%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL943^24 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 08:15:26 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 9
% Syntax : Number of formulae : 92 ( 56 unt; 0 typ; 3 def)
% Number of atoms : 806 ( 127 equ; 0 cnn)
% Maximal formula atoms : 24 ( 8 avg)
% Number of connectives : 1208 ( 22 ~; 99 |; 0 &; 841 @)
% ( 3 <=>; 149 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 34 usr; 11 con; 0-4 aty)
% ( 94 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 244 ( 0 sgn 63 !; 0 ?; 244 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
p: mworld > $o ).
thf(func_def_12,type,
q: mworld > $o ).
thf(func_def_13,type,
r: mworld > $o ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
vIMP: $o > $o > $o ).
thf(func_def_22,type,
vIFF: $o > $o > $o ).
thf(func_def_23,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
sK0: mworld ).
thf(func_def_28,type,
sK1: mworld > mworld ).
thf(func_def_29,type,
sK2: mworld > mworld ).
thf(func_def_30,type,
sK3: mworld ).
thf(func_def_31,type,
sK4: mworld ).
thf(func_def_32,type,
sK5: mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f4,axiom,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
thf(f10,conjecture,
mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel5) ).
thf(f11,negated_conjecture,
~ ( mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f12,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f17,plain,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f18,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f20,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f23,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f24,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f27,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
inference(rectify,[],[f9]) ).
thf(f28,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(fool_elimination,[],[f27]) ).
thf(f29,plain,
~ ( mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f30,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f29]) ).
thf(f31,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f30]) ).
thf(f32,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f35,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f36,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f38,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f40,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(cnf_transformation,[],[f28]) ).
thf(f41,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f44,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ r ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ r ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f41,f32,f38,f36,f38,f36,f35,f38,f38,f35,f38,f38,f35,f38,f38,f36,f38,f38]) ).
thf(f45,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( $false
= ( ( mrel @ mactual @ sK0 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f47]) ).
thf(f50,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f48]) ).
thf(f51,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f48]) ).
thf(f52,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ sK0 @ X1 )
=> ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f55]) ).
thf(f69,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f56]) ).
thf(f70,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( mrel @ X1 @ ( sK2 @ X1 ) )
=> ( q @ ( sK2 @ X1 ) ) ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( r @ X2 ) ) )
| ( $true
= ( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( q @ ( sK2 @ X1 ) ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( r @ X2 ) ) )
| ( $true
= ( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f73]) ).
thf(f78,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( q @ ( sK2 @ X1 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) ) )
| ( $true
= ( r @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f74]) ).
thf(f79,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( q @ ( sK2 @ X1 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f78]) ).
thf(f80,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f50]) ).
thf(f81,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f50]) ).
thf(f82,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f81]) ).
thf(f83,plain,
( $false
= ( ( mrel @ sK0 @ sK3 )
=> ( p @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
( $false
= ( p @ sK3 ) ),
inference(imp_proxy_clausification,[],[f83]) ).
thf(f86,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f80]) ).
thf(f87,plain,
( $false
= ( ( mrel @ sK0 @ sK4 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( q @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f88,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( q @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( r @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f87]) ).
thf(f90,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( r @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f88]) ).
thf(f91,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f88]) ).
thf(f92,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( q @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ sK4 @ X1 )
=> ( q @ X1 ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK4 @ X1 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f95,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( r @ Y0 ) )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f90]) ).
thf(f96,plain,
( $false
= ( ( mrel @ sK4 @ sK5 )
=> ( r @ sK5 ) ) ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
( $false
= ( r @ sK5 ) ),
inference(imp_proxy_clausification,[],[f96]) ).
thf(f117,definition,
( spl6_1
<=> ! [X3: mworld] :
( $true
= ( p @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f118,plain,
( ! [X3: mworld] :
( $true
= ( p @ X3 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f120,definition,
( spl6_2
<=> ! [X2: mworld] :
( $true
= ( r @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f121,plain,
( ! [X2: mworld] :
( $true
= ( r @ X2 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f120]) ).
thf(f126,plain,
( ( $true = $false )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f121,f97]) ).
thf(f130,plain,
( $false
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f131,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f130]) ).
thf(f134,plain,
! [X1: mworld] :
( ( $true = $false )
| ( $true
= ( q @ X1 ) ) ),
inference(forward_demodulation,[],[f94,f40]) ).
thf(f135,plain,
! [X1: mworld] :
( $true
= ( q @ X1 ) ),
inference(trivial_inequality_removal,[],[f134]) ).
thf(f136,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true = $false )
| ( $false
= ( q @ ( sK2 @ X1 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) ) ),
inference(forward_demodulation,[],[f79,f40]) ).
thf(f137,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( q @ ( sK2 @ X1 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f138,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true = $false )
| ( $false
= ( q @ ( sK2 @ X1 ) ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) ) ),
inference(forward_demodulation,[],[f137,f40]) ).
thf(f139,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( q @ ( sK2 @ X1 ) ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f138]) ).
thf(f140,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true = $false )
| ( $false
= ( q @ ( sK2 @ X1 ) ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) ) ),
inference(forward_demodulation,[],[f139,f40]) ).
thf(f141,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( q @ ( sK2 @ X1 ) ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f143,definition,
( spl6_4
<=> ! [X1: mworld] :
( $false
= ( q @ ( sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f144,plain,
( ! [X1: mworld] :
( $false
= ( q @ ( sK2 @ X1 ) ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f145,plain,
( spl6_1
| spl6_2
| spl6_4 ),
inference(avatar_split_clause,[],[f141,f143,f120,f117]) ).
thf(f146,plain,
( ( $true = $false )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f118,f84]) ).
thf(f156,plain,
( $false
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f146]) ).
thf(f157,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f156]) ).
thf(f160,plain,
( ( $true = $false )
| ~ spl6_4 ),
inference(constrained_superposition,[],[f135,f144]) ).
thf(f164,plain,
( $false
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f160]) ).
thf(f165,plain,
~ spl6_4,
inference(avatar_contradiction_clause,[],[f164]) ).
cnf(s3,plain,
~ spl6_2,
inference(sat_conversion,[],[f131]) ).
cnf(s4,plain,
( spl6_1
| spl6_2
| spl6_4 ),
inference(sat_conversion,[],[f145]) ).
cnf(s8,plain,
~ spl6_1,
inference(sat_conversion,[],[f157]) ).
cnf(s10,plain,
~ spl6_4,
inference(sat_conversion,[],[f165]) ).
cnf(s11,plain,
spl6_2,
inference(rat,[],[s4,s10,s8]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s3,s11]) ).
thf(f166,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL943^24 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n010.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 10:45:33 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.19/0.28 % (2691505)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (2691510)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=87420420_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (2691511)% WARNING: option uhcvi not known.
% 0.19/0.28 % (2691511)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2194090996:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (2691513)dis+10_1_sil=32000:sp=arity:random_seed=3323988314:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (2691512)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2844473903:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (2691511)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (2691511)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.28 % (2691518)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4286597039:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.28 % (2691514)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3687583036:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (2691514)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (2691513) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2691505-2691513"...
% 0.19/0.28 % (2691513)...printing done.
% 0.19/0.28 % (2691513)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (2691513)------------------------------
% 0.19/0.29 % (2691513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2691513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2691513)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2691513)Termination reason: Refutation
% 0.19/0.29 % (2691513)Time elapsed: 0.009 s
% 0.19/0.29 % (2691513)Peak memory usage: 12 MB
% 0.19/0.29 % (2691513)Instructions burned: 15 (million)
% 0.19/0.29 % (2691505)Success in time 0.046 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------