%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL703^1 : 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 : n013.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 08:14:31 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of formulae : 85 ( 69 unt; 0 typ; 0 def)
% Number of atoms : 477 ( 97 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 774 ( 108 ~; 62 |; 15 &; 515 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 139 ( 139 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 50 usr; 6 con; 0-4 aty)
% ( 58 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 224 ( 182 ^; 41 !; 1 ?; 224 :)
% 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,
vNOT: $o > $o ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vAND: $o > $o > $o ).
thf(func_def_41,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $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(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
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,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f17,axiom,
( mdia
= ( ^ [X0: $i > $i > $o,X1: $i > $o] : ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mdia) ).
thf(f22,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X3: $i,X2: $i,X1: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) )
= meuclidean ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( meuclidean @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( meuclidean @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f34,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f35,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f37,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f57,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f66,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X1 )
& ( X0 @ X3 @ X2 ) )
=> ( X0 @ X2 @ X1 ) ) )
= meuclidean ),
inference(rectify,[],[f22]) ).
thf(f67,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f68,plain,
~ ! [X0: $i > $i > $o] :
( ( meuclidean @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f69,plain,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
= $true )
=> ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ X0 @ Y0 ) @ ( mbox @ X0 @ ( mdia @ X0 @ Y0 ) ) ) ) )
= $true ) ),
inference(fool_elimination,[],[f68]) ).
thf(f70,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f71,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f74,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f75,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f77,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f78,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f85,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ X0 @ Y0 ) @ ( mbox @ X0 @ ( mdia @ X0 @ Y0 ) ) ) ) )
!= $true )
& ( ( meuclidean @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f69]) ).
thf(f88,plain,
( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ sK0 @ Y0 ) @ ( mbox @ sK0 @ ( mdia @ sK0 @ Y0 ) ) ) ) )
!= $true )
& ( ( meuclidean @ sK0 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f89,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f91,plain,
( ( meuclidean @ sK0 )
= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f92,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ sK0 @ Y0 ) @ ( mbox @ sK0 @ ( mdia @ sK0 @ Y0 ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f95,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f97,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f98,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f105,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f108,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f111,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f117,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f125,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,[],[f117,f95,f108]) ).
thf(f132,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,[],[f97,f108,f105,f108]) ).
thf(f133,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,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 ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f92,f98,f89,f125,f132,f105,f132]) ).
thf(f134,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f91,f111]) ).
thf(f135,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X1 @ X2 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ X2 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( sK0 @ X1 @ X2 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ X2 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( sK0 @ X1 @ X2 )
& ( sK0 @ X1 @ X3 ) )
=> ( sK0 @ X2 @ X3 ) )
= $true ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X2 @ X3 )
= $true )
| ( ( ( sK0 @ X1 @ X2 )
& ( sK0 @ X1 @ X3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X2 @ X3 )
= $true )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( !! @ $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 ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f145,plain,
( ( ^ [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 ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
( ( ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( ~ ( sK2 @ sK3 )
| ~ ( sK0 @ sK1 @ sK3 ) )
= $false ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
( ( ~ ( sK0 @ sK1 @ sK3 ) )
= $false ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( ~ ( sK2 @ sK3 ) )
= $false ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f157,plain,
( ( sK2 @ sK3 )
= $true ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( sK0 @ sK1 @ sK3 )
= $true ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f159,plain,
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f149]) ).
thf(f160,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) ) )
| ~ ( sK0 @ sK1 @ sK4 ) )
= $false ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( ( ~ ( sK0 @ sK1 @ sK4 ) )
= $false ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( ~ ( sK2 @ X1 )
| ~ ( sK0 @ sK4 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( ( ~ ( sK2 @ X1 ) )
= $true )
| ( ( ~ ( sK0 @ sK4 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( ( ~ ( sK0 @ sK4 @ X1 ) )
= $true )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( ( sK0 @ sK4 @ X1 )
= $false )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( sK0 @ sK1 @ sK4 )
= $true ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f185,plain,
! [X0: $i] :
( ( ( sK0 @ X0 @ sK3 )
= $true )
| ( ( sK0 @ sK1 @ X0 )
= $false )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f158,f143]) ).
thf(f187,plain,
! [X0: $i] :
( ( ( sK0 @ sK1 @ X0 )
= $false )
| ( ( sK0 @ X0 @ sK3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f185]) ).
thf(f227,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( $false = $true )
| ( ( sK0 @ sK1 @ sK4 )
= $false ) ),
inference(constrained_superposition,[],[f168,f187]) ).
thf(f231,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(trivial_inequality_removal,[],[f227]) ).
thf(f241,plain,
( ( $false = $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(forward_demodulation,[],[f231,f169]) ).
thf(f242,plain,
( ( sK2 @ sK3 )
= $false ),
inference(trivial_inequality_removal,[],[f241]) ).
thf(f254,plain,
$false = $true,
inference(forward_demodulation,[],[f242,f157]) ).
thf(f255,plain,
$false,
inference(trivial_inequality_removal,[],[f254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL703^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n013.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 09:42:36 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.23/0.30 % (1872682)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (1872690)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=1147797804: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)
% 0.23/0.30 % (1872687)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3637135510:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (1872689)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=634531839:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (1872688)lrs+10_16_si=on:nwc=1.5:random_seed=31257928:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (1872689)Instruction limit reached!
% 0.23/0.30 % (1872689)------------------------------
% 0.23/0.30 % (1872689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1872689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1872689)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1872689)Termination reason: Instruction limit
% 0.23/0.30 % (1872689)Termination phase: Property scanning
% 0.23/0.30 % (1872689)Time elapsed: 0.002 s
% 0.23/0.30 % (1872689)Peak memory usage: 10 MB
% 0.23/0.30 % (1872689)Instructions burned: 4 (million)
% 0.23/0.30 % (1872692)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=127305855:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.30 % (1872693)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.30 % (1872693)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
% 0.23/0.30 % (1872687) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1872682-1872687"...
% 0.23/0.30 % (1872688)Instruction limit reached!
% 0.23/0.30 % (1872688)------------------------------
% 0.23/0.30 % (1872688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1872688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1872688)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1872688)Termination reason: Instruction limit
% 0.23/0.30 % (1872688)Termination phase: Saturation
% 0.23/0.30 % (1872688)Time elapsed: 0.010 s
% 0.23/0.30 % (1872688)Peak memory usage: 12 MB
% 0.23/0.30 % (1872688)Instructions burned: 18 (million)
% 0.23/0.30 % (1872693)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=2040600091:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.30 % (1872691)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4087360523:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (1872687)...printing done.
% 0.23/0.30 % (1872687)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.30 % (1872687)------------------------------
% 0.23/0.30 % (1872687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1872687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1872687)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1872687)Termination reason: Refutation
% 0.23/0.30 % (1872687)Time elapsed: 0.011 s
% 0.23/0.30 % (1872687)Peak memory usage: 12 MB
% 0.23/0.30 % (1872687)Instructions burned: 20 (million)
% 0.23/0.30 % (1872682)Success in time 0.047 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------