%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO485^6 : 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 : n019.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 08:48:05 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 78 ( 56 unt; 0 typ; 2 def)
% Number of atoms : 320 ( 90 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 423 ( 86 ~; 29 |; 0 &; 268 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 53 usr; 7 con; 0-4 aty)
% ( 38 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 174 ( 4 sgn 28 !; 0 ?; 174 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_38,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vIMP: $o > $o > $o ).
thf(func_def_40,type,
vAND: $o > $o > $o ).
thf(func_def_41,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_50,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sK1: mu ).
thf(f1,axiom,
( ( ^ [X0: mu,X1: mu,X2: $i] : ( X0 = X1 ) )
= meq_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',meq_ind) ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f10,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_ind) ).
thf(f12,axiom,
( ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) )
= mexists_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mexists_ind) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f34,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a1) ).
thf(f37,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mdia_s5
@ ( mexists_ind
@ ^ [X1: mu] : ( meq_ind @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mdia_s5
@ ( mexists_ind
@ ^ [X1: mu] : ( meq_ind @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) )
= mexists_ind ),
inference(rectify,[],[f12]) ).
thf(f40,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f42,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f45,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f46,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f52,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mdia_s5
@ ( mexists_ind
@ ^ [X1: mu] : ( meq_ind @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f53,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mdia_s5
@ ( mexists_ind
@ ^ [Y1: mu] : ( meq_ind @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f52]) ).
thf(f54,plain,
mreflexive @ rel_s5,
inference(rectify,[],[f34]) ).
thf(f55,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
inference(rectify,[],[f10]) ).
thf(f57,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f66,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f69,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f70,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f85,plain,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f86,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f97,plain,
( meq_ind
= ( ^ [Y0: mu,Y1: mu,Y2: $i] : ( Y0 = Y1 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f101,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mdia_s5
@ ( mexists_ind
@ ^ [Y1: mu] : ( meq_ind @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(flattening,[],[f53]) ).
thf(f104,plain,
( meq_ind
= ( ^ [Y0: mu,Y1: mu,Y2: $i] : ( Y0 = Y1 ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f105,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f108,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f112,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f115,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f116,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f55]) ).
thf(f118,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f131,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f132,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f134,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mdia_s5
@ ( mexists_ind
@ ^ [Y1: mu] : ( meq_ind @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
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,[],[f118,f112,f105,f112]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f108,f112,f132,f112]) ).
thf(f152,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f116,f115]) ).
thf(f154,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s5 @ Y3 @ Y4 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( Y1 @ Y2 ) ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: mu,Y3: mu,Y4: $i] : ( Y2 = Y3 )
@ Y0
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f134,f131,f105,f150,f146,f104]) ).
thf(f155,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y3: mu] : ( Y1 != Y3 ) )
| ~ ( rel_s5 @ Y0 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y3: mu] : ( Y1 != Y3 ) )
| ~ ( rel_s5 @ Y0 @ Y2 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y2: mu] : ( Y0 != Y2 ) )
| ~ ( rel_s5 @ sK0 @ Y1 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( ( ^ [Y0: mu] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y2: mu] : ( Y0 != Y2 ) )
| ~ ( rel_s5 @ sK0 @ Y1 ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y1: mu] : ( sK1 != Y1 ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y1: mu] : ( sK1 != Y1 ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y1: mu] : ( sK1 != Y1 ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( $true
= ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] : ( sK1 != Y0 ) )
| ~ ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] : ( sK1 != Y0 ) ) ) )
| ( ( ~ ( rel_s5 @ sK0 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK0 @ X1 ) )
= $true )
| ( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] : ( sK1 != Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] : ( sK1 != Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( !! @ mu
@ ^ [Y0: mu] : ( sK1 != Y0 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( ^ [Y0: mu] : ( sK1 != Y0 )
@ X2 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( sK1 != X2 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X2: mu,X1: $i] :
( ( $false
= ( sK1 = X2 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: mu,X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( sK1 != X2 ) ),
inference(equality_proxy_clausification,[],[f169]) ).
thf(f186,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f187,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( rel_s5 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f190,definition,
( spl2_1
<=> ! [X2: mu] : ( sK1 != X2 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f191,plain,
( ! [X2: mu] : ( sK1 != X2 )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f190]) ).
thf(f193,definition,
( spl2_2
<=> ! [X1: $i] :
( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f194,plain,
( ! [X1: $i] :
( ( rel_s5 @ sK0 @ X1 )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f193]) ).
thf(f195,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f170,f193,f190]) ).
thf(f197,plain,
( ( $true = $false )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f194,f188]) ).
thf(f200,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f197]) ).
thf(f201,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f200]) ).
thf(f202,plain,
( $false
| ~ spl2_1 ),
inference(equality_resolution,[],[f191]) ).
thf(f203,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f202]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f195]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f201]) ).
cnf(s4,plain,
~ spl2_1,
inference(sat_conversion,[],[f203]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
thf(f204,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO485^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:08:48 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.27 % (1090267)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (1090280)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2409065679:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.27 % (1090283)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.27 % (1090283)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
% 0.21/0.27 % (1090276)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2573174427:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (1090277)lrs+10_16_si=on:nwc=1.5:random_seed=88437864:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (1090278)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1472571245:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.27 % (1090279)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=890257085: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)
% 0.21/0.27 % (1090280)Instruction limit reached!
% 0.21/0.27 % (1090280)------------------------------
% 0.21/0.27 % (1090280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1090280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1090280)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1090280)Termination reason: Instruction limit
% 0.21/0.27 % (1090280)Termination phase: Saturation
% 0.21/0.27 % (1090280)Time elapsed: 0.008 s
% 0.21/0.27 % (1090280)Peak memory usage: 11 MB
% 0.21/0.27 % (1090280)Instructions burned: 25 (million)
% 0.21/0.27 % (1090282)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=795301250:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.27 % (1090283)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=339117513:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.27 % (1090278)Instruction limit reached!
% 0.21/0.27 % (1090278)------------------------------
% 0.21/0.27 % (1090278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1090278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1090278)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1090278)Termination reason: Instruction limit
% 0.21/0.27 % (1090278)Termination phase: shuffling
% 0.21/0.27 % (1090278)Time elapsed: 0.002 s
% 0.21/0.27 % (1090278)Peak memory usage: 10 MB
% 0.21/0.27 % (1090278)Instructions burned: 4 (million)
% 0.21/0.27 % (1090277) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1090267-1090277"...
% 0.21/0.27 % (1090276) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1090267-1090276"...
% 0.21/0.27 % (1090282) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1090267-1090282"...
% 0.21/0.27 % (1090283) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1090267-1090283"...
% 0.21/0.27 % (1090277)...printing done.
% 0.21/0.27 % (1090276)...printing done.
% 0.21/0.27 % (1090277)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (1090277)------------------------------
% 0.21/0.28 % (1090277)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1090277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1090277)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1090277)Termination reason: Refutation
% 0.21/0.28 % (1090277)Time elapsed: 0.008 s
% 0.21/0.28 % (1090277)Peak memory usage: 13 MB
% 0.21/0.28 % (1090277)Instructions burned: 13 (million)
% 0.21/0.28 % (1090267)Success in time 0.033 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------