%------------------------------------------------------------------------------
% File : Vampire-SAT---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/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:48:51 AM UTC 2026
% Result : Theorem 0.80s 0.43s
% Output : Refutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 10
% Syntax : Number of formulae : 93 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 718 ( 152 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 973 ( 56 ~; 82 |; 3 &; 689 @)
% ( 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 : 224 ( 157 ^; 67 !; 0 ?; 224 :)
% 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_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_28,type,
vOR: $o > $o > $o ).
thf(func_def_29,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
vAND: $o > $o > $o ).
thf(func_def_31,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
vIMP: $o > $o > $o ).
thf(func_def_33,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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/sandbox2/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f2,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X1 @ X2 )
& ( irel @ X0 @ X1 ) )
=> ( irel @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',trans_axiom) ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f9,axiom,
( inot
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL010^0.ax',ior) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,conjecture,
ivalid @ ( inot @ ( inot @ ( ior @ ( iatom @ a ) @ ( inot @ ( iatom @ a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f23,negated_conjecture,
~ ( ivalid @ ( inot @ ( inot @ ( ior @ ( iatom @ a ) @ ( inot @ ( iatom @ a ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
thf(f24,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f25,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X1 @ X2 )
& ( irel @ X0 @ X1 ) )
=> ( irel @ X0 @ X2 ) ),
inference(rectify,[],[f2]) ).
thf(f27,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( ( irel @ X1 @ X2 )
= $true )
& ( ( irel @ X0 @ X1 )
= $true ) )
=> ( ( irel @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f26]) ).
thf(f28,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f29,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f31,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f30]) ).
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(f37,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f38,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f41,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f46,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f47,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f54,plain,
~ ( ivalid @ ( inot @ ( inot @ ( ior @ ( iatom @ a ) @ ( inot @ ( iatom @ a ) ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f55,plain,
( ( ivalid @ ( inot @ ( inot @ ( ior @ ( iatom @ a ) @ ( inot @ ( iatom @ a ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( ( ivalid @ ( inot @ ( inot @ ( ior @ ( iatom @ a ) @ ( inot @ ( iatom @ a ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f55]) ).
thf(f57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X0 @ X2 )
= $true )
| ( ( irel @ X1 @ X2 )
!= $true )
| ( ( irel @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f27]) ).
thf(f58,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X0 @ X2 )
= $true )
| ( ( irel @ X1 @ X2 )
!= $true )
| ( ( irel @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f57]) ).
thf(f59,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f25]) ).
thf(f60,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
!= $true )
| ( ( irel @ X0 @ X2 )
= $true )
| ( ( irel @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f61,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f62,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f65,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f66,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f67,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f71,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f76,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
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,[],[f67,f61,f65]) ).
thf(f87,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ 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,[],[f71,f62,f65,f65]) ).
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] :
( ( Y2 @ Y4 )
| ( Y3 @ 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,f76,f84,f84,f87,f66,f84,f66]) ).
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 )
=> ( a @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
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 )
=> ( a @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a @ Y4 ) ) ) ) ) ) ) ) ) )
@ 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 )
=> ( a @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a @ Y3 ) ) ) ) ) ) ) ) )
@ X1 ) ),
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 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) ) ) ) ) ) ),
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 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) ) )
@ ( sK1 @ 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 )
=> ( a @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f103,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ( a @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK1 @ X1 ) ) )
| ( $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 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f103]) ).
thf(f106,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f103]) ).
thf(f107,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ( a @ Y0 ) )
@ ( sK2 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ( irel @ ( sK1 @ X1 ) @ ( sK2 @ X1 ) )
=> ( a @ ( sK2 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( a @ ( sK2 @ X1 ) ) ) ),
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 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ ( sK1 @ X1 ) @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
@ ( sK3 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f105]) ).
thf(f112,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ( irel @ ( sK1 @ X1 ) @ ( sK3 @ X1 ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f113,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f112]) ).
thf(f114,plain,
! [X1: $i] :
( ( $true
= ( irel @ ( sK1 @ X1 ) @ ( sK3 @ X1 ) ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f112]) ).
thf(f115,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f113]) ).
thf(f116,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( a @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( ( irel @ ( sK3 @ X1 ) @ X2 )
=> ( a @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ ( sK3 @ X1 ) @ X2 ) )
| ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( a @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f117]) ).
thf(f190,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( irel @ X1 @ ( sK2 @ X0 ) ) )
| ( $true
!= ( irel @ X1 @ ( sK1 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f60,f110]) ).
thf(f191,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( irel @ X1 @ ( sK3 @ X0 ) ) )
| ( $true
!= ( irel @ X1 @ ( sK1 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f60,f114]) ).
thf(f195,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( irel @ X1 @ ( sK1 @ X0 ) ) )
| ( $true
= ( irel @ X1 @ ( sK3 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f191]) ).
thf(f196,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( irel @ X1 @ ( sK1 @ X0 ) ) )
| ( $true
= ( irel @ X1 @ ( sK2 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f190]) ).
thf(f233,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( irel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f195,f104]) ).
thf(f242,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( irel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f233]) ).
thf(f243,plain,
! [X0: $i] :
( ( $true
= ( irel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f242]) ).
thf(f249,plain,
( ( $true = $false )
| ( $false
= ( a @ ( sK2 @ ( sK3 @ sK0 ) ) ) )
| ( $false
= ( irel @ sK0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f109,f243]) ).
thf(f259,plain,
( ( $false
= ( a @ ( sK2 @ ( sK3 @ sK0 ) ) ) )
| ( $false
= ( irel @ sK0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f249]) ).
thf(f268,plain,
( ( $true = $false )
| ( $false
= ( a @ ( sK2 @ ( sK3 @ sK0 ) ) ) ) ),
inference(forward_demodulation,[],[f259,f59]) ).
thf(f269,plain,
( $false
= ( a @ ( sK2 @ ( sK3 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[],[f268]) ).
thf(f327,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( irel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f196,f104]) ).
thf(f336,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( irel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f327]) ).
thf(f337,plain,
! [X0: $i] :
( ( $true
= ( irel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f336]) ).
thf(f343,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( a @ ( sK2 @ ( sK3 @ X0 ) ) ) )
| ( $false
= ( irel @ sK0 @ ( sK3 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f118,f337]) ).
thf(f350,plain,
! [X0: $i] :
( ( $false
= ( irel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( a @ ( sK2 @ ( sK3 @ X0 ) ) ) )
| ( $false
= ( irel @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f343]) ).
thf(f415,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK0 ) )
| ( $true
= ( a @ ( sK2 @ ( sK3 @ sK0 ) ) ) )
| ( $false
= ( irel @ sK0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f243,f350]) ).
thf(f419,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK0 ) )
| ( $true
= ( a @ ( sK2 @ ( sK3 @ sK0 ) ) ) ) ),
inference(duplicate_literal_removal,[],[f415]) ).
thf(f420,plain,
( ( $false
= ( irel @ sK0 @ sK0 ) )
| ( $true
= ( a @ ( sK2 @ ( sK3 @ sK0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f419]) ).
thf(f426,plain,
( ( $true = $false )
| ( $true
= ( a @ ( sK2 @ ( sK3 @ sK0 ) ) ) ) ),
inference(forward_demodulation,[],[f420,f59]) ).
thf(f427,plain,
( $true
= ( a @ ( sK2 @ ( sK3 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[],[f426]) ).
thf(f430,plain,
$true = $false,
inference(forward_demodulation,[],[f427,f269]) ).
thf(f431,plain,
$false,
inference(trivial_inequality_removal,[],[f430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO062^4.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 % Computer : n020.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Sep 29 16:27:04 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.27 Running first-order model finding
% 0.08/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.80/0.43 % (1255610)Will run a generic schedule for satisfiability detection.
% 0.80/0.43 % (1255621)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=221749346:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.80/0.43 % (1255615)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=499614790_2999 on theBenchmark for (2999ds/0Mi)
% 0.80/0.43 % Exception at run slice level
% 0.80/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.80/0.43 % (1255616)% WARNING: option uhcvi not known.
% 0.80/0.43 % (1255618)dis+10_1_sil=32000:sp=arity:random_seed=3704218554:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.80/0.43 % (1255620)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2300938498:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.80/0.43 % (1255619)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1681269009:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.80/0.43 % (1255616)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2616646915:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.80/0.43 % (1255617)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=887778905:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.80/0.43 % (1255619)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.80/0.43 % (1255616)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.80/0.43 % (1255616)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.80/0.43 % (1255624)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1509881552:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.80/0.43 % Exception at run slice level
% 0.80/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.80/0.43 % (1255631)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1656342747:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.80/0.43 % (1255621)Instruction limit reached!
% 0.80/0.43 % (1255621)------------------------------
% 0.80/0.43 % (1255621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.43 % (1255621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.43 % (1255621)CaDiCaL version: 2.1.3
% 0.80/0.43 % (1255621)Termination reason: Instruction limit
% 0.80/0.43 % (1255621)Termination phase: Saturation
% 0.80/0.43 % (1255621)Time elapsed: 0.074 s
% 0.80/0.43 % (1255621)Peak memory usage: 12 MB
% 0.80/0.43 % (1255621)Instructions burned: 159 (million)
% 0.80/0.43 % (1255633)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4225771895:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.80/0.43 % (1255633)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.80/0.43 % (1255633)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.80/0.43 % (1255618)Instruction limit reached!
% 0.80/0.43 % (1255618)------------------------------
% 0.80/0.43 % (1255618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.43 % (1255618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.43 % (1255618)CaDiCaL version: 2.1.3
% 0.80/0.43 % (1255618)Termination reason: Instruction limit
% 0.80/0.43 % (1255618)Termination phase: Saturation
% 0.80/0.43 % (1255618)Time elapsed: 0.086 s
% 0.80/0.43 % (1255618)Peak memory usage: 12 MB
% 0.80/0.43 % (1255618)Instructions burned: 103 (million)
% 0.80/0.43 % (1255619)Instruction limit reached!
% 0.80/0.43 % (1255619)------------------------------
% 0.80/0.43 % (1255619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.43 % (1255619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.43 % (1255619)CaDiCaL version: 2.1.3
% 0.80/0.43 % (1255619)Termination reason: Instruction limit
% 0.80/0.43 % (1255619)Termination phase: Saturation
% 0.80/0.43 % (1255619)Time elapsed: 0.097 s
% 0.80/0.43 % (1255619)Peak memory usage: 12 MB
% 0.80/0.43 % (1255619)Instructions burned: 116 (million)
% 0.80/0.43 % (1255633) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1255610-1255633"...
% 0.80/0.43 % (1255635)ott-21_1_sil=16000:fs=off:random_seed=3531050348:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.80/0.43 % (1255633)...printing done.
% 0.80/0.43 % (1255633)Refutation found. Thanks to Tanya!
% 0.80/0.43 % SZS status Theorem for theBenchmark
% 0.80/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.80/0.43 % (1255633)------------------------------
% 0.80/0.43 % (1255633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.43 % (1255633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.43 % (1255633)CaDiCaL version: 2.1.3
% 0.80/0.43 % (1255633)Termination reason: Refutation
% 0.80/0.43 % (1255633)Time elapsed: 0.023 s
% 0.80/0.43 % (1255633)Peak memory usage: 13 MB
% 0.80/0.43 % (1255633)Instructions burned: 37 (million)
% 0.80/0.43 % (1255610)Success in time 0.144 s
% 0.80/0.43 % Vampire exiting
%------------------------------------------------------------------------------