%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN041^4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:41:37 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 10
% Syntax : Number of formulae : 99 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 758 ( 139 equ; 0 cnn)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 1060 ( 70 ~; 75 |; 3 &; 747 @)
% ( 0 <=>; 89 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 38 usr; 6 con; 0-4 aty)
% ( 76 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 258 ( 207 ^; 51 !; 0 ?; 258 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
p: $i > $o ).
thf(func_def_22,type,
q: $i > $o ).
thf(func_def_23,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_26,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vIMP: $o > $o > $o ).
thf(func_def_28,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vOR: $o > $o > $o ).
thf(func_def_32,type,
vNOT: $o > $o ).
thf(func_def_33,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
vAND: $o > $o > $o ).
thf(func_def_36,type,
sK1: $i > $i ).
thf(func_def_37,type,
sK2: $i > $i ).
thf(f2,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ X0 @ X1 )
& ( irel @ X1 @ X2 ) )
=> ( irel @ X0 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',trans_axiom) ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mimplies) ).
thf(f7,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f9,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ X0 ) ) )
= inot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',inot) ).
thf(f14,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) )
= iimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,conjecture,
ivalid @ ( iimplies @ ( inot @ ( iimplies @ ( iatom @ p ) @ ( iatom @ q ) ) ) @ ( iimplies @ ( iatom @ q ) @ ( iatom @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel3) ).
thf(f23,negated_conjecture,
~ ( ivalid @ ( iimplies @ ( inot @ ( iimplies @ ( iatom @ p ) @ ( iatom @ q ) ) ) @ ( iimplies @ ( iatom @ q ) @ ( iatom @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
thf(f24,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f25,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f7]) ).
thf(f26,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f28,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f30,plain,
~ ( ivalid @ ( iimplies @ ( inot @ ( iimplies @ ( iatom @ p ) @ ( iatom @ q ) ) ) @ ( iimplies @ ( iatom @ q ) @ ( iatom @ p ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f31,plain,
( ( ivalid @ ( iimplies @ ( inot @ ( iimplies @ ( iatom @ p ) @ ( iatom @ q ) ) ) @ ( iimplies @ ( iatom @ q ) @ ( iatom @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f33,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f34,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f35,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f37,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f48,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f52,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X1 @ X2 )
& ( irel @ X2 @ X0 ) )
=> ( irel @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f53,plain,
! [X2: $i,X1: $i,X0: $i] :
( ( ( ( irel @ X2 @ X0 )
= $true )
& ( ( irel @ X1 @ X2 )
= $true ) )
=> ( ( irel @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f52]) ).
thf(f56,plain,
( ( ivalid @ ( iimplies @ ( inot @ ( iimplies @ ( iatom @ p ) @ ( iatom @ q ) ) ) @ ( iimplies @ ( iatom @ q ) @ ( iatom @ p ) ) ) )
!= $true ),
inference(flattening,[],[f31]) ).
thf(f57,plain,
! [X2: $i,X1: $i,X0: $i] :
( ( ( irel @ X1 @ X0 )
= $true )
| ( ( irel @ X2 @ X0 )
!= $true )
| ( ( irel @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f53]) ).
thf(f58,plain,
! [X1: $i,X0: $i,X2: $i] :
( ( ( irel @ X1 @ X2 )
!= $true )
| ( ( irel @ X2 @ X0 )
!= $true )
| ( ( irel @ X1 @ X0 )
= $true ) ),
inference(flattening,[],[f57]) ).
thf(f59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X0 @ X2 )
!= $true )
| ( ( irel @ X2 @ X1 )
!= $true )
| ( ( irel @ X0 @ X1 )
= $true ) ),
inference(rectify,[],[f58]) ).
thf(f60,plain,
( ( ivalid @ ( iimplies @ ( inot @ ( iimplies @ ( iatom @ p ) @ ( iatom @ q ) ) ) @ ( iimplies @ ( iatom @ q ) @ ( iatom @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f62,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f63,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ X2 @ X1 )
!= $true )
| ( ( irel @ X0 @ X2 )
!= $true )
| ( ( irel @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f64,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f66,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f67,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f68,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f76,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f77,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f81,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f84,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f64,f67,f77]) ).
thf(f85,plain,
( inot
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f68,f77,f66]) ).
thf(f89,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f62,f84,f66,f66]) ).
thf(f93,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p )
@ ( ^ [Y0: $i > $o] : Y0
@ q ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ q )
@ ( ^ [Y0: $i > $o] : Y0
@ p ) ) ) ) ),
inference(definition_unfolding,[],[f60,f76,f89,f85,f89,f81,f81,f89,f81,f81]) ).
thf(f94,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( q @ Y3 ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( q @ Y3 ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f94]) ).
thf(f96,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f96]) ).
thf(f98,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f96]) ).
thf(f99,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK0 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f102,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) )
@ ( sK1 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ( q @ Y0 ) ) ) ) ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f106,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ( q @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X1: $i] :
( ( ( irel @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f108,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f106]) ).
thf(f114,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f108]) ).
thf(f115,plain,
! [X1: $i] :
( ( $false
= ( ( irel @ ( sK1 @ X1 ) @ ( sK2 @ X1 ) )
=> ( q @ ( sK2 @ X1 ) ) ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( q @ ( sK2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X1: $i] :
( ( $true
= ( irel @ ( sK1 @ X1 ) @ ( sK2 @ X1 ) ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f115]) ).
thf(f118,plain,
( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f97]) ).
thf(f119,plain,
( $false
= ( ( irel @ sK0 @ sK3 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f121,plain,
( ( irel @ sK0 @ sK3 )
= $true ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f122,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f120]) ).
thf(f123,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f120]) ).
thf(f124,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK3 @ X1 )
=> ( q @ X1 ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
! [X1: $i] :
( ( ( irel @ sK3 @ X1 )
= $false )
| ( $true
= ( q @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f128,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f122]) ).
thf(f129,plain,
( $false
= ( ( irel @ sK3 @ sK4 )
=> ( p @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f128]) ).
thf(f131,plain,
( $true
= ( irel @ sK3 @ sK4 ) ),
inference(imp_proxy_clausification,[],[f129]) ).
thf(f222,plain,
! [X0: $i,X1: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( irel @ X1 @ X0 )
!= $true )
| ( $true
= ( irel @ X1 @ ( sK1 @ X0 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f63,f107]) ).
thf(f223,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( irel @ X1 @ ( sK1 @ X0 ) ) )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( ( irel @ X1 @ ( sK2 @ X0 ) )
= $true ) ),
inference(constrained_superposition,[],[f63,f117]) ).
thf(f226,plain,
! [X0: $i] :
( ( ( irel @ X0 @ sK3 )
!= $true )
| ( ( irel @ X0 @ sK4 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f63,f131]) ).
thf(f228,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( irel @ X1 @ ( sK1 @ X0 ) ) )
| ( ( irel @ X1 @ ( sK2 @ X0 ) )
= $true )
| ( ( irel @ sK0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f229,plain,
! [X0: $i,X1: $i] :
( ( ( irel @ X1 @ X0 )
!= $true )
| ( $true
= ( irel @ X1 @ ( sK1 @ X0 ) ) )
| ( ( irel @ sK0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f222]) ).
thf(f230,plain,
! [X0: $i] :
( ( ( irel @ X0 @ sK3 )
!= $true )
| ( ( irel @ X0 @ sK4 )
= $true ) ),
inference(trivial_inequality_removal,[],[f226]) ).
thf(f244,plain,
( ( $true != $true )
| ( $true
= ( irel @ sK0 @ sK4 ) ) ),
inference(constrained_superposition,[],[f230,f121]) ).
thf(f245,plain,
( $true
= ( irel @ sK0 @ sK4 ) ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f252,plain,
( ( $false
= ( q @ ( sK2 @ sK4 ) ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f116,f245]) ).
thf(f254,plain,
( $false
= ( q @ ( sK2 @ sK4 ) ) ),
inference(trivial_inequality_removal,[],[f252]) ).
thf(f274,plain,
( ( $true != $true )
| ( ( irel @ sK3 @ ( sK1 @ sK4 ) )
= $true )
| ( $false
= ( irel @ sK0 @ sK4 ) ) ),
inference(constrained_superposition,[],[f229,f131]) ).
thf(f281,plain,
( ( ( irel @ sK3 @ ( sK1 @ sK4 ) )
= $true )
| ( $false
= ( irel @ sK0 @ sK4 ) ) ),
inference(trivial_inequality_removal,[],[f274]) ).
thf(f282,plain,
( ( $false = $true )
| ( ( irel @ sK3 @ ( sK1 @ sK4 ) )
= $true ) ),
inference(forward_demodulation,[],[f281,f245]) ).
thf(f283,plain,
( ( irel @ sK3 @ ( sK1 @ sK4 ) )
= $true ),
inference(trivial_inequality_removal,[],[f282]) ).
thf(f347,plain,
( ( $false
= ( irel @ sK0 @ sK4 ) )
| ( $true != $true )
| ( ( irel @ sK3 @ ( sK2 @ sK4 ) )
= $true ) ),
inference(constrained_superposition,[],[f228,f283]) ).
thf(f354,plain,
( ( ( irel @ sK3 @ ( sK2 @ sK4 ) )
= $true )
| ( $false
= ( irel @ sK0 @ sK4 ) ) ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f360,plain,
( ( ( irel @ sK3 @ ( sK2 @ sK4 ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f354,f245]) ).
thf(f361,plain,
( ( irel @ sK3 @ ( sK2 @ sK4 ) )
= $true ),
inference(trivial_inequality_removal,[],[f360]) ).
thf(f379,plain,
( ( ( q @ ( sK2 @ sK4 ) )
= $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f127,f361]) ).
thf(f384,plain,
( ( q @ ( sK2 @ sK4 ) )
= $true ),
inference(trivial_inequality_removal,[],[f379]) ).
thf(f388,plain,
$false = $true,
inference(forward_demodulation,[],[f384,f254]) ).
thf(f389,plain,
$false,
inference(trivial_inequality_removal,[],[f388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN041^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:17:18 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.21/0.31 % (3720422)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (3720429)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3394896838:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (3720429)Instruction limit reached!
% 0.21/0.31 % (3720429)------------------------------
% 0.21/0.31 % (3720429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3720429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3720429)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3720429)Termination reason: Instruction limit
% 0.21/0.31 % (3720429)Termination phase: Saturation
% 0.21/0.31 % (3720429)Time elapsed: 0.002 s
% 0.21/0.31 % (3720429)Peak memory usage: 12 MB
% 0.21/0.31 % (3720429)Instructions burned: 6 (million)
% 0.21/0.31 % (3720430)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=1680046177:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.31 % (3720427)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2210347390:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (3720428)lrs+10_16_si=on:nwc=1.5:random_seed=2852248783:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (3720433)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (3720433)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.31 % (3720432)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3557003851:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (3720433)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=2497852642:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (3720428)Instruction limit reached!
% 0.21/0.31 % (3720428)------------------------------
% 0.21/0.31 % (3720428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3720428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3720428)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3720428)Termination reason: Instruction limit
% 0.21/0.31 % (3720428)Termination phase: Saturation
% 0.21/0.31 % (3720428)Time elapsed: 0.010 s
% 0.21/0.31 % (3720428)Peak memory usage: 12 MB
% 0.21/0.31 % (3720428)Instructions burned: 20 (million)
% 0.21/0.31 % (3720427) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3720422-3720427"...
% 0.21/0.31 % (3720431)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3656134949:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (3720427)...printing done.
% 0.21/0.31 % (3720427)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (3720427)------------------------------
% 0.21/0.31 % (3720427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3720427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3720427)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3720427)Termination reason: Refutation
% 0.21/0.31 % (3720427)Time elapsed: 0.015 s
% 0.21/0.31 % (3720427)Peak memory usage: 12 MB
% 0.21/0.31 % (3720427)Instructions burned: 27 (million)
% 0.21/0.31 % (3720422)Success in time 0.068 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------