%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO455^2 : 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 : n015.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 08:47:48 AM UTC 2026
% Result : Theorem 0.26s 0.39s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 85 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 502 ( 97 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 681 ( 112 ~; 82 |; 0 &; 446 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 52 usr; 5 con; 0-4 aty)
% ( 35 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 181 ( 155 ^; 24 !; 2 ?; 181 :)
% 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_d: $i > $i > $o ).
thf(func_def_33,type,
mbox_d: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_d: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_49,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
sK1: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f20,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= mserial ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mserial) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_d
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_d @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',mbox_d) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_d @ ( mnot @ X0 ) ) ) )
= mdia_d ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',mdia_d) ).
thf(f34,axiom,
mserial @ rel_d,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',a1) ).
thf(f35,conjecture,
mvalid @ ( mimplies @ ( mand @ ( mbox_d @ p ) @ ( mbox_d @ ( mor @ ( mnot @ p ) @ q ) ) ) @ ( mdia_d @ q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f36,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mand @ ( mbox_d @ p ) @ ( mbox_d @ ( mor @ ( mnot @ p ) @ q ) ) ) @ ( mdia_d @ q ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
thf(f39,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f40,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= mserial ),
inference(rectify,[],[f20]) ).
thf(f42,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f60,plain,
( mdia_d
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_d @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f66,plain,
mserial @ rel_d,
inference(rectify,[],[f34]) ).
thf(f67,plain,
( ( mserial @ rel_d )
= $true ),
inference(fool_elimination,[],[f66]) ).
thf(f68,plain,
( mbox_d
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_d @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f69,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f75,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f78,plain,
~ ( mvalid @ ( mimplies @ ( mand @ ( mbox_d @ p ) @ ( mbox_d @ ( mor @ ( mnot @ p ) @ q ) ) ) @ ( mdia_d @ q ) ) ),
inference(rectify,[],[f36]) ).
thf(f79,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_d @ p ) @ ( mbox_d @ ( mor @ ( mnot @ p ) @ q ) ) ) @ ( mdia_d @ q ) ) )
!= $true ),
inference(fool_elimination,[],[f78]) ).
thf(f80,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f81,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f88,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f89,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f88]) ).
thf(f90,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f95,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_d @ p ) @ ( mbox_d @ ( mor @ ( mnot @ p ) @ q ) ) ) @ ( mdia_d @ q ) ) )
!= $true ),
inference(flattening,[],[f79]) ).
thf(f96,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f106,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f108,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f109,plain,
( ( mserial @ rel_d )
= $true ),
inference(cnf_transformation,[],[f67]) ).
thf(f110,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f111,plain,
( mdia_d
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_d @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f115,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f120,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f121,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f125,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_d @ p ) @ ( mbox_d @ ( mor @ ( mnot @ p ) @ q ) ) ) @ ( mdia_d @ q ) ) )
!= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f133,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f96,f106,f110,f106,f106]) ).
thf(f134,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,[],[f115,f110,f106]) ).
thf(f142,plain,
( mdia_d
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_d @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f111,f106,f121,f106]) ).
thf(f143,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ rel_d ) ),
inference(definition_unfolding,[],[f109,f108]) ).
thf(f144,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_d @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p )
@ q ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_d @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) ),
inference(definition_unfolding,[],[f125,f120,f134,f133,f121,f121,f110,f106,f142]) ).
thf(f145,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_d @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f150,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f154,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( ( ~ ( rel_d @ sK0 @ X1 )
| ( p @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_d @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( q @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f160,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( q @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_d @ sK0 @ X1 )
| ~ ( p @ X1 )
| ( q @ X1 ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_d @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_d @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_d @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK0 @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f167,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_d @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_d @ sK0 @ X1 )
| ~ ( q @ X1 ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_d @ sK0 @ X1 ) ) )
| ( ( ~ ( q @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK0 @ X1 ) )
| ( ( ~ ( q @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK0 @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( rel_d @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f173,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( ?? @ $i @ ( rel_d @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( $true
= ( ?? @ $i @ ( rel_d @ X1 ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( $true
= ( rel_d @ X1 @ ( sK1 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $false = $true )
| ( $false
= ( q @ ( sK1 @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f175,f171]) ).
thf(f178,plain,
( $false
= ( q @ ( sK1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f180,plain,
( ( $true
= ( p @ ( sK1 @ sK0 ) ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f158,f175]) ).
thf(f182,plain,
( $true
= ( p @ ( sK1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f180]) ).
thf(f185,plain,
( ( $false = $true )
| ( ( q @ ( sK1 @ sK0 ) )
= $true )
| ( $false
= ( p @ ( sK1 @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f175,f165]) ).
thf(f186,plain,
( ( ( q @ ( sK1 @ sK0 ) )
= $true )
| ( $false
= ( p @ ( sK1 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[],[f185]) ).
thf(f188,plain,
( ( $false = $true )
| ( $false
= ( p @ ( sK1 @ sK0 ) ) ) ),
inference(forward_demodulation,[],[f186,f178]) ).
thf(f189,plain,
( $false
= ( p @ ( sK1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f188]) ).
thf(f193,plain,
$false = $true,
inference(constrained_superposition,[],[f182,f189]) ).
thf(f194,plain,
$false,
inference(trivial_inequality_removal,[],[f193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO455^2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 % Computer : n015.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 16:58:34 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.31 Running higher-order theorem proving
% 0.21/0.33 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
% 0.26/0.39 % (3801743)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.39 % (3801751)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=2674685556: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)
% 0.26/0.39 % (3801754)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.26/0.39 % (3801754)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
% 0.26/0.39 % (3801748)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3613943899:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.26/0.39 % (3801749)lrs+10_16_si=on:nwc=1.5:random_seed=52533971:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.26/0.39 % (3801752)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=381812574:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.26/0.39 % (3801753)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2238966404:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.26/0.39 % (3801750)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1649993553:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.26/0.39 % (3801754)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=755018913:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.26/0.39 % (3801750)Instruction limit reached!
% 0.26/0.39 % (3801750)------------------------------
% 0.26/0.39 % (3801750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.39 % (3801750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.39 % (3801750)CaDiCaL version: 2.1.3
% 0.26/0.39 % (3801750)Termination reason: Instruction limit
% 0.26/0.39 % (3801750)Termination phase: Property scanning
% 0.26/0.39 % (3801750)Time elapsed: 0.003 s
% 0.26/0.39 % (3801750)Peak memory usage: 9 MB
% 0.26/0.39 % (3801750)Instructions burned: 3 (million)
% 0.26/0.39 % (3801749) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3801743-3801749"...
% 0.26/0.39 % (3801748) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3801743-3801748"...
% 0.26/0.39 % (3801753) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3801743-3801753"...
% 0.26/0.39 % (3801754) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3801743-3801754"...
% 0.26/0.39 % (3801749)...printing done.
% 0.26/0.39 % (3801748)...printing done.
% 0.26/0.39 % (3801753)...printing done.
% 0.26/0.39 % (3801749)Refutation found. Thanks to Tanya!
% 0.26/0.39 % SZS status Theorem for theBenchmark
% 0.26/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.40 % (3801749)------------------------------
% 0.26/0.40 % (3801749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.40 % (3801749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.40 % (3801749)CaDiCaL version: 2.1.3
% 0.26/0.40 % (3801749)Termination reason: Refutation
% 0.26/0.40 % (3801749)Time elapsed: 0.015 s
% 0.26/0.40 % (3801749)Peak memory usage: 12 MB
% 0.26/0.40 % (3801749)Instructions burned: 15 (million)
% 0.26/0.40 % (3801743)Success in time 0.054 s
% 0.26/0.40 % Vampire exiting
%------------------------------------------------------------------------------