%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL607^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:15:02 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 14
% Syntax : Number of formulae : 114 ( 47 unt; 0 typ; 5 def)
% Number of atoms : 701 ( 119 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 899 ( 135 ~; 114 |; 41 &; 526 @)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 117 ( 117 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 40 usr; 12 con; 0-4 aty)
% ( 26 !!; 20 ??; 0 @@+; 0 @@-)
% Number of variables : 216 ( 0 sgn 27 !; 4 ?; 216 :)
% 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(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/LCL008^0.ax',mand) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/LCL008^0.ax',mdia) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,conjecture,
! [X0: $i > $i > $o,X1: $i > $o] : ( mvalid @ ( miff @ ( mdia @ X0 @ X1 ) @ ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f17,negated_conjecture,
~ ! [X0: $i > $i > $o,X1: $i > $o] : ( mvalid @ ( miff @ ( mdia @ X0 @ X1 ) @ ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) ) ),
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(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] : ( mvalid @ ( miff @ ( mdia @ X0 @ X1 ) @ ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f45,plain,
~ ! [X0: $i > $i > $o,X1: $i > $o] :
( ( mvalid @ ( miff @ ( mdia @ X0 @ X1 ) @ ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
? [X0: $i > $i > $o,X1: $i > $o] :
( ( mvalid @ ( miff @ ( mdia @ X0 @ X1 ) @ ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) ) )
!= $true ),
inference(ennf_transformation,[],[f45]) ).
thf(f47,plain,
( $true
!= ( mvalid @ ( miff @ ( mdia @ sK0 @ sK1 ) @ ( mnot @ ( mbox @ sK0 @ ( mnot @ sK1 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[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(f54,plain,
( miff
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimpl @ Y0 @ Y1 ) @ ( mimpl @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
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 @ ( miff @ ( mdia @ sK0 @ sK1 ) @ ( mnot @ ( mbox @ sK0 @ ( mnot @ sK1 ) ) ) ) ) ),
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(f67,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,[],[f54,f52,f66,f66]) ).
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 > $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 ) ) )
@ sK0
@ sK1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ sK1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f63,f59,f67,f56,f50,f55,f50]) ).
thf(f69,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK1 @ Y1 ) ) ) )
& ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK1 @ Y1 ) ) )
| ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
( $false
= ( ^ [Y0: $i] :
( ( ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK1 @ Y1 ) ) ) )
& ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK1 @ Y1 ) ) )
| ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f69]) ).
thf(f71,plain,
( $false
= ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) )
& ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) )
| ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) )
| ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f72]) ).
thf(f75,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f75]) ).
thf(f77,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) )
@ sK3 ) )
| ( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f76]) ).
thf(f79,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) )
@ sK3 ) )
| ( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f77]) ).
thf(f80,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) )
@ sK3 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f79]) ).
thf(f81,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f80]) ).
thf(f82,plain,
( ( $false
= ( ( sK0 @ sK2 @ sK3 )
=> ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK2 @ sK4 )
& ( sK1 @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
( ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK2 @ sK4 )
& ( sK1 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( ( $true
= ( sK0 @ sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK2 @ sK4 )
& ( sK1 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f85,plain,
( ( $true
= ( sK0 @ sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f84]) ).
thf(f86,plain,
( ( $true
= ( sK0 @ sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f84]) ).
thf(f87,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK2 @ sK4 )
& ( sK1 @ sK4 ) ) ) ),
inference(not_proxy_clausification,[],[f83]) ).
thf(f88,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f87]) ).
thf(f89,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f87]) ).
thf(f100,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f73]) ).
thf(f101,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f100]) ).
thf(f109,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f101]) ).
thf(f110,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f109]) ).
thf(f111,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK0 @ sK2 @ X1 )
& ( sK1 @ X1 ) ) )
| ( $true
= ( ( sK0 @ sK2 @ X2 )
=> ~ ( sK1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f112,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( ( sK0 @ sK2 @ X2 )
=> ~ ( sK1 @ X2 ) ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK2 @ X2 ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( sK1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f112]) ).
thf(f114,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK2 @ X2 ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f113]) ).
thf(f116,definition,
( spl6_1
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f118,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f116]) ).
thf(f120,definition,
( spl6_2
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f122,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f120]) ).
thf(f123,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f88,f120,f116]) ).
thf(f125,definition,
( spl6_3
<=> ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f127,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f125]) ).
thf(f128,plain,
( spl6_3
| spl6_2 ),
inference(avatar_split_clause,[],[f89,f120,f125]) ).
thf(f130,definition,
( spl6_4
<=> ( $true
= ( sK0 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f131,plain,
( ( $true
!= ( sK0 @ sK2 @ sK3 ) )
| spl6_4 ),
inference(avatar_component_clause,[],[f130]) ).
thf(f132,plain,
( ( $true
= ( sK0 @ sK2 @ sK3 ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f130]) ).
thf(f133,plain,
( spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f86,f130,f125]) ).
thf(f145,definition,
( spl6_8
<=> ! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f146,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $false
= ( sK1 @ X1 ) ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f145]) ).
thf(f180,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK4 ) )
| ~ spl6_3
| ~ spl6_8 ),
inference(constrained_superposition,[],[f127,f146]) ).
thf(f181,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK3 ) )
| ~ spl6_4
| ~ spl6_8 ),
inference(constrained_superposition,[],[f132,f146]) ).
thf(f182,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl6_4
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f181]) ).
thf(f183,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ~ spl6_3
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f180]) ).
thf(f186,plain,
( ( $false = $true )
| ~ spl6_2
| ~ spl6_4
| ~ spl6_8 ),
inference(constrained_superposition,[],[f182,f122]) ).
thf(f190,plain,
( $false
| ~ spl6_2
| ~ spl6_4
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f186]) ).
thf(f191,plain,
( ~ spl6_2
| ~ spl6_4
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f190]) ).
thf(f194,plain,
( ( $false = $true )
| ~ spl6_1
| ~ spl6_3
| ~ spl6_8 ),
inference(constrained_superposition,[],[f118,f183]) ).
thf(f195,plain,
( $false
| ~ spl6_1
| ~ spl6_3
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f194]) ).
thf(f196,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f195]) ).
thf(f200,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK2 @ sK3 ) )
| ~ spl6_3
| ~ spl6_8 ),
inference(forward_demodulation,[],[f85,f183]) ).
thf(f201,plain,
( ( $true
= ( sK0 @ sK2 @ sK3 ) )
| ~ spl6_3
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f200]) ).
thf(f203,plain,
( $false
| ~ spl6_3
| spl6_4
| ~ spl6_8 ),
inference(forward_subsumption_resolution,[],[f201,f131]) ).
thf(f204,plain,
( ~ spl6_3
| spl6_4
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f203]) ).
thf(f206,plain,
( spl6_8
| spl6_8 ),
inference(avatar_split_clause,[],[f114,f145,f145]) ).
cnf(s14,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f123]) ).
cnf(s18,plain,
( spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f128]) ).
cnf(s22,plain,
( spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f133]) ).
cnf(s55,plain,
( ~ spl6_2
| ~ spl6_4
| ~ spl6_8 ),
inference(sat_conversion,[],[f191]) ).
cnf(s57,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_8 ),
inference(sat_conversion,[],[f196]) ).
cnf(s64,plain,
( ~ spl6_3
| spl6_4
| ~ spl6_8 ),
inference(sat_conversion,[],[f204]) ).
cnf(s78,plain,
( spl6_8
| spl6_8 ),
inference(sat_conversion,[],[f206]) ).
cnf(s79,plain,
spl6_8,
inference(rat,[],[s78]) ).
cnf(s80,plain,
( ~ spl6_3
| spl6_4 ),
inference(rat,[],[s64,s79]) ).
cnf(s82,plain,
( ~ spl6_1
| ~ spl6_3 ),
inference(rat,[],[s57,s79]) ).
cnf(s83,plain,
( ~ spl6_2
| ~ spl6_4 ),
inference(rat,[],[s55,s79]) ).
cnf(s85,plain,
spl6_4,
inference(rat,[],[s22,s80]) ).
cnf(s86,plain,
~ spl6_2,
inference(rat,[],[s83,s85]) ).
cnf(s87,plain,
spl6_3,
inference(rat,[],[s18,s86]) ).
cnf(s88,plain,
spl6_1,
inference(rat,[],[s14,s86]) ).
cnf(s90,plain,
$false,
inference(rat,[],[s82,s87,s88]) ).
thf(f207,plain,
$false,
inference(avatar_sat_refutation,[],[s90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL607^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n017.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 09:13:52 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 Running first-order model finding
% 0.10/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.26 % (93863)Will run a generic schedule for satisfiability detection.
% 0.10/0.26 % (93870)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=834593954:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.26 % (93869)% WARNING: option uhcvi not known.
% 0.10/0.26 % (93870) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-93863-93870"...
% 0.10/0.26 % (93870)...printing done.
% 0.10/0.26 % (93868)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1760863498_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.26 % (93869)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1722923148:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.26 % (93869)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.26 % Exception at run slice level
% 0.10/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.26 % (93869)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.10/0.26 % (93870)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (93870)------------------------------
% 0.10/0.26 % (93870)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (93870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (93870)CaDiCaL version: 2.1.3
% 0.10/0.26 % (93870)Termination reason: Refutation
% 0.10/0.26 % (93870)Time elapsed: 0.005 s
% 0.10/0.26 % (93870)Peak memory usage: 13 MB
% 0.10/0.26 % (93870)Instructions burned: 14 (million)
% 0.10/0.26 % (93863)Success in time 0.044 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------