%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL957^6 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:14:56 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 496 ( 54 equ; 0 cnn)
% Maximal formula atoms : 21 ( 8 avg)
% Number of connectives : 1098 ( 7 ~; 2 |; 0 &; 858 @)
% ( 0 <=>; 121 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 34 usr; 6 con; 0-4 aty)
% ( 97 !!; 13 ??; 0 @@+; 0 @@-)
% Number of variables : 261 ( 220 ^; 39 !; 2 ?; 261 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
big_r: $i > $i > mworld > $o ).
thf(func_def_16,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vOR: $o > $o > $o ).
thf(func_def_22,type,
vIMP: $o > $o > $o ).
thf(func_def_23,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vAND: $o > $o > $o ).
thf(func_def_25,type,
vIFF: $o > $o > $o ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(func_def_27,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
sK0: mworld ).
thf(func_def_31,type,
sK1: mworld > $i > mworld ).
thf(func_def_32,type,
sK2: $i > mworld ).
thf(func_def_33,type,
sK3: $i > $i ).
thf(func_def_34,type,
sK4: $i > mworld ).
thf(func_def_35,type,
sK5: $i > mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X1: mworld,X0: mworld] : ( mrel @ X0 @ X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
thf(f10,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f11,axiom,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) )
= mexists_di ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f12,conjecture,
( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( big_r @ X0 @ X0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( big_r @ X1 @ X1 ) ) ) ) ) )
@ ( mexists_di
@ ^ [X2: $i] :
( mbox
@ ( mforall_di
@ ^ [X3: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_r @ X2 @ X2 ) ) @ ( mbox @ ( big_r @ X3 @ X3 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2122) ).
thf(f13,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( big_r @ X0 @ X0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( big_r @ X1 @ X1 ) ) ) ) ) )
@ ( mexists_di
@ ^ [X2: $i] :
( mbox
@ ( mforall_di
@ ^ [X3: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_r @ X2 @ X2 ) ) @ ( mbox @ ( big_r @ X3 @ X3 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
thf(f14,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X1 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f15,plain,
! [X1: mworld,X0: mworld] :
( $true
= ( mrel @ X1 @ X0 ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f17,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f21,plain,
~ ( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( big_r @ X0 @ X0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( big_r @ X1 @ X1 ) ) ) ) ) )
@ ( mexists_di
@ ^ [X2: $i] :
( mbox
@ ( mforall_di
@ ^ [X3: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_r @ X2 @ X2 ) ) @ ( mbox @ ( big_r @ X3 @ X3 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f22,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( big_r @ Y0 @ Y0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( big_r @ Y0 @ Y0 ) ) ) ) ) )
@ ( mexists_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_r @ Y0 @ Y0 ) ) @ ( mbox @ ( big_r @ Y1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f24,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f27,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f28,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f31,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) )
= mexists_di ),
inference(rectify,[],[f11]) ).
thf(f32,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f37,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( big_r @ Y0 @ Y0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( big_r @ Y0 @ Y0 ) ) ) ) ) )
@ ( mexists_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_r @ Y0 @ Y0 ) ) @ ( mbox @ ( big_r @ Y1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f22]) ).
thf(f38,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(rectify,[],[f15]) ).
thf(f39,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f40,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( big_r @ Y0 @ Y0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( big_r @ Y0 @ Y0 ) ) ) ) ) )
@ ( mexists_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_r @ Y0 @ Y0 ) ) @ ( mbox @ ( big_r @ Y1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f41,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f42,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f43,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f46,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(cnf_transformation,[],[f38]) ).
thf(f48,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f53,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( big_r @ Y0 @ Y0 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( big_r @ Y0 @ Y0 ) ) ) ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( big_r @ Y0 @ Y0 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( big_r @ Y1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f40,f48,f43,f39,f43,f39,f42,f43,f43,f41,f43,f42,f43,f41,f43,f39,f43,f43]) ).
thf(f54,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( big_r @ Y2 @ Y2 @ Y3 ) ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( big_r @ Y3 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( big_r @ Y1 @ Y1 @ Y5 ) ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( big_r @ Y3 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( big_r @ Y2 @ Y2 @ Y3 ) ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( big_r @ Y3 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( big_r @ Y1 @ Y1 @ Y5 ) ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( big_r @ Y3 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f54]) ).
thf(f56,plain,
( $false
= ( ( mrel @ mactual @ sK0 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_r @ Y1 @ Y1 @ Y2 ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( big_r @ Y2 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( big_r @ Y0 @ Y0 @ Y4 ) ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( big_r @ Y2 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_r @ Y1 @ Y1 @ Y2 ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( big_r @ Y2 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( big_r @ Y0 @ Y0 @ Y4 ) ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( big_r @ Y2 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f56]) ).
thf(f59,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( big_r @ Y0 @ Y0 @ Y4 ) ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( big_r @ Y2 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f79,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( big_r @ Y0 @ Y0 @ Y4 ) ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( big_r @ Y2 @ Y2 @ Y4 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f59]) ).
thf(f80,plain,
! [X1: $i] :
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( big_r @ X1 @ X1 @ Y3 ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( big_r @ Y1 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( big_r @ X1 @ X1 @ Y3 ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( big_r @ Y1 @ Y1 @ Y3 ) ) ) ) ) ) ) )
@ ( sK2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X1: $i] :
( $false
= ( ( mrel @ sK0 @ ( sK2 @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK2 @ X1 ) @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( big_r @ X1 @ X1 @ Y2 ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( big_r @ Y0 @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X1: $i] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK2 @ X1 ) @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( big_r @ X1 @ X1 @ Y2 ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( big_r @ Y0 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f85,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK2 @ X1 ) @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( big_r @ X1 @ X1 @ Y2 ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( big_r @ Y0 @ Y0 @ Y2 ) ) ) ) ) )
@ ( sK3 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f83]) ).
thf(f86,plain,
! [X1: $i] :
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK2 @ X1 ) @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( big_r @ X1 @ X1 @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( big_r @ ( sK3 @ X1 ) @ ( sK3 @ X1 ) @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f87,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK2 @ X1 ) @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( big_r @ X1 @ X1 @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( big_r @ ( sK3 @ X1 ) @ ( sK3 @ X1 ) @ Y1 ) ) ) ) )
@ ( sK4 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X1: $i] :
( $false
= ( ( mrel @ ( sK2 @ X1 ) @ ( sK4 @ X1 ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK4 @ X1 ) @ Y0 )
=> ( big_r @ X1 @ X1 @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK4 @ X1 ) @ Y0 )
=> ( big_r @ ( sK3 @ X1 ) @ ( sK3 @ X1 ) @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
! [X1: $i] :
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK4 @ X1 ) @ Y0 )
=> ( big_r @ X1 @ X1 @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK4 @ X1 ) @ Y0 )
=> ( big_r @ ( sK3 @ X1 ) @ ( sK3 @ X1 ) @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f88]) ).
thf(f91,plain,
! [X1: $i] :
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK4 @ X1 ) @ Y0 )
=> ( big_r @ ( sK3 @ X1 ) @ ( sK3 @ X1 ) @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f89]) ).
thf(f92,plain,
! [X1: $i] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK4 @ X1 ) @ Y0 )
=> ( big_r @ X1 @ X1 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f89]) ).
thf(f93,plain,
! [X2: mworld,X1: $i] :
( ( ^ [Y0: mworld] :
( ( mrel @ ( sK4 @ X1 ) @ Y0 )
=> ( big_r @ X1 @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X2: mworld,X1: $i] :
( $true
= ( ( mrel @ ( sK4 @ X1 ) @ X2 )
=> ( big_r @ X1 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( mrel @ ( sK4 @ X1 ) @ X2 ) )
| ( $true
= ( big_r @ X1 @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK4 @ X1 ) @ Y0 )
=> ( big_r @ ( sK3 @ X1 ) @ ( sK3 @ X1 ) @ Y0 ) )
@ ( sK5 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f91]) ).
thf(f97,plain,
! [X1: $i] :
( $false
= ( ( mrel @ ( sK4 @ X1 ) @ ( sK5 @ X1 ) )
=> ( big_r @ ( sK3 @ X1 ) @ ( sK3 @ X1 ) @ ( sK5 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f96]) ).
thf(f98,plain,
! [X1: $i] :
( $false
= ( big_r @ ( sK3 @ X1 ) @ ( sK3 @ X1 ) @ ( sK5 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f97]) ).
thf(f102,plain,
! [X2: mworld,X1: $i] :
( ( $true
= ( big_r @ X1 @ X1 @ X2 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f95,f46]) ).
thf(f103,plain,
! [X2: mworld,X1: $i] :
( $true
= ( big_r @ X1 @ X1 @ X2 ) ),
inference(trivial_inequality_removal,[],[f102]) ).
thf(f107,plain,
$false = $true,
inference(constrained_superposition,[],[f103,f98]) ).
thf(f108,plain,
$false,
inference(trivial_inequality_removal,[],[f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL957^6 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 10:58:25 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.27 % (565734)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (565740)lrs+10_16_si=on:nwc=1.5:random_seed=1360215830:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.27 % (565740) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-565734-565740"...
% 0.19/0.27 % (565740)...printing done.
% 0.19/0.27 % (565740)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (565740)------------------------------
% 0.19/0.27 % (565740)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (565740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (565740)CaDiCaL version: 2.1.3
% 0.19/0.27 % (565740)Termination reason: Refutation
% 0.19/0.27 % (565740)Time elapsed: 0.004 s
% 0.19/0.27 % (565740)Peak memory usage: 12 MB
% 0.19/0.27 % (565740)Instructions burned: 13 (million)
% 0.19/0.27 % (565734)Success in time 0.038 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------