%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO048^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:48:48 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : Refutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 18
% Syntax : Number of formulae : 197 ( 56 unt; 0 typ; 9 def)
% Number of atoms : 1974 ( 306 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 2935 ( 710 ~; 610 |; 0 &;1458 @)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 192 ( 192 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 61 usr; 16 con; 0-4 aty)
% ( 148 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 421 ( 0 sgn 58 !; 1 ?; 421 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_49,type,
sK2: $i > $o ).
thf(func_def_50,type,
sK3: $i > $o ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f11,axiom,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mequiv @ ( mbox @ X0 @ ( mand @ X1 @ X2 ) ) @ ( mand @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mequiv @ ( mbox @ X0 @ ( mand @ X1 @ X2 ) ) @ ( mand @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f36,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f37,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f39,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f40,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f41,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f43,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f47,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f48,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f54,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f55,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f77,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f78,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f85,plain,
~ ! [X0: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mequiv @ ( mbox @ X0 @ ( mand @ X1 @ X2 ) ) @ ( mand @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f86,plain,
~ ! [X0: $i > $i > $o] :
( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mequiv @ ( mbox @ X0 @ ( mand @ Y0 @ Y1 ) ) @ ( mand @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mequiv @ ( mbox @ X0 @ ( mand @ Y0 @ Y1 ) ) @ ( mand @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X0 @ Y1 ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f86]) ).
thf(f88,plain,
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mequiv @ ( mbox @ sK0 @ ( mand @ Y0 @ Y1 ) ) @ ( mand @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK0 @ Y1 ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f91,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f92,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f93,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f94,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f96,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f99,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f104,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f116,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f120,plain,
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mequiv @ ( mbox @ sK0 @ ( mand @ Y0 @ Y1 ) ) @ ( mand @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f123,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f93,f91,f92,f91,f91]) ).
thf(f124,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f94,f92,f91]) ).
thf(f126,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f96,f123,f124,f124]) ).
thf(f132,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: ( $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ ( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y5 ) ) )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y3
@ Y2 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ sK0
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ sK0
@ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f120,f116,f99,f99,f126,f104,f123,f123,f104,f104]) ).
thf(f133,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ~ ( ~ ( Y1 @ Y3 )
| ~ ( Y2 @ Y3 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ~ ( ~ ( Y1 @ Y3 )
| ~ ( Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ~ ( ~ ( Y1 @ Y3 )
| ~ ( Y2 @ Y3 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ~ ( ~ ( Y1 @ Y3 )
| ~ ( Y2 @ Y3 ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f133]) ).
thf(f135,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ~ ( ~ ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ~ ( ~ ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ~ ( ~ ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK1 @ Y2 )
| ~ ( ~ ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ~ ( ~ ( sK2 @ Y1 )
| ~ ( Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ~ ( ~ ( sK2 @ Y1 )
| ~ ( Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
( $false
= ( ^ [Y0: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ~ ( ~ ( sK2 @ Y1 )
| ~ ( Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK1 @ Y1 )
| ~ ( ~ ( sK2 @ Y1 )
| ~ ( Y0 @ Y1 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( $false
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ( $true
= ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f142]) ).
thf(f145,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f149,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f153,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f154,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( sK0 @ sK1 @ X1 )
| ( sK2 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 )
| ~ ( ~ ( sK2 @ X2 )
| ~ ( sK3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK2 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 )
| ~ ( ~ ( sK2 @ X2 )
| ~ ( sK3 @ X2 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK2 @ X1 ) )
| ( $true
= ( ~ ( ~ ( sK2 @ X2 )
| ~ ( sK3 @ X2 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK2 @ X1 ) )
| ( $false
= ( ~ ( sK2 @ X2 )
| ~ ( sK3 @ X2 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK2 @ X1 ) )
| ( $false
= ( ~ ( sK2 @ X2 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK2 @ X1 ) )
| ( $true
= ( sK2 @ X2 ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK2 @ X1 ) )
| ( $true
= ( sK2 @ X2 ) )
| ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK2 @ X1 ) )
| ( $true
= ( sK2 @ X2 ) )
| ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f189,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f190,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f193,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f194,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( sK0 @ sK1 @ X1 )
| ( sK3 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 )
| ~ ( ~ ( sK2 @ X2 )
| ~ ( sK3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 )
| ~ ( ~ ( sK2 @ X2 )
| ~ ( sK3 @ X2 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( ~ ( ~ ( sK2 @ X2 )
| ~ ( sK3 @ X2 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $false
= ( ~ ( sK2 @ X2 )
| ~ ( sK3 @ X2 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $false
= ( ~ ( sK3 @ X2 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f229,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
@ sK8 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f230,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
@ sK8 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
@ sK8 ) )
| ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f230]) ).
thf(f260,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
@ sK8 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f231]) ).
thf(f261,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
@ sK8 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f262,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
@ sK8 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f261]) ).
thf(f263,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) )
@ sK9 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f262]) ).
thf(f264,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) )
@ sK9 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f263]) ).
thf(f265,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ~ ( sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK3 @ Y0 ) )
@ sK9 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ( sK2 @ Y0 ) )
@ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f264]) ).
thf(f266,plain,
( ( $false
= ( ~ ( sK0 @ sK1 @ sK8 )
| ~ ( ~ ( sK2 @ sK8 )
| ~ ( sK3 @ sK8 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK9 )
| ( sK3 @ sK9 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 )
| ( sK2 @ sK10 ) ) ) ),
inference(beta-eta_normalization,[],[f265]) ).
thf(f267,plain,
( ( $false
= ( ~ ( ~ ( sK2 @ sK8 )
| ~ ( sK3 @ sK8 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK9 )
| ( sK3 @ sK9 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 )
| ( sK2 @ sK10 ) ) ) ),
inference(or_proxy_clausification,[],[f266]) ).
thf(f268,plain,
( ( $false
= ( ~ ( sK0 @ sK1 @ sK8 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK9 )
| ( sK3 @ sK9 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 )
| ( sK2 @ sK10 ) ) ) ),
inference(or_proxy_clausification,[],[f266]) ).
thf(f269,plain,
( ( $true
= ( sK0 @ sK1 @ sK8 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK9 )
| ( sK3 @ sK9 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 )
| ( sK2 @ sK10 ) ) ) ),
inference(not_proxy_clausification,[],[f268]) ).
thf(f270,plain,
( ( $true
= ( sK0 @ sK1 @ sK8 ) )
| ( $false
= ( sK3 @ sK9 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 )
| ( sK2 @ sK10 ) ) ) ),
inference(or_proxy_clausification,[],[f269]) ).
thf(f271,plain,
( ( $true
= ( sK0 @ sK1 @ sK8 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK9 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 )
| ( sK2 @ sK10 ) ) ) ),
inference(or_proxy_clausification,[],[f269]) ).
thf(f272,plain,
( ( $true
= ( sK0 @ sK1 @ sK8 ) )
| ( $true
= ( sK0 @ sK1 @ sK9 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 )
| ( sK2 @ sK10 ) ) ) ),
inference(not_proxy_clausification,[],[f271]) ).
thf(f273,plain,
( ( $true
= ( sK0 @ sK1 @ sK8 ) )
| ( $true
= ( sK0 @ sK1 @ sK9 ) )
| ( $false
= ( sK2 @ sK10 ) ) ),
inference(or_proxy_clausification,[],[f272]) ).
thf(f274,plain,
( ( $true
= ( sK0 @ sK1 @ sK8 ) )
| ( $true
= ( sK0 @ sK1 @ sK9 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 ) ) ) ),
inference(or_proxy_clausification,[],[f272]) ).
thf(f275,plain,
( ( $true
= ( sK0 @ sK1 @ sK8 ) )
| ( $true
= ( sK0 @ sK1 @ sK9 ) )
| ( $true
= ( sK0 @ sK1 @ sK10 ) ) ),
inference(not_proxy_clausification,[],[f274]) ).
thf(f276,plain,
( ( $true
= ( sK0 @ sK1 @ sK8 ) )
| ( $false
= ( sK3 @ sK9 ) )
| ( $false
= ( sK2 @ sK10 ) ) ),
inference(or_proxy_clausification,[],[f270]) ).
thf(f277,plain,
( ( $true
= ( sK0 @ sK1 @ sK8 ) )
| ( $false
= ( sK3 @ sK9 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 ) ) ) ),
inference(or_proxy_clausification,[],[f270]) ).
thf(f278,plain,
( ( $true
= ( sK0 @ sK1 @ sK8 ) )
| ( $false
= ( sK3 @ sK9 ) )
| ( $true
= ( sK0 @ sK1 @ sK10 ) ) ),
inference(not_proxy_clausification,[],[f277]) ).
thf(f279,plain,
( ( $true
= ( ~ ( sK2 @ sK8 )
| ~ ( sK3 @ sK8 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK9 )
| ( sK3 @ sK9 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 )
| ( sK2 @ sK10 ) ) ) ),
inference(not_proxy_clausification,[],[f267]) ).
thf(f280,plain,
( ( $true
= ( ~ ( sK3 @ sK8 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK9 )
| ( sK3 @ sK9 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 )
| ( sK2 @ sK10 ) ) )
| ( $true
= ( ~ ( sK2 @ sK8 ) ) ) ),
inference(or_proxy_clausification,[],[f279]) ).
thf(f281,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK9 )
| ( sK3 @ sK9 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 )
| ( sK2 @ sK10 ) ) )
| ( $true
= ( ~ ( sK2 @ sK8 ) ) ) ),
inference(not_proxy_clausification,[],[f280]) ).
thf(f282,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $false
= ( sK3 @ sK9 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 )
| ( sK2 @ sK10 ) ) )
| ( $true
= ( ~ ( sK2 @ sK8 ) ) ) ),
inference(or_proxy_clausification,[],[f281]) ).
thf(f283,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK9 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 )
| ( sK2 @ sK10 ) ) )
| ( $true
= ( ~ ( sK2 @ sK8 ) ) ) ),
inference(or_proxy_clausification,[],[f281]) ).
thf(f284,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK1 @ sK9 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 )
| ( sK2 @ sK10 ) ) )
| ( $true
= ( ~ ( sK2 @ sK8 ) ) ) ),
inference(not_proxy_clausification,[],[f283]) ).
thf(f285,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK1 @ sK9 ) )
| ( $false
= ( sK2 @ sK10 ) )
| ( $true
= ( ~ ( sK2 @ sK8 ) ) ) ),
inference(or_proxy_clausification,[],[f284]) ).
thf(f286,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK1 @ sK9 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 ) ) )
| ( $true
= ( ~ ( sK2 @ sK8 ) ) ) ),
inference(or_proxy_clausification,[],[f284]) ).
thf(f287,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK1 @ sK9 ) )
| ( $true
= ( sK0 @ sK1 @ sK10 ) )
| ( $true
= ( ~ ( sK2 @ sK8 ) ) ) ),
inference(not_proxy_clausification,[],[f286]) ).
thf(f288,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK1 @ sK9 ) )
| ( $true
= ( sK0 @ sK1 @ sK10 ) )
| ( $false
= ( sK2 @ sK8 ) ) ),
inference(not_proxy_clausification,[],[f287]) ).
thf(f289,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK1 @ sK9 ) )
| ( $false
= ( sK2 @ sK10 ) )
| ( $false
= ( sK2 @ sK8 ) ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f290,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $false
= ( sK3 @ sK9 ) )
| ( $false
= ( sK2 @ sK10 ) )
| ( $true
= ( ~ ( sK2 @ sK8 ) ) ) ),
inference(or_proxy_clausification,[],[f282]) ).
thf(f291,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $false
= ( sK3 @ sK9 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK10 ) ) )
| ( $true
= ( ~ ( sK2 @ sK8 ) ) ) ),
inference(or_proxy_clausification,[],[f282]) ).
thf(f292,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $false
= ( sK3 @ sK9 ) )
| ( $true
= ( sK0 @ sK1 @ sK10 ) )
| ( $true
= ( ~ ( sK2 @ sK8 ) ) ) ),
inference(not_proxy_clausification,[],[f291]) ).
thf(f293,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $false
= ( sK3 @ sK9 ) )
| ( $true
= ( sK0 @ sK1 @ sK10 ) )
| ( $false
= ( sK2 @ sK8 ) ) ),
inference(not_proxy_clausification,[],[f292]) ).
thf(f294,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ( $false
= ( sK3 @ sK9 ) )
| ( $false
= ( sK2 @ sK10 ) )
| ( $false
= ( sK2 @ sK8 ) ) ),
inference(not_proxy_clausification,[],[f290]) ).
thf(f296,definition,
( spl11_1
<=> ! [X2: $i] :
( ( $true
= ( sK2 @ X2 ) )
| ( $false
= ( sK0 @ sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
thf(f297,plain,
( ! [X2: $i] :
( ( $false
= ( sK0 @ sK1 @ X2 ) )
| ( $true
= ( sK2 @ X2 ) ) )
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f296]) ).
thf(f298,plain,
( spl11_1
| spl11_1 ),
inference(avatar_split_clause,[],[f164,f296,f296]) ).
thf(f300,definition,
( spl11_2
<=> ! [X2: $i] :
( ( $true
= ( sK3 @ X2 ) )
| ( $false
= ( sK0 @ sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f301,plain,
( ! [X2: $i] :
( ( $false
= ( sK0 @ sK1 @ X2 ) )
| ( $true
= ( sK3 @ X2 ) ) )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f300]) ).
thf(f324,plain,
( spl11_2
| spl11_2 ),
inference(avatar_split_clause,[],[f207,f300,f300]) ).
thf(f346,definition,
( spl11_11
<=> ( $true
= ( sK0 @ sK1 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
thf(f348,plain,
( ( $true
= ( sK0 @ sK1 @ sK8 ) )
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f346]) ).
thf(f352,definition,
( spl11_12
<=> ( $false
= ( sK2 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
thf(f354,plain,
( ( $false
= ( sK2 @ sK8 ) )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f352]) ).
thf(f356,definition,
( spl11_13
<=> ( $false
= ( sK3 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition]) ).
thf(f358,plain,
( ( $false
= ( sK3 @ sK8 ) )
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f356]) ).
thf(f362,definition,
( spl11_14
<=> ( $true
= ( sK0 @ sK1 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
thf(f364,plain,
( ( $true
= ( sK0 @ sK1 @ sK10 ) )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f362]) ).
thf(f366,definition,
( spl11_15
<=> ( $true
= ( sK0 @ sK1 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
thf(f368,plain,
( ( $true
= ( sK0 @ sK1 @ sK9 ) )
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f366]) ).
thf(f369,plain,
( spl11_14
| spl11_15
| spl11_11 ),
inference(avatar_split_clause,[],[f275,f346,f366,f362]) ).
thf(f371,definition,
( spl11_16
<=> ( $false
= ( sK2 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_16])],[avatar_definition]) ).
thf(f373,plain,
( ( $false
= ( sK2 @ sK10 ) )
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f371]) ).
thf(f374,plain,
( spl11_16
| spl11_15
| spl11_11 ),
inference(avatar_split_clause,[],[f273,f346,f366,f371]) ).
thf(f376,definition,
( spl11_17
<=> ( $false
= ( sK3 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_17])],[avatar_definition]) ).
thf(f378,plain,
( ( $false
= ( sK3 @ sK9 ) )
| ~ spl11_17 ),
inference(avatar_component_clause,[],[f376]) ).
thf(f379,plain,
( spl11_14
| spl11_17
| spl11_11 ),
inference(avatar_split_clause,[],[f278,f346,f376,f362]) ).
thf(f380,plain,
( spl11_16
| spl11_17
| spl11_11 ),
inference(avatar_split_clause,[],[f276,f346,f376,f371]) ).
thf(f381,plain,
( spl11_12
| spl11_14
| spl11_15
| spl11_13 ),
inference(avatar_split_clause,[],[f288,f356,f366,f362,f352]) ).
thf(f382,plain,
( spl11_12
| spl11_16
| spl11_15
| spl11_13 ),
inference(avatar_split_clause,[],[f289,f356,f366,f371,f352]) ).
thf(f383,plain,
( spl11_12
| spl11_14
| spl11_17
| spl11_13 ),
inference(avatar_split_clause,[],[f293,f356,f376,f362,f352]) ).
thf(f384,plain,
( spl11_12
| spl11_16
| spl11_17
| spl11_13 ),
inference(avatar_split_clause,[],[f294,f356,f376,f371,f352]) ).
thf(f394,plain,
( ( $true = $false )
| ( $true
= ( sK2 @ sK8 ) )
| ~ spl11_1
| ~ spl11_11 ),
inference(constrained_superposition,[],[f297,f348]) ).
thf(f399,plain,
( ( $true
= ( sK2 @ sK8 ) )
| ~ spl11_1
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f394]) ).
thf(f403,plain,
( ( $true = $false )
| ~ spl11_1
| ~ spl11_11
| ~ spl11_12 ),
inference(forward_demodulation,[],[f399,f354]) ).
thf(f404,plain,
( $false
| ~ spl11_1
| ~ spl11_11
| ~ spl11_12 ),
inference(trivial_inequality_removal,[],[f403]) ).
thf(f405,plain,
( ~ spl11_1
| ~ spl11_11
| ~ spl11_12 ),
inference(avatar_contradiction_clause,[],[f404]) ).
thf(f409,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK8 ) )
| ~ spl11_2
| ~ spl11_11 ),
inference(constrained_superposition,[],[f301,f348]) ).
thf(f414,plain,
( ( $true
= ( sK3 @ sK8 ) )
| ~ spl11_2
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f409]) ).
thf(f418,plain,
( ( $true = $false )
| ~ spl11_2
| ~ spl11_11
| ~ spl11_13 ),
inference(forward_demodulation,[],[f414,f358]) ).
thf(f419,plain,
( $false
| ~ spl11_2
| ~ spl11_11
| ~ spl11_13 ),
inference(trivial_inequality_removal,[],[f418]) ).
thf(f420,plain,
( ~ spl11_2
| ~ spl11_11
| ~ spl11_13 ),
inference(avatar_contradiction_clause,[],[f419]) ).
thf(f427,plain,
( ( $true = $false )
| ( $true
= ( sK2 @ sK10 ) )
| ~ spl11_1
| ~ spl11_14 ),
inference(constrained_superposition,[],[f364,f297]) ).
thf(f432,plain,
( ( $true
= ( sK2 @ sK10 ) )
| ~ spl11_1
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f427]) ).
thf(f437,plain,
( ( $true = $false )
| ~ spl11_1
| ~ spl11_14
| ~ spl11_16 ),
inference(forward_demodulation,[],[f432,f373]) ).
thf(f438,plain,
( $false
| ~ spl11_1
| ~ spl11_14
| ~ spl11_16 ),
inference(trivial_inequality_removal,[],[f437]) ).
thf(f439,plain,
( ~ spl11_1
| ~ spl11_14
| ~ spl11_16 ),
inference(avatar_contradiction_clause,[],[f438]) ).
thf(f446,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK9 ) )
| ~ spl11_2
| ~ spl11_15 ),
inference(constrained_superposition,[],[f368,f301]) ).
thf(f453,plain,
( ( $true
= ( sK3 @ sK9 ) )
| ~ spl11_2
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f446]) ).
thf(f457,plain,
( ( $true = $false )
| ~ spl11_2
| ~ spl11_15
| ~ spl11_17 ),
inference(forward_demodulation,[],[f453,f378]) ).
thf(f458,plain,
( $false
| ~ spl11_2
| ~ spl11_15
| ~ spl11_17 ),
inference(trivial_inequality_removal,[],[f457]) ).
thf(f459,plain,
( ~ spl11_2
| ~ spl11_15
| ~ spl11_17 ),
inference(avatar_contradiction_clause,[],[f458]) ).
cnf(s1,plain,
( spl11_1
| spl11_1 ),
inference(sat_conversion,[],[f298]) ).
cnf(s2,plain,
spl11_1,
inference(rat,[],[s1]) ).
cnf(s9,plain,
( spl11_2
| spl11_2 ),
inference(sat_conversion,[],[f324]) ).
cnf(s10,plain,
spl11_2,
inference(rat,[],[s9]) ).
cnf(s19,plain,
( spl11_11
| spl11_14
| spl11_15 ),
inference(sat_conversion,[],[f369]) ).
cnf(s20,plain,
( spl11_11
| spl11_15
| spl11_16 ),
inference(sat_conversion,[],[f374]) ).
cnf(s21,plain,
( spl11_11
| spl11_14
| spl11_17 ),
inference(sat_conversion,[],[f379]) ).
cnf(s22,plain,
( spl11_11
| spl11_16
| spl11_17 ),
inference(sat_conversion,[],[f380]) ).
cnf(s23,plain,
( spl11_12
| spl11_13
| spl11_14
| spl11_15 ),
inference(sat_conversion,[],[f381]) ).
cnf(s24,plain,
( spl11_12
| spl11_13
| spl11_15
| spl11_16 ),
inference(sat_conversion,[],[f382]) ).
cnf(s25,plain,
( spl11_12
| spl11_13
| spl11_14
| spl11_17 ),
inference(sat_conversion,[],[f383]) ).
cnf(s26,plain,
( spl11_12
| spl11_13
| spl11_16
| spl11_17 ),
inference(sat_conversion,[],[f384]) ).
cnf(s28,plain,
( ~ spl11_1
| ~ spl11_11
| ~ spl11_12 ),
inference(sat_conversion,[],[f405]) ).
cnf(s30,plain,
( ~ spl11_2
| ~ spl11_11
| ~ spl11_13 ),
inference(sat_conversion,[],[f420]) ).
cnf(s32,plain,
( ~ spl11_1
| ~ spl11_14
| ~ spl11_16 ),
inference(sat_conversion,[],[f439]) ).
cnf(s34,plain,
( ~ spl11_2
| ~ spl11_15
| ~ spl11_17 ),
inference(sat_conversion,[],[f459]) ).
cnf(s35,plain,
( spl11_14
| spl11_11 ),
inference(rat,[],[s34,s21,s19,s10]) ).
cnf(s36,plain,
( spl11_16
| spl11_11 ),
inference(rat,[],[s34,s20,s22,s10]) ).
cnf(s37,plain,
spl11_11,
inference(rat,[],[s36,s32,s35,s2]) ).
cnf(s38,plain,
~ spl11_13,
inference(rat,[],[s30,s10,s37]) ).
cnf(s39,plain,
~ spl11_12,
inference(rat,[],[s28,s2,s37]) ).
cnf(s40,plain,
spl11_17,
inference(rat,[],[s32,s26,s25,s2,s39,s38]) ).
cnf(s41,plain,
~ spl11_15,
inference(rat,[],[s34,s10,s40]) ).
cnf(s42,plain,
spl11_16,
inference(rat,[],[s24,s39,s38,s41]) ).
cnf(s43,plain,
spl11_14,
inference(rat,[],[s23,s38,s39,s41]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s32,s2,s42,s43]) ).
thf(f460,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO048^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:28:04 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.08/0.27 % (3737482)Will run a generic schedule for satisfiability detection.
% 0.08/0.27 % (3737494)dis+10_1_sil=32000:sp=arity:random_seed=2778551547:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.27 % (3737492)% WARNING: option uhcvi not known.
% 0.08/0.27 % (3737494) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3737482-3737494"...
% 0.08/0.27 % (3737491)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1150530709_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.27 % (3737492)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2297237215:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.27 % (3737495)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3543100167:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.27 % (3737493)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4261875131:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.27 % (3737492)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.27 % (3737495)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.27 % (3737494)...printing done.
% 0.08/0.27 % Exception at run slice level
% 0.08/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.27 % (3737492)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.27 % (3737497)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3772518651:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.27 % (3737494)Refutation found. Thanks to Tanya!
% 0.08/0.27 % SZS status Theorem for theBenchmark
% 0.08/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.34/0.27 % (3737494)------------------------------
% 0.34/0.27 % (3737494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.27 % (3737494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.27 % (3737494)CaDiCaL version: 2.1.3
% 0.34/0.27 % (3737494)Termination reason: Refutation
% 0.34/0.27 % (3737494)Time elapsed: 0.009 s
% 0.34/0.27 % (3737494)Peak memory usage: 13 MB
% 0.34/0.27 % (3737494)Instructions burned: 35 (million)
% 0.34/0.27 % (3737482)Success in time 0.034 s
% 0.34/0.27 % Vampire exiting
%------------------------------------------------------------------------------