%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO497^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:50:19 AM UTC 2026
% Result : Theorem 0.09s 0.18s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of formulae : 134 ( 104 unt; 0 typ; 0 def)
% Number of atoms : 883 ( 166 equ; 0 cnn)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 1457 ( 194 ~; 126 |; 13 &; 988 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 53 usr; 7 con; 0-4 aty)
% ( 114 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 396 ( 313 ^; 83 !; 0 ?; 396 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vAND: $o > $o > $o ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
sK2: mu ).
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(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f10,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mexists_ind) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
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] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ 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(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( f @ X0 ) @ ( mbox_s5 @ ( f @ X0 ) ) ) ) )
@ ( mdia_s5
@ ( mexists_ind
@ ^ [X0: mu] : ( f @ X0 ) ) ) )
@ ( mbox_s5
@ ( mexists_ind
@ ^ [X0: mu] : ( f @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( f @ X0 ) @ ( mbox_s5 @ ( f @ X0 ) ) ) ) )
@ ( mdia_s5
@ ( mexists_ind
@ ^ [X0: mu] : ( f @ X0 ) ) ) )
@ ( mbox_s5
@ ( mexists_ind
@ ^ [X0: mu] : ( f @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f41,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f42,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f44,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f45,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f46,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f50,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f51,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f54,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f55,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f64,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f65,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f68,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f69,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f82,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f83,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f90,plain,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f91,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f90]) ).
thf(f92,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f95,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f96,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f98,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f97]) ).
thf(f99,plain,
~ ( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( f @ X0 ) @ ( mbox_s5 @ ( f @ X0 ) ) ) ) )
@ ( mdia_s5
@ ( mexists_ind
@ ^ [X1: mu] : ( f @ X1 ) ) ) )
@ ( mbox_s5
@ ( mexists_ind
@ ^ [X2: mu] : ( f @ X2 ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f100,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( f @ Y0 ) @ ( mbox_s5 @ ( f @ Y0 ) ) ) ) )
@ ( mdia_s5
@ ( mexists_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) )
@ ( mbox_s5
@ ( mexists_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( f @ Y0 ) @ ( mbox_s5 @ ( f @ Y0 ) ) ) ) )
@ ( mdia_s5
@ ( mexists_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) )
@ ( mbox_s5
@ ( mexists_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) ) ) ),
inference(flattening,[],[f100]) ).
thf(f104,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f105,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f106,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f107,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f111,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f113,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f120,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f122,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f129,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f133,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f134,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f136,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f96]) ).
thf(f137,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f138,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( f @ Y0 ) @ ( mbox_s5 @ ( f @ Y0 ) ) ) ) )
@ ( mdia_s5
@ ( mexists_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) )
@ ( mbox_s5
@ ( mexists_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f141,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,[],[f106,f104,f105,f104,f104]) ).
thf(f142,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,[],[f107,f105,f104]) ).
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,[],[f113,f104,f111,f104]) ).
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,[],[f134,f104,f133,f104]) ).
thf(f152,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f136,f122]) ).
thf(f153,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f137,f120]) ).
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] :
( ( 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_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( f @ Y0 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( f @ Y0 ) ) ) ) )
@ ( ^ [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 > $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] : ( f @ Y0 ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [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] : ( f @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f138,f129,f142,f141,f133,f111,f142,f133,f150,f146,f133,f146]) ).
thf(f155,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ~ ( f @ Y2 @ Y1 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y1 @ Y3 )
| ( f @ Y2 @ Y3 ) ) ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( f @ Y2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( f @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ~ ( f @ Y2 @ Y1 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y1 @ Y3 )
| ( f @ Y2 @ Y3 ) ) ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( f @ Y2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( f @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ~ ( f @ Y1 @ Y0 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ( f @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ~ ( f @ Y1 @ Y0 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ( f @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f160,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ~ ( f @ Y1 @ Y0 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ( f @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ~ ( f @ Y1 @ Y0 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ( f @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ~ ( f @ Y1 @ Y0 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ( f @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f164,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ~ ( f @ Y1 @ Y0 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ( f @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ~ ( f @ Y1 @ Y0 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y0 @ Y2 )
| ( f @ Y1 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ~ ( f @ Y0 @ X1 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ X1 @ Y1 )
| ( f @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ~ ( f @ Y0 @ X1 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ X1 @ Y1 )
| ( f @ Y0 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( ^ [Y0: mu] :
( ~ ( f @ Y0 @ X1 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ X1 @ Y1 )
| ( f @ Y0 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( ^ [Y0: mu] :
( ~ ( f @ Y0 @ X1 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ X1 @ Y1 )
| ( f @ Y0 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( ~ ( f @ X2 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( f @ X2 @ Y0 ) ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( f @ X2 @ Y0 ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( f @ X2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( f @ X2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( f @ X2 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( f @ X2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( f @ X2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X3 )
| ( f @ X2 @ X3 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( f @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( f @ X2 @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( f @ X2 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( f @ X2 @ X3 ) )
| ( $false
= ( f @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ X1 @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f178,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
( $false
= ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK1 ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f183,plain,
( $true
= ( rel_s5 @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK1 ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f185,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( $false
= ( ^ [Y0: mu] :
~ ( f @ Y0 @ sK1 )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( $false
= ( ~ ( f @ sK2 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
( $true
= ( f @ sK2 @ sK1 ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f190,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f193,plain,
( $true
= ( rel_s5 @ sK0 @ sK3 ) ),
inference(not_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f195,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
~ ( f @ Y0 @ sK3 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: mu] :
( $true
= ( ~ ( f @ X1 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f197,plain,
! [X1: mu] :
( $false
= ( f @ X1 @ sK3 ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f199,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f205,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) ) )
| ( $true
= ( rel_s5 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( $true
= ( rel_s5 @ X3 @ X1 ) )
| ( $false
= ( rel_s5 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f211]) ).
thf(f241,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( f @ sK2 @ X0 ) )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f188,f176]) ).
thf(f247,plain,
! [X0: $i] :
( ( $true
= ( f @ sK2 @ X0 ) )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f241]) ).
thf(f257,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( f @ sK2 @ X0 ) )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) ) ),
inference(forward_demodulation,[],[f247,f183]) ).
thf(f258,plain,
! [X0: $i] :
( ( $true
= ( f @ sK2 @ X0 ) )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f257]) ).
thf(f282,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ X0 @ X2 ) ) ),
inference(constrained_superposition,[],[f203,f212]) ).
thf(f285,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f282]) ).
thf(f355,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK3 ) ) ),
inference(constrained_superposition,[],[f193,f285]) ).
thf(f373,plain,
! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f355]) ).
thf(f1029,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK1 @ sK3 ) ) ),
inference(constrained_superposition,[],[f197,f258]) ).
thf(f1030,plain,
( $false
= ( rel_s5 @ sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f1029]) ).
thf(f1043,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f373,f1030]) ).
thf(f1046,plain,
( $false
= ( rel_s5 @ sK0 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f1043]) ).
thf(f1090,plain,
$true = $false,
inference(constrained_superposition,[],[f183,f1046]) ).
thf(f1091,plain,
$false,
inference(trivial_inequality_removal,[],[f1090]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO497^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 17:10:20 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.13 Running first-order model finding
% 0.09/0.13 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % (405162)Will run a generic schedule for satisfiability detection.
% 0.09/0.18 % (405168)% WARNING: option uhcvi not known.
% 0.09/0.18 % (405167)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2465682973_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.18 % (405169)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3509132094:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.18 % (405168)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3670029040:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.18 % (405170)dis+10_1_sil=32000:sp=arity:random_seed=4077196188:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.18 % (405173)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1623160613:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.18 % (405171)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4022342757:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.18 % (405172)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2693439261:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.18 % (405168)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.18 % (405171)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.18 % Exception at run slice level
% 0.09/0.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.18 % (405168)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.18 % (405181)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=57523988:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.09/0.18 % Exception at run slice level
% 0.09/0.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.18 % (405170) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-405162-405170"...
% 0.09/0.18 % (405170)...printing done.
% 0.09/0.18 % (405170)Refutation found. Thanks to Tanya!
% 0.09/0.18 % SZS status Theorem for theBenchmark
% 0.09/0.18 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.18 % (405170)------------------------------
% 0.09/0.18 % (405170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.18 % (405170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.18 % (405170)CaDiCaL version: 2.1.3
% 0.09/0.18 % (405170)Termination reason: Refutation
% 0.09/0.18 % (405170)Time elapsed: 0.022 s
% 0.09/0.18 % (405170)Peak memory usage: 12 MB
% 0.09/0.18 % (405170)Instructions burned: 85 (million)
% 0.09/0.18 % (405162)Success in time 0.05 s
% 0.09/0.18 % Vampire exiting
%------------------------------------------------------------------------------