%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN390^4 : 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 : 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 08:41:53 AM UTC 2026
% Result : Theorem 0.13s 0.23s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 360 ( 70 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 553 ( 27 ~; 26 |; 10 &; 408 @)
% ( 0 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 124 ( 124 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 34 usr; 5 con; 0-4 aty)
% ( 38 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 218 ( 210 ^; 8 !; 0 ?; 218 :)
% 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_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(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(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mimplies) ).
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(f12,axiom,
( iand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iand) ).
thf(f14,axiom,
( iimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f16,axiom,
( iequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( iand @ ( iimplies @ X0 @ X1 ) @ ( iimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iequiv) ).
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 @ ( iequiv @ ( iatom @ p ) @ ( iatom @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel11) ).
thf(f23,negated_conjecture,
~ ( ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ p ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
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(f32,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f33,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
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(f40,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f42,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f44,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f16]) ).
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 @ ( iequiv @ ( iatom @ p ) @ ( iatom @ p ) ) ),
inference(rectify,[],[f23]) ).
thf(f55,plain,
( ( ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ p ) ) )
!= $true ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( ( ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ p ) ) )
!= $true ),
inference(flattening,[],[f55]) ).
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(f63,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f64,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
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(f70,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f72,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f74,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f76,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f80,plain,
( ( ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ p ) ) )
!= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f83,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,f62,f61]) ).
thf(f86,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f70,f63]) ).
thf(f88,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,[],[f72,f83,f65,f65]) ).
thf(f90,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f74,f86,f88,f88]) ).
thf(f92,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 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p )
@ ( ^ [Y0: $i > $o] : Y0
@ p ) ) ) ),
inference(definition_unfolding,[],[f80,f76,f90,f66,f66]) ).
thf(f93,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
( $false
= ( ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f93]) ).
thf(f95,plain,
( $false
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f95]) ).
thf(f97,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f96]) ).
thf(f98,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f96]) ).
thf(f99,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) ),
inference(duplicate_literal_removal,[],[f100]) ).
thf(f102,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK0 @ X1 )
=> ( p @ X1 ) ) ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f103,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f102]) ).
thf(f104,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f97]) ).
thf(f105,plain,
( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( p @ Y0 ) )
@ sK1 ) ),
inference(duplicate_literal_removal,[],[f104]) ).
thf(f106,plain,
( $false
= ( ( irel @ sK0 @ sK1 )
=> ( p @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
( $false
= ( p @ sK1 ) ),
inference(imp_proxy_clausification,[],[f106]) ).
thf(f108,plain,
( $true
= ( irel @ sK0 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f106]) ).
thf(f127,plain,
( ( $true = $false )
| ( $true
= ( p @ sK1 ) ) ),
inference(constrained_superposition,[],[f108,f103]) ).
thf(f129,plain,
( $true
= ( p @ sK1 ) ),
inference(trivial_inequality_removal,[],[f127]) ).
thf(f134,plain,
$true = $false,
inference(forward_demodulation,[],[f129,f107]) ).
thf(f135,plain,
$false,
inference(trivial_inequality_removal,[],[f134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN390^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.16 % Computer : n015.cluster.edu
% 0.13/0.16 % Model : x86_64 x86_64
% 0.13/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.16 % Memory : 8046.5625MB
% 0.13/0.16 % OS : Linux 6.8.0-71-generic
% 0.13/0.16 % CPULimit : 300
% 0.13/0.16 % WCLimit : 300
% 0.13/0.16 % DateTime : Tue Sep 29 16:19:03 UTC 2026
% 0.13/0.16 % CPUTime :
% 0.13/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.19 Running first-order model finding
% 0.13/0.19 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
% 0.13/0.23 % (3724664)Will run a generic schedule for satisfiability detection.
% 0.13/0.23 % (3724670)% WARNING: option uhcvi not known.
% 0.13/0.23 % (3724670)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3112061946:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.23 % (3724670)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.13/0.23 % (3724670)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.13/0.23 % (3724670) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3724664-3724670"...
% 0.13/0.23 % (3724670)...printing done.
% 0.13/0.23 % (3724670)Refutation found. Thanks to Tanya!
% 0.13/0.23 % SZS status Theorem for theBenchmark
% 0.13/0.23 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.24 % (3724670)------------------------------
% 0.13/0.24 % (3724670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.24 % (3724670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.24 % (3724670)CaDiCaL version: 2.1.3
% 0.13/0.24 % (3724670)Termination reason: Refutation
% 0.13/0.24 % (3724670)Time elapsed: 0.003 s
% 0.13/0.24 % (3724670)Peak memory usage: 12 MB
% 0.13/0.24 % (3724670)Instructions burned: 10 (million)
% 0.13/0.24 % (3724664)Success in time 0.036 s
% 0.13/0.24 % Vampire exiting
%------------------------------------------------------------------------------