%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO049^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 18
% Syntax : Number of formulae : 229 ( 58 unt; 0 typ; 8 def)
% Number of atoms : 2278 ( 359 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 3096 ( 738 ~; 726 |; 0 &;1486 @)
% ( 8 <=>; 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 : 214 ( 214 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 15 con; 0-4 aty)
% ( 138 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 425 ( 0 sgn 57 !; 1 ?; 425 :)
% 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/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(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] :
( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mequiv @ ( mdia @ X0 @ ( mor @ X1 @ X2 ) ) @ ( mor @ ( mdia @ X0 @ X1 ) @ ( mdia @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mequiv @ ( mdia @ X0 @ ( mor @ X1 @ X2 ) ) @ ( mor @ ( mdia @ X0 @ X1 ) @ ( mdia @ 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(f56,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
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 @ ( mdia @ X0 @ ( mor @ X1 @ X2 ) ) @ ( mor @ ( mdia @ X0 @ X1 ) @ ( mdia @ 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 @ ( mdia @ X0 @ ( mor @ Y0 @ Y1 ) ) @ ( mor @ ( mdia @ X0 @ Y0 ) @ ( mdia @ 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 @ ( mdia @ X0 @ ( mor @ Y0 @ Y1 ) ) @ ( mor @ ( mdia @ X0 @ Y0 ) @ ( mdia @ X0 @ Y1 ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f86]) ).
thf(f88,plain,
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mequiv @ ( mdia @ sK0 @ ( mor @ Y0 @ Y1 ) ) @ ( mor @ ( mdia @ sK0 @ Y0 ) @ ( mdia @ 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(f105,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
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 @ ( mdia @ sK0 @ ( mor @ Y0 @ Y1 ) ) @ ( mor @ ( mdia @ sK0 @ Y0 ) @ ( mdia @ 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(f131,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(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 > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y5 @ Y7 ) ) )
@ Y2
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ sK0
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y5 @ Y7 ) ) )
@ Y2
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y5 @ Y7 ) ) )
@ Y2
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ sK0
@ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f120,f116,f99,f99,f126,f131,f92,f92,f131,f131]) ).
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,
( ( $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 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) ) ) ),
inference(or_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 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ sK4 ) )
| ( $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 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ sK4 ) )
| ( $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 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ sK4 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f149]) ).
thf(f152,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ sK4 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
@ sK5 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( $false
= ( ~ ( sK0 @ sK1 @ sK4 )
| ~ ( sK3 @ sK4 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK5 )
| ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( ( $false
= ( ~ ( sK3 @ sK4 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK5 )
| ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( ~ ( sK0 @ sK1 @ sK4 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK5 )
| ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f160,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK5 )
| ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK5 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f166,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK2 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f168,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f169,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK6 ) ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 ) ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f172,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $true
= ( sK2 @ sK6 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f174,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK5 )
| ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f175,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $false
= ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK5 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f177,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f180,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK2 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f182,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f183,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 )
| ~ ( sK2 @ sK6 ) ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK6 ) ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK1 @ sK6 ) ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f186,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $true
= ( sK2 @ sK6 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f240,plain,
( ( $true
= ( !! @ $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,[],[f143]) ).
thf(f241,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ 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,[],[f240]) ).
thf(f242,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ 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,[],[f241]) ).
thf(f243,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f242]) ).
thf(f267,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f243]) ).
thf(f268,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f243]) ).
thf(f269,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK2 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( sK0 @ sK1 @ X1 )
| ~ ( ( sK2 @ X1 )
| ( sK3 @ X1 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 )
| ~ ( sK2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f270]) ).
thf(f272,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( ( sK2 @ X1 )
| ( sK3 @ X1 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 )
| ~ ( sK2 @ X2 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK2 @ X1 )
| ( sK3 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 )
| ~ ( sK2 @ X2 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f272]) ).
thf(f275,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 )
| ~ ( sK2 @ X2 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f273]) ).
thf(f276,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( $true
= ( ~ ( sK2 @ X2 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f275]) ).
thf(f277,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( $false
= ( sK2 @ X2 ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f277]) ).
thf(f279,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f278]) ).
thf(f284,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f267]) ).
thf(f285,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| ~ ( sK3 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f284]) ).
thf(f286,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( sK0 @ sK1 @ X1 )
| ~ ( ( sK2 @ X1 )
| ( sK3 @ X1 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 )
| ~ ( sK3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f285]) ).
thf(f287,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( ( sK2 @ X1 )
| ( sK3 @ X1 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 )
| ~ ( sK3 @ X2 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK2 @ X1 )
| ( sK3 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 )
| ~ ( sK3 @ X2 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 )
| ~ ( sK3 @ X2 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f288]) ).
thf(f295,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( $true
= ( ~ ( sK3 @ X2 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f296,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( $false
= ( sK3 @ X2 ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f295]) ).
thf(f297,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( $false
= ( sK3 @ X2 ) )
| ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f296]) ).
thf(f298,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( $false
= ( sK3 @ X2 ) )
| ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f297]) ).
thf(f300,definition,
( spl10_1
<=> ( $true
= ( sK2 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
thf(f301,plain,
( ( $true
!= ( sK2 @ sK6 ) )
| spl10_1 ),
inference(avatar_component_clause,[],[f300]) ).
thf(f302,plain,
( ( $true
= ( sK2 @ sK6 ) )
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f300]) ).
thf(f304,definition,
( spl10_2
<=> ( $true
= ( sK0 @ sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f305,plain,
( ( $true
!= ( sK0 @ sK1 @ sK5 ) )
| spl10_2 ),
inference(avatar_component_clause,[],[f304]) ).
thf(f306,plain,
( ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f304]) ).
thf(f308,definition,
( spl10_3
<=> ( $true
= ( sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f309,plain,
( ( $true
!= ( sK3 @ sK4 ) )
| spl10_3 ),
inference(avatar_component_clause,[],[f308]) ).
thf(f310,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f308]) ).
thf(f311,plain,
( spl10_1
| spl10_2
| spl10_3 ),
inference(avatar_split_clause,[],[f181,f308,f304,f300]) ).
thf(f323,definition,
( spl10_7
<=> ! [X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( $false
= ( sK0 @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f324,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f323]) ).
thf(f346,definition,
( spl10_8
<=> ( $true
= ( sK0 @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
thf(f347,plain,
( ( $true
!= ( sK0 @ sK1 @ sK4 ) )
| spl10_8 ),
inference(avatar_component_clause,[],[f346]) ).
thf(f348,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f346]) ).
thf(f360,definition,
( spl10_11
<=> ! [X1: $i] :
( ( $false
= ( sK3 @ X1 ) )
| ( $false
= ( sK0 @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
thf(f361,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f360]) ).
thf(f408,plain,
( ( $true = $false )
| ( $false
= ( sK3 @ sK4 ) )
| ~ spl10_8
| ~ spl10_11 ),
inference(constrained_superposition,[],[f361,f348]) ).
thf(f409,plain,
( ( $false
= ( sK3 @ sK4 ) )
| ~ spl10_8
| ~ spl10_11 ),
inference(trivial_inequality_removal,[],[f408]) ).
thf(f412,plain,
( ( $true = $false )
| ~ spl10_3
| ~ spl10_8
| ~ spl10_11 ),
inference(constrained_superposition,[],[f310,f409]) ).
thf(f413,plain,
( $false
| ~ spl10_3
| ~ spl10_8
| ~ spl10_11 ),
inference(trivial_inequality_removal,[],[f412]) ).
thf(f414,plain,
( ~ spl10_3
| ~ spl10_8
| ~ spl10_11 ),
inference(avatar_contradiction_clause,[],[f413]) ).
thf(f423,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| spl10_1 ),
inference(forward_subsumption_resolution,[],[f173,f301]) ).
thf(f433,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| spl10_1
| spl10_8 ),
inference(forward_subsumption_resolution,[],[f423,f347]) ).
thf(f438,plain,
( spl10_11
| spl10_11 ),
inference(avatar_split_clause,[],[f298,f360,f360]) ).
thf(f440,definition,
( spl10_13
<=> ( $true
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_13])],[avatar_definition]) ).
thf(f441,plain,
( ( $true
!= ( sK2 @ sK5 ) )
| spl10_13 ),
inference(avatar_component_clause,[],[f440]) ).
thf(f442,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl10_13 ),
inference(avatar_component_clause,[],[f440]) ).
thf(f444,definition,
( spl10_14
<=> ( $true
= ( sK3 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition]) ).
thf(f446,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ~ spl10_14 ),
inference(avatar_component_clause,[],[f444]) ).
thf(f447,plain,
( spl10_13
| spl10_14
| spl10_1
| spl10_8 ),
inference(avatar_split_clause,[],[f433,f346,f300,f444,f440]) ).
thf(f451,plain,
( ( $true = $false )
| ( $false
= ( sK2 @ sK5 ) )
| ~ spl10_2
| ~ spl10_7 ),
inference(constrained_superposition,[],[f306,f324]) ).
thf(f454,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl10_2
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f451]) ).
thf(f457,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_7
| ~ spl10_13 ),
inference(constrained_superposition,[],[f454,f442]) ).
thf(f461,plain,
( $false
| ~ spl10_2
| ~ spl10_7
| ~ spl10_13 ),
inference(trivial_inequality_removal,[],[f457]) ).
thf(f462,plain,
( ~ spl10_2
| ~ spl10_7
| ~ spl10_13 ),
inference(avatar_contradiction_clause,[],[f461]) ).
thf(f466,plain,
( ( $true = $false )
| ( $false
= ( sK3 @ sK5 ) )
| ~ spl10_2
| ~ spl10_11 ),
inference(constrained_superposition,[],[f306,f361]) ).
thf(f469,plain,
( ( $false
= ( sK3 @ sK5 ) )
| ~ spl10_2
| ~ spl10_11 ),
inference(trivial_inequality_removal,[],[f466]) ).
thf(f481,plain,
( spl10_7
| spl10_7 ),
inference(avatar_split_clause,[],[f279,f323,f323]) ).
thf(f482,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_11
| ~ spl10_14 ),
inference(forward_demodulation,[],[f446,f469]) ).
thf(f483,plain,
( $false
| ~ spl10_2
| ~ spl10_11
| ~ spl10_14 ),
inference(trivial_inequality_removal,[],[f482]) ).
thf(f484,plain,
( ~ spl10_2
| ~ spl10_11
| ~ spl10_14 ),
inference(avatar_contradiction_clause,[],[f483]) ).
thf(f507,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $true
= ( sK2 @ sK5 ) )
| spl10_8 ),
inference(forward_subsumption_resolution,[],[f172,f347]) ).
thf(f508,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| spl10_8
| spl10_13 ),
inference(forward_subsumption_resolution,[],[f507,f441]) ).
thf(f509,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ~ spl10_2
| spl10_8
| ~ spl10_11
| spl10_13 ),
inference(forward_demodulation,[],[f508,f469]) ).
thf(f510,plain,
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ~ spl10_2
| spl10_8
| ~ spl10_11
| spl10_13 ),
inference(trivial_inequality_removal,[],[f509]) ).
thf(f513,plain,
( ( $true = $false )
| ( $false
= ( sK2 @ sK6 ) )
| ~ spl10_2
| ~ spl10_7
| spl10_8
| ~ spl10_11
| spl10_13 ),
inference(constrained_superposition,[],[f324,f510]) ).
thf(f516,plain,
( ( $false
= ( sK2 @ sK6 ) )
| ~ spl10_2
| ~ spl10_7
| spl10_8
| ~ spl10_11
| spl10_13 ),
inference(trivial_inequality_removal,[],[f513]) ).
thf(f519,plain,
( ( $true = $false )
| ~ spl10_1
| ~ spl10_2
| ~ spl10_7
| spl10_8
| ~ spl10_11
| spl10_13 ),
inference(constrained_superposition,[],[f516,f302]) ).
thf(f523,plain,
( $false
| ~ spl10_1
| ~ spl10_2
| ~ spl10_7
| spl10_8
| ~ spl10_11
| spl10_13 ),
inference(trivial_inequality_removal,[],[f519]) ).
thf(f524,plain,
( ~ spl10_1
| ~ spl10_2
| ~ spl10_7
| spl10_8
| ~ spl10_11
| spl10_13 ),
inference(avatar_contradiction_clause,[],[f523]) ).
thf(f527,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $true
= ( sK2 @ sK6 ) )
| spl10_13 ),
inference(forward_subsumption_resolution,[],[f187,f441]) ).
thf(f528,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| spl10_13 ),
inference(forward_subsumption_resolution,[],[f186,f441]) ).
thf(f533,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK2 @ sK6 ) )
| ~ spl10_2
| ~ spl10_11
| spl10_13 ),
inference(forward_demodulation,[],[f527,f469]) ).
thf(f534,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK2 @ sK6 ) )
| ~ spl10_2
| ~ spl10_11
| spl10_13 ),
inference(trivial_inequality_removal,[],[f533]) ).
thf(f535,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ~ spl10_2
| ~ spl10_11
| spl10_13 ),
inference(forward_demodulation,[],[f528,f469]) ).
thf(f536,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ~ spl10_2
| ~ spl10_11
| spl10_13 ),
inference(trivial_inequality_removal,[],[f535]) ).
thf(f585,plain,
( ( $true
= ( sK2 @ sK6 ) )
| ~ spl10_2
| spl10_3
| ~ spl10_11
| spl10_13 ),
inference(forward_subsumption_resolution,[],[f534,f309]) ).
thf(f586,plain,
( spl10_1
| ~ spl10_2
| spl10_3
| ~ spl10_11
| spl10_13 ),
inference(avatar_split_clause,[],[f585,f440,f360,f308,f304,f300]) ).
thf(f587,plain,
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ~ spl10_2
| spl10_3
| ~ spl10_11
| spl10_13 ),
inference(forward_subsumption_resolution,[],[f536,f309]) ).
thf(f590,plain,
( ( $true = $false )
| ( $false
= ( sK2 @ sK6 ) )
| ~ spl10_2
| spl10_3
| ~ spl10_7
| ~ spl10_11
| spl10_13 ),
inference(constrained_superposition,[],[f324,f587]) ).
thf(f593,plain,
( ( $false
= ( sK2 @ sK6 ) )
| ~ spl10_2
| spl10_3
| ~ spl10_7
| ~ spl10_11
| spl10_13 ),
inference(trivial_inequality_removal,[],[f590]) ).
thf(f598,plain,
( ( $true = $false )
| ~ spl10_1
| ~ spl10_2
| spl10_3
| ~ spl10_7
| ~ spl10_11
| spl10_13 ),
inference(constrained_superposition,[],[f593,f302]) ).
thf(f604,plain,
( $false
| ~ spl10_1
| ~ spl10_2
| spl10_3
| ~ spl10_7
| ~ spl10_11
| spl10_13 ),
inference(trivial_inequality_removal,[],[f598]) ).
thf(f605,plain,
( ~ spl10_1
| ~ spl10_2
| spl10_3
| ~ spl10_7
| ~ spl10_11
| spl10_13 ),
inference(avatar_contradiction_clause,[],[f604]) ).
thf(f606,plain,
( ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| spl10_3 ),
inference(forward_subsumption_resolution,[],[f180,f309]) ).
thf(f642,plain,
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| spl10_2
| spl10_3 ),
inference(forward_subsumption_resolution,[],[f606,f305]) ).
thf(f700,plain,
( ( $true = $false )
| ( $false
= ( sK2 @ sK6 ) )
| spl10_2
| spl10_3
| ~ spl10_7 ),
inference(constrained_superposition,[],[f324,f642]) ).
thf(f703,plain,
( ( $false
= ( sK2 @ sK6 ) )
| spl10_2
| spl10_3
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f700]) ).
thf(f708,plain,
( ( $true = $false )
| ~ spl10_1
| spl10_2
| spl10_3
| ~ spl10_7 ),
inference(constrained_superposition,[],[f703,f302]) ).
thf(f714,plain,
( $false
| ~ spl10_1
| spl10_2
| spl10_3
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f708]) ).
thf(f715,plain,
( ~ spl10_1
| spl10_2
| spl10_3
| ~ spl10_7 ),
inference(avatar_contradiction_clause,[],[f714]) ).
thf(f716,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| spl10_2 ),
inference(forward_subsumption_resolution,[],[f166,f305]) ).
thf(f725,plain,
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| spl10_2
| spl10_8 ),
inference(forward_subsumption_resolution,[],[f716,f347]) ).
thf(f728,plain,
( ( $true = $false )
| ( $false
= ( sK2 @ sK6 ) )
| spl10_2
| ~ spl10_7
| spl10_8 ),
inference(constrained_superposition,[],[f324,f725]) ).
thf(f731,plain,
( ( $false
= ( sK2 @ sK6 ) )
| spl10_2
| ~ spl10_7
| spl10_8 ),
inference(trivial_inequality_removal,[],[f728]) ).
thf(f745,plain,
( ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK2 @ sK6 ) )
| spl10_8 ),
inference(forward_subsumption_resolution,[],[f167,f347]) ).
thf(f746,plain,
( ( $true
= ( sK2 @ sK6 ) )
| spl10_2
| spl10_8 ),
inference(forward_subsumption_resolution,[],[f745,f305]) ).
thf(f747,plain,
( ( $true = $false )
| spl10_2
| ~ spl10_7
| spl10_8 ),
inference(forward_demodulation,[],[f746,f731]) ).
thf(f748,plain,
( $false
| spl10_2
| ~ spl10_7
| spl10_8 ),
inference(trivial_inequality_removal,[],[f747]) ).
thf(f749,plain,
( spl10_2
| ~ spl10_7
| spl10_8 ),
inference(avatar_contradiction_clause,[],[f748]) ).
cnf(s28,plain,
( spl10_1
| spl10_2
| spl10_3 ),
inference(sat_conversion,[],[f311]) ).
cnf(s92,plain,
( ~ spl10_3
| ~ spl10_8
| ~ spl10_11 ),
inference(sat_conversion,[],[f414]) ).
cnf(s126,plain,
( spl10_11
| spl10_11 ),
inference(sat_conversion,[],[f438]) ).
cnf(s127,plain,
spl10_11,
inference(rat,[],[s126]) ).
cnf(s135,plain,
( spl10_1
| spl10_8
| spl10_13
| spl10_14 ),
inference(sat_conversion,[],[f447]) ).
cnf(s146,plain,
( ~ spl10_2
| ~ spl10_7
| ~ spl10_13 ),
inference(sat_conversion,[],[f462]) ).
cnf(s160,plain,
( spl10_7
| spl10_7 ),
inference(sat_conversion,[],[f481]) ).
cnf(s161,plain,
spl10_7,
inference(rat,[],[s160]) ).
cnf(s164,plain,
( ~ spl10_2
| ~ spl10_11
| ~ spl10_14 ),
inference(sat_conversion,[],[f484]) ).
cnf(s191,plain,
( ~ spl10_1
| ~ spl10_2
| ~ spl10_7
| spl10_8
| ~ spl10_11
| spl10_13 ),
inference(sat_conversion,[],[f524]) ).
cnf(s215,plain,
( spl10_1
| ~ spl10_2
| spl10_3
| ~ spl10_11
| spl10_13 ),
inference(sat_conversion,[],[f586]) ).
cnf(s227,plain,
( ~ spl10_1
| ~ spl10_2
| spl10_3
| ~ spl10_7
| ~ spl10_11
| spl10_13 ),
inference(sat_conversion,[],[f605]) ).
cnf(s277,plain,
( ~ spl10_1
| spl10_2
| spl10_3
| ~ spl10_7 ),
inference(sat_conversion,[],[f715]) ).
cnf(s296,plain,
( spl10_2
| ~ spl10_7
| spl10_8 ),
inference(sat_conversion,[],[f749]) ).
cnf(s298,plain,
( ~ spl10_2
| ~ spl10_13 ),
inference(rat,[],[s146,s161]) ).
cnf(s301,plain,
( ~ spl10_3
| ~ spl10_8 ),
inference(rat,[],[s92,s127]) ).
cnf(s305,plain,
( spl10_2
| spl10_1 ),
inference(rat,[],[s301,s28,s296,s161]) ).
cnf(s306,plain,
spl10_1,
inference(rat,[],[s301,s135,s215,s298,s164,s305,s127]) ).
cnf(s308,plain,
spl10_2,
inference(rat,[],[s301,s277,s296,s306,s161]) ).
cnf(s310,plain,
~ spl10_13,
inference(rat,[],[s298,s308]) ).
cnf(s312,plain,
spl10_3,
inference(rat,[],[s227,s310,s127,s161,s306,s308]) ).
cnf(s313,plain,
spl10_8,
inference(rat,[],[s191,s310,s127,s306,s161,s308]) ).
cnf(s315,plain,
$false,
inference(rat,[],[s301,s313,s312]) ).
thf(f750,plain,
$false,
inference(avatar_sat_refutation,[],[s315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO049^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n014.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
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:24:30 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
% 0.20/0.29 % (2876670)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (2876677)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4190657843:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (2876676)% WARNING: option uhcvi not known.
% 0.20/0.29 % (2876676)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=127998939:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (2876675)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3766696153_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (2876679)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2569644383:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (2876676)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (2876679)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (2876676)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (2876678)dis+10_1_sil=32000:sp=arity:random_seed=768331275:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (2876677) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2876670-2876677"...
% 0.20/0.29 % (2876676) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2876670-2876676"...
% 0.20/0.29 % (2876677)...printing done.
% 0.20/0.29 % (2876677)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (2876677)------------------------------
% 0.20/0.30 % (2876677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2876677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2876677)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2876677)Termination reason: Refutation
% 0.20/0.30 % (2876677)Time elapsed: 0.019 s
% 0.20/0.30 % (2876677)Peak memory usage: 13 MB
% 0.20/0.30 % (2876677)Instructions burned: 55 (million)
% 0.20/0.30 % (2876670)Success in time 0.055 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------