%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL705^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:15:06 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 19
% Syntax : Number of formulae : 167 ( 66 unt; 0 typ; 8 def)
% Number of atoms : 1143 ( 225 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1611 ( 316 ~; 270 |; 12 &; 897 @)
% ( 8 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 183 ( 183 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 60 usr; 16 con; 0-4 aty)
% ( 85 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 358 ( 0 sgn 67 !; 3 ?; 358 :)
% 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_48,type,
sK1: $i > $i ).
thf(func_def_50,type,
sK3: $i > $o ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f17,axiom,
( mdia
= ( ^ [X0: $i > $i > $o,X1: $i > $o] : ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mdia) ).
thf(f24,axiom,
( mfunctional
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] :
( ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X2 = X3 ) )
& ( X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mfunctional) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( mfunctional @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mequiv @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( mfunctional @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mequiv @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ X1 ) ) ) ) ),
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(f56,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f69,plain,
( mfunctional
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] :
( ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X2 = X3 ) )
& ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f70,plain,
( mfunctional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
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] :
( ( mfunctional @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mequiv @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f86,plain,
~ ! [X0: $i > $i > $o] :
( ( ( mfunctional @ X0 )
= $true )
=> ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mequiv @ ( mdia @ X0 @ Y0 ) @ ( mbox @ X0 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mequiv @ ( mdia @ X0 @ Y0 ) @ ( mbox @ X0 @ Y0 ) ) ) ) )
& ( ( mfunctional @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f86]) ).
thf(f88,plain,
( ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mequiv @ ( mdia @ sK0 @ Y0 ) @ ( mbox @ sK0 @ Y0 ) ) ) ) )
& ( $true
= ( mfunctional @ sK0 ) ) ),
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(f105,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f112,plain,
( mfunctional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f116,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f120,plain,
( $true
= ( mfunctional @ sK0 ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f121,plain,
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mequiv @ ( mdia @ sK0 @ Y0 ) @ ( mbox @ sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f124,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(f125,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(f127,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,f124,f125,f125]) ).
thf(f132,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f105,f91,f104,f91]) ).
thf(f133,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,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ Y1
@ Y2 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ Y2
@ Y1 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y4 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f121,f116,f99,f127,f132,f104]) ).
thf(f134,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f120,f112]) ).
thf(f135,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X1: $i] :
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ X1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ X1 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ ( sK1 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X1: $i] :
( $true
= ( ( sK0 @ X1 @ ( sK1 @ X1 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( ( sK1 @ X1 )
= Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( ( sK1 @ X1 )
= Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X1: $i] :
( $true
= ( sK0 @ X1 @ ( sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f139]) ).
thf(f142,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( ( sK1 @ X1 )
= Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f140]) ).
thf(f143,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK0 @ X1 @ X2 )
=> ( ( sK1 @ X1 )
= X2 ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( ( sK1 @ X1 )
= X2 ) ) ),
inference(imp_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X2 ) )
| ( ( sK1 @ X1 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f147,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK2 @ Y1 )
| ~ ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK2 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK2 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK2 @ Y1 )
| ~ ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
( $false
= ( ^ [Y0: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK2 @ Y1 )
| ~ ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK2 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK2 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK2 @ Y1 )
| ~ ( Y0 @ Y1 ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( $false
= ( ~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f156,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f161,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true
= ( ~ ( sK0 @ sK2 @ X1 )
| ( sK3 @ X1 ) ) )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK4 )
| ~ ( sK3 @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK4 )
| ~ ( sK3 @ sK4 ) ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $false
= ( ~ ( sK3 @ sK4 ) ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK4 ) ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f171,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( sK3 @ sK4 ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f159]) ).
thf(f173,plain,
! [X1: $i] :
( ( $true
= ( ~ ( sK0 @ sK2 @ X1 )
| ( sK3 @ X1 ) ) )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK5 )
| ( sK3 @ sK5 ) ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK5 )
| ( sK3 @ sK5 ) ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $false
= ( sK3 @ sK5 ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK5 ) ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $false
= ( sK3 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f180,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f197,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f198,plain,
! [X1: $i] :
( ( $true
= ( ~ ( sK0 @ sK2 @ X1 )
| ~ ( sK3 @ X1 ) ) )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK7 )
| ( sK3 @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( ~ ( sK3 @ X1 ) ) )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK7 )
| ( sK3 @ sK7 ) ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK7 )
| ( sK3 @ sK7 ) ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( $false
= ( sK3 @ sK7 ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( $false
= ( ~ ( sK0 @ sK2 @ sK7 ) ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f203,plain,
! [X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( $true
= ( sK0 @ sK2 @ sK7 ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( $true
= ( sK0 @ sK2 @ sK7 ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( $false
= ( sK3 @ sK7 ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f207,definition,
( spl8_1
<=> ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f209,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f207]) ).
thf(f211,definition,
( spl8_2
<=> ! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f212,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $true
= ( sK3 @ X1 ) ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f213,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f169,f211,f207]) ).
thf(f215,definition,
( spl8_3
<=> ( $true
= ( sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f217,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f215]) ).
thf(f218,plain,
( spl8_3
| spl8_2 ),
inference(avatar_split_clause,[],[f171,f211,f215]) ).
thf(f220,definition,
( spl8_4
<=> ( $true
= ( sK0 @ sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f222,plain,
( ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f220]) ).
thf(f223,plain,
( spl8_4
| spl8_2 ),
inference(avatar_split_clause,[],[f178,f211,f220]) ).
thf(f225,definition,
( spl8_5
<=> ( $false
= ( sK3 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f227,plain,
( ( $false
= ( sK3 @ sK5 ) )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f225]) ).
thf(f228,plain,
( spl8_5
| spl8_2 ),
inference(avatar_split_clause,[],[f179,f211,f225]) ).
thf(f234,definition,
( spl8_7
<=> ! [X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
thf(f235,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f234]) ).
thf(f243,definition,
( spl8_9
<=> ( $true
= ( sK0 @ sK2 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
thf(f245,plain,
( ( $true
= ( sK0 @ sK2 @ sK7 ) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f246,plain,
( spl8_9
| spl8_7 ),
inference(avatar_split_clause,[],[f204,f234,f243]) ).
thf(f248,definition,
( spl8_10
<=> ( $false
= ( sK3 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
thf(f250,plain,
( ( $false
= ( sK3 @ sK7 ) )
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f251,plain,
( spl8_10
| spl8_7 ),
inference(avatar_split_clause,[],[f205,f234,f248]) ).
thf(f263,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ ( sK1 @ sK2 ) ) )
| ~ spl8_2 ),
inference(constrained_superposition,[],[f141,f212]) ).
thf(f264,plain,
( ( $true
= ( sK3 @ ( sK1 @ sK2 ) ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f263]) ).
thf(f269,plain,
( ( $true = $false )
| ( $false
= ( sK3 @ ( sK1 @ sK2 ) ) )
| ~ spl8_7 ),
inference(constrained_superposition,[],[f141,f235]) ).
thf(f270,plain,
( ( $false
= ( sK3 @ ( sK1 @ sK2 ) ) )
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f273,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_7 ),
inference(constrained_superposition,[],[f270,f264]) ).
thf(f279,plain,
( $false
| ~ spl8_2
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f273]) ).
thf(f280,plain,
( ~ spl8_2
| ~ spl8_7 ),
inference(avatar_contradiction_clause,[],[f279]) ).
thf(f292,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK7 ) )
| ~ spl8_2
| ~ spl8_9 ),
inference(constrained_superposition,[],[f245,f212]) ).
thf(f297,plain,
( ( $true
= ( sK3 @ sK7 ) )
| ~ spl8_2
| ~ spl8_9 ),
inference(trivial_inequality_removal,[],[f292]) ).
thf(f303,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_9
| ~ spl8_10 ),
inference(forward_demodulation,[],[f297,f250]) ).
thf(f304,plain,
( $false
| ~ spl8_2
| ~ spl8_9
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f303]) ).
thf(f305,plain,
( ~ spl8_2
| ~ spl8_9
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f304]) ).
thf(f312,plain,
( ( $true = $false )
| ( sK4
= ( sK1 @ sK2 ) )
| ~ spl8_1 ),
inference(constrained_superposition,[],[f145,f209]) ).
thf(f313,plain,
( ( sK4
= ( sK1 @ sK2 ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f312]) ).
thf(f317,plain,
( ( $true = $false )
| ( sK5
= ( sK1 @ sK2 ) )
| ~ spl8_4 ),
inference(constrained_superposition,[],[f145,f222]) ).
thf(f318,plain,
( ( sK5
= ( sK1 @ sK2 ) )
| ~ spl8_4 ),
inference(trivial_inequality_removal,[],[f317]) ).
thf(f320,plain,
( ( sK4 = sK5 )
| ~ spl8_1
| ~ spl8_4 ),
inference(forward_demodulation,[],[f318,f313]) ).
thf(f323,plain,
( ( $false
= ( sK3 @ sK4 ) )
| ~ spl8_1
| ~ spl8_4
| ~ spl8_5 ),
inference(constrained_superposition,[],[f227,f320]) ).
thf(f352,plain,
( ( $true = $false )
| ~ spl8_1
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(constrained_superposition,[],[f323,f217]) ).
thf(f358,plain,
( $false
| ~ spl8_1
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f352]) ).
thf(f359,plain,
( ~ spl8_1
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(avatar_contradiction_clause,[],[f358]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f213]) ).
cnf(s2,plain,
( spl8_2
| spl8_3 ),
inference(sat_conversion,[],[f218]) ).
cnf(s3,plain,
( spl8_2
| spl8_4 ),
inference(sat_conversion,[],[f223]) ).
cnf(s4,plain,
( spl8_2
| spl8_5 ),
inference(sat_conversion,[],[f228]) ).
cnf(s7,plain,
( spl8_7
| spl8_9 ),
inference(sat_conversion,[],[f246]) ).
cnf(s8,plain,
( spl8_7
| spl8_10 ),
inference(sat_conversion,[],[f251]) ).
cnf(s10,plain,
( ~ spl8_2
| ~ spl8_7 ),
inference(sat_conversion,[],[f280]) ).
cnf(s12,plain,
( ~ spl8_2
| ~ spl8_9
| ~ spl8_10 ),
inference(sat_conversion,[],[f305]) ).
cnf(s16,plain,
( ~ spl8_1
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(sat_conversion,[],[f359]) ).
cnf(s17,plain,
~ spl8_2,
inference(rat,[],[s12,s7,s8,s10]) ).
cnf(s18,plain,
spl8_5,
inference(rat,[],[s4,s17]) ).
cnf(s19,plain,
spl8_4,
inference(rat,[],[s3,s17]) ).
cnf(s20,plain,
spl8_3,
inference(rat,[],[s2,s17]) ).
cnf(s21,plain,
spl8_1,
inference(rat,[],[s1,s17]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s16,s18,s21,s19,s20]) ).
thf(f360,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL705^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 09:44:48 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.28 % (536279)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (536294)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3588011462:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.28 % (536294)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % (536291)% WARNING: option uhcvi not known.
% 0.21/0.28 % (536294) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-536279-536294"...
% 0.21/0.28 % (536290)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=889262318_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.28 % (536293)dis+10_1_sil=32000:sp=arity:random_seed=2244403913:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.28 % (536291)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2172647066:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.28 % (536295)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=353743993:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.28 % (536292)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2805810695:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.28 % (536296)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2349150507:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.28 % (536291)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % (536294)...printing done.
% 0.21/0.28 % (536294)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (536294)------------------------------
% 0.21/0.29 % (536294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (536294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (536294)CaDiCaL version: 2.1.3
% 0.21/0.29 % (536294)Termination reason: Refutation
% 0.21/0.29 % (536294)Time elapsed: 0.008 s
% 0.21/0.29 % (536294)Peak memory usage: 12 MB
% 0.21/0.29 % (536294)Instructions burned: 26 (million)
% 0.21/0.29 % (536279)Success in time 0.043 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------