%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO062^4.002 : 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 : n018.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 08:46:26 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 10
% Syntax : Number of formulae : 88 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 674 ( 140 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 932 ( 53 ~; 75 |; 3 &; 658 @)
% ( 0 <=>; 77 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 36 usr; 4 con; 0-4 aty)
% ( 66 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 223 ( 157 ^; 66 !; 0 ?; 223 :)
% 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,
a: $i > $o ).
thf(func_def_22,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(func_def_28,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_30,type,
vIMP: $o > $o > $o ).
thf(func_def_31,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
vAND: $o > $o > $o ).
thf(func_def_33,type,
vOR: $o > $o > $o ).
thf(func_def_35,type,
sK1: $i > $i ).
thf(func_def_36,type,
sK2: $i > $i ).
thf(func_def_37,type,
sK3: $i > $i ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f2,axiom,
! [X1: $i,X2: $i,X0: $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,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f7,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o] : X0 )
= iatom ),
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(f13,axiom,
( ior
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ior) ).
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 @ ( inot @ ( inot @ ( ior @ ( iatom @ a ) @ ( inot @ ( iatom @ a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f23,negated_conjecture,
~ ( ivalid @ ( inot @ ( inot @ ( ior @ ( iatom @ a ) @ ( inot @ ( iatom @ a ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
thf(f25,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f26,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f29,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f31,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f32,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f31]) ).
thf(f35,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f36,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f39,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f40,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
~ ( ivalid @ ( inot @ ( inot @ ( ior @ ( iatom @ a ) @ ( inot @ ( iatom @ a ) ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f42,plain,
( ( ivalid @ ( inot @ ( inot @ ( ior @ ( iatom @ a ) @ ( inot @ ( iatom @ a ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
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(f52,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X2 @ X0 )
& ( irel @ X0 @ X1 ) )
=> ( irel @ X2 @ X1 ) ),
inference(rectify,[],[f2]) ).
thf(f53,plain,
! [X1: $i,X0: $i,X2: $i] :
( ( ( ( irel @ X2 @ X0 )
= $true )
& ( ( irel @ X0 @ X1 )
= $true ) )
=> ( ( irel @ X2 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f52]) ).
thf(f56,plain,
( ( ivalid @ ( inot @ ( inot @ ( ior @ ( iatom @ a ) @ ( inot @ ( iatom @ a ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f42]) ).
thf(f57,plain,
! [X1: $i,X0: $i,X2: $i] :
( ( ( irel @ X2 @ X1 )
= $true )
| ( ( irel @ X2 @ X0 )
!= $true )
| ( ( irel @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f53]) ).
thf(f58,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X2 @ X0 )
!= $true )
| ( ( irel @ X2 @ X1 )
= $true )
| ( ( irel @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f57]) ).
thf(f61,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f63,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f32]) ).
thf(f64,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f70,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f72,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f76,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f77,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f78,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ X2 @ X0 )
!= $true )
| ( ( irel @ X0 @ X1 )
!= $true )
| ( ( irel @ X2 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f79,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f80,plain,
( ( ivalid @ ( inot @ ( inot @ ( ior @ ( iatom @ a ) @ ( inot @ ( iatom @ a ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f84,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,[],[f64,f77,f76]) ).
thf(f87,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [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,[],[f70,f61,f76,f76]) ).
thf(f92,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ 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] :
~ ( 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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [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
@ a )
@ ( ^ [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] : Y0
@ a ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f80,f72,f84,f84,f87,f79,f84,f79]) ).
thf(f93,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a @ Y4 ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
( $false
= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a @ Y4 ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a @ Y3 ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f93]) ).
thf(f95,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK0 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) )
@ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f103,plain,
! [X1: $i] :
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ( a @ Y0 ) ) ) ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X1: $i] :
( ( ( irel @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f102]) ).
thf(f105,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f103]) ).
thf(f106,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f103]) ).
thf(f107,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
@ ( sK2 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X1: $i] :
( ( $false
= ( ( irel @ ( sK1 @ X1 ) @ ( sK2 @ X1 ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK2 @ X1 ) @ Y0 )
=> ( a @ Y0 ) ) ) ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK2 @ X1 ) @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f108]) ).
thf(f110,plain,
! [X1: $i] :
( ( $true
= ( irel @ ( sK1 @ X1 ) @ ( sK2 @ X1 ) ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f108]) ).
thf(f111,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK2 @ X1 ) @ Y0 )
=> ( a @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f109]) ).
thf(f112,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ ( sK2 @ X1 ) @ Y0 )
=> ( a @ Y0 ) )
@ X2 ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ ( sK2 @ X1 ) @ X2 )
=> ( a @ X2 ) )
= $true )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ ( sK2 @ X1 ) @ X2 ) )
| ( ( a @ X2 )
= $true )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ( a @ Y0 ) )
@ ( sK3 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f105]) ).
thf(f116,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ( irel @ ( sK1 @ X1 ) @ ( sK3 @ X1 ) )
=> ( a @ ( sK3 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f115]) ).
thf(f117,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( a @ ( sK3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X1: $i] :
( ( ( irel @ ( sK1 @ X1 ) @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f116]) ).
thf(f122,plain,
! [X0: $i,X1: $i] :
( ( ( irel @ ( sK1 @ X0 ) @ X1 )
!= $true )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true != $true )
| ( ( irel @ X0 @ X1 )
= $true ) ),
inference(constrained_superposition,[],[f78,f104]) ).
thf(f124,plain,
! [X0: $i,X1: $i] :
( ( ( irel @ ( sK1 @ X0 ) @ X1 )
!= $true )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( ( irel @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f122]) ).
thf(f130,plain,
! [X0: $i] :
( ( $true != $true )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( irel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f124,f110]) ).
thf(f131,plain,
! [X0: $i] :
( ( $true != $true )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( irel @ X0 @ ( sK3 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f124,f118]) ).
thf(f134,plain,
! [X0: $i] :
( ( $true != $true )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( irel @ X0 @ ( sK3 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[],[f131]) ).
thf(f135,plain,
! [X0: $i] :
( ( $true
= ( irel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f134]) ).
thf(f136,plain,
! [X0: $i] :
( ( $true
= ( irel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[],[f130]) ).
thf(f137,plain,
! [X0: $i] :
( ( $true
= ( irel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f153,plain,
! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( ( a @ ( sK3 @ ( sK2 @ X0 ) ) )
= $true )
| ( $false
= ( irel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f114,f135]) ).
thf(f161,plain,
! [X0: $i] :
( ( $false
= ( irel @ sK0 @ ( sK2 @ X0 ) ) )
| ( ( a @ ( sK3 @ ( sK2 @ X0 ) ) )
= $true )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f153]) ).
thf(f271,plain,
! [X0: $i] :
( ( $false = $true )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( irel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ ( sK2 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f161,f117]) ).
thf(f274,plain,
! [X0: $i] :
( ( $false
= ( irel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f271]) ).
thf(f275,plain,
! [X0: $i] :
( ( $false
= ( irel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f274]) ).
thf(f299,plain,
( ( $false
= ( irel @ sK0 @ sK0 ) )
| ( $false
= ( irel @ sK0 @ sK0 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f137,f275]) ).
thf(f300,plain,
( ( $false
= ( irel @ sK0 @ sK0 ) )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f299]) ).
thf(f301,plain,
( $false
= ( irel @ sK0 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f300]) ).
thf(f304,plain,
$false = $true,
inference(forward_demodulation,[],[f301,f63]) ).
thf(f305,plain,
$false,
inference(trivial_inequality_removal,[],[f304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO062^4.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n018.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:28:12 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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
% 0.21/0.29 % (293519)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (293529)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3232475495:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (293530)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (293530)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
% 0.21/0.29 % (293524)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3170524501:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (293525)lrs+10_16_si=on:nwc=1.5:random_seed=2174560317:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (293526)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1426718185:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (293528)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3495221239:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (293527)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=2324745353: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)
% 0.21/0.29 % (293530)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=3458561743:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (293526)Instruction limit reached!
% 0.21/0.29 % (293526)------------------------------
% 0.21/0.29 % (293526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (293529) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-293519-293529"...
% 0.21/0.29 % (293526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (293526)CaDiCaL version: 2.1.3
% 0.21/0.29 % (293526)Termination reason: Instruction limit
% 0.21/0.29 % (293526)Termination phase: Saturation
% 0.21/0.29 % (293526)Time elapsed: 0.002 s
% 0.21/0.29 % (293526)Peak memory usage: 11 MB
% 0.21/0.29 % (293526)Instructions burned: 3 (million)
% 0.21/0.29 % (293529)...printing done.
% 0.21/0.29 % (293529)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (293529)------------------------------
% 0.21/0.29 % (293529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (293529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (293529)CaDiCaL version: 2.1.3
% 0.21/0.29 % (293529)Termination reason: Refutation
% 0.21/0.29 % (293529)Time elapsed: 0.011 s
% 0.21/0.29 % (293529)Peak memory usage: 12 MB
% 0.21/0.29 % (293529)Instructions burned: 39 (million)
% 0.21/0.29 % (293519)Success in time 0.044 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------