ( a @ X2 ) ) ),
inference(and_proxy_clausification,[],[f84]) ).
thf(f98,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f75]) ).
thf(f100,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f98]) ).
thf(f101,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( r @ sK0 @ X1 )
=> ( b @ X1 ) ) )
| ( $true
= ( ( r @ sK0 @ X2 )
=> ( ( a @ X2 )
& ( b @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK0 @ X1 ) )
| ( $true
= ( ( r @ sK0 @ X2 )
=> ( ( a @ X2 )
& ( b @ X2 ) ) ) )
| ( $true
= ( b @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK0 @ X1 ) )
| ( $false
= ( r @ sK0 @ X2 ) )
| ( $true
= ( b @ X1 ) )
| ( $true
= ( ( a @ X2 )
& ( b @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK0 @ X1 ) )
| ( $false
= ( r @ sK0 @ X2 ) )
| ( $true
= ( b @ X1 ) )
| ( $true
= ( b @ X2 ) ) ),
inference(and_proxy_clausification,[],[f105]) ).
thf(f119,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) )
@ sK5 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f72]) ).
thf(f120,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) )
@ sK5 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f119]) ).
thf(f134,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f120]) ).
thf(f135,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) )
@ sK6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f134]) ).
thf(f136,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( a @ Y0 )
& ( b @ Y0 ) ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( a @ Y0 ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( ( $false
= ( ( r @ sK0 @ sK5 )
=> ( ( a @ sK5 )
& ( b @ sK5 ) ) ) )
| ( $false
= ( ( r @ sK0 @ sK6 )
=> ( b @ sK6 ) ) )
| ( $false
= ( ( r @ sK0 @ sK7 )
=> ( a @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
( ( $false
= ( ( a @ sK5 )
& ( b @ sK5 ) ) )
| ( $false
= ( ( r @ sK0 @ sK6 )
=> ( b @ sK6 ) ) )
| ( $false
= ( ( r @ sK0 @ sK7 )
=> ( a @ sK7 ) ) ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( ( $true
= ( r @ sK0 @ sK5 ) )
| ( $false
= ( ( r @ sK0 @ sK6 )
=> ( b @ sK6 ) ) )
| ( $false
= ( ( r @ sK0 @ sK7 )
=> ( a @ sK7 ) ) ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f140,plain,
( ( $true
= ( r @ sK0 @ sK5 ) )
| ( $false
= ( b @ sK6 ) )
| ( $false
= ( ( r @ sK0 @ sK7 )
=> ( a @ sK7 ) ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ( $true
= ( r @ sK0 @ sK5 ) )
| ( $true
= ( r @ sK0 @ sK6 ) )
| ( $false
= ( ( r @ sK0 @ sK7 )
=> ( a @ sK7 ) ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f142,plain,
( ( $true
= ( r @ sK0 @ sK5 ) )
| ( $true
= ( r @ sK0 @ sK6 ) )
| ( $false
= ( a @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( ( $true
= ( r @ sK0 @ sK5 ) )
| ( $true
= ( r @ sK0 @ sK6 ) )
| ( $true
= ( r @ sK0 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f144,plain,
( ( $true
= ( r @ sK0 @ sK5 ) )
| ( $false
= ( b @ sK6 ) )
| ( $false
= ( a @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f145,plain,
( ( $true
= ( r @ sK0 @ sK5 ) )
| ( $false
= ( b @ sK6 ) )
| ( $true
= ( r @ sK0 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f146,plain,
( ( $false
= ( b @ sK5 ) )
| ( $false
= ( ( r @ sK0 @ sK6 )
=> ( b @ sK6 ) ) )
| ( $false
= ( ( r @ sK0 @ sK7 )
=> ( a @ sK7 ) ) )
| ( $false
= ( a @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f138]) ).
thf(f147,plain,
( ( $false
= ( b @ sK5 ) )
| ( $false
= ( b @ sK6 ) )
| ( $false
= ( ( r @ sK0 @ sK7 )
=> ( a @ sK7 ) ) )
| ( $false
= ( a @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( $false
= ( b @ sK5 ) )
| ( $true
= ( r @ sK0 @ sK6 ) )
| ( $false
= ( ( r @ sK0 @ sK7 )
=> ( a @ sK7 ) ) )
| ( $false
= ( a @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f149,plain,
( ( $false
= ( b @ sK5 ) )
| ( $true
= ( r @ sK0 @ sK6 ) )
| ( $false
= ( a @ sK7 ) )
| ( $false
= ( a @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( $false
= ( b @ sK5 ) )
| ( $true
= ( r @ sK0 @ sK6 ) )
| ( $true
= ( r @ sK0 @ sK7 ) )
| ( $false
= ( a @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( $false
= ( b @ sK5 ) )
| ( $false
= ( b @ sK6 ) )
| ( $false
= ( a @ sK7 ) )
| ( $false
= ( a @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f152,plain,
( ( $false
= ( b @ sK5 ) )
| ( $false
= ( b @ sK6 ) )
| ( $true
= ( r @ sK0 @ sK7 ) )
| ( $false
= ( a @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f154,definition,
( spl8_1
<=> ! [X2: $i] :
( ( $false
= ( r @ sK0 @ X2 ) )
| ( $true
= ( a @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f155,plain,
( ! [X2: $i] :
( ( $false
= ( r @ sK0 @ X2 ) )
| ( $true
= ( a @ X2 ) ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f154]) ).
thf(f156,plain,
( spl8_1
| spl8_1 ),
inference(avatar_split_clause,[],[f86,f154,f154]) ).
thf(f158,definition,
( spl8_2
<=> ! [X2: $i] :
( ( $false
= ( r @ sK0 @ X2 ) )
| ( $true
= ( b @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f159,plain,
( ! [X2: $i] :
( ( $false
= ( r @ sK0 @ X2 ) )
| ( $true
= ( b @ X2 ) ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f158]) ).
thf(f182,plain,
( spl8_2
| spl8_2 ),
inference(avatar_split_clause,[],[f106,f158,f158]) ).
thf(f204,definition,
( spl8_11
<=> ( $true
= ( r @ sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_11])],[avatar_definition]) ).
thf(f206,plain,
( ( $true
= ( r @ sK0 @ sK5 ) )
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f204]) ).
thf(f210,definition,
( spl8_12
<=> ( $false
= ( a @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_12])],[avatar_definition]) ).
thf(f212,plain,
( ( $false
= ( a @ sK5 ) )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f214,definition,
( spl8_13
<=> ( $false
= ( b @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_13])],[avatar_definition]) ).
thf(f216,plain,
( ( $false
= ( b @ sK5 ) )
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f214]) ).
thf(f220,definition,
( spl8_14
<=> ( $true
= ( r @ sK0 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_14])],[avatar_definition]) ).
thf(f222,plain,
( ( $true
= ( r @ sK0 @ sK7 ) )
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f220]) ).
thf(f224,definition,
( spl8_15
<=> ( $true
= ( r @ sK0 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_15])],[avatar_definition]) ).
thf(f226,plain,
( ( $true
= ( r @ sK0 @ sK6 ) )
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f224]) ).
thf(f227,plain,
( spl8_14
| spl8_15
| spl8_11 ),
inference(avatar_split_clause,[],[f143,f204,f224,f220]) ).
thf(f229,definition,
( spl8_16
<=> ( $false
= ( a @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_16])],[avatar_definition]) ).
thf(f231,plain,
( ( $false
= ( a @ sK7 ) )
| ~ spl8_16 ),
inference(avatar_component_clause,[],[f229]) ).
thf(f232,plain,
( spl8_16
| spl8_15
| spl8_11 ),
inference(avatar_split_clause,[],[f142,f204,f224,f229]) ).
thf(f234,definition,
( spl8_17
<=> ( $false
= ( b @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_17])],[avatar_definition]) ).
thf(f236,plain,
( ( $false
= ( b @ sK6 ) )
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f234]) ).
thf(f237,plain,
( spl8_14
| spl8_17
| spl8_11 ),
inference(avatar_split_clause,[],[f145,f204,f234,f220]) ).
thf(f238,plain,
( spl8_16
| spl8_17
| spl8_11 ),
inference(avatar_split_clause,[],[f144,f204,f234,f229]) ).
thf(f239,plain,
( spl8_12
| spl8_14
| spl8_15
| spl8_13 ),
inference(avatar_split_clause,[],[f150,f214,f224,f220,f210]) ).
thf(f240,plain,
( spl8_12
| spl8_16
| spl8_15
| spl8_13 ),
inference(avatar_split_clause,[],[f149,f214,f224,f229,f210]) ).
thf(f241,plain,
( spl8_12
| spl8_14
| spl8_17
| spl8_13 ),
inference(avatar_split_clause,[],[f152,f214,f234,f220,f210]) ).
thf(f242,plain,
( spl8_12
| spl8_16
| spl8_17
| spl8_13 ),
inference(avatar_split_clause,[],[f151,f214,f234,f229,f210]) ).
thf(f252,plain,
( ( $false = $true )
| ( $true
= ( a @ sK5 ) )
| ~ spl8_1
| ~ spl8_11 ),
inference(constrained_superposition,[],[f155,f206]) ).
thf(f257,plain,
( ( $true
= ( a @ sK5 ) )
| ~ spl8_1
| ~ spl8_11 ),
inference(trivial_inequality_removal,[],[f252]) ).
thf(f261,plain,
( ( $false = $true )
| ~ spl8_1
| ~ spl8_11
| ~ spl8_12 ),
inference(forward_demodulation,[],[f257,f212]) ).
thf(f262,plain,
( $false
| ~ spl8_1
| ~ spl8_11
| ~ spl8_12 ),
inference(trivial_inequality_removal,[],[f261]) ).
thf(f263,plain,
( ~ spl8_1
| ~ spl8_11
| ~ spl8_12 ),
inference(avatar_contradiction_clause,[],[f262]) ).
thf(f267,plain,
( ( $false = $true )
| ( $true
= ( b @ sK5 ) )
| ~ spl8_2
| ~ spl8_11 ),
inference(constrained_superposition,[],[f159,f206]) ).
thf(f272,plain,
( ( $true
= ( b @ sK5 ) )
| ~ spl8_2
| ~ spl8_11 ),
inference(trivial_inequality_removal,[],[f267]) ).
thf(f276,plain,
( ( $false = $true )
| ~ spl8_2
| ~ spl8_11
| ~ spl8_13 ),
inference(forward_demodulation,[],[f272,f216]) ).
thf(f277,plain,
( $false
| ~ spl8_2
| ~ spl8_11
| ~ spl8_13 ),
inference(trivial_inequality_removal,[],[f276]) ).
thf(f278,plain,
( ~ spl8_2
| ~ spl8_11
| ~ spl8_13 ),
inference(avatar_contradiction_clause,[],[f277]) ).
thf(f285,plain,
( ( $false = $true )
| ( $true
= ( a @ sK7 ) )
| ~ spl8_1
| ~ spl8_14 ),
inference(constrained_superposition,[],[f222,f155]) ).
thf(f290,plain,
( ( $true
= ( a @ sK7 ) )
| ~ spl8_1
| ~ spl8_14 ),
inference(trivial_inequality_removal,[],[f285]) ).
thf(f295,plain,
( ( $false = $true )
| ~ spl8_1
| ~ spl8_14
| ~ spl8_16 ),
inference(forward_demodulation,[],[f290,f231]) ).
thf(f296,plain,
( $false
| ~ spl8_1
| ~ spl8_14
| ~ spl8_16 ),
inference(trivial_inequality_removal,[],[f295]) ).
thf(f297,plain,
( ~ spl8_1
| ~ spl8_14
| ~ spl8_16 ),
inference(avatar_contradiction_clause,[],[f296]) ).
thf(f304,plain,
( ( $false = $true )
| ( $true
= ( b @ sK6 ) )
| ~ spl8_2
| ~ spl8_15 ),
inference(constrained_superposition,[],[f226,f159]) ).
thf(f311,plain,
( ( $true
= ( b @ sK6 ) )
| ~ spl8_2
| ~ spl8_15 ),
inference(trivial_inequality_removal,[],[f304]) ).
thf(f315,plain,
( ( $false = $true )
| ~ spl8_2
| ~ spl8_15
| ~ spl8_17 ),
inference(forward_demodulation,[],[f311,f236]) ).
thf(f316,plain,
( $false
| ~ spl8_2
| ~ spl8_15
| ~ spl8_17 ),
inference(trivial_inequality_removal,[],[f315]) ).
thf(f317,plain,
( ~ spl8_2
| ~ spl8_15
| ~ spl8_17 ),
inference(avatar_contradiction_clause,[],[f316]) ).
cnf(s1,plain,
( spl8_1
| spl8_1 ),
inference(sat_conversion,[],[f156]) ).
cnf(s2,plain,
spl8_1,
inference(rat,[],[s1]) ).
cnf(s9,plain,
( spl8_2
| spl8_2 ),
inference(sat_conversion,[],[f182]) ).
cnf(s10,plain,
spl8_2,
inference(rat,[],[s9]) ).
cnf(s19,plain,
( spl8_11
| spl8_14
| spl8_15 ),
inference(sat_conversion,[],[f227]) ).
cnf(s20,plain,
( spl8_11
| spl8_15
| spl8_16 ),
inference(sat_conversion,[],[f232]) ).
cnf(s21,plain,
( spl8_11
| spl8_14
| spl8_17 ),
inference(sat_conversion,[],[f237]) ).
cnf(s22,plain,
( spl8_11
| spl8_16
| spl8_17 ),
inference(sat_conversion,[],[f238]) ).
cnf(s23,plain,
( spl8_12
| spl8_13
| spl8_14
| spl8_15 ),
inference(sat_conversion,[],[f239]) ).
cnf(s24,plain,
( spl8_12
| spl8_13
| spl8_15
| spl8_16 ),
inference(sat_conversion,[],[f240]) ).
cnf(s25,plain,
( spl8_12
| spl8_13
| spl8_14
| spl8_17 ),
inference(sat_conversion,[],[f241]) ).
cnf(s26,plain,
( spl8_12
| spl8_13
| spl8_16
| spl8_17 ),
inference(sat_conversion,[],[f242]) ).
cnf(s28,plain,
( ~ spl8_1
| ~ spl8_11
| ~ spl8_12 ),
inference(sat_conversion,[],[f263]) ).
cnf(s30,plain,
( ~ spl8_2
| ~ spl8_11
| ~ spl8_13 ),
inference(sat_conversion,[],[f278]) ).
cnf(s32,plain,
( ~ spl8_1
| ~ spl8_14
| ~ spl8_16 ),
inference(sat_conversion,[],[f297]) ).
cnf(s34,plain,
( ~ spl8_2
| ~ spl8_15
| ~ spl8_17 ),
inference(sat_conversion,[],[f317]) ).
cnf(s35,plain,
( spl8_14
| spl8_11 ),
inference(rat,[],[s34,s21,s19,s10]) ).
cnf(s36,plain,
( spl8_16
| spl8_11 ),
inference(rat,[],[s34,s20,s22,s10]) ).
cnf(s37,plain,
spl8_11,
inference(rat,[],[s36,s32,s35,s2]) ).
cnf(s38,plain,
~ spl8_13,
inference(rat,[],[s30,s10,s37]) ).
cnf(s39,plain,
~ spl8_12,
inference(rat,[],[s28,s2,s37]) ).
cnf(s40,plain,
spl8_17,
inference(rat,[],[s32,s26,s25,s2,s39,s38]) ).
cnf(s41,plain,
~ spl8_15,
inference(rat,[],[s34,s10,s40]) ).
cnf(s42,plain,
spl8_16,
inference(rat,[],[s24,s39,s38,s41]) ).
cnf(s43,plain,
spl8_14,
inference(rat,[],[s23,s38,s39,s41]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s32,s2,s42,s43]) ).
thf(f318,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL584^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.26 % Computer : n017.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 08:53:37 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.32 Running first-order model finding
% 0.24/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.38 % (78746)Will run a generic schedule for satisfiability detection.
% 0.46/0.38 % (78751)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=904537578_2999 on theBenchmark for (2999ds/0Mi)
% 0.46/0.38 % Exception at run slice level
% 0.46/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.46/0.38 % (78752)% WARNING: option uhcvi not known.
% 0.46/0.38 % (78756)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=666723644:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.46/0.38 % (78755)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3564142765:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.46/0.38 % (78752)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=899939863:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.46/0.38 % (78753)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1311516796:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.46/0.38 % (78754)dis+10_1_sil=32000:sp=arity:random_seed=342366740:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.46/0.38 % (78757)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1095692259:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.46/0.38 % (78755)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.46/0.38 % (78752)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.46/0.38 % (78752)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.46/0.38 % (78759)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1737116941:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.46/0.38 % Exception at run slice level
% 0.46/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.46/0.38 % (78756) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-78746-78756"...
% 0.46/0.38 % (78755) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-78746-78755"...
% 0.46/0.38 % (78752) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-78746-78752"...
% 0.46/0.38 % (78754) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-78746-78754"...
% 0.46/0.38 % (78757) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-78746-78757"...
% 0.46/0.38 % (78756)...printing done.
% 0.46/0.38 % (78752)...printing done.
% 0.46/0.38 % (78755)...printing done.
% 0.46/0.38 % (78754)...printing done.
% 0.46/0.38 % (78756)Refutation found. Thanks to Tanya!
% 0.46/0.38 % SZS status Theorem for theBenchmark
% 0.46/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.46/0.39 % (78756)------------------------------
% 0.46/0.39 % (78756)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.39 % (78756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.39 % (78756)CaDiCaL version: 2.1.3
% 0.46/0.39 % (78756)Termination reason: Refutation
% 0.46/0.39 % (78756)Time elapsed: 0.019 s
% 0.46/0.39 % (78756)Peak memory usage: 13 MB
% 0.46/0.39 % (78756)Instructions burned: 18 (million)
% 0.46/0.39 % (78746)Success in time 0.055 s
% 0.46/0.39 % Vampire exiting
%------------------------------------------------------------------------------