%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n007.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 08:14:26 AM UTC 2026
% Result : Theorem 0.14s 0.27s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 14
% Syntax : Number of formulae : 109 ( 48 unt; 0 typ; 5 def)
% Number of atoms : 663 ( 117 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 843 ( 117 ~; 96 |; 39 &; 512 @)
% ( 5 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 120 ( 120 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 40 usr; 12 con; 0-4 aty)
% ( 26 !!; 18 ??; 0 @@+; 0 @@-)
% Number of variables : 213 ( 0 sgn 26 !; 6 ?; 213 :)
% 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,
vOR: $o > $o > $o ).
thf(func_def_24,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_29,type,
vAND: $o > $o > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
sK0: $i > $i > $o ).
thf(func_def_34,type,
sK1: $i > $o ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
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,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimpl @ X0 @ X1 ) @ ( mimpl @ X1 @ X0 ) ) )
= miff ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',miff) ).
thf(f8,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f9,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X0 @ X2 @ X3 )
& ( X1 @ X3 ) ) )
= mdia ),
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,
! [X1: $i > $o,X0: $i > $i > $o] : ( mvalid @ ( miff @ ( mdia @ X0 @ X1 ) @ ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f17,negated_conjecture,
~ ! [X1: $i > $o,X0: $i > $i > $o] : ( mvalid @ ( miff @ ( mdia @ X0 @ X1 ) @ ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f18,plain,
~ ! [X0: $i > $o,X1: $i > $i > $o] : ( mvalid @ ( miff @ ( mdia @ X1 @ X0 ) @ ( mnot @ ( mbox @ X1 @ ( mnot @ X0 ) ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f19,plain,
~ ! [X0: $i > $o,X1: $i > $i > $o] :
( $true
= ( mvalid @ ( miff @ ( mdia @ X1 @ X0 ) @ ( mnot @ ( mbox @ X1 @ ( mnot @ X0 ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f21,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f22,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f29,plain,
( miff
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimpl @ Y0 @ Y1 ) @ ( mimpl @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f30,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f31,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
inference(rectify,[],[f5]) ).
thf(f32,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f33,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f34,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f35,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f36,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f39,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X0 @ X2 @ X3 )
& ( X1 @ X3 ) ) )
= mdia ),
inference(rectify,[],[f9]) ).
thf(f40,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f44,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f45,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
? [X1: $i > $i > $o,X0: $i > $o] :
( $true
!= ( mvalid @ ( miff @ ( mdia @ X1 @ X0 ) @ ( mnot @ ( mbox @ X1 @ ( mnot @ X0 ) ) ) ) ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f47,plain,
? [X0: $i > $i > $o,X1: $i > $o] :
( ( mvalid @ ( miff @ ( mdia @ X0 @ X1 ) @ ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) ) )
!= $true ),
inference(rectify,[],[f46]) ).
thf(f48,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)],[f47]) ).
thf(f49,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f54,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f56,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f57,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f58,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f60,plain,
( $true
!= ( mvalid @ ( miff @ ( mdia @ sK0 @ sK1 ) @ ( mnot @ ( mbox @ sK0 @ ( mnot @ sK1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f61,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f62,plain,
( miff
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimpl @ Y0 @ Y1 ) @ ( mimpl @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f63,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f67,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,[],[f57,f58,f63]) ).
thf(f68,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,[],[f62,f54,f67,f67]) ).
thf(f69,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] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ 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,[],[f60,f61,f68,f56,f63,f49,f63]) ).
thf(f70,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
& ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK1 @ Y1 ) ) ) )
& ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK1 @ Y1 ) ) )
| ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
& ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
( ( ^ [Y0: $i] :
( ( ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
& ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK1 @ Y1 ) ) ) )
& ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK1 @ Y1 ) ) )
| ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
& ( sK0 @ Y0 @ Y1 ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) )
& ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) )
| ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f73,plain,
( ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) )
| ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) )
= $false )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f73]) ).
thf(f77,plain,
( ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) ) ) )
= $false )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f75]) ).
thf(f78,plain,
( ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f78]) ).
thf(f80,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f79]) ).
thf(f81,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) )
@ sK3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f80]) ).
thf(f82,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) )
@ sK3 ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f81]) ).
thf(f83,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ( sK0 @ sK2 @ sK3 ) ) )
| ( ( ( sK0 @ sK2 @ sK4 )
=> ~ ( sK1 @ sK4 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
( ( ( ( sK0 @ sK2 @ sK4 )
=> ~ ( sK1 @ sK4 ) )
= $false )
| ( $true
= ( sK0 @ sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f83]) ).
thf(f85,plain,
( ( ( ( sK0 @ sK2 @ sK4 )
=> ~ ( sK1 @ sK4 ) )
= $false )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f83]) ).
thf(f86,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( ( ~ ( sK1 @ sK4 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f88,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f86]) ).
thf(f89,plain,
( ( ( ~ ( sK1 @ sK4 ) )
= $false )
| ( $true
= ( sK0 @ sK2 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f90,plain,
( ( $true
= ( sK0 @ sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f91,plain,
( ( $true
= ( sK0 @ sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(not_proxy_clausification,[],[f89]) ).
thf(f105,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f74]) ).
thf(f114,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) )
@ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f105]) ).
thf(f115,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) )
@ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( sK0 @ sK2 @ Y0 ) )
@ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( sK0 @ sK2 @ X2 )
=> ~ ( sK1 @ X2 ) ) )
| ( ( ( sK1 @ X1 )
& ( sK0 @ sK2 @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( sK1 @ X2 ) ) )
| ( ( sK0 @ sK2 @ X2 )
= $false )
| ( ( ( sK1 @ X1 )
& ( sK0 @ sK2 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X2 )
= $false )
| ( ( ( sK1 @ X1 )
& ( sK0 @ sK2 @ X1 ) )
= $false )
| ( ( sK0 @ sK2 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ sK2 @ X2 )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( sK1 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f119]) ).
thf(f122,definition,
( spl7_1
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f124,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f122]) ).
thf(f126,definition,
( spl7_2
<=> ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f128,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f126]) ).
thf(f129,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f87,f126,f122]) ).
thf(f131,definition,
( spl7_3
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f133,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f131]) ).
thf(f134,plain,
( spl7_3
| spl7_1 ),
inference(avatar_split_clause,[],[f88,f122,f131]) ).
thf(f136,definition,
( spl7_4
<=> ( $true
= ( sK0 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f138,plain,
( ( $true
= ( sK0 @ sK2 @ sK3 ) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f136]) ).
thf(f139,plain,
( spl7_2
| spl7_4 ),
inference(avatar_split_clause,[],[f90,f136,f126]) ).
thf(f140,plain,
( spl7_4
| spl7_3 ),
inference(avatar_split_clause,[],[f91,f131,f136]) ).
thf(f146,definition,
( spl7_6
<=> ! [X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ sK2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f147,plain,
( ! [X1: $i] :
( ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f146]) ).
thf(f164,plain,
( spl7_6
| spl7_6 ),
inference(avatar_split_clause,[],[f120,f146,f146]) ).
thf(f165,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( $true = $false )
| ~ spl7_2
| ~ spl7_6 ),
inference(constrained_superposition,[],[f128,f147]) ).
thf(f168,plain,
( ( ( sK1 @ sK4 )
= $false )
| ~ spl7_2
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f165]) ).
thf(f172,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_3
| ~ spl7_6 ),
inference(forward_demodulation,[],[f168,f133]) ).
thf(f173,plain,
( $false
| ~ spl7_2
| ~ spl7_3
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f174,plain,
( ~ spl7_2
| ~ spl7_3
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f173]) ).
thf(f176,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( $true = $false )
| ~ spl7_4
| ~ spl7_6 ),
inference(constrained_superposition,[],[f138,f147]) ).
thf(f179,plain,
( ( ( sK1 @ sK3 )
= $false )
| ~ spl7_4
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f183,plain,
( ( $true = $false )
| ~ spl7_1
| ~ spl7_4
| ~ spl7_6 ),
inference(forward_demodulation,[],[f179,f124]) ).
thf(f184,plain,
( $false
| ~ spl7_1
| ~ spl7_4
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f183]) ).
thf(f185,plain,
( ~ spl7_1
| ~ spl7_4
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f184]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f129]) ).
cnf(s2,plain,
( spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f134]) ).
cnf(s3,plain,
( spl7_2
| spl7_4 ),
inference(sat_conversion,[],[f139]) ).
cnf(s4,plain,
( spl7_3
| spl7_4 ),
inference(sat_conversion,[],[f140]) ).
cnf(s9,plain,
( spl7_6
| spl7_6 ),
inference(sat_conversion,[],[f164]) ).
cnf(s10,plain,
spl7_6,
inference(rat,[],[s9]) ).
cnf(s12,plain,
( ~ spl7_2
| ~ spl7_3
| ~ spl7_6 ),
inference(sat_conversion,[],[f174]) ).
cnf(s14,plain,
( ~ spl7_1
| ~ spl7_4
| ~ spl7_6 ),
inference(sat_conversion,[],[f185]) ).
cnf(s15,plain,
spl7_1,
inference(rat,[],[s12,s1,s2,s10]) ).
cnf(s16,plain,
~ spl7_4,
inference(rat,[],[s14,s10,s15]) ).
cnf(s17,plain,
spl7_3,
inference(rat,[],[s4,s16]) ).
cnf(s18,plain,
spl7_2,
inference(rat,[],[s3,s16]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s12,s10,s17,s18]) ).
thf(f186,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 THM
% 0.14/0.18 % Computer : n007.cluster.edu
% 0.14/0.18 % Model : x86_64 x86_64
% 0.14/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.18 % Memory : 8046.5625MB
% 0.14/0.18 % OS : Linux 6.8.0-71-generic
% 0.14/0.18 % CPULimit : 300
% 0.14/0.18 % WCLimit : 300
% 0.14/0.18 % DateTime : Tue Sep 29 09:16:11 UTC 2026
% 0.14/0.18 % CPUTime :
% 0.14/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.22 Running higher-order theorem proving
% 0.14/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.27 % (3106883)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.14/0.27 % (3106894)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.14/0.27 % (3106894)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
% 0.14/0.27 % (3106889)lrs+10_16_si=on:nwc=1.5:random_seed=1548757592:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.14/0.27 % (3106888)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=833975888:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.14/0.27 % (3106890)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1548453026:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.14/0.27 % (3106892)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3082029294:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.14/0.27 % (3106894)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3184282184:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.14/0.27 % (3106890)Refutation not found, incomplete strategy
% 0.14/0.27 % (3106890)------------------------------
% 0.14/0.27 % (3106890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.27 % (3106890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.27 % (3106890)CaDiCaL version: 2.1.3
% 0.14/0.27 % (3106890)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.27 % (3106890)Time elapsed: 0.003 s
% 0.14/0.27 % (3106890)Peak memory usage: 12 MB
% 0.14/0.27 % (3106890)Instructions burned: 4 (million)
% 0.14/0.27 % (3106890)------------------------------
% 0.14/0.27 % (3106890)------------------------------
% 0.14/0.27 % (3106891)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=4196975364: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)
% 0.14/0.27 % (3106888) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3106883-3106888"...
% 0.14/0.27 % (3106889) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3106883-3106889"...
% 0.14/0.27 % (3106894) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3106883-3106894"...
% 0.14/0.27 % (3106888)...printing done.
% 0.14/0.27 % (3106889)...printing done.
% 0.14/0.27 % (3106888)Refutation found. Thanks to Tanya!
% 0.14/0.27 % SZS status Theorem for theBenchmark
% 0.14/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.27 % (3106888)------------------------------
% 0.14/0.27 % (3106888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.27 % (3106888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.27 % (3106888)CaDiCaL version: 2.1.3
% 0.14/0.27 % (3106888)Termination reason: Refutation
% 0.14/0.27 % (3106888)Time elapsed: 0.007 s
% 0.14/0.27 % (3106888)Peak memory usage: 13 MB
% 0.14/0.27 % (3106888)Instructions burned: 12 (million)
% 0.14/0.27 % (3106883)Success in time 0.041 s
% 0.14/0.27 % Vampire exiting
%------------------------------------------------------------------------------