%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV432^2 : 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 : n002.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 0.23s 0.28s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 97 ( 71 unt; 0 typ; 0 def)
% Number of atoms : 672 ( 131 equ; 0 cnn)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 918 ( 56 ~; 98 |; 0 &; 655 @)
% ( 0 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 159 ( 159 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 49 usr; 6 con; 0-4 aty)
% ( 52 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 274 ( 228 ^; 46 !; 0 ?; 274 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_35,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
vAND: $o > $o > $o ).
thf(func_def_37,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
vIMP: $o > $o > $o ).
thf(func_def_46,type,
sK0: $i > ( $i > $o ) > $i ).
thf(func_def_50,type,
sK4: $i > ( $i > $o ) > $i ).
thf(func_def_52,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimpl ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
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(f17,axiom,
( ( ^ [X0: $i > $o] : X0 )
= icl_princ ),
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,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mor @ X0 @ X1 ) ) )
= icl_says ),
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(f25,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^1.ax',refl_axiom) ).
thf(f27,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mimpl @ X0 @ X1 ) ) )
= icl_impl_princ ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^2.ax',icl_impl_princ) ).
thf(f28,conjecture,
iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ b ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',handoff) ).
thf(f29,negated_conjecture,
~ ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ b ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
thf(f33,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f17]) ).
thf(f34,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f37,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f42,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) ),
inference(rectify,[],[f25]) ).
thf(f43,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) )
= $true ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( icl_impl_princ
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f53,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f54,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f55,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f57,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f59,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f60,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f61,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f65,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f66,plain,
~ ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ b ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f67,plain,
( ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ b ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) )
!= $true ),
inference(fool_elimination,[],[f66]) ).
thf(f70,plain,
( ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ b ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) )
!= $true ),
inference(flattening,[],[f67]) ).
thf(f71,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f73,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f75,plain,
( icl_impl_princ
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f76,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f77,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f84,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f86,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f88,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f90,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f92,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f94,plain,
( ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ b ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f70]) ).
thf(f96,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) )
= $true ),
inference(cnf_transformation,[],[f43]) ).
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,[],[f86,f90,f84]) ).
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,[],[f73,f76,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,[],[f71,f76,f90]) ).
thf(f110,plain,
( iclval
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f88,f92]) ).
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,[],[f75,f76,f101]) ).
thf(f113,plain,
( $true
!= ( ^ [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] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [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] : 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] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) ) ) ) ),
inference(definition_unfolding,[],[f94,f110,f106,f109,f77,f111,f77,f77,f111,f77,f77]) ).
thf(f114,plain,
! [X0: $i > $o] :
( $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 > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ X0 )
@ X0 ) ) ),
inference(definition_unfolding,[],[f96,f92,f101,f76]) ).
thf(f115,plain,
! [X0: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( X0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( X0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) )
| ( X0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X0: $i > $o,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK0 @ X1 @ X0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X0: $i > $o,X1: $i] :
( ( $false
= ( ( rel @ X1 @ ( sK0 @ X1 @ X0 ) )
=> ( X0 @ ( sK0 @ X1 @ X0 ) ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( sK0 @ X1 @ X0 ) )
= $false )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK0 @ X1 @ X0 ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f121]) ).
thf(f124,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( b @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ~ ( a @ Y3 )
| ( b @ Y3 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ~ ( a @ Y2 )
| ( b @ Y2 ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f125,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( b @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ~ ( a @ Y3 )
| ( b @ Y3 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ~ ( a @ Y2 )
| ( b @ Y2 ) ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f124]) ).
thf(f126,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ~ ( a @ Y2 )
| ( b @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
( ( ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ~ ( a @ Y2 )
| ( b @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f126]) ).
thf(f128,plain,
( ( ( rel @ sK1 @ sK2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f127]) ).
thf(f129,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f128]) ).
thf(f131,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f129]) ).
thf(f132,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f129]) ).
thf(f133,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X1: $i] :
( $true
= ( ( rel @ sK2 @ X1 )
=> ( ( b @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
! [X1: $i] :
( ( ( rel @ sK2 @ X1 )
= $false )
| ( ( ( b @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X1: $i] :
( ( $true
= ( b @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) )
= $true )
| ( ( rel @ sK2 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X1: $i] :
( ( ( rel @ sK2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) )
@ X2 ) )
| ( $true
= ( b @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( rel @ X1 @ X2 )
=> ( ~ ( a @ X2 )
| ( b @ X2 ) ) ) )
| ( ( rel @ sK2 @ X1 )
= $false )
| ( $true
= ( b @ X1 ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
! [X2: $i,X1: $i] :
( ( ( rel @ X1 @ X2 )
= $false )
| ( $true
= ( b @ X1 ) )
| ( ( rel @ sK2 @ X1 )
= $false )
| ( $true
= ( ~ ( a @ X2 )
| ( b @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( b @ X1 ) )
| ( ( rel @ X1 @ X2 )
= $false )
| ( ( rel @ sK2 @ X1 )
= $false )
| ( ( b @ X2 )
= $true )
| ( $true
= ( ~ ( a @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f140]) ).
thf(f142,plain,
! [X2: $i,X1: $i] :
( ( ( rel @ sK2 @ X1 )
= $false )
| ( ( rel @ X1 @ X2 )
= $false )
| ( $false
= ( a @ X2 ) )
| ( ( b @ X2 )
= $true )
| ( $true
= ( b @ X1 ) ) ),
inference(not_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( $false
= ( ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f131]) ).
thf(f144,plain,
( $false
= ( ( rel @ sK2 @ sK3 )
=> ( ~ ( a @ sK3 )
| ( b @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
( $false
= ( ~ ( a @ sK3 )
| ( b @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( $true
= ( rel @ sK2 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f147,plain,
( $false
= ( b @ sK3 ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( ~ ( a @ sK3 ) )
= $false ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f149,plain,
( $true
= ( a @ sK3 ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f213,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( rel @ X0 @ X0 ) )
| ( $true
= ( rel @ X0 @ X0 ) ) ),
inference(constrained_superposition,[],[f122,f123]) ).
thf(f215,plain,
! [X0: $i] :
( ( $true
= ( rel @ X0 @ X0 ) )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f213]) ).
thf(f216,plain,
! [X0: $i] :
( $true
= ( rel @ X0 @ X0 ) ),
inference(trivial_inequality_removal,[],[f215]) ).
thf(f222,plain,
! [X0: $i] :
( ( ( a @ X0 )
= $false )
| ( ( rel @ sK2 @ X0 )
= $false )
| ( $false = $true )
| ( $true
= ( b @ X0 ) )
| ( $true
= ( b @ X0 ) ) ),
inference(constrained_superposition,[],[f216,f142]) ).
thf(f227,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( rel @ sK2 @ X0 )
= $false )
| ( $true
= ( b @ X0 ) )
| ( ( a @ X0 )
= $false ) ),
inference(duplicate_literal_removal,[],[f222]) ).
thf(f228,plain,
! [X0: $i] :
( ( ( rel @ sK2 @ X0 )
= $false )
| ( ( a @ X0 )
= $false )
| ( $true
= ( b @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f227]) ).
thf(f236,plain,
( ( $true
= ( b @ sK3 ) )
| ( $false = $true )
| ( $false
= ( a @ sK3 ) ) ),
inference(constrained_superposition,[],[f146,f228]) ).
thf(f237,plain,
( ( $false
= ( a @ sK3 ) )
| ( $true
= ( b @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f236]) ).
thf(f243,plain,
( ( $false = $true )
| ( $true
= ( b @ sK3 ) ) ),
inference(forward_demodulation,[],[f237,f149]) ).
thf(f244,plain,
( $true
= ( b @ sK3 ) ),
inference(trivial_inequality_removal,[],[f243]) ).
thf(f247,plain,
$false = $true,
inference(forward_demodulation,[],[f244,f147]) ).
thf(f248,plain,
$false,
inference(trivial_inequality_removal,[],[f247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV432^2 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:05:37 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.23/0.28 % (1470294)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.28 % (1470311)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=3549204902: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)
% 0.23/0.28 % (1470310)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2394889190:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.28 % (1470309)lrs+10_16_si=on:nwc=1.5:random_seed=4203324276:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.28 % (1470308)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=376516445:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.28 % (1470310)Instruction limit reached!
% 0.23/0.28 % (1470310)------------------------------
% 0.23/0.28 % (1470310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.28 % (1470310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.28 % (1470310)CaDiCaL version: 2.1.3
% 0.23/0.28 % (1470310)Termination reason: Instruction limit
% 0.23/0.28 % (1470310)Termination phase: Saturation
% 0.23/0.28 % (1470310)Time elapsed: 0.003 s
% 0.23/0.28 % (1470310)Peak memory usage: 11 MB
% 0.23/0.28 % (1470310)Instructions burned: 7 (million)
% 0.23/0.28 % (1470314)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.28 % (1470314)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
% 0.23/0.28 % (1470308) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1470294-1470308"...
% 0.23/0.28 % (1470314)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=467084965:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.28 % (1470312)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3238680605:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.28 % (1470309)Instruction limit reached!
% 0.23/0.28 % (1470309)------------------------------
% 0.23/0.28 % (1470309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.28 % (1470309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.28 % (1470309)CaDiCaL version: 2.1.3
% 0.23/0.28 % (1470309)Termination reason: Instruction limit
% 0.23/0.28 % (1470309)Termination phase: Saturation
% 0.23/0.28 % (1470309)Time elapsed: 0.011 s
% 0.23/0.28 % (1470309)Peak memory usage: 12 MB
% 0.23/0.28 % (1470309)Instructions burned: 19 (million)
% 0.23/0.28 % (1470308)...printing done.
% 0.23/0.28 % (1470308)Refutation found. Thanks to Tanya!
% 0.23/0.28 % SZS status Theorem for theBenchmark
% 0.23/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.29 % (1470308)------------------------------
% 0.23/0.29 % (1470308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (1470308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (1470308)CaDiCaL version: 2.1.3
% 0.23/0.29 % (1470308)Termination reason: Refutation
% 0.23/0.29 % (1470308)Time elapsed: 0.011 s
% 0.23/0.29 % (1470308)Peak memory usage: 12 MB
% 0.23/0.29 % (1470308)Instructions burned: 20 (million)
% 0.23/0.29 % (1470294)Success in time 0.043 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------