%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO434^1 : 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 : n006.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 08:47:41 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 11
% Syntax : Number of formulae : 99 ( 72 unt; 0 typ; 0 def)
% Number of atoms : 574 ( 119 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 814 ( 91 ~; 84 |; 13 &; 551 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 52 usr; 5 con; 0-4 aty)
% ( 63 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 210 ( 158 ^; 52 !; 0 ?; 210 :)
% 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_s4: $i > $i > $o ).
thf(func_def_33,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vOR: $o > $o > $o ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_46,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_53,type,
sK2: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
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(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X3: $i,X1: $i,X2: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X0 ) ) ) )
= mdia_s4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mdia_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f40,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f41,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f43,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f42]) ).
thf(f47,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f50,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f51,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f54,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X1 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f55,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f62,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f63,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f62]) ).
thf(f70,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f75,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f76,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f77,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f78,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f86,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f87,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f95,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f96,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) )
!= $true ),
inference(flattening,[],[f41]) ).
thf(f99,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f100,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f101,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f43]) ).
thf(f103,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f109,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f115,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f117,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f119,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f120,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f121,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f63]) ).
thf(f122,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f138,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,[],[f99,f115,f100]) ).
thf(f146,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f117,f100,f103,f100]) ).
thf(f147,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f101,f120]) ).
thf(f148,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f121,f109]) ).
thf(f149,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] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ p ) ) ) ) ) ),
inference(definition_unfolding,[],[f122,f119,f138,f103,f103,f146,f103]) ).
thf(f150,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ Y2 ) )
=> ( rel_s4 @ Y1 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f151,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ Y2 ) )
=> ( rel_s4 @ Y1 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ X1 )
& ( rel_s4 @ X1 @ Y1 ) )
=> ( rel_s4 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ X1 )
& ( rel_s4 @ X1 @ Y1 ) )
=> ( rel_s4 @ Y0 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ X2 @ X1 )
& ( rel_s4 @ X1 @ Y0 ) )
=> ( rel_s4 @ X2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s4 @ X2 @ X1 )
& ( rel_s4 @ X1 @ Y0 ) )
=> ( rel_s4 @ X2 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s4 @ X2 @ X1 )
& ( rel_s4 @ X1 @ X3 ) )
=> ( rel_s4 @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s4 @ X2 @ X3 ) )
| ( ( ( rel_s4 @ X2 @ X1 )
& ( rel_s4 @ X1 @ X3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s4 @ X2 @ X3 ) )
| ( $false
= ( rel_s4 @ X2 @ X1 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f160,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f163,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( $true
= ( ( p @ X1 )
| ~ ( rel_s4 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f165]) ).
thf(f173,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
( ( ~ ( rel_s4 @ sK0 @ sK1 ) )
= $false ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f176,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
| ~ ( rel_s4 @ sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK1 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
= $false )
| ( ( rel_s4 @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ ( sK2 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( ( ( p @ ( sK2 @ X1 ) )
| ~ ( rel_s4 @ X1 @ ( sK2 @ X1 ) ) )
= $false )
| ( ( rel_s4 @ sK1 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK1 @ X1 )
= $false )
| ( $false
= ( ~ ( rel_s4 @ X1 @ ( sK2 @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK1 @ X1 )
= $false )
| ( $false
= ( p @ ( sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f186,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ X1 @ ( sK2 @ X1 ) ) )
| ( ( rel_s4 @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f187,plain,
( $true
= ( rel_s4 @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f217,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK2 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f185,f161]) ).
thf(f219,plain,
( $false
= ( p @ ( sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f217]) ).
thf(f222,plain,
! [X0: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X0 )
= $false )
| ( $true = $false )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( p @ X0 ) ) ),
inference(constrained_superposition,[],[f158,f171]) ).
thf(f251,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( rel_s4 @ X1 @ X0 )
= $false )
| ( $true
= ( p @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f222]) ).
thf(f284,plain,
! [X0: $i] :
( ( $true
= ( p @ ( sK2 @ X0 ) ) )
| ( ( rel_s4 @ sK1 @ X0 )
= $false )
| ( $false
= ( rel_s4 @ sK0 @ X0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f186,f251]) ).
thf(f289,plain,
! [X0: $i] :
( ( ( rel_s4 @ sK1 @ X0 )
= $false )
| ( $true
= ( p @ ( sK2 @ X0 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f284]) ).
thf(f342,plain,
( ( $true
= ( p @ ( sK2 @ sK1 ) ) )
| ( $true = $false )
| ( ( rel_s4 @ sK0 @ sK1 )
= $false ) ),
inference(constrained_superposition,[],[f161,f289]) ).
thf(f347,plain,
( ( ( rel_s4 @ sK0 @ sK1 )
= $false )
| ( $true
= ( p @ ( sK2 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f342]) ).
thf(f356,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK2 @ sK1 ) ) ) ),
inference(forward_demodulation,[],[f347,f187]) ).
thf(f357,plain,
( $true
= ( p @ ( sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f356]) ).
thf(f368,plain,
$true = $false,
inference(forward_demodulation,[],[f357,f219]) ).
thf(f369,plain,
$false,
inference(trivial_inequality_removal,[],[f368]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO434^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n006.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:51:25 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 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
% 0.21/0.30 % (1008422)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (1008429)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3068452193:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (1008429)Instruction limit reached!
% 0.21/0.30 % (1008429)------------------------------
% 0.21/0.30 % (1008429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1008429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1008429)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1008429)Termination reason: Instruction limit
% 0.21/0.30 % (1008429)Termination phase: Function definition elimination
% 0.21/0.30 % (1008429)Time elapsed: 0.001 s
% 0.21/0.30 % (1008429)Peak memory usage: 10 MB
% 0.21/0.30 % (1008429)Instructions burned: 6 (million)
% 0.21/0.30 % (1008428)lrs+10_16_si=on:nwc=1.5:random_seed=3180626036:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (1008427)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3807176577:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (1008431)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=833189809:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (1008430)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=2311530242: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)
% 0.21/0.30 % (1008433)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (1008433)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
% 0.21/0.30 % (1008435)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3111483659:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.30 % (1008433)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=179542489:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (1008435)Instruction limit reached!
% 0.21/0.30 % (1008435)------------------------------
% 0.21/0.30 % (1008435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1008435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1008435)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1008435)Termination reason: Instruction limit
% 0.21/0.30 % (1008435)Termination phase: Property scanning
% 0.21/0.30 % (1008435)Time elapsed: 0.001 s
% 0.21/0.30 % (1008435)Peak memory usage: 10 MB
% 0.21/0.30 % (1008435)Instructions burned: 4 (million)
% 0.21/0.30 % (1008428)Instruction limit reached!
% 0.21/0.30 % (1008428)------------------------------
% 0.21/0.30 % (1008428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1008428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1008428)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1008428)Termination reason: Instruction limit
% 0.21/0.30 % (1008428)Termination phase: Saturation
% 0.21/0.30 % (1008428)Time elapsed: 0.009 s
% 0.21/0.30 % (1008428)Peak memory usage: 12 MB
% 0.21/0.30 % (1008428)Instructions burned: 18 (million)
% 0.21/0.30 % (1008427) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1008422-1008427"...
% 0.21/0.30 % (1008432)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2641578607:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (1008431)Instruction limit reached!
% 0.21/0.30 % (1008431)------------------------------
% 0.21/0.30 % (1008431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1008431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1008431)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1008431)Termination reason: Instruction limit
% 0.21/0.30 % (1008431)Termination phase: Saturation
% 0.21/0.30 % (1008431)Time elapsed: 0.014 s
% 0.21/0.30 % (1008431)Peak memory usage: 11 MB
% 0.21/0.30 % (1008431)Instructions burned: 24 (million)
% 0.21/0.30 % (1008427)...printing done.
% 0.21/0.30 % (1008427)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (1008427)------------------------------
% 0.21/0.30 % (1008427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1008427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1008427)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1008427)Termination reason: Refutation
% 0.21/0.30 % (1008427)Time elapsed: 0.014 s
% 0.21/0.30 % (1008427)Peak memory usage: 12 MB
% 0.21/0.30 % (1008427)Instructions burned: 25 (million)
% 0.21/0.30 % (1008422)Success in time 0.061 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------