%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO488^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:48:06 AM UTC 2026
% Result : Theorem 0.25s 0.34s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 368 ( 69 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 581 ( 99 ~; 39 |; 0 &; 398 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 81 ( 81 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 52 usr; 6 con; 0-4 aty)
% ( 45 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 187 ( 174 ^; 13 !; 0 ?; 187 :)
% 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,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
f: mu > $i > $o ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vIMP: $o > $o > $o ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_49,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sK1: mu ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f10,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_ind) ).
thf(f12,axiom,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mexists_ind) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) )
= mdia_s5 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f37,conjecture,
( mvalid
@ ( mimplies
@ ( mdia_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( f @ X0 ) ) )
@ ( mnot
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s5 @ ( mnot @ ( f @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mdia_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( f @ X0 ) ) )
@ ( mnot
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s5 @ ( mnot @ ( f @ X0 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f45,plain,
~ ( mvalid
@ ( mimplies
@ ( mdia_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( f @ X0 ) ) )
@ ( mnot
@ ( mexists_ind
@ ^ [X1: mu] : ( mbox_s5 @ ( mnot @ ( f @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f46,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mdia_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) )
@ ( mnot
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s5 @ ( mnot @ ( f @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f55,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f56,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f58,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f63,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f64,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f69,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f70,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f78,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f79,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f78]) ).
thf(f86,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f91,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
inference(rectify,[],[f10]) ).
thf(f92,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f98,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f99,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f98]) ).
thf(f101,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mdia_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) )
@ ( mnot
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s5 @ ( mnot @ ( f @ Y0 ) ) ) ) ) ) ) ),
inference(flattening,[],[f46]) ).
thf(f121,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f123,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f99]) ).
thf(f126,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f127,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f128,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f130,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f135,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f137,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f138,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mdia_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) )
@ ( mnot
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s5 @ ( mnot @ ( f @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f142,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,[],[f121,f137,f135]) ).
thf(f146,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f123,f135,f130,f135]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f126,f135,f127,f135]) ).
thf(f154,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] : ( f @ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( f @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f138,f128,f142,f150,f130,f135,f146,f127,f135]) ).
thf(f170,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ~ ( f @ Y1 @ Y2 ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ mu
@ ^ [Y2: mu] : ( f @ Y2 @ Y1 ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f171,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ~ ( f @ Y1 @ Y2 ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ mu
@ ^ [Y2: mu] : ( f @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( $false
= ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK0 @ Y1 )
| ~ ( f @ Y0 @ Y1 ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] : ( f @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] : ( f @ Y1 @ Y0 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( $false
= ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK0 @ Y1 )
| ~ ( f @ Y0 @ Y1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK0 @ Y1 )
| ~ ( f @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK0 @ Y1 )
| ~ ( f @ Y0 @ Y1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( $false
= ( ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ sK0 @ Y1 )
| ~ ( f @ Y0 @ Y1 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( f @ sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( f @ sK1 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( f @ sK1 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( f @ sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $true
= ( ~ ( f @ sK1 @ X1 ) ) )
| ( ( ~ ( rel_s5 @ sK0 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK0 @ X1 ) )
= $true )
| ( ( f @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( ( f @ sK1 @ X1 )
= $false )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] : ( f @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f186,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] : ( f @ Y1 @ Y0 ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] : ( f @ Y1 @ Y0 ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( !! @ mu
@ ^ [Y0: mu] : ( f @ Y0 @ sK2 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] : ( f @ Y0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f191,plain,
( $true
= ( rel_s5 @ sK0 @ sK2 ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( !! @ mu
@ ^ [Y0: mu] : ( f @ Y0 @ sK2 ) )
= $true ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f193,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] : ( f @ Y0 @ sK2 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: mu] :
( $true
= ( f @ X1 @ sK2 ) ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f198,plain,
( ( $false = $true )
| ( $false
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(constrained_superposition,[],[f184,f194]) ).
thf(f200,plain,
( $false
= ( rel_s5 @ sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f198]) ).
thf(f203,plain,
$false = $true,
inference(constrained_superposition,[],[f191,f200]) ).
thf(f204,plain,
$false,
inference(trivial_inequality_removal,[],[f203]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO488^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n005.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 17:09:40 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.28 Running higher-order theorem proving
% 0.25/0.30 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.25/0.34 % (1944874)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.34 % (1944880)lrs+10_16_si=on:nwc=1.5:random_seed=995313052:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.34 % (1944880) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1944874-1944880"...
% 0.25/0.34 % (1944880)...printing done.
% 0.25/0.34 % (1944886)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.34 % (1944886)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
% 0.25/0.34 % (1944880)Refutation found. Thanks to Tanya!
% 0.25/0.34 % SZS status Theorem for theBenchmark
% 0.25/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.34 % (1944880)------------------------------
% 0.25/0.34 % (1944880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.34 % (1944880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.34 % (1944880)CaDiCaL version: 2.1.3
% 0.25/0.34 % (1944880)Termination reason: Refutation
% 0.25/0.34 % (1944880)Time elapsed: 0.008 s
% 0.25/0.34 % (1944880)Peak memory usage: 12 MB
% 0.25/0.34 % (1944880)Instructions burned: 15 (million)
% 0.25/0.34 % (1944874)Success in time 0.033 s
% 0.25/0.34 % Vampire exiting
%------------------------------------------------------------------------------