%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL624^1 : 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 : n003.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 08:15:04 AM UTC 2026
% Result : Theorem 0.06s 0.25s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 10
% Syntax : Number of formulae : 90 ( 56 unt; 0 typ; 2 def)
% Number of atoms : 611 ( 110 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 828 ( 29 ~; 52 |; 63 &; 602 @)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 107 ( 107 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 38 usr; 8 con; 0-4 aty)
% ( 23 !!; 32 ??; 0 @@+; 0 @@-)
% Number of variables : 215 ( 0 sgn 43 !; 5 ?; 215 :)
% 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_22,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_23,type,
vNOT: $o > $o ).
thf(func_def_24,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vOR: $o > $o > $o ).
thf(func_def_27,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vAND: $o > $o > $o ).
thf(func_def_29,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_30,type,
vIMP: $o > $o > $o ).
thf(func_def_31,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
sK0: $i > $i > $o ).
thf(func_def_34,type,
sK1: $i > $o ).
thf(func_def_35,type,
sK2: $i > $o ).
thf(func_def_38,type,
sK5: $i > $i ).
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(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(f9,axiom,
( mdia
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mdia) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,conjecture,
! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] : ( mvalid @ ( mimpl @ ( mand @ ( mdia @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ X2 ) ) ) @ ( mdia @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f17,negated_conjecture,
~ ! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] : ( mvalid @ ( mimpl @ ( mand @ ( mdia @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ X2 ) ) ) @ ( mdia @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) ),
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(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(f30,plain,
( mdia
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f31,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f30]) ).
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,
~ ! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] : ( mvalid @ ( mimpl @ ( mand @ ( mdia @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ X2 ) ) ) @ ( mdia @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f45,plain,
~ ! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
( ( mvalid @ ( mimpl @ ( mand @ ( mdia @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ X2 ) ) ) @ ( mdia @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
? [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
( ( mvalid @ ( mimpl @ ( mand @ ( mdia @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ X2 ) ) ) @ ( mdia @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) )
!= $true ),
inference(ennf_transformation,[],[f45]) ).
thf(f47,plain,
( $true
!= ( mvalid @ ( mimpl @ ( mand @ ( mdia @ sK0 @ ( mbox @ sK0 @ sK1 ) ) @ ( mbox @ sK0 @ ( mdia @ sK0 @ sK2 ) ) ) @ ( mdia @ sK0 @ ( mdia @ sK0 @ ( mand @ sK1 @ sK2 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f46]) ).
thf(f50,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f51,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f52,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f53,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f55,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f56,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f59,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f63,plain,
( $true
!= ( mvalid @ ( mimpl @ ( mand @ ( mdia @ sK0 @ ( mbox @ sK0 @ sK1 ) ) @ ( mbox @ sK0 @ ( mdia @ sK0 @ sK2 ) ) ) @ ( mdia @ sK0 @ ( mdia @ sK0 @ ( mand @ sK1 @ sK2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f66,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,[],[f53,f51,f50]) ).
thf(f68,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] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [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 ) ) )
@ sK0
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ sK1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ sK0
@ sK2 ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ sK0
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ sK0
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ sK1
@ sK2 ) ) ) ) ) ),
inference(definition_unfolding,[],[f63,f59,f66,f52,f56,f55,f55,f56,f56,f56,f52]) ).
thf(f69,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK2 @ Y2 ) ) ) ) ) )
| ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK1 @ Y2 )
& ( sK2 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK2 @ Y2 ) ) ) ) ) )
| ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK1 @ Y2 )
& ( sK2 @ Y2 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f69]) ).
thf(f71,plain,
( $false
= ( ~ ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) ) )
| ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( $false
= ( ~ ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f71]) ).
thf(f74,plain,
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f74]) ).
thf(f77,plain,
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( $true
= ( ( sK0 @ sK3 @ sK4 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f80,plain,
( $true
= ( sK0 @ sK3 @ sK4 ) ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f81,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f79]) ).
thf(f82,plain,
! [X1: $i] :
( $true
= ( ( sK0 @ sK4 @ X1 )
=> ( sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f75]) ).
thf(f85,plain,
! [X1: $i] :
( $true
= ( ( sK0 @ sK3 @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f84]) ).
thf(f86,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f87,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( sK2 @ Y0 ) )
@ ( sK5 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( $true
= ( ( sK0 @ X1 @ ( sK5 @ X1 ) )
& ( sK2 @ ( sK5 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( $true
= ( sK2 @ ( sK5 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ ( sK5 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f88]) ).
thf(f91,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 )
& ( sK2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f72]) ).
thf(f92,plain,
! [X1: $i] :
( $false
= ( ( sK0 @ sK3 @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f91]) ).
thf(f93,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ sK3 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
@ X2 ) )
| ( $false
= ( sK0 @ sK3 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X1 @ X2 )
& ( sK1 @ X2 )
& ( sK2 @ X2 ) ) )
| ( $false
= ( sK0 @ sK3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK1 @ X2 )
& ( sK2 @ X2 ) ) )
| ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f96]) ).
thf(f99,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK1 @ ( sK5 @ sK4 ) ) ) ),
inference(constrained_superposition,[],[f90,f83]) ).
thf(f104,plain,
( ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK1 @ ( sK5 @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f107,definition,
( spl6_1
<=> ( $false
= ( sK0 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f109,plain,
( ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f107]) ).
thf(f111,definition,
( spl6_2
<=> ( $true
= ( sK1 @ ( sK5 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f113,plain,
( ( $true
= ( sK1 @ ( sK5 @ sK4 ) ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f111]) ).
thf(f124,plain,
( spl6_2
| spl6_1 ),
inference(avatar_split_clause,[],[f104,f107,f111]) ).
thf(f131,plain,
! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ sK3 @ X0 ) )
| ( $false
= ( sK0 @ sK3 @ X0 ) )
| ( $false
= ( sK2 @ ( sK5 @ X0 ) ) )
| ( $false
= ( sK1 @ ( sK5 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f90,f97]) ).
thf(f136,plain,
! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ sK3 @ X0 ) )
| ( $false
= ( sK2 @ ( sK5 @ X0 ) ) )
| ( $false
= ( sK1 @ ( sK5 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[],[f131]) ).
thf(f137,plain,
! [X0: $i] :
( ( $false
= ( sK2 @ ( sK5 @ X0 ) ) )
| ( $false
= ( sK0 @ sK3 @ X0 ) )
| ( $false
= ( sK1 @ ( sK5 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f145,plain,
! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ sK3 @ X0 ) )
| ( $false
= ( sK0 @ sK3 @ X0 ) )
| ( $false
= ( sK1 @ ( sK5 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f89,f137]) ).
thf(f148,plain,
! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ sK3 @ X0 ) )
| ( $false
= ( sK1 @ ( sK5 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[],[f145]) ).
thf(f149,plain,
! [X0: $i] :
( ( $false
= ( sK0 @ sK3 @ X0 ) )
| ( $false
= ( sK1 @ ( sK5 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f148]) ).
thf(f156,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f113,f149]) ).
thf(f157,plain,
( ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f156]) ).
thf(f161,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f157,f111,f107]) ).
thf(f162,plain,
( ( $false = $true )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f109,f80]) ).
thf(f166,plain,
( $false
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f162]) ).
thf(f167,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f166]) ).
cnf(s3,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f124]) ).
cnf(s5,plain,
( spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f161]) ).
cnf(s8,plain,
~ spl6_1,
inference(sat_conversion,[],[f167]) ).
cnf(s9,plain,
~ spl6_2,
inference(rat,[],[s5,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s3,s9,s8]) ).
thf(f168,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL624^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.19 % Computer : n003.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Sep 29 09:30:59 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.22 Running first-order model finding
% 0.06/0.22 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
% 0.06/0.25 % (2290879)Will run a generic schedule for satisfiability detection.
% 0.06/0.25 % (2290890)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3528772497:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.25 % (2290890) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2290879-2290890"...
% 0.06/0.25 % (2290885)% WARNING: option uhcvi not known.
% 0.06/0.25 % (2290890)...printing done.
% 0.06/0.25 % (2290890)Refutation found. Thanks to Tanya!
% 0.06/0.25 % SZS status Theorem for theBenchmark
% 0.06/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.26 % (2290890)------------------------------
% 0.06/0.26 % (2290890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.26 % (2290890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.26 % (2290890)CaDiCaL version: 2.1.3
% 0.06/0.26 % (2290890)Termination reason: Refutation
% 0.06/0.26 % (2290890)Time elapsed: 0.005 s
% 0.06/0.26 % (2290890)Peak memory usage: 13 MB
% 0.06/0.26 % (2290890)Instructions burned: 15 (million)
% 0.06/0.26 % (2290879)Success in time 0.03 s
% 0.06/0.26 % Vampire exiting
%------------------------------------------------------------------------------