%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO893^11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 08:50:33 AM UTC 2026
% Result : Theorem 0.17s 0.37s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 19
% Syntax : Number of formulae : 303 ( 38 unt; 0 typ; 11 def)
% Number of atoms : 2557 ( 557 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 3378 ( 486 ~; 774 |; 96 &;1795 @)
% ( 13 <=>; 93 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 42 usr; 18 con; 0-4 aty)
% ( 61 !!; 60 ??; 0 @@+; 0 @@-)
% Number of variables : 393 ( 0 sgn 184 !; 2 ?; 393 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vAND: $o > $o > $o ).
thf(func_def_17,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vOR: $o > $o > $o ).
thf(func_def_19,type,
vIMP: $o > $o > $o ).
thf(func_def_20,type,
vIFF: $o > $o > $o ).
thf(func_def_21,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_22,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
sK0: mworld > mworld ).
thf(func_def_26,type,
sK1: mworld > mworld ).
thf(func_def_27,type,
sK2: mworld ).
thf(func_def_28,type,
sK3: mworld ).
thf(func_def_29,type,
sK4: mworld > mworld ).
thf(func_def_30,type,
sK5: mworld > mworld ).
thf(func_def_31,type,
sK6: mworld > mworld ).
thf(func_def_32,type,
sK7: mworld > mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def) ).
thf(f6,axiom,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f10,axiom,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X1 )
& ( mrel @ X0 @ X2 ) )
=> ( mrel @ X2 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_euclidean) ).
thf(f11,conjecture,
mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f12,negated_conjecture,
~ ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f13,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f14,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f15,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f22,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f23,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f24,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f25,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f27,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f28,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f29,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X1 )
& ( mrel @ X0 @ X2 ) )
=> ( mrel @ X2 @ X1 ) ),
inference(rectify,[],[f10]) ).
thf(f31,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( ( mrel @ X0 @ X1 )
= $true )
& ( ( mrel @ X0 @ X2 )
= $true ) )
=> ( ( mrel @ X2 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
~ ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f33,plain,
( ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f33]) ).
thf(f35,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X2 @ X1 )
= $true )
| ( ( mrel @ X0 @ X1 )
!= $true )
| ( ( mrel @ X0 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f31]) ).
thf(f36,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X2 @ X1 )
= $true )
| ( ( mrel @ X0 @ X1 )
!= $true )
| ( ( mrel @ X0 @ X2 )
!= $true ) ),
inference(flattening,[],[f35]) ).
thf(f37,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f38,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f42,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f43,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f44,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f45,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f29]) ).
thf(f46,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X2 )
!= $true )
| ( ( mrel @ X0 @ X1 )
!= $true )
| ( ( mrel @ X2 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f47,plain,
( ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f34]) ).
thf(f50,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ 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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ p ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f47,f37,f42,f38,f43,f44,f43,f44,f43,f44,f38]) ).
thf(f51,plain,
( $true
!= ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
!= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f51]) ).
thf(f53,plain,
( ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(xor_proxy_clausification,[],[f52]) ).
thf(f54,plain,
( ( $false
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(xor_proxy_clausification,[],[f52]) ).
thf(f55,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
| ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ mactual @ X1 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ( mrel @ mactual @ X2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( mrel @ mactual @ X2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(and_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) )
@ ( sK0 @ X2 ) ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) )
@ ( sK0 @ X2 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
@ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( mrel @ X2 @ ( sK0 @ X2 ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK0 @ X2 ) @ Y0 )
& ~ ( p @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ X1 @ ( sK1 @ X1 ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK1 @ X1 ) @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK0 @ X2 ) @ Y0 )
& ~ ( p @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ X1 @ ( sK1 @ X1 ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK1 @ X1 ) @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( mrel @ X2 @ ( sK0 @ X2 ) ) )
| ( $true
= ( ( mrel @ X1 @ ( sK1 @ X1 ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK1 @ X1 ) @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f66,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( mrel @ X2 @ ( sK0 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK1 @ X1 ) @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( mrel @ X2 @ ( sK0 @ X2 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f68,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( mrel @ X2 @ ( sK0 @ X2 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK1 @ X1 ) @ Y0 )
=> ( p @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f66]) ).
thf(f69,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( mrel @ X2 @ ( sK0 @ X2 ) ) )
| ( $true
= ( ( mrel @ ( sK1 @ X1 ) @ X3 )
=> ( p @ X3 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( mrel @ X2 @ ( sK0 @ X2 ) ) )
| ( $false
= ( mrel @ ( sK1 @ X1 ) @ X3 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $true
= ( p @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK0 @ X2 ) @ Y0 )
& ~ ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ X1 @ ( sK1 @ X1 ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK1 @ X1 ) @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f64]) ).
thf(f72,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK0 @ X2 ) @ Y0 )
& ~ ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK1 @ X1 ) @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(and_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK0 @ X2 ) @ Y0 )
& ~ ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(and_proxy_clausification,[],[f71]) ).
thf(f74,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( mrel @ ( sK0 @ X2 ) @ X3 )
& ~ ( p @ X3 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ~ ( p @ X3 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ ( sK0 @ X2 ) @ X3 ) ) ),
inference(and_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ ( sK0 @ X2 ) @ X3 ) ) ),
inference(not_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK0 @ X2 ) @ Y0 )
& ~ ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK1 @ X1 ) @ Y0 )
=> ( p @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f72]) ).
thf(f78,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( mrel @ ( sK0 @ X2 ) @ X3 )
& ~ ( p @ X3 ) ) )
| ( $true
= ( ( mrel @ ( sK1 @ X1 ) @ X4 )
=> ( p @ X4 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ~ ( p @ X3 ) ) )
| ( $true
= ( ( mrel @ ( sK1 @ X1 ) @ X4 )
=> ( p @ X4 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ ( sK0 @ X2 ) @ X3 ) ) ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( ( mrel @ ( sK1 @ X1 ) @ X4 )
=> ( p @ X4 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ ( sK0 @ X2 ) @ X3 ) ) ),
inference(not_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( p @ X3 ) )
| ( $false
= ( mrel @ ( sK1 @ X1 ) @ X4 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ ( sK0 @ X2 ) @ X3 ) )
| ( $true
= ( p @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f82,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f53]) ).
thf(f83,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) )
@ sK2 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f83]) ).
thf(f85,plain,
( ( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ( mrel @ mactual @ sK3 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f84]) ).
thf(f86,plain,
( ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( ( mrel @ mactual @ sK3 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( ( mrel @ mactual @ sK3 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f88,plain,
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f87]) ).
thf(f89,plain,
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( mrel @ mactual @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f87]) ).
thf(f90,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f88]) ).
thf(f91,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( ( mrel @ sK3 @ X1 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ~ ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( mrel @ sK3 @ X1 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ~ ( p @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( mrel @ sK3 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ~ ( p @ Y0 ) )
@ ( sK4 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( mrel @ sK3 @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
& ~ ( p @ ( sK4 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( mrel @ sK3 @ X1 ) )
| ( $true
= ( ~ ( p @ ( sK4 @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( mrel @ sK3 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK4 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f94]) ).
thf(f97,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( mrel @ sK3 @ X1 ) )
| ( $false
= ( p @ ( sK4 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f95]) ).
thf(f98,plain,
! [X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ( mrel @ mactual @ sK3 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f86]) ).
thf(f99,plain,
! [X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( mrel @ mactual @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f98]) ).
thf(f101,plain,
! [X1: mworld] :
( ( $false
= ( ( mrel @ sK2 @ X1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( $true
= ( mrel @ mactual @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f102,plain,
! [X1: mworld] :
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $true
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X1: mworld] :
( ( $false
= ( ( mrel @ X1 @ ( sK5 @ X1 ) )
=> ( p @ ( sK5 @ X1 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f105,plain,
! [X1: mworld] :
( ( $false
= ( p @ ( sK5 @ X1 ) ) )
| ( $true
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f104]) ).
thf(f107,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f99]) ).
thf(f108,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ( mrel @ sK2 @ X1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK3 @ X2 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
& ~ ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK3 @ X2 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
& ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f108]) ).
thf(f110,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ ( sK6 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK3 @ X2 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
& ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f109]) ).
thf(f111,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ ( sK6 @ X1 ) ) )
| ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
& ~ ( p @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f112,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ ( sK6 @ X1 ) ) )
| ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
& ~ ( p @ Y0 ) )
@ ( sK7 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ( mrel @ X1 @ ( sK6 @ X1 ) )
=> ( p @ ( sK6 @ X1 ) ) ) )
| ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( ( mrel @ X2 @ ( sK7 @ X2 ) )
& ~ ( p @ ( sK7 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( p @ ( sK6 @ X1 ) ) )
| ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( ( mrel @ X2 @ ( sK7 @ X2 ) )
& ~ ( p @ ( sK7 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( ( mrel @ X2 @ ( sK7 @ X2 ) )
& ~ ( p @ ( sK7 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f113]) ).
thf(f116,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( ~ ( p @ ( sK7 @ X2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( mrel @ X2 @ ( sK7 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f115]) ).
thf(f118,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $false
= ( p @ ( sK7 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f116]) ).
thf(f119,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( p @ ( sK6 @ X1 ) ) )
| ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( ~ ( p @ ( sK7 @ X2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f114]) ).
thf(f120,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( p @ ( sK6 @ X1 ) ) )
| ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( mrel @ X2 @ ( sK7 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f114]) ).
thf(f121,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( p @ ( sK6 @ X1 ) ) )
| ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $false
= ( p @ ( sK7 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f119]) ).
thf(f123,definition,
( spl8_1
<=> ( $true
= ( mrel @ mactual @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f124,plain,
( ( $true
!= ( mrel @ mactual @ sK3 ) )
| spl8_1 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f125,plain,
( ( $true
= ( mrel @ mactual @ sK3 ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f127,definition,
( spl8_2
<=> ( $true
= ( mrel @ mactual @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f128,plain,
( ( $true
!= ( mrel @ mactual @ sK2 ) )
| spl8_2 ),
inference(avatar_component_clause,[],[f127]) ).
thf(f129,plain,
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f127]) ).
thf(f130,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f89,f127,f123]) ).
thf(f138,definition,
( spl8_5
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK3 @ X1 ) )
| ( $false
= ( p @ ( sK4 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f139,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ sK3 @ X1 ) )
| ( $false
= ( p @ ( sK4 @ X1 ) ) ) )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f138]) ).
thf(f140,plain,
( spl8_5
| spl8_2 ),
inference(avatar_split_clause,[],[f97,f127,f138]) ).
thf(f197,definition,
( spl8_10
<=> ! [X2: mworld] :
( ( $true
= ( mrel @ X2 @ ( sK0 @ X2 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
thf(f198,plain,
( ! [X2: mworld] :
( ( $true
= ( mrel @ X2 @ ( sK0 @ X2 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) )
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f203,definition,
( spl8_12
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_12])],[avatar_definition]) ).
thf(f204,plain,
( ! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f205,plain,
( spl8_10
| spl8_12 ),
inference(avatar_split_clause,[],[f67,f203,f197]) ).
thf(f260,definition,
( spl8_14
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $false
= ( p @ ( sK7 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_14])],[avatar_definition]) ).
thf(f261,plain,
( ! [X2: mworld] :
( ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $false
= ( p @ ( sK7 @ X2 ) ) ) )
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f269,definition,
( spl8_17
<=> ! [X1: mworld] :
( ( $false
= ( p @ ( sK6 @ X1 ) ) )
| ( $false
= ( mrel @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_17])],[avatar_definition]) ).
thf(f270,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $false
= ( p @ ( sK6 @ X1 ) ) ) )
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f271,plain,
( spl8_14
| spl8_17 ),
inference(avatar_split_clause,[],[f121,f269,f260]) ).
thf(f301,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $false
= ( p @ ( sK5 @ X1 ) ) ) )
| spl8_1 ),
inference(forward_subsumption_resolution,[],[f105,f124]) ).
thf(f307,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( p @ ( sK5 @ ( sK0 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_10 ),
inference(constrained_superposition,[],[f198,f301]) ).
thf(f308,plain,
( ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( p @ ( sK5 @ ( sK0 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f307]) ).
thf(f311,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK5 @ ( sK0 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_2
| ~ spl8_10 ),
inference(forward_demodulation,[],[f308,f129]) ).
thf(f312,plain,
( ( $false
= ( p @ ( sK5 @ ( sK0 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_2
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f311]) ).
thf(f317,plain,
( ! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( mrel @ sK2 @ X1 ) ) )
| spl8_1 ),
inference(forward_subsumption_resolution,[],[f106,f124]) ).
thf(f348,definition,
( spl8_22
<=> ! [X2: mworld,X3: mworld] :
( ( $true
= ( p @ X3 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ ( sK0 @ X2 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_22])],[avatar_definition]) ).
thf(f349,plain,
( ! [X2: mworld,X3: mworld] :
( ( $false
= ( mrel @ ( sK0 @ X2 ) @ X3 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $true
= ( p @ X3 ) ) )
| ~ spl8_22 ),
inference(avatar_component_clause,[],[f348]) ).
thf(f350,plain,
( spl8_22
| spl8_12 ),
inference(avatar_split_clause,[],[f76,f203,f348]) ).
thf(f411,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK2 @ ( sK0 @ X0 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( p @ ( sK5 @ ( sK0 @ X0 ) ) ) ) )
| spl8_1
| ~ spl8_22 ),
inference(constrained_superposition,[],[f317,f349]) ).
thf(f412,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ sK2 @ ( sK0 @ X0 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( p @ ( sK5 @ ( sK0 @ X0 ) ) ) ) )
| spl8_1
| ~ spl8_22 ),
inference(trivial_inequality_removal,[],[f411]) ).
thf(f493,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( p @ ( sK5 @ ( sK0 @ sK2 ) ) ) )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| spl8_1
| ~ spl8_10
| ~ spl8_22 ),
inference(constrained_superposition,[],[f412,f198]) ).
thf(f497,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( p @ ( sK5 @ ( sK0 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_10
| ~ spl8_22 ),
inference(duplicate_literal_removal,[],[f493]) ).
thf(f498,plain,
( ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( p @ ( sK5 @ ( sK0 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_10
| ~ spl8_22 ),
inference(trivial_inequality_removal,[],[f497]) ).
thf(f502,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK5 @ ( sK0 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_2
| ~ spl8_10
| ~ spl8_22 ),
inference(forward_demodulation,[],[f498,f129]) ).
thf(f503,plain,
( ( $true
= ( p @ ( sK5 @ ( sK0 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_2
| ~ spl8_10
| ~ spl8_22 ),
inference(trivial_inequality_removal,[],[f502]) ).
thf(f507,plain,
( ( $true = $false )
| spl8_1
| ~ spl8_2
| ~ spl8_10
| ~ spl8_22 ),
inference(forward_demodulation,[],[f503,f312]) ).
thf(f508,plain,
( $false
| spl8_1
| ~ spl8_2
| ~ spl8_10
| ~ spl8_22 ),
inference(trivial_inequality_removal,[],[f507]) ).
thf(f509,plain,
( spl8_1
| ~ spl8_2
| ~ spl8_10
| ~ spl8_22 ),
inference(avatar_contradiction_clause,[],[f508]) ).
thf(f518,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK5 @ ( sK1 @ sK2 ) ) ) )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| spl8_1
| ~ spl8_12 ),
inference(constrained_superposition,[],[f301,f204]) ).
thf(f521,plain,
( ( $false
= ( p @ ( sK5 @ ( sK1 @ sK2 ) ) ) )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| spl8_1
| ~ spl8_12 ),
inference(trivial_inequality_removal,[],[f518]) ).
thf(f524,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK5 @ ( sK1 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_2
| ~ spl8_12 ),
inference(forward_demodulation,[],[f521,f129]) ).
thf(f525,plain,
( ( $false
= ( p @ ( sK5 @ ( sK1 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_2
| ~ spl8_12 ),
inference(trivial_inequality_removal,[],[f524]) ).
thf(f534,definition,
( spl8_30
<=> ! [X4: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( mrel @ ( sK1 @ X1 ) @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_30])],[avatar_definition]) ).
thf(f535,plain,
( ! [X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ ( sK1 @ X1 ) @ X4 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl8_30 ),
inference(avatar_component_clause,[],[f534]) ).
thf(f536,plain,
( spl8_22
| spl8_30 ),
inference(avatar_split_clause,[],[f81,f534,f348]) ).
thf(f576,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK2 @ ( sK1 @ X0 ) ) )
| ( $true
= ( p @ ( sK5 @ ( sK1 @ X0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) )
| spl8_1
| ~ spl8_30 ),
inference(constrained_superposition,[],[f317,f535]) ).
thf(f579,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ sK2 @ ( sK1 @ X0 ) ) )
| ( $true
= ( p @ ( sK5 @ ( sK1 @ X0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) )
| spl8_1
| ~ spl8_30 ),
inference(trivial_inequality_removal,[],[f576]) ).
thf(f613,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( p @ ( sK5 @ ( sK1 @ sK2 ) ) ) )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| spl8_1
| ~ spl8_12
| ~ spl8_30 ),
inference(constrained_superposition,[],[f204,f579]) ).
thf(f614,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( p @ ( sK5 @ ( sK1 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_12
| ~ spl8_30 ),
inference(duplicate_literal_removal,[],[f613]) ).
thf(f615,plain,
( ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( p @ ( sK5 @ ( sK1 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_12
| ~ spl8_30 ),
inference(trivial_inequality_removal,[],[f614]) ).
thf(f619,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK5 @ ( sK1 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_2
| ~ spl8_12
| ~ spl8_30 ),
inference(forward_demodulation,[],[f615,f129]) ).
thf(f620,plain,
( ( $true
= ( p @ ( sK5 @ ( sK1 @ sK2 ) ) ) )
| spl8_1
| ~ spl8_2
| ~ spl8_12
| ~ spl8_30 ),
inference(trivial_inequality_removal,[],[f619]) ).
thf(f623,plain,
( ( $true = $false )
| spl8_1
| ~ spl8_2
| ~ spl8_12
| ~ spl8_30 ),
inference(forward_demodulation,[],[f620,f525]) ).
thf(f624,plain,
( $false
| spl8_1
| ~ spl8_2
| ~ spl8_12
| ~ spl8_30 ),
inference(trivial_inequality_removal,[],[f623]) ).
thf(f625,plain,
( spl8_1
| ~ spl8_2
| ~ spl8_12
| ~ spl8_30 ),
inference(avatar_contradiction_clause,[],[f624]) ).
thf(f644,definition,
( spl8_36
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ sK3 @ X2 ) )
| ( $true
= ( mrel @ X2 @ ( sK7 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_36])],[avatar_definition]) ).
thf(f645,plain,
( ! [X2: mworld] :
( ( $true
= ( mrel @ X2 @ ( sK7 @ X2 ) ) )
| ( $false
= ( mrel @ sK3 @ X2 ) ) )
| ~ spl8_36 ),
inference(avatar_component_clause,[],[f644]) ).
thf(f650,definition,
( spl8_38
<=> ! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( mrel @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_38])],[avatar_definition]) ).
thf(f651,plain,
( ! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( mrel @ sK2 @ X1 ) ) )
| ~ spl8_38 ),
inference(avatar_component_clause,[],[f650]) ).
thf(f652,plain,
( spl8_36
| spl8_38 ),
inference(avatar_split_clause,[],[f117,f650,f644]) ).
thf(f727,plain,
( spl8_14
| spl8_38 ),
inference(avatar_split_clause,[],[f118,f650,f260]) ).
thf(f737,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( p @ ( sK6 @ ( sK1 @ X0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ sK2 @ ( sK1 @ X0 ) ) ) )
| ~ spl8_30
| ~ spl8_38 ),
inference(constrained_superposition,[],[f535,f651]) ).
thf(f738,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ sK2 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( p @ ( sK6 @ ( sK1 @ X0 ) ) ) ) )
| ~ spl8_30
| ~ spl8_38 ),
inference(trivial_inequality_removal,[],[f737]) ).
thf(f765,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( p @ ( sK6 @ ( sK1 @ sK2 ) ) ) )
| ~ spl8_12
| ~ spl8_17 ),
inference(constrained_superposition,[],[f204,f270]) ).
thf(f768,plain,
( ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( p @ ( sK6 @ ( sK1 @ sK2 ) ) ) )
| ~ spl8_12
| ~ spl8_17 ),
inference(trivial_inequality_removal,[],[f765]) ).
thf(f774,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK6 @ ( sK1 @ sK2 ) ) ) )
| ~ spl8_2
| ~ spl8_12
| ~ spl8_17 ),
inference(forward_demodulation,[],[f768,f129]) ).
thf(f775,plain,
( ( $false
= ( p @ ( sK6 @ ( sK1 @ sK2 ) ) ) )
| ~ spl8_2
| ~ spl8_12
| ~ spl8_17 ),
inference(trivial_inequality_removal,[],[f774]) ).
thf(f873,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( p @ ( sK6 @ ( sK1 @ sK2 ) ) ) )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ~ spl8_12
| ~ spl8_30
| ~ spl8_38 ),
inference(constrained_superposition,[],[f738,f204]) ).
thf(f877,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( p @ ( sK6 @ ( sK1 @ sK2 ) ) ) )
| ~ spl8_12
| ~ spl8_30
| ~ spl8_38 ),
inference(duplicate_literal_removal,[],[f873]) ).
thf(f878,plain,
( ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( p @ ( sK6 @ ( sK1 @ sK2 ) ) ) )
| ~ spl8_12
| ~ spl8_30
| ~ spl8_38 ),
inference(trivial_inequality_removal,[],[f877]) ).
thf(f882,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK6 @ ( sK1 @ sK2 ) ) ) )
| ~ spl8_2
| ~ spl8_12
| ~ spl8_30
| ~ spl8_38 ),
inference(forward_demodulation,[],[f878,f129]) ).
thf(f883,plain,
( ( $true
= ( p @ ( sK6 @ ( sK1 @ sK2 ) ) ) )
| ~ spl8_2
| ~ spl8_12
| ~ spl8_30
| ~ spl8_38 ),
inference(trivial_inequality_removal,[],[f882]) ).
thf(f887,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_12
| ~ spl8_17
| ~ spl8_30
| ~ spl8_38 ),
inference(forward_demodulation,[],[f883,f775]) ).
thf(f888,plain,
( $false
| ~ spl8_2
| ~ spl8_12
| ~ spl8_17
| ~ spl8_30
| ~ spl8_38 ),
inference(trivial_inequality_removal,[],[f887]) ).
thf(f889,plain,
( ~ spl8_2
| ~ spl8_12
| ~ spl8_17
| ~ spl8_30
| ~ spl8_38 ),
inference(avatar_contradiction_clause,[],[f888]) ).
thf(f890,plain,
( spl8_36
| spl8_17 ),
inference(avatar_split_clause,[],[f120,f269,f644]) ).
thf(f905,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( p @ ( sK7 @ ( sK1 @ sK3 ) ) ) )
| ~ spl8_12
| ~ spl8_14 ),
inference(constrained_superposition,[],[f204,f261]) ).
thf(f910,plain,
( ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( p @ ( sK7 @ ( sK1 @ sK3 ) ) ) )
| ~ spl8_12
| ~ spl8_14 ),
inference(trivial_inequality_removal,[],[f905]) ).
thf(f917,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK7 @ ( sK1 @ sK3 ) ) ) )
| ~ spl8_1
| ~ spl8_12
| ~ spl8_14 ),
inference(forward_demodulation,[],[f910,f125]) ).
thf(f918,plain,
( ( $false
= ( p @ ( sK7 @ ( sK1 @ sK3 ) ) ) )
| ~ spl8_1
| ~ spl8_12
| ~ spl8_14 ),
inference(trivial_inequality_removal,[],[f917]) ).
thf(f955,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( p @ ( sK7 @ ( sK1 @ X0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ sK3 @ ( sK1 @ X0 ) ) ) )
| ~ spl8_30
| ~ spl8_36 ),
inference(constrained_superposition,[],[f535,f645]) ).
thf(f958,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ sK3 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( p @ ( sK7 @ ( sK1 @ X0 ) ) ) ) )
| ~ spl8_30
| ~ spl8_36 ),
inference(trivial_inequality_removal,[],[f955]) ).
thf(f970,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $true
= ( p @ ( sK7 @ ( sK1 @ sK3 ) ) ) )
| ( $false
= ( mrel @ mactual @ sK3 ) )
| ~ spl8_12
| ~ spl8_30
| ~ spl8_36 ),
inference(constrained_superposition,[],[f958,f204]) ).
thf(f974,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $true
= ( p @ ( sK7 @ ( sK1 @ sK3 ) ) ) )
| ~ spl8_12
| ~ spl8_30
| ~ spl8_36 ),
inference(duplicate_literal_removal,[],[f970]) ).
thf(f975,plain,
( ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $true
= ( p @ ( sK7 @ ( sK1 @ sK3 ) ) ) )
| ~ spl8_12
| ~ spl8_30
| ~ spl8_36 ),
inference(trivial_inequality_removal,[],[f974]) ).
thf(f979,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK7 @ ( sK1 @ sK3 ) ) ) )
| ~ spl8_1
| ~ spl8_12
| ~ spl8_30
| ~ spl8_36 ),
inference(forward_demodulation,[],[f975,f125]) ).
thf(f980,plain,
( ( $true
= ( p @ ( sK7 @ ( sK1 @ sK3 ) ) ) )
| ~ spl8_1
| ~ spl8_12
| ~ spl8_30
| ~ spl8_36 ),
inference(trivial_inequality_removal,[],[f979]) ).
thf(f984,plain,
( ( $true = $false )
| ~ spl8_1
| ~ spl8_12
| ~ spl8_14
| ~ spl8_30
| ~ spl8_36 ),
inference(forward_demodulation,[],[f980,f918]) ).
thf(f985,plain,
( $false
| ~ spl8_1
| ~ spl8_12
| ~ spl8_14
| ~ spl8_30
| ~ spl8_36 ),
inference(trivial_inequality_removal,[],[f984]) ).
thf(f986,plain,
( ~ spl8_1
| ~ spl8_12
| ~ spl8_14
| ~ spl8_30
| ~ spl8_36 ),
inference(avatar_contradiction_clause,[],[f985]) ).
thf(f992,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( p @ ( sK6 @ ( sK0 @ sK2 ) ) ) )
| ~ spl8_10
| ~ spl8_17 ),
inference(constrained_superposition,[],[f198,f270]) ).
thf(f999,plain,
( ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( p @ ( sK6 @ ( sK0 @ sK2 ) ) ) )
| ~ spl8_10
| ~ spl8_17 ),
inference(trivial_inequality_removal,[],[f992]) ).
thf(f1007,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK6 @ ( sK0 @ sK2 ) ) ) )
| ~ spl8_2
| ~ spl8_10
| ~ spl8_17 ),
inference(forward_demodulation,[],[f999,f129]) ).
thf(f1008,plain,
( ( $false
= ( p @ ( sK6 @ ( sK0 @ sK2 ) ) ) )
| ~ spl8_2
| ~ spl8_10
| ~ spl8_17 ),
inference(trivial_inequality_removal,[],[f1007]) ).
thf(f1053,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK2 @ ( sK0 @ X0 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( p @ ( sK6 @ ( sK0 @ X0 ) ) ) ) )
| ~ spl8_22
| ~ spl8_38 ),
inference(constrained_superposition,[],[f651,f349]) ).
thf(f1054,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK3 @ ( sK0 @ X0 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( p @ ( sK7 @ ( sK0 @ X0 ) ) ) ) )
| ~ spl8_22
| ~ spl8_36 ),
inference(constrained_superposition,[],[f645,f349]) ).
thf(f1057,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ sK3 @ ( sK0 @ X0 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( p @ ( sK7 @ ( sK0 @ X0 ) ) ) ) )
| ~ spl8_22
| ~ spl8_36 ),
inference(trivial_inequality_removal,[],[f1054]) ).
thf(f1058,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ sK2 @ ( sK0 @ X0 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( p @ ( sK6 @ ( sK0 @ X0 ) ) ) ) )
| ~ spl8_22
| ~ spl8_38 ),
inference(trivial_inequality_removal,[],[f1053]) ).
thf(f1136,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( p @ ( sK6 @ ( sK0 @ sK2 ) ) ) )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ~ spl8_10
| ~ spl8_22
| ~ spl8_38 ),
inference(constrained_superposition,[],[f1058,f198]) ).
thf(f1140,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( p @ ( sK6 @ ( sK0 @ sK2 ) ) ) )
| ~ spl8_10
| ~ spl8_22
| ~ spl8_38 ),
inference(duplicate_literal_removal,[],[f1136]) ).
thf(f1141,plain,
( ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $true
= ( p @ ( sK6 @ ( sK0 @ sK2 ) ) ) )
| ~ spl8_10
| ~ spl8_22
| ~ spl8_38 ),
inference(trivial_inequality_removal,[],[f1140]) ).
thf(f1145,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK6 @ ( sK0 @ sK2 ) ) ) )
| ~ spl8_2
| ~ spl8_10
| ~ spl8_22
| ~ spl8_38 ),
inference(forward_demodulation,[],[f1141,f129]) ).
thf(f1146,plain,
( ( $true
= ( p @ ( sK6 @ ( sK0 @ sK2 ) ) ) )
| ~ spl8_2
| ~ spl8_10
| ~ spl8_22
| ~ spl8_38 ),
inference(trivial_inequality_removal,[],[f1145]) ).
thf(f1150,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_10
| ~ spl8_17
| ~ spl8_22
| ~ spl8_38 ),
inference(forward_demodulation,[],[f1146,f1008]) ).
thf(f1151,plain,
( $false
| ~ spl8_2
| ~ spl8_10
| ~ spl8_17
| ~ spl8_22
| ~ spl8_38 ),
inference(trivial_inequality_removal,[],[f1150]) ).
thf(f1152,plain,
( ~ spl8_2
| ~ spl8_10
| ~ spl8_17
| ~ spl8_22
| ~ spl8_38 ),
inference(avatar_contradiction_clause,[],[f1151]) ).
thf(f1155,plain,
( spl8_10
| spl8_30 ),
inference(avatar_split_clause,[],[f70,f534,f197]) ).
thf(f1226,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( p @ ( sK7 @ ( sK0 @ sK3 ) ) ) )
| ~ spl8_10
| ~ spl8_14 ),
inference(constrained_superposition,[],[f198,f261]) ).
thf(f1230,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $true
= ( p @ ( sK7 @ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( mrel @ mactual @ sK3 ) )
| ~ spl8_10
| ~ spl8_22
| ~ spl8_36 ),
inference(constrained_superposition,[],[f1057,f198]) ).
thf(f1233,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $true
= ( p @ ( sK7 @ ( sK0 @ sK3 ) ) ) )
| ~ spl8_10
| ~ spl8_22
| ~ spl8_36 ),
inference(duplicate_literal_removal,[],[f1230]) ).
thf(f1234,plain,
( ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $true
= ( p @ ( sK7 @ ( sK0 @ sK3 ) ) ) )
| ~ spl8_10
| ~ spl8_22
| ~ spl8_36 ),
inference(trivial_inequality_removal,[],[f1233]) ).
thf(f1238,plain,
( ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( p @ ( sK7 @ ( sK0 @ sK3 ) ) ) )
| ~ spl8_10
| ~ spl8_14 ),
inference(trivial_inequality_removal,[],[f1226]) ).
thf(f1248,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK7 @ ( sK0 @ sK3 ) ) ) )
| ~ spl8_1
| ~ spl8_10
| ~ spl8_14 ),
inference(forward_demodulation,[],[f1238,f125]) ).
thf(f1249,plain,
( ( $false
= ( p @ ( sK7 @ ( sK0 @ sK3 ) ) ) )
| ~ spl8_1
| ~ spl8_10
| ~ spl8_14 ),
inference(trivial_inequality_removal,[],[f1248]) ).
thf(f1262,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK7 @ ( sK0 @ sK3 ) ) ) )
| ~ spl8_1
| ~ spl8_10
| ~ spl8_22
| ~ spl8_36 ),
inference(forward_demodulation,[],[f1234,f125]) ).
thf(f1263,plain,
( ( $true
= ( p @ ( sK7 @ ( sK0 @ sK3 ) ) ) )
| ~ spl8_1
| ~ spl8_10
| ~ spl8_22
| ~ spl8_36 ),
inference(trivial_inequality_removal,[],[f1262]) ).
thf(f1270,plain,
( ( $true = $false )
| ~ spl8_1
| ~ spl8_10
| ~ spl8_14
| ~ spl8_22
| ~ spl8_36 ),
inference(forward_demodulation,[],[f1263,f1249]) ).
thf(f1271,plain,
( $false
| ~ spl8_1
| ~ spl8_10
| ~ spl8_14
| ~ spl8_22
| ~ spl8_36 ),
inference(trivial_inequality_removal,[],[f1270]) ).
thf(f1272,plain,
( ~ spl8_1
| ~ spl8_10
| ~ spl8_14
| ~ spl8_22
| ~ spl8_36 ),
inference(avatar_contradiction_clause,[],[f1271]) ).
thf(f1292,plain,
( ! [X0: mworld] :
( ( $true != $true )
| ( $true
!= ( mrel @ mactual @ X0 ) )
| ( $true
= ( mrel @ sK3 @ X0 ) ) )
| ~ spl8_1 ),
inference(constrained_superposition,[],[f46,f125]) ).
thf(f1296,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ mactual @ X0 ) )
| ( $true
= ( mrel @ sK3 @ X0 ) ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f1292]) ).
thf(f1327,plain,
( ( $true != $true )
| ( $true
= ( mrel @ sK3 @ ( sK0 @ mactual ) ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl8_1
| ~ spl8_10 ),
inference(constrained_superposition,[],[f1296,f198]) ).
thf(f1328,plain,
( ( $true != $true )
| ( $true
= ( mrel @ sK3 @ ( sK1 @ mactual ) ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl8_1
| ~ spl8_12 ),
inference(constrained_superposition,[],[f1296,f204]) ).
thf(f1330,plain,
( ( $true != $true )
| ( $true
= ( mrel @ sK3 @ mactual ) )
| ~ spl8_1 ),
inference(constrained_superposition,[],[f1296,f45]) ).
thf(f1335,plain,
( ( $true
= ( mrel @ sK3 @ mactual ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f1330]) ).
thf(f1337,plain,
( ( $true
= ( mrel @ sK3 @ ( sK1 @ mactual ) ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl8_1
| ~ spl8_12 ),
inference(trivial_inequality_removal,[],[f1328]) ).
thf(f1338,plain,
( ( $true
= ( mrel @ sK3 @ ( sK0 @ mactual ) ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl8_1
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f1327]) ).
thf(f1340,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK3 @ ( sK1 @ mactual ) ) )
| ~ spl8_1
| ~ spl8_12 ),
inference(forward_demodulation,[],[f1337,f45]) ).
thf(f1341,plain,
( ( $true
= ( mrel @ sK3 @ ( sK1 @ mactual ) ) )
| ~ spl8_1
| ~ spl8_12 ),
inference(trivial_inequality_removal,[],[f1340]) ).
thf(f1342,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK3 @ ( sK0 @ mactual ) ) )
| ~ spl8_1
| ~ spl8_10 ),
inference(forward_demodulation,[],[f1338,f45]) ).
thf(f1343,plain,
( ( $true
= ( mrel @ sK3 @ ( sK0 @ mactual ) ) )
| ~ spl8_1
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f1342]) ).
thf(f1396,plain,
( ! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK4 @ X1 ) ) )
| ( $false
= ( mrel @ sK3 @ X1 ) ) )
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f96,f128]) ).
thf(f1426,plain,
( ! [X0: mworld] :
( ( $true != $true )
| ( $true
!= ( mrel @ sK3 @ X0 ) )
| ( $true
= ( mrel @ ( sK1 @ mactual ) @ X0 ) ) )
| ~ spl8_1
| ~ spl8_12 ),
inference(constrained_superposition,[],[f46,f1341]) ).
thf(f1427,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ sK3 @ X0 ) )
| ( $true
= ( mrel @ ( sK1 @ mactual ) @ X0 ) ) )
| ~ spl8_1
| ~ spl8_12 ),
inference(trivial_inequality_removal,[],[f1426]) ).
thf(f1429,plain,
( ! [X0: mworld] :
( ( $true != $true )
| ( $true
!= ( mrel @ sK3 @ X0 ) )
| ( $true
= ( mrel @ ( sK0 @ mactual ) @ X0 ) ) )
| ~ spl8_1
| ~ spl8_10 ),
inference(constrained_superposition,[],[f46,f1343]) ).
thf(f1432,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ sK3 @ X0 ) )
| ( $true
= ( mrel @ ( sK0 @ mactual ) @ X0 ) ) )
| ~ spl8_1
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f1429]) ).
thf(f1451,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK4 @ mactual ) ) )
| ~ spl8_1
| ~ spl8_5 ),
inference(constrained_superposition,[],[f1335,f139]) ).
thf(f1452,plain,
( ( $false
= ( p @ ( sK4 @ mactual ) ) )
| ~ spl8_1
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f1451]) ).
thf(f1779,plain,
( ( $true != $true )
| ( $true
= ( mrel @ sK3 @ ( sK4 @ mactual ) ) )
| ( $false
= ( mrel @ sK3 @ mactual ) )
| ~ spl8_1
| spl8_2 ),
inference(constrained_superposition,[],[f1296,f1396]) ).
thf(f1792,plain,
( ( $true
= ( mrel @ sK3 @ ( sK4 @ mactual ) ) )
| ( $false
= ( mrel @ sK3 @ mactual ) )
| ~ spl8_1
| spl8_2 ),
inference(trivial_inequality_removal,[],[f1779]) ).
thf(f1807,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK3 @ ( sK4 @ mactual ) ) )
| ~ spl8_1
| spl8_2 ),
inference(forward_demodulation,[],[f1792,f1335]) ).
thf(f1808,plain,
( ( $true
= ( mrel @ sK3 @ ( sK4 @ mactual ) ) )
| ~ spl8_1
| spl8_2 ),
inference(trivial_inequality_removal,[],[f1807]) ).
thf(f2024,plain,
( ( $true != $true )
| ( $true
= ( mrel @ ( sK1 @ mactual ) @ ( sK4 @ mactual ) ) )
| ~ spl8_1
| spl8_2
| ~ spl8_12 ),
inference(constrained_superposition,[],[f1427,f1808]) ).
thf(f2032,plain,
( ( $true
= ( mrel @ ( sK1 @ mactual ) @ ( sK4 @ mactual ) ) )
| ~ spl8_1
| spl8_2
| ~ spl8_12 ),
inference(trivial_inequality_removal,[],[f2024]) ).
thf(f2077,plain,
( ( $true != $true )
| ( $true
= ( mrel @ ( sK0 @ mactual ) @ ( sK4 @ mactual ) ) )
| ~ spl8_1
| spl8_2
| ~ spl8_10 ),
inference(constrained_superposition,[],[f1432,f1808]) ).
thf(f2085,plain,
( ( $true
= ( mrel @ ( sK0 @ mactual ) @ ( sK4 @ mactual ) ) )
| ~ spl8_1
| spl8_2
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f2077]) ).
thf(f2239,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ( $true
= ( p @ ( sK4 @ mactual ) ) )
| ~ spl8_1
| spl8_2
| ~ spl8_10
| ~ spl8_22 ),
inference(constrained_superposition,[],[f2085,f349]) ).
thf(f2244,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( $true
= ( p @ ( sK4 @ mactual ) ) )
| ~ spl8_1
| spl8_2
| ~ spl8_10
| ~ spl8_22 ),
inference(trivial_inequality_removal,[],[f2239]) ).
thf(f2247,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK4 @ mactual ) ) )
| ~ spl8_1
| spl8_2
| ~ spl8_10
| ~ spl8_22 ),
inference(forward_demodulation,[],[f2244,f45]) ).
thf(f2248,plain,
( ( $true
= ( p @ ( sK4 @ mactual ) ) )
| ~ spl8_1
| spl8_2
| ~ spl8_10
| ~ spl8_22 ),
inference(trivial_inequality_removal,[],[f2247]) ).
thf(f2252,plain,
( ( $true = $false )
| ~ spl8_1
| spl8_2
| ~ spl8_5
| ~ spl8_10
| ~ spl8_22 ),
inference(forward_demodulation,[],[f2248,f1452]) ).
thf(f2253,plain,
( $false
| ~ spl8_1
| spl8_2
| ~ spl8_5
| ~ spl8_10
| ~ spl8_22 ),
inference(trivial_inequality_removal,[],[f2252]) ).
thf(f2254,plain,
( ~ spl8_1
| spl8_2
| ~ spl8_5
| ~ spl8_10
| ~ spl8_22 ),
inference(avatar_contradiction_clause,[],[f2253]) ).
thf(f2562,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK4 @ mactual ) ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl8_1
| spl8_2
| ~ spl8_12
| ~ spl8_30 ),
inference(constrained_superposition,[],[f2032,f535]) ).
thf(f2567,plain,
( ( $true
= ( p @ ( sK4 @ mactual ) ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl8_1
| spl8_2
| ~ spl8_12
| ~ spl8_30 ),
inference(trivial_inequality_removal,[],[f2562]) ).
thf(f2570,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl8_1
| spl8_2
| ~ spl8_5
| ~ spl8_12
| ~ spl8_30 ),
inference(forward_demodulation,[],[f2567,f1452]) ).
thf(f2571,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl8_1
| spl8_2
| ~ spl8_5
| ~ spl8_12
| ~ spl8_30 ),
inference(trivial_inequality_removal,[],[f2570]) ).
thf(f2575,plain,
( ( $true = $false )
| ~ spl8_1
| spl8_2
| ~ spl8_5
| ~ spl8_12
| ~ spl8_30 ),
inference(forward_demodulation,[],[f2571,f45]) ).
thf(f2576,plain,
( $false
| ~ spl8_1
| spl8_2
| ~ spl8_5
| ~ spl8_12
| ~ spl8_30 ),
inference(trivial_inequality_removal,[],[f2575]) ).
thf(f2577,plain,
( ~ spl8_1
| spl8_2
| ~ spl8_5
| ~ spl8_12
| ~ spl8_30 ),
inference(avatar_contradiction_clause,[],[f2576]) ).
cnf(s20,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f130]) ).
cnf(s24,plain,
( spl8_2
| spl8_5 ),
inference(sat_conversion,[],[f140]) ).
cnf(s43,plain,
( spl8_10
| spl8_12 ),
inference(sat_conversion,[],[f205]) ).
cnf(s78,plain,
( spl8_14
| spl8_17 ),
inference(sat_conversion,[],[f271]) ).
cnf(s117,plain,
( spl8_12
| spl8_22 ),
inference(sat_conversion,[],[f350]) ).
cnf(s186,plain,
( spl8_1
| ~ spl8_2
| ~ spl8_10
| ~ spl8_22 ),
inference(sat_conversion,[],[f509]) ).
cnf(s197,plain,
( spl8_22
| spl8_30 ),
inference(sat_conversion,[],[f536]) ).
cnf(s227,plain,
( spl8_1
| ~ spl8_2
| ~ spl8_12
| ~ spl8_30 ),
inference(sat_conversion,[],[f625]) ).
cnf(s244,plain,
( spl8_36
| spl8_38 ),
inference(sat_conversion,[],[f652]) ).
cnf(s283,plain,
( spl8_14
| spl8_38 ),
inference(sat_conversion,[],[f727]) ).
cnf(s346,plain,
( ~ spl8_2
| ~ spl8_12
| ~ spl8_17
| ~ spl8_30
| ~ spl8_38 ),
inference(sat_conversion,[],[f889]) ).
cnf(s352,plain,
( spl8_17
| spl8_36 ),
inference(sat_conversion,[],[f890]) ).
cnf(s390,plain,
( ~ spl8_1
| ~ spl8_12
| ~ spl8_14
| ~ spl8_30
| ~ spl8_36 ),
inference(sat_conversion,[],[f986]) ).
cnf(s452,plain,
( ~ spl8_2
| ~ spl8_10
| ~ spl8_17
| ~ spl8_22
| ~ spl8_38 ),
inference(sat_conversion,[],[f1152]) ).
cnf(s459,plain,
( spl8_10
| spl8_30 ),
inference(sat_conversion,[],[f1155]) ).
cnf(s497,plain,
( ~ spl8_1
| ~ spl8_10
| ~ spl8_14
| ~ spl8_22
| ~ spl8_36 ),
inference(sat_conversion,[],[f1272]) ).
cnf(s854,plain,
( ~ spl8_1
| spl8_2
| ~ spl8_5
| ~ spl8_10
| ~ spl8_22 ),
inference(sat_conversion,[],[f2254]) ).
cnf(s1008,plain,
( ~ spl8_1
| spl8_2
| ~ spl8_5
| ~ spl8_12
| ~ spl8_30 ),
inference(sat_conversion,[],[f2577]) ).
cnf(s1010,plain,
( spl8_10
| spl8_1 ),
inference(rat,[],[s227,s43,s459,s20]) ).
cnf(s1011,plain,
( ~ spl8_10
| ~ spl8_2
| spl8_1 ),
inference(rat,[],[s227,s117,s197,s186]) ).
cnf(s1012,plain,
spl8_1,
inference(rat,[],[s1011,s1010,s20]) ).
cnf(s1014,plain,
( spl8_14
| spl8_10
| ~ spl8_2 ),
inference(rat,[],[s346,s78,s283,s459,s43]) ).
cnf(s1015,plain,
( spl8_10
| ~ spl8_2 ),
inference(rat,[],[s346,s244,s352,s390,s1014,s43,s459,s1012]) ).
cnf(s1016,plain,
( spl8_14
| ~ spl8_30
| ~ spl8_12
| ~ spl8_2 ),
inference(rat,[],[s346,s78,s283]) ).
cnf(s1017,plain,
( ~ spl8_30
| ~ spl8_12
| ~ spl8_2 ),
inference(rat,[],[s346,s244,s352,s390,s1016,s1012]) ).
cnf(s1018,plain,
( spl8_14
| ~ spl8_22
| ~ spl8_2 ),
inference(rat,[],[s452,s78,s283,s1015]) ).
cnf(s1019,plain,
( ~ spl8_22
| ~ spl8_2 ),
inference(rat,[],[s452,s244,s352,s497,s1018,s1015,s1012]) ).
cnf(s1020,plain,
~ spl8_2,
inference(rat,[],[s1017,s117,s197,s1019]) ).
cnf(s1022,plain,
spl8_5,
inference(rat,[],[s24,s1020]) ).
cnf(s1024,plain,
spl8_30,
inference(rat,[],[s854,s197,s459,s1012,s1020,s1022]) ).
cnf(s1025,plain,
~ spl8_12,
inference(rat,[],[s1008,s1022,s1020,s1012,s1024]) ).
cnf(s1028,plain,
spl8_22,
inference(rat,[],[s117,s1025]) ).
cnf(s1029,plain,
spl8_10,
inference(rat,[],[s43,s1025]) ).
cnf(s1030,plain,
$false,
inference(rat,[],[s854,s1022,s1020,s1012,s1028,s1029]) ).
thf(f2578,plain,
$false,
inference(avatar_sat_refutation,[],[s1030]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO893^11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n006.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 17:25:54 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.37 % (1049385)Will run a generic schedule for satisfiability detection.
% 0.17/0.37 % (1049391)% WARNING: option uhcvi not known.
% 0.17/0.37 % (1049396)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1461114796:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.37 % (1049394)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2959662910:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.37 % (1049390)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3969241337_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.37 % (1049393)dis+10_1_sil=32000:sp=arity:random_seed=575215138:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.37 % (1049392)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4065579844:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.37 % (1049391)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3262287513:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.37 % (1049394)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.17/0.37 % (1049391)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.17/0.37 % (1049395)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2978688536:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.37 % Exception at run slice level
% 0.17/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.37 % (1049391)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.17/0.37 % (1049404)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=246957898:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.17/0.37 % Exception at run slice level
% 0.17/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.37 % (1049396)Instruction limit reached!
% 0.17/0.37 % (1049396)------------------------------
% 0.17/0.37 % (1049396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.37 % (1049396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.37 % (1049396)CaDiCaL version: 2.1.3
% 0.17/0.37 % (1049396)Termination reason: Instruction limit
% 0.17/0.37 % (1049396)Termination phase: Saturation
% 0.17/0.37 % (1049396)Time elapsed: 0.051 s
% 0.17/0.37 % (1049396)Peak memory usage: 12 MB
% 0.17/0.37 % (1049396)Instructions burned: 161 (million)
% 0.17/0.37 % (1049406)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=31417848:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.37 % (1049393)Instruction limit reached!
% 0.17/0.37 % (1049393)------------------------------
% 0.17/0.37 % (1049393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.37 % (1049393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.37 % (1049393)CaDiCaL version: 2.1.3
% 0.17/0.37 % (1049393)Termination reason: Instruction limit
% 0.17/0.37 % (1049393)Termination phase: Saturation
% 0.17/0.37 % (1049393)Time elapsed: 0.055 s
% 0.17/0.37 % (1049393)Peak memory usage: 12 MB
% 0.17/0.37 % (1049393)Instructions burned: 103 (million)
% 0.17/0.37 % (1049407)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=3303869805:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.17/0.37 % (1049407)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.17/0.37 % (1049407)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.17/0.37 % (1049394)Instruction limit reached!
% 0.17/0.37 % (1049394)------------------------------
% 0.17/0.37 % (1049394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.37 % (1049394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.37 % (1049394)CaDiCaL version: 2.1.3
% 0.17/0.37 % (1049394)Termination reason: Instruction limit
% 0.17/0.37 % (1049394)Termination phase: Saturation
% 0.17/0.37 % (1049394)Time elapsed: 0.062 s
% 0.17/0.37 % (1049394)Peak memory usage: 12 MB
% 0.17/0.37 % (1049394)Instructions burned: 117 (million)
% 0.17/0.37 % (1049409)ott-21_1_sil=16000:fs=off:random_seed=3828776212:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.17/0.37 % (1049411)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4261732491:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.17/0.37 % (1049395)Instruction limit reached!
% 0.17/0.37 % (1049395)------------------------------
% 0.17/0.37 % (1049395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.37 % (1049395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.37 % (1049395)CaDiCaL version: 2.1.3
% 0.17/0.37 % (1049395)Termination reason: Instruction limit
% 0.17/0.37 % (1049395)Termination phase: Saturation
% 0.17/0.37 % (1049395)Time elapsed: 0.097 s
% 0.17/0.37 % (1049395)Peak memory usage: 12 MB
% 0.17/0.37 % (1049395)Instructions burned: 134 (million)
% 0.17/0.37 % (1049392) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1049385-1049392"...
% 0.17/0.37 % (1049406)Instruction limit reached!
% 0.17/0.37 % (1049406)------------------------------
% 0.17/0.37 % (1049406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.37 % (1049406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.37 % (1049406)CaDiCaL version: 2.1.3
% 0.17/0.37 % (1049406)Termination reason: Instruction limit
% 0.17/0.37 % (1049406)Termination phase: Saturation
% 0.17/0.37 % (1049406)Time elapsed: 0.060 s
% 0.17/0.37 % (1049406)Peak memory usage: 12 MB
% 0.17/0.37 % (1049406)Instructions burned: 132 (million)
% 0.17/0.37 % (1049392)...printing done.
% 0.17/0.37 % (1049392)Refutation found. Thanks to Tanya!
% 0.17/0.37 % SZS status Theorem for theBenchmark
% 0.17/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.37 % (1049392)------------------------------
% 0.17/0.37 % (1049392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.37 % (1049392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.37 % (1049392)CaDiCaL version: 2.1.3
% 0.17/0.37 % (1049392)Termination reason: Refutation
% 0.17/0.37 % (1049392)Time elapsed: 0.109 s
% 0.17/0.37 % (1049392)Peak memory usage: 13 MB
% 0.17/0.37 % (1049392)Instructions burned: 185 (million)
% 0.17/0.37 % (1049385)Success in time 0.149 s
% 0.17/0.37 % Vampire exiting
%------------------------------------------------------------------------------