%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL713^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:14:32 AM UTC 2026
% Result : Theorem 0.80s 0.38s
% Output : Refutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 11
% Syntax : Number of formulae : 99 ( 57 unt; 0 typ; 2 def)
% Number of atoms : 658 ( 159 equ; 1 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 1073 ( 154 ~; 142 |; 15 &; 676 @)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 159 ( 159 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 52 usr; 9 con; 0-4 aty)
% ( 68 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 307 ( 0 sgn 113 !; 1 ?; 307 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db1:
!>[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,
vOR: $o > $o > $o ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_48,type,
sK1: $i > ( $i > $o ) > $i ).
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] :
( ( X1 @ X2 )
| ( X0 @ 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,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
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] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ 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(f22,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X3: $i,X1: $i,X2: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X2 @ X3 ) ) )
= meuclidean ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
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] : ( mimplies @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) ) ) )
=> ( meuclidean @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) ) ) )
=> ( meuclidean @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f43,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f44,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f47,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f48,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f50,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f52,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f55,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f56,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f66,plain,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) ) ) )
=> ( meuclidean @ X0 ) ),
inference(rectify,[],[f33]) ).
thf(f67,plain,
~ ! [X0: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ X0 @ Y0 ) @ ( mbox @ X0 @ ( mdia @ X0 @ Y0 ) ) ) ) ) )
=> ( ( meuclidean @ X0 )
= $true ) ),
inference(fool_elimination,[],[f66]) ).
thf(f75,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f76,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f81,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X3 @ X1 ) ) )
= meuclidean ),
inference(rectify,[],[f22]) ).
thf(f82,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
!= $true )
& ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ X0 @ Y0 ) @ ( mbox @ X0 @ ( mdia @ X0 @ Y0 ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f67]) ).
thf(f88,plain,
( ( $true
!= ( meuclidean @ sK0 ) )
& ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ sK0 @ Y0 ) @ ( mbox @ sK0 @ ( mdia @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f90,plain,
( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ sK0 @ Y0 ) @ ( mbox @ sK0 @ ( mdia @ sK0 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f91,plain,
( $true
!= ( meuclidean @ sK0 ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f93,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f98,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f99,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f100,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f102,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f103,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f104,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f105,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f109,plain,
( mimplies
= ( ^ [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,[],[f105,f104,f98]) ).
thf(f114,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] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f93,f98,f103,f98]) ).
thf(f115,plain,
( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f91,f100]) ).
thf(f116,plain,
( $true
= ( ^ [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,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f90,f99,f102,f109,f114,f103,f114]) ).
thf(f117,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X1 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X1 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( X2 @ X4 )
| ~ ( sK0 @ X1 @ X4 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f126]) ).
thf(f128,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( X2 @ X4 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( sK0 @ X1 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( X2 @ X4 )
= $false )
| ( $true
= ( ~ ( sK0 @ X1 @ X4 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( X2 @ X4 )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f129]) ).
thf(f131,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) ) ) )
| ( ( X2 @ X4 )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( $true
= ( ~ ( sK0 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( X2 @ X4 )
= $false )
| ( $true
= ( ~ ( sK0 @ X1 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f131]) ).
thf(f133,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( X2 @ X4 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) )
= $false )
| ( $false
= ( sK0 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( X2 @ X4 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) )
@ ( sK1 @ X3 @ X2 ) )
= $false )
| ( $false
= ( sK0 @ X1 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( X2 @ X4 )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( ~ ( X2 @ ( sK1 @ X3 @ X2 ) )
| ~ ( sK0 @ X3 @ ( sK1 @ X3 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( X2 @ X4 )
= $false )
| ( ( ~ ( sK0 @ X3 @ ( sK1 @ X3 @ X2 ) ) )
= $false )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( sK0 @ X1 @ X4 )
= $false ) ),
inference(or_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( X2 @ X4 )
= $false )
| ( ( ~ ( X2 @ ( sK1 @ X3 @ X2 ) ) )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false ) ),
inference(or_proxy_clausification,[],[f135]) ).
thf(f138,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( X2 @ ( sK1 @ X3 @ X2 ) ) )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( X2 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X3 @ ( sK1 @ X3 @ X2 ) )
= $true )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( X2 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f136]) ).
thf(f140,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f115]) ).
thf(f141,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ sK2 @ Y1 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ sK2 @ Y1 ) ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK3 @ Y0 )
& ( sK0 @ sK3 @ sK2 ) )
=> ( sK0 @ sK2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
( ( ^ [Y0: $i] :
( ( ( sK0 @ sK3 @ Y0 )
& ( sK0 @ sK3 @ sK2 ) )
=> ( sK0 @ sK2 @ Y0 ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( ( ( sK0 @ sK3 @ sK4 )
& ( sK0 @ sK3 @ sK2 ) )
=> ( sK0 @ sK2 @ sK4 ) )
= $false ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
( ( sK0 @ sK2 @ sK4 )
= $false ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( $true
= ( ( sK0 @ sK3 @ sK4 )
& ( sK0 @ sK3 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f149,plain,
( $true
= ( sK0 @ sK3 @ sK2 ) ),
inference(and_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( $true
= ( sK0 @ sK3 @ sK4 ) ),
inference(and_proxy_clausification,[],[f148]) ).
thf(f151,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK1 @ X0 @ ( (=) @ X1 ) )
= X1 )
| ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X2 @ X0 )
= $false ) ),
inference(leibniz_equality_elimination,[],[f138]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X4 @ X0 )
= $false )
| ( $true
= ( sK0 @ X1 @ X0 ) )
| ( ( sK0 @ X2 @ X3 )
= $false )
| ( ( sK0 @ X4 @ X1 )
= $false )
| ( ( X0 = X3 )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $false ) ),
inference(superposition,[],[f139,f151]) ).
thf(f181,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( ( sK0 @ X4 @ X1 )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X2 @ X3 )
= $false )
| ( ( sK0 @ X4 @ X0 )
= $false )
| ( X0 != X3 ) ),
inference(equality_proxy_clausification,[],[f177]) ).
thf(f226,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ sK2 )
= $false )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( $true = $false )
| ( ( sK0 @ X0 @ sK4 )
= $false )
| ( ( sK0 @ X1 @ sK2 )
= $false )
| ( sK4 != X2 ) ),
inference(superposition,[],[f147,f181]) ).
thf(f238,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ sK4 )
= $false )
| ( ( sK0 @ X0 @ sK2 )
= $false )
| ( ( sK0 @ X1 @ sK2 )
= $false )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( sK4 != X2 ) ),
inference(trivial_inequality_removal,[],[f226]) ).
thf(f240,definition,
( spl5_4
<=> ! [X0: $i] :
( ( ( sK0 @ X0 @ sK4 )
= $false )
| ( ( sK0 @ X0 @ sK2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f241,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK4 )
= $false )
| ( ( sK0 @ X0 @ sK2 )
= $false ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f240]) ).
thf(f243,definition,
( spl5_5
<=> ! [X2: $i,X1: $i] :
( ( ( sK0 @ X1 @ sK2 )
= $false )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( sK4 != X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f244,plain,
( ! [X2: $i,X1: $i] :
( ( sK4 != X2 )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X1 @ sK2 )
= $false ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f246,plain,
( spl5_4
| spl5_5 ),
inference(avatar_split_clause,[],[f238,f243,f240]) ).
thf(f247,plain,
( ( $true = $false )
| ( ( sK0 @ sK3 @ sK2 )
= $false )
| ~ spl5_4 ),
inference(superposition,[],[f241,f150]) ).
thf(f255,plain,
( ( ( sK0 @ sK3 @ sK2 )
= $false )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f247]) ).
thf(f277,plain,
( ( $true = $false )
| ~ spl5_4 ),
inference(superposition,[],[f255,f149]) ).
thf(f289,plain,
( $false
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f277]) ).
thf(f290,plain,
~ spl5_4,
inference(avatar_contradiction_clause,[],[f289]) ).
thf(f312,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK4 )
= $false )
| ( ( sK0 @ X0 @ sK2 )
= $false ) )
| ~ spl5_5 ),
inference(equality_resolution,[],[f244]) ).
thf(f314,plain,
( spl5_4
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f312,f243,f240]) ).
cnf(s4,plain,
( spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f246]) ).
cnf(s6,plain,
~ spl5_4,
inference(sat_conversion,[],[f290]) ).
cnf(s13,plain,
( spl5_4
| ~ spl5_5 ),
inference(sat_conversion,[],[f314]) ).
cnf(s15,plain,
~ spl5_5,
inference(rat,[],[s13,s6]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s4,s15,s6]) ).
thf(f315,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL713^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n014.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 09:48:00 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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
% 0.21/0.36 % (2460275)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.36 % (2460282)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=932036499:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.36 % (2460282)Instruction limit reached!
% 0.21/0.36 % (2460282)------------------------------
% 0.21/0.36 % (2460282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2460282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2460282)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2460282)Termination reason: Instruction limit
% 0.21/0.36 % (2460282)Termination phase: Function definition elimination
% 0.21/0.36 % (2460282)Time elapsed: 0.001 s
% 0.21/0.36 % (2460282)Peak memory usage: 10 MB
% 0.21/0.36 % (2460282)Instructions burned: 5 (million)
% 0.21/0.36 % (2460280)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2969199732:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.36 % (2460281)lrs+10_16_si=on:nwc=1.5:random_seed=3811844548:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.36 % (2460288)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3776139404:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (2460288)Instruction limit reached!
% 0.21/0.36 % (2460288)------------------------------
% 0.21/0.36 % (2460288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2460288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2460288)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2460288)Termination reason: Instruction limit
% 0.21/0.36 % (2460288)Termination phase: Preprocessing 3
% 0.21/0.36 % (2460288)Time elapsed: 0.001 s
% 0.21/0.36 % (2460288)Peak memory usage: 10 MB
% 0.21/0.36 % (2460288)Instructions burned: 4 (million)
% 0.21/0.36 % (2460281)Instruction limit reached!
% 0.21/0.36 % (2460281)------------------------------
% 0.21/0.36 % (2460281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2460281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2460281)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2460281)Termination reason: Instruction limit
% 0.21/0.36 % (2460281)Termination phase: Saturation
% 0.21/0.36 % (2460281)Time elapsed: 0.009 s
% 0.21/0.36 % (2460281)Peak memory usage: 12 MB
% 0.21/0.36 % (2460281)Instructions burned: 18 (million)
% 0.21/0.36 % (2460284)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2538500783:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.36 % (2460292)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=990797719:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.36 % (2460292)Instruction limit reached!
% 0.21/0.36 % (2460292)------------------------------
% 0.21/0.36 % (2460292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2460292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2460292)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2460292)Termination reason: Instruction limit
% 0.21/0.36 % (2460292)Termination phase: Saturation
% 0.21/0.36 % (2460292)Time elapsed: 0.002 s
% 0.21/0.36 % (2460292)Peak memory usage: 11 MB
% 0.21/0.36 % (2460292)Instructions burned: 8 (million)
% 0.21/0.36 % (2460286)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.36 % (2460286)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
% 0.21/0.36 % (2460293)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.36 % (2460283)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=3619232864: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)
% 0.21/0.36 % (2460293)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4289265329:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.80/0.38 % (2460286)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=613852902:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.80/0.38 % (2460293)Instruction limit reached!
% 0.80/0.38 % (2460293)------------------------------
% 0.80/0.38 % (2460293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460293)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460293)Termination reason: Instruction limit
% 0.80/0.38 % (2460293)Termination phase: Saturation
% 0.80/0.38 % (2460293)Time elapsed: 0.004 s
% 0.80/0.38 % (2460293)Peak memory usage: 11 MB
% 0.80/0.38 % (2460293)Instructions burned: 9 (million)
% 0.80/0.38 % (2460285)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=992626031:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.80/0.38 % (2460284)Instruction limit reached!
% 0.80/0.38 % (2460284)------------------------------
% 0.80/0.38 % (2460284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460284)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460284)Termination reason: Instruction limit
% 0.80/0.38 % (2460284)Termination phase: Saturation
% 0.80/0.38 % (2460284)Time elapsed: 0.025 s
% 0.80/0.38 % (2460284)Peak memory usage: 12 MB
% 0.80/0.38 % (2460284)Instructions burned: 24 (million)
% 0.80/0.38 % (2460296)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2175496713:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.80/0.38 % (2460280)Instruction limit reached!
% 0.80/0.38 % (2460280)------------------------------
% 0.80/0.38 % (2460280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460280)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460280)Termination reason: Instruction limit
% 0.80/0.38 % (2460280)Termination phase: Saturation
% 0.80/0.38 % (2460280)Time elapsed: 0.044 s
% 0.80/0.38 % (2460280)Peak memory usage: 12 MB
% 0.80/0.38 % (2460280)Instructions burned: 88 (million)
% 0.80/0.38 % (2460296)Instruction limit reached!
% 0.80/0.38 % (2460296)------------------------------
% 0.80/0.38 % (2460296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460296)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460296)Termination reason: Instruction limit
% 0.80/0.38 % (2460296)Termination phase: Saturation
% 0.80/0.38 % (2460296)Time elapsed: 0.006 s
% 0.80/0.38 % (2460296)Peak memory usage: 12 MB
% 0.80/0.38 % (2460296)Instructions burned: 12 (million)
% 0.80/0.38 % (2460286)Refutation not found, incomplete strategy
% 0.80/0.38 % (2460286)------------------------------
% 0.80/0.38 % (2460286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460301)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
% 0.80/0.38 % (2460286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460286)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460286)Termination reason: Refutation not found, incomplete strategy
% 0.80/0.38 % (2460286)Time elapsed: 0.017 s
% 0.80/0.38 % (2460286)Peak memory usage: 12 MB
% 0.80/0.38 % (2460301)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.80/0.38 % (2460286)Instructions burned: 15 (million)
% 0.80/0.38 % (2460302)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3101689534:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.80/0.38 % (2460301)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3029640215:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.80/0.38 % (2460286)------------------------------
% 0.80/0.38 % (2460286)------------------------------
% 0.80/0.38 % (2460305)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.80/0.38 % (2460304)lrs+10_1_si=on:cs=on:random_seed=1815314662:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.80/0.38 % (2460305)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2335841844:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.80/0.38 % (2460308)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=509824303:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.80/0.38 % (2460304)Instruction limit reached!
% 0.80/0.38 % (2460304)------------------------------
% 0.80/0.38 % (2460304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460304)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460304)Termination reason: Instruction limit
% 0.80/0.38 % (2460304)Termination phase: Saturation
% 0.80/0.38 % (2460304)Time elapsed: 0.005 s
% 0.80/0.38 % (2460304)Peak memory usage: 11 MB
% 0.80/0.38 % (2460304)Instructions burned: 10 (million)
% 0.80/0.38 % (2460305)Instruction limit reached!
% 0.80/0.38 % (2460305)------------------------------
% 0.80/0.38 % (2460305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460305)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460305)Termination reason: Instruction limit
% 0.80/0.38 % (2460305)Termination phase: Function definition elimination
% 0.80/0.38 % (2460305)Time elapsed: 0.003 s
% 0.80/0.38 % (2460305)Peak memory usage: 10 MB
% 0.80/0.38 % (2460305)Instructions burned: 5 (million)
% 0.80/0.38 % (2460308)Refutation not found, incomplete strategy
% 0.80/0.38 % (2460308)------------------------------
% 0.80/0.38 % (2460308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460308)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460308)Termination reason: Refutation not found, incomplete strategy
% 0.80/0.38 % (2460308)Time elapsed: 0.003 s
% 0.80/0.38 % (2460308)Peak memory usage: 12 MB
% 0.80/0.38 % (2460308)Instructions burned: 11 (million)
% 0.80/0.38 % (2460301)Instruction limit reached!
% 0.80/0.38 % (2460301)------------------------------
% 0.80/0.38 % (2460301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460301)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460301)Termination reason: Instruction limit
% 0.80/0.38 % (2460301)Termination phase: Saturation
% 0.80/0.38 % (2460301)Time elapsed: 0.017 s
% 0.80/0.38 % (2460301)Peak memory usage: 12 MB
% 0.80/0.38 % (2460301)Instructions burned: 29 (million)
% 0.80/0.38 % (2460308)------------------------------
% 0.80/0.38 % (2460308)------------------------------
% 0.80/0.38 % (2460314)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3151862394:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.80/0.38 % (2460285)Instruction limit reached!
% 0.80/0.38 % (2460285)------------------------------
% 0.80/0.38 % (2460285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460285)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460285)Termination reason: Instruction limit
% 0.80/0.38 % (2460285)Termination phase: Saturation
% 0.80/0.38 % (2460285)Time elapsed: 0.051 s
% 0.80/0.38 % (2460285)Peak memory usage: 13 MB
% 0.80/0.38 % (2460285)Instructions burned: 75 (million)
% 0.80/0.38 % (2460314)Instruction limit reached!
% 0.80/0.38 % (2460314)------------------------------
% 0.80/0.38 % (2460314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460314)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460314)Termination reason: Instruction limit
% 0.80/0.38 % (2460314)Termination phase: Saturation
% 0.80/0.38 % (2460314)Time elapsed: 0.004 s
% 0.80/0.38 % (2460314)Peak memory usage: 12 MB
% 0.80/0.38 % (2460314)Instructions burned: 16 (million)
% 0.80/0.38 % (2460313)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3690647857:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.80/0.38 % (2460315)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3497117178:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.80/0.38 % (2460318)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3270481723:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.80/0.38 % (2460318)Instruction limit reached!
% 0.80/0.38 % (2460318)------------------------------
% 0.80/0.38 % (2460318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460318)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460318)Termination reason: Instruction limit
% 0.80/0.38 % (2460318)Termination phase: SInE selection
% 0.80/0.38 % (2460318)Time elapsed: 0.001 s
% 0.80/0.38 % (2460318)Peak memory usage: 10 MB
% 0.80/0.38 % (2460318)Instructions burned: 4 (million)
% 0.80/0.38 % (2460312)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=69565455:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.80/0.38 % (2460315) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2460275-2460315"...
% 0.80/0.38 % (2460317)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1218616803:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.80/0.38 % (2460313)Instruction limit reached!
% 0.80/0.38 % (2460313)------------------------------
% 0.80/0.38 % (2460313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460313)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460313)Termination reason: Instruction limit
% 0.80/0.38 % (2460313)Termination phase: Saturation
% 0.80/0.38 % (2460313)Time elapsed: 0.015 s
% 0.80/0.38 % (2460313)Peak memory usage: 12 MB
% 0.80/0.38 % (2460313)Instructions burned: 26 (million)
% 0.80/0.38 % (2460315)...printing done.
% 0.80/0.38 % (2460315)Refutation found. Thanks to Tanya!
% 0.80/0.38 % SZS status Theorem for theBenchmark
% 0.80/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.80/0.38 % (2460315)------------------------------
% 0.80/0.38 % (2460315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (2460315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (2460315)CaDiCaL version: 2.1.3
% 0.80/0.38 % (2460315)Termination reason: Refutation
% 0.80/0.38 % (2460315)Time elapsed: 0.016 s
% 0.80/0.38 % (2460315)Peak memory usage: 13 MB
% 0.80/0.38 % (2460315)Instructions burned: 29 (million)
% 0.80/0.38 % (2460275)Success in time 0.145 s
% 0.80/0.38 % Vampire exiting
%------------------------------------------------------------------------------