%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV434^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 08:39:58 AM UTC 2026
% Result : Theorem 0.08s 0.18s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of formulae : 93 ( 70 unt; 0 typ; 0 def)
% Number of atoms : 543 ( 114 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 715 ( 26 ~; 57 |; 0 &; 522 @)
% ( 0 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 47 usr; 6 con; 0-4 aty)
% ( 52 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 244 ( 199 ^; 45 !; 0 ?; 244 :)
% 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,
s: $i > $o ).
thf(func_def_31,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
vNOT: $o > $o ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
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_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vOR: $o > $o > $o ).
thf(func_def_41,type,
vAND: $o > $o > $o ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_48,type,
sK4: $i > ( $i > $o ) > $i ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( ( ^ [X0: $i] : $false )
= mfalse ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mfalse) ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
( icl_atom
= ( ^ [X0: $i > $o] : ( mbox @ rel @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_atom) ).
thf(f20,axiom,
( icl_impl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mimpl @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_impl) ).
thf(f22,axiom,
icl_false = mfalse,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_false) ).
thf(f23,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mor @ X0 @ X1 ) ) )
= icl_says ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_says) ).
thf(f24,axiom,
( iclval
= ( ^ [X0: $i > $o] : ( mvalid @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_s4_valid) ).
thf(f25,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^1.ax',refl_axiom) ).
thf(f27,conjecture,
iclval @ ( icl_impl @ ( icl_says @ icl_false @ ( icl_atom @ s ) ) @ ( icl_atom @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trust) ).
thf(f28,negated_conjecture,
~ ( iclval @ ( icl_impl @ ( icl_says @ icl_false @ ( icl_atom @ s ) ) @ ( icl_atom @ s ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
thf(f33,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f34,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f35,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f36,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f38,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f39,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f40,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) ),
inference(rectify,[],[f25]) ).
thf(f41,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) )
= $true ),
inference(fool_elimination,[],[f40]) ).
thf(f45,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f46,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f48,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f52,plain,
~ ( iclval @ ( icl_impl @ ( icl_says @ icl_false @ ( icl_atom @ s ) ) @ ( icl_atom @ s ) ) ),
inference(rectify,[],[f28]) ).
thf(f53,plain,
( ( iclval @ ( icl_impl @ ( icl_says @ icl_false @ ( icl_atom @ s ) ) @ ( icl_atom @ s ) ) )
!= $true ),
inference(fool_elimination,[],[f52]) ).
thf(f59,plain,
( mfalse
= ( ^ [Y0: $i] : $false ) ),
inference(fool_elimination,[],[f1]) ).
thf(f62,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f63,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f67,plain,
( icl_atom
= ( ^ [Y0: $i > $o] : ( mbox @ rel @ Y0 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f68,plain,
( ( iclval @ ( icl_impl @ ( icl_says @ icl_false @ ( icl_atom @ s ) ) @ ( icl_atom @ s ) ) )
!= $true ),
inference(flattening,[],[f53]) ).
thf(f70,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f72,plain,
mfalse = icl_false,
inference(cnf_transformation,[],[f22]) ).
thf(f73,plain,
( icl_atom
= ( ^ [Y0: $i > $o] : ( mbox @ rel @ Y0 ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f76,plain,
( mfalse
= ( ^ [Y0: $i] : $false ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f79,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f81,plain,
( ( iclval @ ( icl_impl @ ( icl_says @ icl_false @ ( icl_atom @ s ) ) @ ( icl_atom @ s ) ) )
!= $true ),
inference(cnf_transformation,[],[f68]) ).
thf(f83,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f85,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f86,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f89,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f90,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f92,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f95,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) )
= $true ),
inference(cnf_transformation,[],[f41]) ).
thf(f98,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f92,f83,f86]) ).
thf(f100,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,[],[f73,f79]) ).
thf(f103,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] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f85,f79,f98]) ).
thf(f105,plain,
( icl_false
= ( ^ [Y0: $i] : $false ) ),
inference(definition_unfolding,[],[f72,f76]) ).
thf(f106,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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f70,f79,f83]) ).
thf(f107,plain,
( iclval
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f89,f90]) ).
thf(f108,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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ^ [Y0: $i] : $false
@ ( ^ [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 > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) ) )
!= $true ),
inference(definition_unfolding,[],[f81,f107,f103,f106,f105,f100,f100]) ).
thf(f110,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] :
( ( Y3 @ Y4 )
| ( Y2 @ 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 ) )
= $true ),
inference(definition_unfolding,[],[f95,f90,f98,f79]) ).
thf(f111,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) )
| $false ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f112,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) )
| $false ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f111]) ).
thf(f113,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK0 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| $false ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
( ( ^ [Y0: $i] :
( ( rel @ sK0 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| $false ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f113]) ).
thf(f115,plain,
( ( ( rel @ sK0 @ sK1 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( s @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| $false ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( s @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| $false ) ) ) ) ),
inference(imp_proxy_clausification,[],[f115]) ).
thf(f118,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| $false ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f116]) ).
thf(f119,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( s @ Y0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f116]) ).
thf(f120,plain,
( $false
= ( ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( s @ Y0 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f119]) ).
thf(f121,plain,
( ( ( rel @ sK1 @ sK2 )
=> ( s @ sK2 ) )
= $false ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
( $false
= ( s @ sK2 ) ),
inference(imp_proxy_clausification,[],[f121]) ).
thf(f123,plain,
( $true
= ( rel @ sK1 @ sK2 ) ),
inference(imp_proxy_clausification,[],[f121]) ).
thf(f124,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| $false ) ) ) ),
inference(not_proxy_clausification,[],[f118]) ).
thf(f125,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| $false ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X1: $i] :
( $true
= ( ( rel @ sK1 @ X1 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) ) )
| $false ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) ) )
| $false ) )
| ( ( rel @ sK1 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X1: $i] :
( ( ( rel @ sK1 @ X1 )
= $false )
| ( $true = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: $i,X1: $i] :
( ( ( rel @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) )
@ X2 )
= $true )
| ( $true = $false ) ),
inference(pi_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) )
@ X2 )
= $true )
| ( ( rel @ sK1 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f129]) ).
thf(f131,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( rel @ X1 @ X2 )
=> ( s @ X2 ) ) )
| ( ( rel @ sK1 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f130]) ).
thf(f132,plain,
! [X2: $i,X1: $i] :
( ( ( rel @ sK1 @ X1 )
= $false )
| ( ( rel @ X1 @ X2 )
= $false )
| ( $true
= ( s @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f131]) ).
thf(f151,plain,
! [X0: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f152,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ( X0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X0: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false )
| ( ( X0 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK4 @ X1 @ X0 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( ( ( rel @ X1 @ ( sK4 @ X1 @ X0 ) )
=> ( X0 @ ( sK4 @ X1 @ X0 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( sK4 @ X1 @ X0 ) )
= $false )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK4 @ X1 @ X0 ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f192,plain,
! [X0: $i,X1: $i > $o] :
( ( $true = $false )
| ( $true
= ( s @ ( sK4 @ X0 @ X1 ) ) )
| ( ( rel @ sK1 @ X0 )
= $false )
| ( $true
= ( X1 @ X0 ) ) ),
inference(constrained_superposition,[],[f159,f132]) ).
thf(f196,plain,
! [X0: $i,X1: $i > $o] :
( ( $true
= ( s @ ( sK4 @ X0 @ X1 ) ) )
| ( $true
= ( X1 @ X0 ) )
| ( ( rel @ sK1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f192]) ).
thf(f202,plain,
! [X0: $i] :
( ( $true
= ( s @ X0 ) )
| ( $true
= ( s @ X0 ) )
| ( $true = $false )
| ( ( rel @ sK1 @ X0 )
= $false ) ),
inference(constrained_superposition,[],[f196,f158]) ).
thf(f204,plain,
! [X0: $i] :
( ( $true
= ( s @ X0 ) )
| ( $true = $false )
| ( ( rel @ sK1 @ X0 )
= $false ) ),
inference(duplicate_literal_removal,[],[f202]) ).
thf(f205,plain,
! [X0: $i] :
( ( ( rel @ sK1 @ X0 )
= $false )
| ( $true
= ( s @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f204]) ).
thf(f209,plain,
( ( $true
= ( s @ sK2 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f205,f123]) ).
thf(f212,plain,
( $true
= ( s @ sK2 ) ),
inference(trivial_inequality_removal,[],[f209]) ).
thf(f216,plain,
$true = $false,
inference(forward_demodulation,[],[f212,f122]) ).
thf(f217,plain,
$false,
inference(trivial_inequality_removal,[],[f216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV434^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 16:02:49 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % (291874)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.18 % (291896)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.18 % (291896)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
% 0.08/0.18 % (291890)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3194350557:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.18 % (291891)lrs+10_16_si=on:nwc=1.5:random_seed=2544239256:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.18 % (291892)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1539750558:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.18 % (291893)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=20174009: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)
% 0.08/0.18 % (291895)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1803668644:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.18 % (291894)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=373533532:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.18 % (291896)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=768122533:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.18 % (291892)Instruction limit reached!
% 0.08/0.18 % (291892)------------------------------
% 0.08/0.18 % (291892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.18 % (291892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.18 % (291892)CaDiCaL version: 2.1.3
% 0.08/0.18 % (291892)Termination reason: Instruction limit
% 0.08/0.18 % (291892)Termination phase: Function definition elimination
% 0.08/0.18 % (291892)Time elapsed: 0.001 s
% 0.08/0.18 % (291892)Peak memory usage: 10 MB
% 0.08/0.18 % (291892)Instructions burned: 3 (million)
% 0.08/0.18 % (291890) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-291874-291890"...
% 0.08/0.18 % (291896) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-291874-291896"...
% 0.08/0.18 % (291890)...printing done.
% 0.08/0.18 % (291890)Refutation found. Thanks to Tanya!
% 0.08/0.18 % SZS status Theorem for theBenchmark
% 0.08/0.18 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.18 % (291890)------------------------------
% 0.08/0.18 % (291890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.18 % (291890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.18 % (291890)CaDiCaL version: 2.1.3
% 0.08/0.18 % (291890)Termination reason: Refutation
% 0.08/0.18 % (291890)Time elapsed: 0.005 s
% 0.08/0.18 % (291890)Peak memory usage: 12 MB
% 0.08/0.18 % (291890)Instructions burned: 16 (million)
% 0.08/0.18 % (291874)Success in time 0.042 s
% 0.08/0.18 % Vampire exiting
%------------------------------------------------------------------------------