%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV431^2 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:39:58 AM UTC 2026
% Result : Theorem 0.64s 0.41s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 26
% Syntax : Number of formulae : 205 ( 71 unt; 0 typ; 13 def)
% Number of atoms : 1722 ( 310 equ; 0 cnn)
% Maximal formula atoms : 18 ( 8 avg)
% Number of connectives : 2433 ( 196 ~; 381 |; 0 &;1544 @)
% ( 12 <=>; 159 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 369 ( 369 >; 0 *; 0 +; 0 <<)
% Number of symbols : 75 ( 71 usr; 21 con; 0-4 aty)
% ( 141 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 672 ( 0 sgn 121 !; 0 ?; 672 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
rel: $i > $i > $o ).
thf(func_def_21,type,
icl_atom: ( $i > $o ) > $i > $o ).
thf(func_def_22,type,
icl_princ: ( $i > $o ) > $i > $o ).
thf(func_def_23,type,
icl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_24,type,
icl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_25,type,
icl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_26,type,
icl_true: $i > $o ).
thf(func_def_27,type,
icl_false: $i > $o ).
thf(func_def_28,type,
icl_says: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_29,type,
iclval: ( $i > $o ) > $o ).
thf(func_def_30,type,
icl_impl_princ: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_31,type,
a: $i > $o ).
thf(func_def_32,type,
b: $i > $o ).
thf(func_def_33,type,
s: $i > $o ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vIMP: $o > $o > $o ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
sF0: $o ).
thf(func_def_48,type,
sK1: $i > ( $i > $o ) > $i ).
thf(func_def_54,type,
sK7: $i > $i ).
thf(func_def_55,type,
sK8: $i > $i ).
thf(func_def_56,type,
sK9: $i > $i ).
thf(func_def_57,type,
sK10: $i > $i ).
thf(func_def_58,type,
sK11: $i > $i ).
thf(func_def_59,type,
sK12: $i > $i ).
thf(func_def_60,type,
sK13: $i > $i ).
thf(func_def_61,type,
sK14: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
( ( ^ [X0: $i > $o] : ( mbox @ rel @ X0 ) )
= icl_atom ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_atom) ).
thf(f17,axiom,
( icl_princ
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_princ) ).
thf(f20,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mimpl @ X0 @ X1 ) ) )
= icl_impl ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_impl) ).
thf(f23,axiom,
( icl_says
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mor @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_says) ).
thf(f24,axiom,
( ( ^ [X0: $i > $o] : ( mvalid @ X0 ) )
= iclval ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_s4_valid) ).
thf(f26,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^1.ax',trans_axiom) ).
thf(f27,axiom,
( icl_impl_princ
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mimpl @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^2.ax',icl_impl_princ) ).
thf(f28,conjecture,
iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',speaking_for) ).
thf(f29,negated_conjecture,
~ ( iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
thf(f30,plain,
( icl_atom
= ( ^ [Y0: $i > $o] : ( mbox @ rel @ Y0 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f33,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f34,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f35,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f38,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f39,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f40,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f41,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f17]) ).
thf(f43,plain,
~ ( iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f44,plain,
( ( iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f43]) ).
thf(f47,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f48,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f54,plain,
( icl_impl_princ
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f55,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f56,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f59,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f60,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f59]) ).
thf(f66,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f70,plain,
( ( iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ) )
!= $true ),
inference(flattening,[],[f44]) ).
thf(f73,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f76,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f77,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f81,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f83,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f84,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f85,plain,
( ( iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f70]) ).
thf(f86,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f60]) ).
thf(f88,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f89,plain,
( icl_impl_princ
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f94,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f97,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f98,plain,
( icl_atom
= ( ^ [Y0: $i > $o] : ( mbox @ rel @ Y0 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f101,plain,
( mimpl
= ( ^ [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,[],[f81,f84,f83]) ).
thf(f103,plain,
( icl_atom
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 ) ) ),
inference(definition_unfolding,[],[f98,f94]) ).
thf(f106,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f76,f94,f101]) ).
thf(f109,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f97,f94,f84]) ).
thf(f110,plain,
( iclval
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f88,f73]) ).
thf(f111,plain,
( icl_impl_princ
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f89,f94,f101]) ).
thf(f112,plain,
( ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f85,f110,f106,f111,f77,f77,f106,f109,f77,f103,f109,f77,f103]) ).
thf(f113,plain,
! [X0: $i > $o] :
( ( ^ [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 > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ X0 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ X0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f86,f73,f101,f94,f94,f94]) ).
thf(f115,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f116,plain,
( ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) ) ) ) )
= sF0 ),
inference(reorient_equations,[],[f115]) ).
thf(f117,plain,
sF0 != $true,
inference(definition_folding,[],[f112,f116]) ).
thf(f118,plain,
! [X0: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( X0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f119,plain,
! [X0: $i > $o,X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( X0 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X0: $i > $o,X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f121,plain,
! [X0: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK1 @ X1 @ X0 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( ( rel @ X1 @ ( sK1 @ X1 @ X0 ) )
=> ( X0 @ ( sK1 @ X1 @ X0 ) ) ) )
| ( $true
= ( ( rel @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f124]) ).
thf(f126,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( ( rel @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( $false
= ( X0 @ ( sK1 @ X1 @ X0 ) ) ) ),
inference(imp_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK1 @ X1 @ X0 ) ) )
| ( $true
= ( ( rel @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f125]) ).
thf(f128,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( rel @ X1 @ ( sK1 @ X1 @ X0 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X3 ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( rel @ X1 @ ( sK1 @ X1 @ X0 ) ) ) ),
inference(pi_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( ( rel @ X2 @ X3 )
=> ( X0 @ X3 ) )
= $true )
| ( $true
= ( rel @ X1 @ ( sK1 @ X1 @ X0 ) ) )
| ( $false
= ( rel @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f131,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK1 @ X1 @ X0 ) ) )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( $true
= ( X0 @ X3 ) )
| ( $false
= ( rel @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $true )
| ( $false
= ( X0 @ ( sK1 @ X1 @ X0 ) ) )
| ( $false
= ( rel @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f133,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK1 @ X1 @ X0 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X3 ) )
| ( $false
= ( rel @ X1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK1 @ X1 @ X0 ) ) )
| ( ( ( rel @ X2 @ X3 )
=> ( X0 @ X3 ) )
= $true )
| ( $false
= ( rel @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f135,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK1 @ X1 @ X0 ) ) )
| ( $true
= ( X0 @ X3 ) )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( $false
= ( rel @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f134]) ).
thf(f137,plain,
( ( ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f116]) ).
thf(f138,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ~ ( a @ Y2 )
| ( b @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( a @ Y3 )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( rel @ Y3 @ Y4 )
=> ( s @ Y4 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( b @ Y3 )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( rel @ Y3 @ Y4 )
=> ( s @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ~ ( a @ Y2 )
| ( b @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( a @ Y3 )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( rel @ Y3 @ Y4 )
=> ( s @ Y4 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( b @ Y3 )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( rel @ Y3 @ Y4 )
=> ( s @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f138]) ).
thf(f140,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( a @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( b @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( a @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( b @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) ) ) ) ) ) ) ) ) )
@ sK3 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( ( $false
= ( ( rel @ sK2 @ sK3 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( a @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( a @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f145,plain,
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( a @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f146,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f147,plain,
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X1: $i] :
( ( ( ( rel @ sK3 @ X1 )
=> ( ~ ( a @ X1 )
| ( b @ X1 ) ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( ( ( ~ ( a @ X1 )
| ( b @ X1 ) )
= $true )
| ( sF0 = $true )
| ( $false
= ( rel @ sK3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( ( $true
= ( ~ ( a @ X1 ) ) )
| ( $false
= ( rel @ sK3 @ X1 ) )
| ( sF0 = $true )
| ( $true
= ( b @ X1 ) ) ),
inference(or_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( $false
= ( a @ X1 ) )
| ( $false
= ( rel @ sK3 @ X1 ) )
| ( $true
= ( b @ X1 ) ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( a @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) ) ) ) ) ) )
@ sK4 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f154,plain,
( ( sF0 = $true )
| ( $false
= ( ( rel @ sK3 @ sK4 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( a @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( a @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( ( rel @ sK3 @ sK4 )
= $true )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f154]) ).
thf(f157,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( a @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f159,plain,
( ( sF0 = $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( a @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( a @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) ) ) )
@ X1 ) )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ( rel @ sK4 @ X1 )
=> ( ( a @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( $true
= ( ( a @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) ) ) ) )
| ( $false
= ( rel @ sK4 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( ( a @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) ) ) )
| ( sF0 = $true )
| ( $false
= ( rel @ sK4 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 )
= $true )
| ( sF0 = $true )
| ( $false
= ( rel @ sK4 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 )
= $true )
| ( sF0 = $true )
| ( $true
= ( ( rel @ X1 @ X2 )
=> ( s @ X2 ) ) )
| ( $false
= ( rel @ sK4 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X1: $i] :
( ( ( s @ X2 )
= $true )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( ( a @ X1 )
= $true )
| ( $false
= ( rel @ sK4 @ X1 ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) ) ) )
@ sK5 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f168,plain,
( ( sF0 = $true )
| ( $false
= ( ( rel @ sK4 @ sK5 )
=> ( ( b @ sK5 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK5 @ Y0 )
=> ( s @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
( ( $false
= ( ( b @ sK5 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK5 @ Y0 )
=> ( s @ Y0 ) ) ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( ( rel @ sK4 @ sK5 )
= $true )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f171,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK5 @ Y0 )
=> ( s @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f172,plain,
( ( $false
= ( b @ sK5 ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f173,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( rel @ sK5 @ Y0 )
=> ( s @ Y0 ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( sF0 = $true )
| ( $false
= ( ( rel @ sK5 @ sK6 )
=> ( s @ sK6 ) ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
( ( sF0 = $true )
| ( $false
= ( s @ sK6 ) ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( ( rel @ sK5 @ sK6 )
= $true )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f283,definition,
( spl15_1
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
thf(f292,definition,
( spl15_3
<=> ! [X1: $i] :
( ( $false
= ( a @ X1 ) )
| ( $true
= ( b @ X1 ) )
| ( $false
= ( rel @ sK3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
thf(f293,plain,
( ! [X1: $i] :
( ( $false
= ( rel @ sK3 @ X1 ) )
| ( $false
= ( a @ X1 ) )
| ( $true
= ( b @ X1 ) ) )
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f292]) ).
thf(f294,plain,
( spl15_3
| spl15_1 ),
inference(avatar_split_clause,[],[f152,f283,f292]) ).
thf(f296,definition,
( spl15_4
<=> ( ( rel @ sK3 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
thf(f298,plain,
( ( ( rel @ sK3 @ sK4 )
= $true )
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f296]) ).
thf(f299,plain,
( spl15_4
| spl15_1 ),
inference(avatar_split_clause,[],[f156,f283,f296]) ).
thf(f301,definition,
( spl15_5
<=> ! [X2: $i,X1: $i] :
( ( ( s @ X2 )
= $true )
| ( $false
= ( rel @ sK4 @ X1 ) )
| ( ( a @ X1 )
= $true )
| ( $false
= ( rel @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
thf(f302,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( rel @ sK4 @ X1 ) )
| ( ( s @ X2 )
= $true )
| ( ( a @ X1 )
= $true )
| ( $false
= ( rel @ X1 @ X2 ) ) )
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f301]) ).
thf(f303,plain,
( spl15_1
| spl15_5 ),
inference(avatar_split_clause,[],[f166,f301,f283]) ).
thf(f305,definition,
( spl15_6
<=> ( ( rel @ sK4 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
thf(f307,plain,
( ( ( rel @ sK4 @ sK5 )
= $true )
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f305]) ).
thf(f308,plain,
( spl15_6
| spl15_1 ),
inference(avatar_split_clause,[],[f170,f283,f305]) ).
thf(f310,definition,
( spl15_7
<=> ( $false
= ( b @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
thf(f312,plain,
( ( $false
= ( b @ sK5 ) )
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f310]) ).
thf(f313,plain,
( spl15_1
| spl15_7 ),
inference(avatar_split_clause,[],[f172,f310,f283]) ).
thf(f315,definition,
( spl15_8
<=> ( ( rel @ sK5 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).
thf(f317,plain,
( ( ( rel @ sK5 @ sK6 )
= $true )
| ~ spl15_8 ),
inference(avatar_component_clause,[],[f315]) ).
thf(f318,plain,
( spl15_8
| spl15_1 ),
inference(avatar_split_clause,[],[f176,f283,f315]) ).
thf(f320,definition,
( spl15_9
<=> ( $false
= ( s @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_9])],[avatar_definition]) ).
thf(f322,plain,
( ( $false
= ( s @ sK6 ) )
| ~ spl15_9 ),
inference(avatar_component_clause,[],[f320]) ).
thf(f323,plain,
( spl15_9
| spl15_1 ),
inference(avatar_split_clause,[],[f175,f283,f320]) ).
thf(f376,plain,
~ spl15_1,
inference(avatar_split_clause,[],[f117,f283]) ).
thf(f443,plain,
( ! [X0: $i] :
( ( $true
= ( a @ sK5 ) )
| ( $false
= ( rel @ sK5 @ X0 ) )
| ( $false = $true )
| ( $true
= ( s @ X0 ) ) )
| ~ spl15_5
| ~ spl15_6 ),
inference(constrained_superposition,[],[f307,f302]) ).
thf(f452,plain,
( ! [X0: $i] :
( ( $true
= ( a @ sK5 ) )
| ( $false
= ( rel @ sK5 @ X0 ) )
| ( $true
= ( s @ X0 ) ) )
| ~ spl15_5
| ~ spl15_6 ),
inference(trivial_inequality_removal,[],[f443]) ).
thf(f456,definition,
( spl15_27
<=> ( $true
= ( a @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_27])],[avatar_definition]) ).
thf(f458,plain,
( ( $true
= ( a @ sK5 ) )
| ~ spl15_27 ),
inference(avatar_component_clause,[],[f456]) ).
thf(f460,definition,
( spl15_28
<=> ! [X0: $i] :
( ( $true
= ( s @ X0 ) )
| ( $false
= ( rel @ sK5 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_28])],[avatar_definition]) ).
thf(f461,plain,
( ! [X0: $i] :
( ( $false
= ( rel @ sK5 @ X0 ) )
| ( $true
= ( s @ X0 ) ) )
| ~ spl15_28 ),
inference(avatar_component_clause,[],[f460]) ).
thf(f467,plain,
( spl15_27
| spl15_28
| ~ spl15_5
| ~ spl15_6 ),
inference(avatar_split_clause,[],[f452,f305,f301,f460,f456]) ).
thf(f500,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( rel @ X0 @ X4 ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $false
= ( rel @ X4 @ X3 ) )
| ( $true
= ( rel @ X0 @ X3 ) )
| ( $true
= ( rel @ X0 @ X2 ) )
| ( $false = $true )
| ( $false
= ( rel @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f131,f135]) ).
thf(f509,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( rel @ X0 @ X3 ) )
| ( $false
= ( rel @ X4 @ X3 ) )
| ( $true
= ( rel @ X0 @ X2 ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $false
= ( rel @ X0 @ X4 ) )
| ( $false
= ( rel @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f500]) ).
thf(f586,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( a @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( ( rel @ sK3 @ X2 )
= $true )
| ( $false
= ( rel @ X3 @ X2 ) )
| ( $false
= ( rel @ sK3 @ X3 ) )
| ( $false = $true )
| ( $false
= ( rel @ X1 @ X0 ) )
| ( $false
= ( rel @ sK3 @ X1 ) ) )
| ~ spl15_3 ),
inference(constrained_superposition,[],[f509,f293]) ).
thf(f608,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( rel @ sK3 @ X2 )
= $true )
| ( $false
= ( rel @ sK3 @ X1 ) )
| ( $true
= ( b @ X0 ) )
| ( $false
= ( rel @ X3 @ X2 ) )
| ( $false
= ( rel @ X1 @ X0 ) )
| ( $false
= ( rel @ sK3 @ X3 ) )
| ( $false
= ( a @ X0 ) ) )
| ~ spl15_3 ),
inference(trivial_inequality_removal,[],[f586]) ).
thf(f620,definition,
( spl15_38
<=> ! [X2: $i,X3: $i] :
( ( $false
= ( rel @ sK3 @ X3 ) )
| ( $false
= ( rel @ X3 @ X2 ) )
| ( ( rel @ sK3 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl15_38])],[avatar_definition]) ).
thf(f621,plain,
( ! [X2: $i,X3: $i] :
( ( $false
= ( rel @ sK3 @ X3 ) )
| ( $false
= ( rel @ X3 @ X2 ) )
| ( ( rel @ sK3 @ X2 )
= $true ) )
| ~ spl15_38 ),
inference(avatar_component_clause,[],[f620]) ).
thf(f623,definition,
( spl15_39
<=> ! [X0: $i,X1: $i] :
( ( $false
= ( rel @ sK3 @ X1 ) )
| ( $false
= ( a @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $false
= ( rel @ X1 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_39])],[avatar_definition]) ).
thf(f624,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel @ sK3 @ X1 ) )
| ( $false
= ( rel @ X1 @ X0 ) )
| ( $false
= ( a @ X0 ) )
| ( $true
= ( b @ X0 ) ) )
| ~ spl15_39 ),
inference(avatar_component_clause,[],[f623]) ).
thf(f626,plain,
( spl15_38
| spl15_39
| ~ spl15_3 ),
inference(avatar_split_clause,[],[f608,f292,f623,f620]) ).
thf(f632,plain,
( ! [X0: $i] :
( ( $false
= ( rel @ sK4 @ X0 ) )
| ( $true
= ( rel @ sK3 @ X0 ) )
| ( $false = $true ) )
| ~ spl15_4
| ~ spl15_38 ),
inference(constrained_superposition,[],[f621,f298]) ).
thf(f641,plain,
( ! [X0: $i] :
( ( $true
= ( rel @ sK3 @ X0 ) )
| ( $false
= ( rel @ sK4 @ X0 ) ) )
| ~ spl15_4
| ~ spl15_38 ),
inference(trivial_inequality_removal,[],[f632]) ).
thf(f654,plain,
( ! [X0: $i] :
( ( $true
= ( b @ X0 ) )
| ( $false
= ( a @ X0 ) )
| ( $false = $true )
| ( $false
= ( rel @ sK4 @ X0 ) ) )
| ~ spl15_3
| ~ spl15_4
| ~ spl15_38 ),
inference(constrained_superposition,[],[f641,f293]) ).
thf(f661,plain,
( ! [X0: $i] :
( ( $false
= ( rel @ sK4 @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $false
= ( a @ X0 ) ) )
| ~ spl15_3
| ~ spl15_4
| ~ spl15_38 ),
inference(trivial_inequality_removal,[],[f654]) ).
thf(f679,plain,
( ( $false
= ( a @ sK5 ) )
| ( $true
= ( b @ sK5 ) )
| ( $false = $true )
| ~ spl15_3
| ~ spl15_4
| ~ spl15_6
| ~ spl15_38 ),
inference(constrained_superposition,[],[f307,f661]) ).
thf(f690,plain,
( ( $true
= ( b @ sK5 ) )
| ( $false
= ( a @ sK5 ) )
| ~ spl15_3
| ~ spl15_4
| ~ spl15_6
| ~ spl15_38 ),
inference(trivial_inequality_removal,[],[f679]) ).
thf(f698,plain,
( ( $false
= ( a @ sK5 ) )
| ( $false = $true )
| ~ spl15_3
| ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_38 ),
inference(forward_demodulation,[],[f690,f312]) ).
thf(f699,plain,
( ( $false
= ( a @ sK5 ) )
| ~ spl15_3
| ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_38 ),
inference(trivial_inequality_removal,[],[f698]) ).
thf(f703,plain,
( ( $false = $true )
| ~ spl15_3
| ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_27
| ~ spl15_38 ),
inference(forward_demodulation,[],[f699,f458]) ).
thf(f704,plain,
( $false
| ~ spl15_3
| ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_27
| ~ spl15_38 ),
inference(trivial_inequality_removal,[],[f703]) ).
thf(f705,plain,
( ~ spl15_3
| ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_27
| ~ spl15_38 ),
inference(avatar_contradiction_clause,[],[f704]) ).
thf(f721,plain,
( ( ( s @ sK6 )
= $true )
| ( $false = $true )
| ~ spl15_8
| ~ spl15_28 ),
inference(constrained_superposition,[],[f317,f461]) ).
thf(f732,plain,
( ( ( s @ sK6 )
= $true )
| ~ spl15_8
| ~ spl15_28 ),
inference(trivial_inequality_removal,[],[f721]) ).
thf(f744,plain,
( ( $false = $true )
| ~ spl15_8
| ~ spl15_9
| ~ spl15_28 ),
inference(forward_demodulation,[],[f732,f322]) ).
thf(f745,plain,
( $false
| ~ spl15_8
| ~ spl15_9
| ~ spl15_28 ),
inference(trivial_inequality_removal,[],[f744]) ).
thf(f746,plain,
( ~ spl15_8
| ~ spl15_9
| ~ spl15_28 ),
inference(avatar_contradiction_clause,[],[f745]) ).
thf(f766,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( rel @ sK4 @ X0 ) )
| ( $false
= ( a @ X0 ) )
| ( $true
= ( b @ X0 ) ) )
| ~ spl15_4
| ~ spl15_39 ),
inference(constrained_superposition,[],[f624,f298]) ).
thf(f775,plain,
( ! [X0: $i] :
( ( $false
= ( rel @ sK4 @ X0 ) )
| ( $false
= ( a @ X0 ) )
| ( $true
= ( b @ X0 ) ) )
| ~ spl15_4
| ~ spl15_39 ),
inference(trivial_inequality_removal,[],[f766]) ).
thf(f803,plain,
( ( $true
= ( b @ sK5 ) )
| ( $false
= ( a @ sK5 ) )
| ( $false = $true )
| ~ spl15_4
| ~ spl15_6
| ~ spl15_39 ),
inference(constrained_superposition,[],[f307,f775]) ).
thf(f811,plain,
( ( $true
= ( b @ sK5 ) )
| ( $false
= ( a @ sK5 ) )
| ~ spl15_4
| ~ spl15_6
| ~ spl15_39 ),
inference(trivial_inequality_removal,[],[f803]) ).
thf(f819,plain,
( ( $false = $true )
| ( $false
= ( a @ sK5 ) )
| ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_39 ),
inference(forward_demodulation,[],[f811,f312]) ).
thf(f820,plain,
( ( $false
= ( a @ sK5 ) )
| ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_39 ),
inference(trivial_inequality_removal,[],[f819]) ).
thf(f825,plain,
( ( $false = $true )
| ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_27
| ~ spl15_39 ),
inference(forward_demodulation,[],[f820,f458]) ).
thf(f826,plain,
( $false
| ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_27
| ~ spl15_39 ),
inference(trivial_inequality_removal,[],[f825]) ).
thf(f827,plain,
( ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_27
| ~ spl15_39 ),
inference(avatar_contradiction_clause,[],[f826]) ).
cnf(s2,plain,
( spl15_1
| spl15_3 ),
inference(sat_conversion,[],[f294]) ).
cnf(s3,plain,
( spl15_1
| spl15_4 ),
inference(sat_conversion,[],[f299]) ).
cnf(s4,plain,
( spl15_1
| spl15_5 ),
inference(sat_conversion,[],[f303]) ).
cnf(s5,plain,
( spl15_1
| spl15_6 ),
inference(sat_conversion,[],[f308]) ).
cnf(s6,plain,
( spl15_1
| spl15_7 ),
inference(sat_conversion,[],[f313]) ).
cnf(s7,plain,
( spl15_1
| spl15_8 ),
inference(sat_conversion,[],[f318]) ).
cnf(s8,plain,
( spl15_1
| spl15_9 ),
inference(sat_conversion,[],[f323]) ).
cnf(s21,plain,
~ spl15_1,
inference(sat_conversion,[],[f376]) ).
cnf(s27,plain,
( ~ spl15_5
| ~ spl15_6
| spl15_27
| spl15_28 ),
inference(sat_conversion,[],[f467]) ).
cnf(s40,plain,
( ~ spl15_3
| spl15_38
| spl15_39 ),
inference(sat_conversion,[],[f626]) ).
cnf(s45,plain,
( ~ spl15_3
| ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_27
| ~ spl15_38 ),
inference(sat_conversion,[],[f705]) ).
cnf(s49,plain,
( ~ spl15_8
| ~ spl15_9
| ~ spl15_28 ),
inference(sat_conversion,[],[f746]) ).
cnf(s57,plain,
( ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_27
| ~ spl15_39 ),
inference(sat_conversion,[],[f827]) ).
cnf(s58,plain,
spl15_9,
inference(rat,[],[s8,s21]) ).
cnf(s59,plain,
spl15_8,
inference(rat,[],[s7,s21]) ).
cnf(s60,plain,
~ spl15_28,
inference(rat,[],[s49,s58,s59]) ).
cnf(s61,plain,
spl15_7,
inference(rat,[],[s6,s21]) ).
cnf(s62,plain,
spl15_6,
inference(rat,[],[s5,s21]) ).
cnf(s63,plain,
spl15_5,
inference(rat,[],[s4,s21]) ).
cnf(s64,plain,
spl15_27,
inference(rat,[],[s27,s60,s62,s63]) ).
cnf(s65,plain,
spl15_4,
inference(rat,[],[s3,s21]) ).
cnf(s66,plain,
~ spl15_39,
inference(rat,[],[s57,s64,s62,s61,s65]) ).
cnf(s67,plain,
spl15_3,
inference(rat,[],[s2,s21]) ).
cnf(s68,plain,
~ spl15_38,
inference(rat,[],[s45,s65,s64,s61,s62,s67]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s40,s66,s68,s67]) ).
thf(f828,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV431^2 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 % Computer : n007.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 16:01:26 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.28 Running higher-order theorem proving
% 0.23/0.30 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.41 % (3552924)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.64/0.41 % (3552932)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=2837463992: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)
% 0.64/0.41 % (3552933)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=906650852:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.64/0.41 % (3552935)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.64/0.41 % (3552935)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
% 0.64/0.41 % (3552929)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3074621035:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.64/0.41 % (3552930)lrs+10_16_si=on:nwc=1.5:random_seed=2546888072:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.64/0.41 % (3552931)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1949830932:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.64/0.41 % (3552935)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=162070796:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.64/0.41 % (3552934)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=513176875:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.64/0.41 % (3552931)Instruction limit reached!
% 0.64/0.41 % (3552931)------------------------------
% 0.64/0.41 % (3552931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (3552931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (3552931)CaDiCaL version: 2.1.3
% 0.64/0.41 % (3552931)Termination reason: Instruction limit
% 0.64/0.41 % (3552931)Termination phase: Property scanning
% 0.64/0.41 % (3552931)Time elapsed: 0.003 s
% 0.64/0.41 % (3552931)Peak memory usage: 10 MB
% 0.64/0.41 % (3552931)Instructions burned: 3 (million)
% 0.64/0.41 % (3552930)Instruction limit reached!
% 0.64/0.41 % (3552930)------------------------------
% 0.64/0.41 % (3552930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (3552930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (3552930)CaDiCaL version: 2.1.3
% 0.64/0.41 % (3552930)Termination reason: Instruction limit
% 0.64/0.41 % (3552930)Termination phase: Saturation
% 0.64/0.41 % (3552930)Time elapsed: 0.016 s
% 0.64/0.41 % (3552930)Peak memory usage: 12 MB
% 0.64/0.41 % (3552930)Instructions burned: 18 (million)
% 0.64/0.41 % (3552933)Instruction limit reached!
% 0.64/0.41 % (3552933)------------------------------
% 0.64/0.41 % (3552933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (3552933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (3552933)CaDiCaL version: 2.1.3
% 0.64/0.41 % (3552933)Termination reason: Instruction limit
% 0.64/0.41 % (3552933)Termination phase: Saturation
% 0.64/0.41 % (3552933)Time elapsed: 0.027 s
% 0.64/0.41 % (3552933)Peak memory usage: 12 MB
% 0.64/0.41 % (3552933)Instructions burned: 24 (million)
% 0.64/0.41 % (3552943)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3830970586:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.64/0.41 % (3552943)Instruction limit reached!
% 0.64/0.41 % (3552943)------------------------------
% 0.64/0.41 % (3552943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (3552943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (3552943)CaDiCaL version: 2.1.3
% 0.64/0.41 % (3552943)Termination reason: Instruction limit
% 0.64/0.41 % (3552943)Termination phase: Property scanning
% 0.64/0.41 % (3552943)Time elapsed: 0.002 s
% 0.64/0.41 % (3552943)Peak memory usage: 10 MB
% 0.64/0.41 % (3552943)Instructions burned: 2 (million)
% 0.64/0.41 % (3552935) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3552924-3552935"...
% 0.64/0.41 % (3552945)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.64/0.41 % (3552944)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2717842036:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.64/0.41 % (3552945)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1659841339:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.64/0.41 % (3552944)Instruction limit reached!
% 0.64/0.41 % (3552944)------------------------------
% 0.64/0.41 % (3552944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (3552944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (3552944)CaDiCaL version: 2.1.3
% 0.64/0.41 % (3552944)Termination reason: Instruction limit
% 0.64/0.41 % (3552944)Termination phase: Saturation
% 0.64/0.41 % (3552944)Time elapsed: 0.003 s
% 0.64/0.41 % (3552944)Peak memory usage: 10 MB
% 0.64/0.41 % (3552944)Instructions burned: 5 (million)
% 0.64/0.41 % (3552935)...printing done.
% 0.64/0.41 % (3552945)Instruction limit reached!
% 0.64/0.41 % (3552945)------------------------------
% 0.64/0.41 % (3552945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (3552945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (3552945)CaDiCaL version: 2.1.3
% 0.64/0.41 % (3552945)Termination reason: Instruction limit
% 0.64/0.41 % (3552945)Termination phase: Saturation
% 0.64/0.41 % (3552945)Time elapsed: 0.007 s
% 0.64/0.41 % (3552945)Peak memory usage: 11 MB
% 0.64/0.41 % (3552945)Instructions burned: 8 (million)
% 0.64/0.41 % (3552935)Refutation found. Thanks to Tanya!
% 0.64/0.41 % SZS status Theorem for theBenchmark
% 0.64/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.64/0.41 % (3552935)------------------------------
% 0.64/0.41 % (3552935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (3552935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (3552935)CaDiCaL version: 2.1.3
% 0.64/0.41 % (3552935)Termination reason: Refutation
% 0.64/0.41 % (3552935)Time elapsed: 0.055 s
% 0.64/0.41 % (3552935)Peak memory usage: 13 MB
% 0.64/0.41 % (3552935)Instructions burned: 62 (million)
% 0.64/0.41 % (3552924)Success in time 0.096 s
% 0.64/0.41 % Vampire exiting
%------------------------------------------------------------------------------