%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO047^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:46:22 AM UTC 2026
% Result : Theorem 0.23s 0.27s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 8
% Syntax : Number of formulae : 76 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 468 ( 87 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 798 ( 148 ~; 94 |; 0 &; 504 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 163 ( 163 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 50 usr; 5 con; 0-4 aty)
% ( 52 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 215 ( 193 ^; 21 !; 1 ?; 215 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_35,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_49,type,
sK2: $i > $o ).
thf(func_def_50,type,
sK3: $i > $o ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f17,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o] : ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) )
= mdia ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mdia) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mimplies @ X1 @ X2 ) ) @ ( mimplies @ ( mdia @ X0 @ X1 ) @ ( mdia @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mimplies @ X1 @ X2 ) ) @ ( mimplies @ ( mdia @ X0 @ X1 ) @ ( mdia @ X0 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f34,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f37,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f57,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f58,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
~ ! [X0: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mimplies @ X1 @ X2 ) ) @ ( mimplies @ ( mdia @ X0 @ X1 ) @ ( mdia @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f60,plain,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mimplies @ Y0 @ Y1 ) ) @ ( mimplies @ ( mdia @ X0 @ Y0 ) @ ( mdia @ X0 @ Y1 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f59]) ).
thf(f66,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f67,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f68,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f69,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f74,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f75,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f80,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f81,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mimplies @ Y0 @ Y1 ) ) @ ( mimplies @ ( mdia @ X0 @ Y0 ) @ ( mdia @ X0 @ Y1 ) ) ) ) ) )
!= $true ),
inference(ennf_transformation,[],[f60]) ).
thf(f88,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ sK0 @ ( mimplies @ Y0 @ Y1 ) ) @ ( mimplies @ ( mdia @ sK0 @ Y0 ) @ ( mdia @ sK0 @ Y1 ) ) ) ) ) )
!= $true ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f91,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f93,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f97,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f101,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f103,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f105,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f109,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ sK0 @ ( mimplies @ Y0 @ Y1 ) ) @ ( mimplies @ ( mdia @ sK0 @ Y0 ) @ ( mdia @ sK0 @ Y1 ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f117,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f124,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f103,f97,f91]) ).
thf(f131,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f101,f91,f93,f91]) ).
thf(f132,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: ( $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ sK0
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y5 @ Y7 ) ) )
@ Y2
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y5 @ Y7 ) ) )
@ Y2
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ sK0
@ Y1 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f109,f117,f105,f105,f124,f93,f124,f124,f131,f131]) ).
thf(f133,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ~ ( Y2 @ Y3 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ~ ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y2 @ Y3 )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,plain,
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ~ ( Y2 @ Y3 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ~ ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y2 @ Y3 )
| ~ ( Y1 @ Y3 ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f133]) ).
thf(f135,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ~ ( Y1 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
( ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ~ ( Y1 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ~ ( Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ~ ( sK2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ( Y0 @ Y1 )
| ~ ( sK2 @ Y1 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
( ( ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ~ ( Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ~ ( sK2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ( Y0 @ Y1 )
| ~ ( sK2 @ Y1 ) ) ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f139]) ).
thf(f142,plain,
( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f141]) ).
thf(f144,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X1: $i] :
( $true
= ( ~ ( sK0 @ sK1 @ X1 )
| ~ ( sK3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
! [X1: $i] :
( ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X1: $i] :
( ( $true
= ( ~ ( sK3 @ X1 ) ) )
| ( ( sK0 @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ X1 )
= $false )
| ( ( sK3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f142]) ).
thf(f151,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) )
= $false ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( ~ ( sK0 @ sK1 @ sK4 )
| ~ ( sK2 @ sK4 ) )
= $false ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
( ( ~ ( sK2 @ sK4 ) )
= $false ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( ~ ( sK0 @ sK1 @ sK4 ) )
= $false ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f156,plain,
( $true
= ( sK0 @ sK1 @ sK4 ) ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( $true
= ( sK2 @ sK4 ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f158,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f140]) ).
thf(f159,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 )
| ~ ( sK2 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( $true
= ( ~ ( sK0 @ sK1 @ X1 )
| ( sK3 @ X1 )
| ~ ( sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( ( ( sK3 @ X1 )
| ~ ( sK2 @ X1 ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( ~ ( sK2 @ X1 ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( sK0 @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ X1 )
= $false )
| ( ( sK3 @ X1 )
= $true )
| ( ( sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f166,plain,
( ( $true = $false )
| ( ( sK2 @ sK4 )
= $false )
| ( $true
= ( sK3 @ sK4 ) ) ),
inference(constrained_superposition,[],[f164,f156]) ).
thf(f167,plain,
( ( ( sK2 @ sK4 )
= $false )
| ( $true
= ( sK3 @ sK4 ) ) ),
inference(trivial_inequality_removal,[],[f166]) ).
thf(f169,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f167,f157]) ).
thf(f170,plain,
( $true
= ( sK3 @ sK4 ) ),
inference(trivial_inequality_removal,[],[f169]) ).
thf(f174,plain,
( ( ( sK3 @ sK4 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f156,f149]) ).
thf(f175,plain,
( ( sK3 @ sK4 )
= $false ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f177,plain,
$true = $false,
inference(constrained_superposition,[],[f175,f170]) ).
thf(f179,plain,
$false,
inference(trivial_inequality_removal,[],[f177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO047^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n016.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:29:20 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.23/0.27 % (558715)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.27 % (558721)lrs+10_16_si=on:nwc=1.5:random_seed=598772506:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.27 % (558721) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-558715-558721"...
% 0.23/0.27 % (558726)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.27 % (558726)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
% 0.23/0.27 % (558721)...printing done.
% 0.23/0.27 % (558721)Refutation found. Thanks to Tanya!
% 0.23/0.27 % SZS status Theorem for theBenchmark
% 0.23/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.27 % (558721)------------------------------
% 0.23/0.27 % (558721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.27 % (558721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.27 % (558721)CaDiCaL version: 2.1.3
% 0.23/0.27 % (558721)Termination reason: Refutation
% 0.23/0.27 % (558721)Time elapsed: 0.005 s
% 0.23/0.27 % (558721)Peak memory usage: 12 MB
% 0.23/0.27 % (558721)Instructions burned: 17 (million)
% 0.23/0.27 % (558715)Success in time 0.022 s
% 0.23/0.27 % Vampire exiting
%------------------------------------------------------------------------------