%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL880^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:15:13 AM UTC 2026
% Result : Theorem 10.19s 1.71s
% Output : Refutation 10.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 17
% Syntax : Number of formulae : 277 ( 31 unt; 0 typ; 10 def)
% Number of atoms : 2724 ( 551 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 3465 ( 670 ~; 792 |; 14 &;1825 @)
% ( 15 <=>; 5 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 252 ( 252 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 76 usr; 25 con; 0-4 aty)
% ( 142 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 628 ( 0 sgn 274 !; 14 ?; 628 :)
% 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 > $o ).
thf(func_def_52,type,
sK5: $i > ( $i > $o ) > $i ).
thf(func_def_54,type,
sK7: $i > $o ).
thf(func_def_58,type,
sK11: $i > $o ).
thf(func_def_62,type,
sK15: $i > $o ).
thf(func_def_66,type,
sK19: $i > $i ).
thf(func_def_67,type,
sK20: ( $i > $o ) > ( $i > $i ) > $i ).
thf(func_def_68,type,
sK21: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ X2 ) ) ) ) ) )
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( ( X0 @ X3 @ X5 )
& ( X1 @ X3 @ X4 ) )
=> ( X0 @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ X2 ) ) ) ) ) )
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( ( X0 @ X3 @ X5 )
& ( X1 @ X3 @ X4 ) )
=> ( X0 @ X4 @ X5 ) ) ),
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(f41,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f47,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f48,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f54,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f55,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f77,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f78,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f85,plain,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ X2 ) ) ) ) ) )
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( ( X0 @ X3 @ X5 )
& ( X1 @ X3 @ X4 ) )
=> ( X0 @ X4 @ X5 ) ) ),
inference(rectify,[],[f33]) ).
thf(f86,plain,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) )
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( ( ( X0 @ X3 @ X5 )
= $true )
& ( ( X1 @ X3 @ X4 )
= $true ) )
=> ( ( X0 @ X4 @ X5 )
= $true ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) )
<=> ! [X2: $i,X3: $i,X4: $i] :
( ( ( ( X0 @ X2 @ X4 )
= $true )
& ( $true
= ( X1 @ X2 @ X3 ) ) )
=> ( ( X0 @ X3 @ X4 )
= $true ) ) ),
inference(rectify,[],[f86]) ).
thf(f88,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) )
<~> ! [X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X3 @ X4 )
= $true )
| ( ( X0 @ X2 @ X4 )
!= $true )
| ( $true
!= ( X1 @ X2 @ X3 ) ) ) ),
inference(ennf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) )
<~> ! [X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X3 @ X4 )
= $true )
| ( ( X0 @ X2 @ X4 )
!= $true )
| ( $true
!= ( X1 @ X2 @ X3 ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ? [X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X3 @ X4 )
!= $true )
& ( ( X0 @ X2 @ X4 )
= $true )
& ( $true
= ( X1 @ X2 @ X3 ) ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) ) )
& ( ! [X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X3 @ X4 )
= $true )
| ( ( X0 @ X2 @ X4 )
!= $true )
| ( $true
!= ( X1 @ X2 @ X3 ) ) )
| ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) ) ) ),
inference(nnf_transformation,[],[f89]) ).
thf(f91,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ? [X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X3 @ X4 )
!= $true )
& ( ( X0 @ X2 @ X4 )
= $true )
& ( $true
= ( X1 @ X2 @ X3 ) ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( $true
= ( X0 @ X6 @ X7 ) )
| ( $true
!= ( X0 @ X5 @ X7 ) )
| ( $true
!= ( X1 @ X5 @ X6 ) ) )
| ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f90]) ).
thf(f92,plain,
( ( ( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
& ( $true
= ( sK0 @ sK2 @ sK4 ) )
& ( $true
= ( sK1 @ sK2 @ sK3 ) ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK1 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) ) )
| ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK1 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f91]) ).
thf(f95,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f96,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f98,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f103,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f108,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f120,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f124,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK1 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f125,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK1 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f126,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK1 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f127,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK1 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f131,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,[],[f98,f96,f95]) ).
thf(f139,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $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] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK1
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f127,f120,f103,f131,f95,f108,f108,f95,f108]) ).
thf(f140,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $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] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK1
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f126,f120,f103,f131,f95,f108,f108,f95,f108]) ).
thf(f141,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $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] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK1
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f125,f120,f103,f131,f95,f108,f108,f95,f108]) ).
thf(f142,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $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] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK1
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f124,f120,f103,f131,f95,f108,f108,f95,f108]) ).
thf(f143,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK1 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
! [X8: $i,X6: $i,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK1 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X8: $i,X6: $i,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ X8 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK1 @ X8 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
! [X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ X8 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK1 @ X8 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X8 @ Y0 )
| ( X9 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ X8 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X9 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ X8 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X9 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X8 @ Y0 )
| ( X9 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK1 @ X8 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X9 @ Y1 ) ) ) )
@ X10 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X8 @ Y0 )
| ( X9 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK1 @ X8 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X9 @ Y1 ) ) ) )
@ X10 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X8 @ Y0 )
| ( X9 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK1 @ X8 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X9 @ Y1 ) ) ) )
@ X10 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X8 @ Y0 )
| ( X9 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK1 @ X8 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X9 @ Y1 ) ) ) )
@ X10 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X8 @ Y0 )
| ( X9 @ Y0 ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ~ ( sK1 @ X8 @ X10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( sK0 @ X8 @ X11 )
| ( X9 @ X11 ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( sK0 @ X8 @ X11 )
| ( X9 @ X11 ) ) )
| ( $true
= ( ~ ( sK1 @ X8 @ X10 ) ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) ) ) )
| ( $true
= ( ~ ( sK0 @ X8 @ X11 )
| ( X9 @ X11 ) ) )
| ( $true
= ( ~ ( sK1 @ X8 @ X10 ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) )
@ ( sK5 @ X10 @ X9 ) ) )
| ( $true
= ( ~ ( sK0 @ X8 @ X11 )
| ( X9 @ X11 ) ) )
| ( $true
= ( ~ ( sK1 @ X8 @ X10 ) ) ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) )
@ ( sK5 @ X10 @ X9 ) ) )
| ( $true
= ( X9 @ X11 ) )
| ( $true
= ( ~ ( sK1 @ X8 @ X10 ) ) )
| ( $true
= ( ~ ( sK0 @ X8 @ X11 ) ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) )
@ ( sK5 @ X10 @ X9 ) ) )
| ( $true
= ( X9 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $true
= ( ~ ( sK0 @ X8 @ X11 ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) )
@ ( sK5 @ X10 @ X9 ) ) )
| ( $true
= ( X9 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $false
= ( sK0 @ X8 @ X11 ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $false
= ( ~ ( sK0 @ X10 @ ( sK5 @ X10 @ X9 ) )
| ( X9 @ ( sK5 @ X10 @ X9 ) ) ) )
| ( $true
= ( X9 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $false
= ( sK0 @ X8 @ X11 ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $false
= ( X9 @ ( sK5 @ X10 @ X9 ) ) )
| ( $true
= ( X9 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $false
= ( sK0 @ X8 @ X11 ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $false
= ( ~ ( sK0 @ X10 @ ( sK5 @ X10 @ X9 ) ) ) )
| ( $true
= ( X9 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $false
= ( sK0 @ X8 @ X11 ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( sK0 @ X10 @ ( sK5 @ X10 @ X9 ) ) )
| ( $true
= ( X9 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $false
= ( sK0 @ X8 @ X11 ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK1 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f165,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK1 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK6 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK1 @ sK6 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK6 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK1 @ sK6 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK6 @ Y0 )
| ( sK7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ sK6 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK7 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ sK6 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK7 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK6 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f171,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK6 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK6 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK6 @ Y0 )
| ( sK7 @ Y0 ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK6 @ sK8 )
| ( sK7 @ sK8 ) ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( sK7 @ sK8 ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK6 @ sK8 ) ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f177,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK6 @ sK8 ) ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK1 @ sK6 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK7 @ Y1 ) ) ) )
@ sK9 ) ) ),
inference(sigma_proxy_clausification,[],[f169]) ).
thf(f179,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK6 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK9 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK9 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK6 @ sK9 ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK6 @ sK9 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK9 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f184,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK9 @ Y0 )
| ( sK7 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK9 @ X1 )
| ( sK7 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( sK7 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK9 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( sK7 @ X1 ) )
| ( $false
= ( sK0 @ sK9 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK1 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f189,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK1 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
@ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK10 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK1 @ sK10 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK10 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK1 @ sK10 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) )
@ sK11 ) ) ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK10 @ Y0 )
| ( sK11 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ sK10 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK11 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ sK10 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK11 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK10 @ Y0 )
| ( sK11 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f195,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK10 @ Y0 )
| ( sK11 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK10 @ Y0 )
| ( sK11 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK10 @ Y0 )
| ( sK11 @ Y0 ) )
@ sK12 ) ) ),
inference(sigma_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK10 @ sK12 )
| ( sK11 @ sK12 ) ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( sK11 @ sK12 ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK10 @ sK12 ) ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f201,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( sK0 @ sK10 @ sK12 ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK1 @ sK10 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK11 @ Y1 ) ) ) )
@ sK13 ) ) ),
inference(sigma_proxy_clausification,[],[f193]) ).
thf(f203,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ~ ( sK1 @ sK10 @ sK13 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK13 @ Y0 )
| ( sK11 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK13 @ Y0 )
| ( sK11 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f205,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ~ ( sK1 @ sK10 @ sK13 ) ) ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f206,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( sK1 @ sK10 @ sK13 ) ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f207,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK13 @ Y0 )
| ( sK11 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f204]) ).
thf(f208,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK13 @ Y0 )
| ( sK11 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( ~ ( sK0 @ sK13 @ X1 )
| ( sK11 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( sK11 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK13 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( sK11 @ X1 ) )
| ( $false
= ( sK0 @ sK13 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK1 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f213,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK1 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
@ sK14 ) ) ),
inference(sigma_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK14 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK1 @ sK14 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK14 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK1 @ sK14 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) )
@ sK15 ) ) ),
inference(sigma_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK14 @ Y0 )
| ( sK15 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ sK14 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK15 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ sK14 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK15 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK14 @ Y0 )
| ( sK15 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f219,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK14 @ Y0 )
| ( sK15 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f220,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK14 @ Y0 )
| ( sK15 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f221,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK14 @ Y0 )
| ( sK15 @ Y0 ) )
@ sK16 ) ) ),
inference(sigma_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK14 @ sK16 )
| ( sK15 @ sK16 ) ) ) ),
inference(beta-eta_normalization,[],[f221]) ).
thf(f223,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( sK15 @ sK16 ) ) ),
inference(or_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK14 @ sK16 ) ) ) ),
inference(or_proxy_clausification,[],[f222]) ).
thf(f225,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK0 @ sK14 @ sK16 ) ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f226,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK1 @ sK14 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK15 @ Y1 ) ) ) )
@ sK17 ) ) ),
inference(sigma_proxy_clausification,[],[f217]) ).
thf(f227,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ~ ( sK1 @ sK14 @ sK17 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK17 @ Y0 )
| ( sK15 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK17 @ Y0 )
| ( sK15 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f227]) ).
thf(f229,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ~ ( sK1 @ sK14 @ sK17 ) ) ) ),
inference(or_proxy_clausification,[],[f227]) ).
thf(f230,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK1 @ sK14 @ sK17 ) ) ),
inference(not_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK17 @ Y0 )
| ( sK15 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f232,plain,
! [X1: $i] :
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK17 @ Y0 )
| ( sK15 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X1: $i] :
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( ~ ( sK0 @ sK17 @ X1 )
| ( sK15 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK15 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK17 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X1: $i] :
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK15 @ X1 ) )
| ( $false
= ( sK0 @ sK17 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f234]) ).
thf(f237,definition,
( spl18_1
<=> ( $false
= ( sK7 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
thf(f239,plain,
( ( $false
= ( sK7 @ sK8 ) )
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f241,definition,
( spl18_2
<=> ( $true
= ( sK1 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
thf(f242,plain,
( ( $true
!= ( sK1 @ sK2 @ sK3 ) )
| spl18_2 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f243,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f244,plain,
( spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f175,f241,f237]) ).
thf(f253,definition,
( spl18_3
<=> ( $false
= ( sK11 @ sK12 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
thf(f255,plain,
( ( $false
= ( sK11 @ sK12 ) )
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f257,definition,
( spl18_4
<=> ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).
thf(f258,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| spl18_4 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f259,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f260,plain,
( spl18_3
| spl18_4 ),
inference(avatar_split_clause,[],[f199,f257,f253]) ).
thf(f262,definition,
( spl18_5
<=> ! [X10: $i,X11: $i,X9: $i > $o,X8: $i] :
( ( $false
= ( X9 @ ( sK5 @ X10 @ X9 ) ) )
| ( $false
= ( sK0 @ X8 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $true
= ( X9 @ X11 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
thf(f263,plain,
( ! [X10: $i,X11: $i,X8: $i,X9: $i > $o] :
( ( $false
= ( X9 @ ( sK5 @ X10 @ X9 ) ) )
| ( $false
= ( sK0 @ X8 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $true
= ( X9 @ X11 ) ) )
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f262]) ).
thf(f265,definition,
( spl18_6
<=> ! [X6: $i,X5: $i,X7: $i] :
( ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
thf(f266,plain,
( ! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK0 @ X5 @ X7 ) ) )
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f267,plain,
( spl18_5
| spl18_6 ),
inference(avatar_split_clause,[],[f161,f265,f262]) ).
thf(f270,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( sK5 @ X0
@ ^ [Y0: $i] : ( Y0 != X1 ) )
= X1 )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK1 @ X2 @ X0 ) ) )
| ~ spl18_5 ),
inference(leibniz_equality_elimination,[],[f263]) ).
thf(f401,definition,
( spl18_7
<=> ( $false
= ( sK15 @ sK16 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_7])],[avatar_definition]) ).
thf(f403,plain,
( ( $false
= ( sK15 @ sK16 ) )
| ~ spl18_7 ),
inference(avatar_component_clause,[],[f401]) ).
thf(f405,definition,
( spl18_8
<=> ( $true
= ( sK0 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_8])],[avatar_definition]) ).
thf(f406,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl18_8 ),
inference(avatar_component_clause,[],[f405]) ).
thf(f407,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| spl18_8 ),
inference(avatar_component_clause,[],[f405]) ).
thf(f408,plain,
( spl18_7
| ~ spl18_8 ),
inference(avatar_split_clause,[],[f223,f405,f401]) ).
thf(f410,definition,
( spl18_9
<=> ! [X10: $i,X11: $i,X9: $i > $o,X8: $i] :
( ( $true
= ( sK0 @ X10 @ ( sK5 @ X10 @ X9 ) ) )
| ( $false
= ( sK0 @ X8 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $true
= ( X9 @ X11 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_9])],[avatar_definition]) ).
thf(f411,plain,
( ! [X10: $i,X11: $i,X8: $i,X9: $i > $o] :
( ( $true
= ( sK0 @ X10 @ ( sK5 @ X10 @ X9 ) ) )
| ( $false
= ( sK0 @ X8 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $true
= ( X9 @ X11 ) ) )
| ~ spl18_9 ),
inference(avatar_component_clause,[],[f410]) ).
thf(f412,plain,
( spl18_9
| spl18_6 ),
inference(avatar_split_clause,[],[f163,f265,f410]) ).
thf(f423,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
= ( sK0 @ sK3 @ X0 ) )
| ( $true
!= ( sK0 @ sK2 @ X0 ) ) )
| ~ spl18_2
| ~ spl18_6 ),
inference(constrained_superposition,[],[f266,f243]) ).
thf(f432,plain,
( ! [X0: $i] :
( ( $true
!= ( sK0 @ sK2 @ X0 ) )
| ( $true
= ( sK0 @ sK3 @ X0 ) ) )
| ~ spl18_2
| ~ spl18_6 ),
inference(trivial_inequality_removal,[],[f423]) ).
thf(f449,definition,
( spl18_10
<=> ( $true
= ( sK0 @ sK10 @ sK12 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_10])],[avatar_definition]) ).
thf(f451,plain,
( ( $true
= ( sK0 @ sK10 @ sK12 ) )
| ~ spl18_10 ),
inference(avatar_component_clause,[],[f449]) ).
thf(f452,plain,
( spl18_10
| spl18_4 ),
inference(avatar_split_clause,[],[f201,f257,f449]) ).
thf(f460,plain,
( ( $true != $true )
| ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl18_2
| ~ spl18_4
| ~ spl18_6 ),
inference(constrained_superposition,[],[f432,f259]) ).
thf(f471,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl18_2
| ~ spl18_4
| ~ spl18_6 ),
inference(trivial_inequality_removal,[],[f460]) ).
thf(f472,plain,
( $false
| ~ spl18_2
| ~ spl18_4
| ~ spl18_6
| spl18_8 ),
inference(forward_subsumption_resolution,[],[f471,f407]) ).
thf(f473,plain,
( ~ spl18_2
| ~ spl18_4
| ~ spl18_6
| spl18_8 ),
inference(avatar_contradiction_clause,[],[f472]) ).
thf(f494,plain,
( ( $true
= ( sK0 @ sK14 @ sK16 ) )
| ~ spl18_8 ),
inference(forward_subsumption_resolution,[],[f225,f406]) ).
thf(f501,plain,
( ( $true
= ( sK1 @ sK14 @ sK17 ) )
| ~ spl18_8 ),
inference(forward_subsumption_resolution,[],[f230,f406]) ).
thf(f504,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
= ( sK0 @ sK17 @ X0 ) )
| ( $true
!= ( sK0 @ sK14 @ X0 ) ) )
| ~ spl18_6
| ~ spl18_8 ),
inference(constrained_superposition,[],[f266,f501]) ).
thf(f505,plain,
( ! [X0: $i] :
( ( $true
!= ( sK0 @ sK14 @ X0 ) )
| ( $true
= ( sK0 @ sK17 @ X0 ) ) )
| ~ spl18_6
| ~ spl18_8 ),
inference(trivial_inequality_removal,[],[f504]) ).
thf(f514,plain,
( ( $true != $true )
| ( $true
= ( sK0 @ sK17 @ sK16 ) )
| ~ spl18_6
| ~ spl18_8 ),
inference(constrained_superposition,[],[f505,f494]) ).
thf(f517,plain,
( ( $true
= ( sK0 @ sK17 @ sK16 ) )
| ~ spl18_6
| ~ spl18_8 ),
inference(trivial_inequality_removal,[],[f514]) ).
thf(f523,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK17 @ X1 ) )
| ( $true
= ( sK15 @ X1 ) ) )
| ~ spl18_8 ),
inference(forward_subsumption_resolution,[],[f235,f406]) ).
thf(f532,plain,
( ( $true = $false )
| ( $true
= ( sK15 @ sK16 ) )
| ~ spl18_6
| ~ spl18_8 ),
inference(constrained_superposition,[],[f523,f517]) ).
thf(f543,plain,
( ( $true
= ( sK15 @ sK16 ) )
| ~ spl18_6
| ~ spl18_8 ),
inference(trivial_inequality_removal,[],[f532]) ).
thf(f551,plain,
( ( $true = $false )
| ~ spl18_6
| ~ spl18_7
| ~ spl18_8 ),
inference(forward_demodulation,[],[f543,f403]) ).
thf(f552,plain,
( $false
| ~ spl18_6
| ~ spl18_7
| ~ spl18_8 ),
inference(trivial_inequality_removal,[],[f551]) ).
thf(f553,plain,
( ~ spl18_6
| ~ spl18_7
| ~ spl18_8 ),
inference(avatar_contradiction_clause,[],[f552]) ).
thf(f1074,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( sK1 @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != X0 )
@ X3 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) )
| ( $false
= ( sK1 @ X4 @ X1 ) ) )
| ~ spl18_5
| ~ spl18_9 ),
inference(constrained_superposition,[],[f411,f270]) ).
thf(f1111,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( sK1 @ X2 @ X1 ) )
| ( $true
= ( X3 != X0 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) )
| ( $false
= ( sK1 @ X4 @ X1 ) ) )
| ~ spl18_5
| ~ spl18_9 ),
inference(beta-eta_normalization,[],[f1074]) ).
thf(f1112,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( sK1 @ X2 @ X1 ) )
| ( $false
= ( X3 = X0 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) )
| ( $false
= ( sK1 @ X4 @ X1 ) ) )
| ~ spl18_5
| ~ spl18_9 ),
inference(not_proxy_clausification,[],[f1111]) ).
thf(f1113,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( sK1 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) )
| ( $false
= ( sK1 @ X4 @ X1 ) )
| ( X0 != X3 ) )
| ~ spl18_5
| ~ spl18_9 ),
inference(equality_proxy_clausification,[],[f1112]) ).
thf(f15676,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( sK1 @ X0 @ X2 ) )
| ( $false
= ( sK1 @ X0 @ X2 ) )
| ( X1 != X1 ) )
| ~ spl18_5
| ~ spl18_9 ),
inference(equality_factoring,[],[f1113]) ).
thf(f15679,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( sK1 @ X0 @ X2 ) )
| ( X1 != X1 ) )
| ~ spl18_5
| ~ spl18_9 ),
inference(duplicate_literal_removal,[],[f15676]) ).
thf(f15680,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( sK1 @ X0 @ X2 ) ) )
| ~ spl18_5
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f15679]) ).
thf(f16279,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( sK0 @ sK3 @ X0 ) )
| ( $false
= ( sK0 @ sK2 @ X0 ) ) )
| ~ spl18_2
| ~ spl18_5
| ~ spl18_9 ),
inference(constrained_superposition,[],[f243,f15680]) ).
thf(f16281,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ sK3 @ X0 ) )
| ( $false
= ( sK0 @ sK2 @ X0 ) ) )
| ~ spl18_2
| ~ spl18_5
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f16279]) ).
thf(f17205,plain,
( ( $true != $true )
| ( ( sK0 @ sK2 @ sK4 )
= $false )
| ~ spl18_2
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(constrained_superposition,[],[f407,f16281]) ).
thf(f17206,plain,
( ( ( sK0 @ sK2 @ sK4 )
= $false )
| ~ spl18_2
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f17205]) ).
thf(f17357,plain,
( ( $true = $false )
| ~ spl18_2
| ~ spl18_4
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(constrained_superposition,[],[f17206,f259]) ).
thf(f17471,plain,
( $false
| ~ spl18_2
| ~ spl18_4
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f17357]) ).
thf(f17472,plain,
( ~ spl18_2
| ~ spl18_4
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(avatar_contradiction_clause,[],[f17471]) ).
thf(f17532,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK10 @ sK13 ) )
| ~ spl18_2
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(forward_demodulation,[],[f206,f17206]) ).
thf(f17533,plain,
( ( $true
= ( sK1 @ sK10 @ sK13 ) )
| ~ spl18_2
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f17532]) ).
thf(f17534,plain,
( ! [X1: $i] :
( ( $true = $false )
| ( $true
= ( sK11 @ X1 ) )
| ( $false
= ( sK0 @ sK13 @ X1 ) ) )
| ~ spl18_2
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(forward_demodulation,[],[f211,f17206]) ).
thf(f17535,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK13 @ X1 ) )
| ( $true
= ( sK11 @ X1 ) ) )
| ~ spl18_2
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f17534]) ).
thf(f17668,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( sK0 @ sK13 @ X0 ) )
| ( $false
= ( sK0 @ sK10 @ X0 ) ) )
| ~ spl18_2
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(constrained_superposition,[],[f15680,f17533]) ).
thf(f17675,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ sK13 @ X0 ) )
| ( $false
= ( sK0 @ sK10 @ X0 ) ) )
| ~ spl18_2
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f17668]) ).
thf(f18819,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( sK11 @ X0 ) )
| ( $false
= ( sK0 @ sK10 @ X0 ) ) )
| ~ spl18_2
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(constrained_superposition,[],[f17535,f17675]) ).
thf(f18886,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK10 @ X0 ) )
| ( $true
= ( sK11 @ X0 ) ) )
| ~ spl18_2
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f18819]) ).
thf(f20089,plain,
( ( $true = $false )
| ( $true
= ( sK11 @ sK12 ) )
| ~ spl18_2
| ~ spl18_5
| spl18_8
| ~ spl18_9
| ~ spl18_10 ),
inference(constrained_superposition,[],[f18886,f451]) ).
thf(f20248,plain,
( ( $true
= ( sK11 @ sK12 ) )
| ~ spl18_2
| ~ spl18_5
| spl18_8
| ~ spl18_9
| ~ spl18_10 ),
inference(trivial_inequality_removal,[],[f20089]) ).
thf(f20335,plain,
( ( $true = $false )
| ~ spl18_2
| ~ spl18_3
| ~ spl18_5
| spl18_8
| ~ spl18_9
| ~ spl18_10 ),
inference(forward_demodulation,[],[f20248,f255]) ).
thf(f20336,plain,
( $false
| ~ spl18_2
| ~ spl18_3
| ~ spl18_5
| spl18_8
| ~ spl18_9
| ~ spl18_10 ),
inference(trivial_inequality_removal,[],[f20335]) ).
thf(f20337,plain,
( ~ spl18_2
| ~ spl18_3
| ~ spl18_5
| spl18_8
| ~ spl18_9
| ~ spl18_10 ),
inference(avatar_contradiction_clause,[],[f20336]) ).
thf(f20965,plain,
( ( $true
= ( sK0 @ sK6 @ sK8 ) )
| spl18_2 ),
inference(forward_subsumption_resolution,[],[f177,f242]) ).
thf(f21057,plain,
( ( $true
= ( sK1 @ sK6 @ sK9 ) )
| spl18_2 ),
inference(forward_subsumption_resolution,[],[f182,f242]) ).
thf(f21099,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( sK0 @ sK9 @ X0 ) )
| ( $false
= ( sK0 @ sK6 @ X0 ) ) )
| spl18_2
| ~ spl18_5
| ~ spl18_9 ),
inference(constrained_superposition,[],[f15680,f21057]) ).
thf(f21106,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ sK9 @ X0 ) )
| ( $false
= ( sK0 @ sK6 @ X0 ) ) )
| spl18_2
| ~ spl18_5
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f21099]) ).
thf(f21173,plain,
( ( $true
= ( sK1 @ sK10 @ sK13 ) )
| spl18_4 ),
inference(forward_subsumption_resolution,[],[f206,f258]) ).
thf(f21289,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK9 @ X1 ) )
| ( $true
= ( sK7 @ X1 ) ) )
| spl18_2 ),
inference(forward_subsumption_resolution,[],[f187,f242]) ).
thf(f21825,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( sK7 @ X0 ) )
| ( $false
= ( sK0 @ sK6 @ X0 ) ) )
| spl18_2
| ~ spl18_5
| ~ spl18_9 ),
inference(constrained_superposition,[],[f21289,f21106]) ).
thf(f21890,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK6 @ X0 ) )
| ( $true
= ( sK7 @ X0 ) ) )
| spl18_2
| ~ spl18_5
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f21825]) ).
thf(f21976,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK13 @ X1 ) )
| ( $true
= ( sK11 @ X1 ) ) )
| spl18_4 ),
inference(forward_subsumption_resolution,[],[f211,f258]) ).
thf(f22303,plain,
( ( $true = $false )
| ( $true
= ( sK7 @ sK8 ) )
| spl18_2
| ~ spl18_5
| ~ spl18_9 ),
inference(constrained_superposition,[],[f21890,f20965]) ).
thf(f22456,plain,
( ( $true
= ( sK7 @ sK8 ) )
| spl18_2
| ~ spl18_5
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f22303]) ).
thf(f22539,plain,
( ( $true = $false )
| ~ spl18_1
| spl18_2
| ~ spl18_5
| ~ spl18_9 ),
inference(forward_demodulation,[],[f22456,f239]) ).
thf(f22540,plain,
( $false
| ~ spl18_1
| spl18_2
| ~ spl18_5
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f22539]) ).
thf(f22541,plain,
( ~ spl18_1
| spl18_2
| ~ spl18_5
| ~ spl18_9 ),
inference(avatar_contradiction_clause,[],[f22540]) ).
thf(f22561,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
= ( sK0 @ sK9 @ X0 ) )
| ( $true
!= ( sK0 @ sK6 @ X0 ) ) )
| spl18_2
| ~ spl18_6 ),
inference(constrained_superposition,[],[f266,f21057]) ).
thf(f22562,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
= ( sK0 @ sK13 @ X0 ) )
| ( $true
!= ( sK0 @ sK10 @ X0 ) ) )
| spl18_4
| ~ spl18_6 ),
inference(constrained_superposition,[],[f266,f21173]) ).
thf(f22565,plain,
( ! [X0: $i] :
( ( $true
!= ( sK0 @ sK10 @ X0 ) )
| ( $true
= ( sK0 @ sK13 @ X0 ) ) )
| spl18_4
| ~ spl18_6 ),
inference(trivial_inequality_removal,[],[f22562]) ).
thf(f22566,plain,
( ! [X0: $i] :
( ( $true
!= ( sK0 @ sK6 @ X0 ) )
| ( $true
= ( sK0 @ sK9 @ X0 ) ) )
| spl18_2
| ~ spl18_6 ),
inference(trivial_inequality_removal,[],[f22561]) ).
thf(f22604,plain,
( ( $true != $true )
| ( $true
= ( sK0 @ sK13 @ sK12 ) )
| spl18_4
| ~ spl18_6
| ~ spl18_10 ),
inference(constrained_superposition,[],[f22565,f451]) ).
thf(f22607,plain,
( ( $true
= ( sK0 @ sK13 @ sK12 ) )
| spl18_4
| ~ spl18_6
| ~ spl18_10 ),
inference(trivial_inequality_removal,[],[f22604]) ).
thf(f22694,plain,
( ( $true = $false )
| ( $true
= ( sK11 @ sK12 ) )
| spl18_4
| ~ spl18_6
| ~ spl18_10 ),
inference(constrained_superposition,[],[f22607,f21976]) ).
thf(f22709,plain,
( ( $true
= ( sK11 @ sK12 ) )
| spl18_4
| ~ spl18_6
| ~ spl18_10 ),
inference(trivial_inequality_removal,[],[f22694]) ).
thf(f22717,plain,
( ( $true = $false )
| ~ spl18_3
| spl18_4
| ~ spl18_6
| ~ spl18_10 ),
inference(forward_demodulation,[],[f22709,f255]) ).
thf(f22718,plain,
( $false
| ~ spl18_3
| spl18_4
| ~ spl18_6
| ~ spl18_10 ),
inference(trivial_inequality_removal,[],[f22717]) ).
thf(f22719,plain,
( ~ spl18_3
| spl18_4
| ~ spl18_6
| ~ spl18_10 ),
inference(avatar_contradiction_clause,[],[f22718]) ).
thf(f22769,plain,
( ( $true != $true )
| ( $true
= ( sK0 @ sK9 @ sK8 ) )
| spl18_2
| ~ spl18_6 ),
inference(constrained_superposition,[],[f22566,f20965]) ).
thf(f22772,plain,
( ( $true
= ( sK0 @ sK9 @ sK8 ) )
| spl18_2
| ~ spl18_6 ),
inference(trivial_inequality_removal,[],[f22769]) ).
thf(f22806,plain,
( ( $true = $false )
| ( $true
= ( sK7 @ sK8 ) )
| spl18_2
| ~ spl18_6 ),
inference(constrained_superposition,[],[f22772,f21289]) ).
thf(f22821,plain,
( ( $true
= ( sK7 @ sK8 ) )
| spl18_2
| ~ spl18_6 ),
inference(trivial_inequality_removal,[],[f22806]) ).
thf(f22829,plain,
( ( $true = $false )
| ~ spl18_1
| spl18_2
| ~ spl18_6 ),
inference(forward_demodulation,[],[f22821,f239]) ).
thf(f22830,plain,
( $false
| ~ spl18_1
| spl18_2
| ~ spl18_6 ),
inference(trivial_inequality_removal,[],[f22829]) ).
thf(f22831,plain,
( ~ spl18_1
| spl18_2
| ~ spl18_6 ),
inference(avatar_contradiction_clause,[],[f22830]) ).
thf(f23674,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK17 @ X1 ) )
| ( $true
= ( sK15 @ X1 ) ) )
| ~ spl18_8 ),
inference(forward_subsumption_resolution,[],[f235,f406]) ).
thf(f25176,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( sK0 @ sK17 @ X0 ) )
| ( $false
= ( sK0 @ sK14 @ X0 ) ) )
| ~ spl18_5
| ~ spl18_8
| ~ spl18_9 ),
inference(constrained_superposition,[],[f501,f15680]) ).
thf(f25178,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ sK17 @ X0 ) )
| ( $false
= ( sK0 @ sK14 @ X0 ) ) )
| ~ spl18_5
| ~ spl18_8
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f25176]) ).
thf(f25323,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( sK15 @ X0 ) )
| ( $false
= ( sK0 @ sK14 @ X0 ) ) )
| ~ spl18_5
| ~ spl18_8
| ~ spl18_9 ),
inference(constrained_superposition,[],[f23674,f25178]) ).
thf(f25348,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK14 @ X0 ) )
| ( $true
= ( sK15 @ X0 ) ) )
| ~ spl18_5
| ~ spl18_8
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f25323]) ).
thf(f26520,plain,
( ( $true = $false )
| ( $true
= ( sK15 @ sK16 ) )
| ~ spl18_5
| ~ spl18_8
| ~ spl18_9 ),
inference(constrained_superposition,[],[f25348,f494]) ).
thf(f26608,plain,
( ( $true
= ( sK15 @ sK16 ) )
| ~ spl18_5
| ~ spl18_8
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f26520]) ).
thf(f26654,plain,
( ( $true = $false )
| ~ spl18_5
| ~ spl18_7
| ~ spl18_8
| ~ spl18_9 ),
inference(forward_demodulation,[],[f26608,f403]) ).
thf(f26655,plain,
( $false
| ~ spl18_5
| ~ spl18_7
| ~ spl18_8
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f26654]) ).
thf(f26656,plain,
( ~ spl18_5
| ~ spl18_7
| ~ spl18_8
| ~ spl18_9 ),
inference(avatar_contradiction_clause,[],[f26655]) ).
cnf(s1,plain,
( spl18_1
| spl18_2 ),
inference(sat_conversion,[],[f244]) ).
cnf(s2,plain,
( spl18_3
| spl18_4 ),
inference(sat_conversion,[],[f260]) ).
cnf(s3,plain,
( spl18_5
| spl18_6 ),
inference(sat_conversion,[],[f267]) ).
cnf(s4,plain,
( spl18_7
| ~ spl18_8 ),
inference(sat_conversion,[],[f408]) ).
cnf(s5,plain,
( spl18_6
| spl18_9 ),
inference(sat_conversion,[],[f412]) ).
cnf(s6,plain,
( spl18_4
| spl18_10 ),
inference(sat_conversion,[],[f452]) ).
cnf(s7,plain,
( ~ spl18_2
| ~ spl18_4
| ~ spl18_6
| spl18_8 ),
inference(sat_conversion,[],[f473]) ).
cnf(s9,plain,
( ~ spl18_6
| ~ spl18_7
| ~ spl18_8 ),
inference(sat_conversion,[],[f553]) ).
cnf(s11,plain,
( ~ spl18_2
| ~ spl18_4
| ~ spl18_5
| spl18_8
| ~ spl18_9 ),
inference(sat_conversion,[],[f17472]) ).
cnf(s16,plain,
( ~ spl18_2
| ~ spl18_3
| ~ spl18_5
| spl18_8
| ~ spl18_9
| ~ spl18_10 ),
inference(sat_conversion,[],[f20337]) ).
cnf(s18,plain,
( ~ spl18_1
| spl18_2
| ~ spl18_5
| ~ spl18_9 ),
inference(sat_conversion,[],[f22541]) ).
cnf(s20,plain,
( ~ spl18_3
| spl18_4
| ~ spl18_6
| ~ spl18_10 ),
inference(sat_conversion,[],[f22719]) ).
cnf(s22,plain,
( ~ spl18_1
| spl18_2
| ~ spl18_6 ),
inference(sat_conversion,[],[f22831]) ).
cnf(s24,plain,
( ~ spl18_5
| ~ spl18_7
| ~ spl18_8
| ~ spl18_9 ),
inference(sat_conversion,[],[f26656]) ).
cnf(s25,plain,
( ~ spl18_6
| ~ spl18_4
| ~ spl18_2 ),
inference(rat,[],[s9,s4,s7]) ).
cnf(s26,plain,
( ~ spl18_5
| ~ spl18_9
| ~ spl18_8 ),
inference(rat,[],[s4,s24]) ).
cnf(s27,plain,
( ~ spl18_5
| ~ spl18_9
| ~ spl18_2
| ~ spl18_4 ),
inference(rat,[],[s26,s11]) ).
cnf(s28,plain,
( ~ spl18_4
| ~ spl18_2 ),
inference(rat,[],[s27,s3,s5,s25]) ).
cnf(s29,plain,
~ spl18_2,
inference(rat,[],[s16,s26,s3,s5,s20,s2,s6,s28]) ).
cnf(s30,plain,
spl18_1,
inference(rat,[],[s1,s29]) ).
cnf(s31,plain,
~ spl18_6,
inference(rat,[],[s22,s29,s30]) ).
cnf(s32,plain,
spl18_9,
inference(rat,[],[s5,s31]) ).
cnf(s33,plain,
spl18_5,
inference(rat,[],[s3,s31]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s18,s30,s29,s32,s33]) ).
thf(f26657,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL880^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 10:24:45 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.43/0.93 % (2490881)Will run a generic schedule for satisfiability detection.
% 4.43/0.93 % (2490886)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=215853294_2999 on theBenchmark for (2999ds/0Mi)
% 4.43/0.93 % Exception at run slice level
% 4.43/0.93 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.43/0.93 % (2490887)% WARNING: option uhcvi not known.
% 4.43/0.93 % (2490887)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2633131802:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.43/0.93 % (2490887)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.43/0.93 % (2490887)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.43/0.93 % (2490894)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3147271297:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.43/0.93 % Exception at run slice level
% 4.43/0.93 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.43/0.93 % (2490892)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3942359990:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.43/0.93 % (2490893)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2720011541:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.43/0.93 % (2490897)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3614278493:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.43/0.93 % (2490889)dis+10_1_sil=32000:sp=arity:random_seed=3142902351:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.43/0.93 % (2490888)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2978235609:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.43/0.93 % (2490890)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=980724920:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.43/0.93 % (2490890)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.43/0.93 % (2490897)Instruction limit reached!
% 4.43/0.93 % (2490897)------------------------------
% 4.43/0.93 % (2490897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.43/0.93 % (2490897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/0.93 % (2490897)CaDiCaL version: 2.1.3
% 4.43/0.93 % (2490897)Termination reason: Instruction limit
% 4.43/0.93 % (2490897)Termination phase: Saturation
% 4.43/0.93 % (2490897)Time elapsed: 0.035 s
% 4.43/0.93 % (2490897)Peak memory usage: 12 MB
% 4.43/0.93 % (2490897)Instructions burned: 133 (million)
% 4.43/0.93 % (2490904)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=579315205:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.43/0.93 % (2490904)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.43/0.93 % (2490904)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.43/0.93 % (2490892)Instruction limit reached!
% 4.43/0.93 % (2490892)------------------------------
% 4.43/0.93 % (2490892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.43/0.93 % (2490892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/0.93 % (2490892)CaDiCaL version: 2.1.3
% 4.43/0.93 % (2490892)Termination reason: Instruction limit
% 4.43/0.93 % (2490892)Termination phase: Saturation
% 4.43/0.93 % (2490892)Time elapsed: 0.065 s
% 4.43/0.93 % (2490892)Peak memory usage: 13 MB
% 4.43/0.93 % (2490892)Instructions burned: 132 (million)
% 4.43/0.93 % (2490889)Instruction limit reached!
% 4.43/0.93 % (2490889)------------------------------
% 4.43/0.93 % (2490889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.43/0.93 % (2490889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/0.93 % (2490889)CaDiCaL version: 2.1.3
% 4.43/0.93 % (2490889)Termination reason: Instruction limit
% 4.43/0.93 % (2490889)Termination phase: Saturation
% 4.43/0.93 % (2490889)Time elapsed: 0.050 s
% 4.43/0.93 % (2490889)Peak memory usage: 12 MB
% 4.43/0.93 % (2490889)Instructions burned: 104 (million)
% 4.43/0.93 % (2490893)Instruction limit reached!
% 4.43/0.93 % (2490893)------------------------------
% 4.43/0.93 % (2490893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.71 % (2490893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.71 % (2490893)CaDiCaL version: 2.1.3
% 10.19/1.71 % (2490893)Termination reason: Instruction limit
% 10.19/1.71 % (2490893)Termination phase: Saturation
% 10.19/1.71 % (2490893)Time elapsed: 0.080 s
% 10.19/1.71 % (2490893)Peak memory usage: 13 MB
% 10.19/1.71 % (2490893)Instructions burned: 160 (million)
% 10.19/1.71 % (2490890)Instruction limit reached!
% 10.19/1.71 % (2490890)------------------------------
% 10.19/1.71 % (2490890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.71 % (2490890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.71 % (2490890)CaDiCaL version: 2.1.3
% 10.19/1.71 % (2490890)Termination reason: Instruction limit
% 10.19/1.71 % (2490890)Termination phase: Saturation
% 10.19/1.71 % (2490890)Time elapsed: 0.056 s
% 10.19/1.71 % (2490890)Peak memory usage: 12 MB
% 10.19/1.71 % (2490890)Instructions burned: 116 (million)
% 10.19/1.71 % (2490906)ott-21_1_sil=16000:fs=off:random_seed=3075124458:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 10.19/1.71 % (2490907)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1559756159:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 10.19/1.71 % (2490909)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2224162701:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 10.19/1.71 % (2490908)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=888311665:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 10.19/1.71 % Exception at run slice level
% 10.19/1.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.19/1.71 % (2490914)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1214127282:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 10.19/1.71 % Exception at run slice level
% 10.19/1.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.19/1.71 % (2490916)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3852518988:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 10.19/1.71 % (2490916)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.19/1.71 % (2490906)Instruction limit reached!
% 10.19/1.71 % (2490906)------------------------------
% 10.19/1.71 % (2490906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.71 % (2490906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.71 % (2490906)CaDiCaL version: 2.1.3
% 10.19/1.71 % (2490906)Termination reason: Instruction limit
% 10.19/1.71 % (2490906)Termination phase: Saturation
% 10.19/1.71 % (2490906)Time elapsed: 0.081 s
% 10.19/1.71 % (2490906)Peak memory usage: 13 MB
% 10.19/1.71 % (2490906)Instructions burned: 181 (million)
% 10.19/1.71 % (2490918)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2183102899:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 10.19/1.71 % (2490918)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.19/1.71 % (2490904)Instruction limit reached!
% 10.19/1.71 % (2490904)------------------------------
% 10.19/1.71 % (2490904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.71 % (2490904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.71 % (2490904)CaDiCaL version: 2.1.3
% 10.19/1.71 % (2490904)Termination reason: Instruction limit
% 10.19/1.71 % (2490904)Termination phase: Saturation
% 10.19/1.71 % (2490904)Time elapsed: 0.173 s
% 10.19/1.71 % (2490904)Peak memory usage: 15 MB
% 10.19/1.71 % (2490904)Instructions burned: 688 (million)
% 10.19/1.71 % (2490920)fmb+10_1_sil=64000:random_seed=3848869639:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 10.19/1.71 % (2490920)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 10.19/1.71 % Exception at run slice level
% 10.19/1.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.19/1.71 % (2490922)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=4192933032:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 10.19/1.71 % Exception at run slice level
% 10.19/1.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.19/1.71 % (2490924)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=4087415540:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 10.19/1.71 % Exception at run slice level
% 10.19/1.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.19/1.71 % (2490926)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3255767083:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 10.19/1.71 % (2490926)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.19/1.71 % (2490907)Instruction limit reached!
% 10.19/1.71 % (2490907)------------------------------
% 10.19/1.71 % (2490907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.71 % (2490907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.71 % (2490907)CaDiCaL version: 2.1.3
% 10.19/1.71 % (2490907)Termination reason: Instruction limit
% 10.19/1.71 % (2490907)Termination phase: Saturation
% 10.19/1.71 % (2490907)Time elapsed: 0.386 s
% 10.19/1.71 % (2490907)Peak memory usage: 14 MB
% 10.19/1.71 % (2490907)Instructions burned: 477 (million)
% 10.19/1.71 % (2490928)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1976423610:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 10.19/1.71 % (2490928)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 10.19/1.71 % (2490928)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 10.19/1.71 % (2490916)Instruction limit reached!
% 10.19/1.71 % (2490916)------------------------------
% 10.19/1.71 % (2490916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.71 % (2490916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.71 % (2490916)CaDiCaL version: 2.1.3
% 10.19/1.71 % (2490916)Termination reason: Instruction limit
% 10.19/1.71 % (2490916)Termination phase: Saturation
% 10.19/1.71 % (2490916)Time elapsed: 0.358 s
% 10.19/1.71 % (2490916)Peak memory usage: 15 MB
% 10.19/1.71 % (2490916)Instructions burned: 693 (million)
% 10.19/1.71 % (2490930)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=4006670542:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 10.19/1.71 % Exception at run slice level
% 10.19/1.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.19/1.71 % (2490932)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2953273731:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 10.19/1.71 % Exception at run slice level
% 10.19/1.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.19/1.71 % (2490918)Instruction limit reached!
% 10.19/1.71 % (2490918)------------------------------
% 10.19/1.71 % (2490918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.71 % (2490918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.71 % (2490918)CaDiCaL version: 2.1.3
% 10.19/1.71 % (2490918)Termination reason: Instruction limit
% 10.19/1.71 % (2490918)Termination phase: Saturation
% 10.19/1.71 % (2490918)Time elapsed: 0.404 s
% 10.19/1.71 % (2490918)Peak memory usage: 15 MB
% 10.19/1.71 % (2490918)Instructions burned: 879 (million)
% 10.19/1.71 % (2490934)ott-2_1_sil=16000:newcnf=on:random_seed=2549165703:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 10.19/1.71 % (2490934)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.19/1.71 % (2490936)ott+10_1_sil=32000:tgt=ground:random_seed=1686152368:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 10.19/1.71 % (2490909)Instruction limit reached!
% 10.19/1.71 % (2490909)------------------------------
% 10.19/1.71 % (2490909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.71 % (2490909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.71 % (2490909)CaDiCaL version: 2.1.3
% 10.19/1.71 % (2490909)Termination reason: Instruction limit
% 10.19/1.71 % (2490909)Termination phase: Saturation
% 10.19/1.71 % (2490909)Time elapsed: 0.538 s
% 10.19/1.71 % (2490909)Peak memory usage: 16 MB
% 10.19/1.71 % (2490909)Instructions burned: 1180 (million)
% 10.19/1.71 % (2490938)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2828939232:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 10.19/1.71 % Exception at run slice level
% 10.19/1.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.19/1.71 % (2490940)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=4176995627:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 10.19/1.71 % (2490940)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 10.19/1.71 % (2490934)Instruction limit reached!
% 10.19/1.71 % (2490934)------------------------------
% 10.19/1.71 % (2490934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.71 % (2490934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.71 % (2490934)CaDiCaL version: 2.1.3
% 10.19/1.71 % (2490934)Termination reason: Instruction limit
% 10.19/1.71 % (2490934)Termination phase: Saturation
% 10.19/1.71 % (2490934)Time elapsed: 0.718 s
% 10.19/1.71 % (2490934)Peak memory usage: 16 MB
% 10.19/1.71 % (2490934)Instructions burned: 869 (million)
% 10.19/1.71 % (2490944)dis+21_1_sil=32000:sas=cadical:random_seed=3491988728:i=3773:amm=off_2986 on theBenchmark for (2986ds/3773Mi)
% 10.19/1.71 % (2490928)Instruction limit reached!
% 10.19/1.71 % (2490928)------------------------------
% 10.19/1.71 % (2490928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.71 % (2490928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.71 % (2490928)CaDiCaL version: 2.1.3
% 10.19/1.71 % (2490928)Termination reason: Instruction limit
% 10.19/1.71 % (2490928)Termination phase: Saturation
% 10.19/1.71 % (2490928)Time elapsed: 0.922 s
% 10.19/1.71 % (2490928)Peak memory usage: 19 MB
% 10.19/1.71 % (2490928)Instructions burned: 1472 (million)
% 10.19/1.71 % (2490926) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2490881-2490926"...
% 10.19/1.71 % (2490926)...printing done.
% 10.19/1.71 % (2490926)Refutation found. Thanks to Tanya!
% 10.19/1.71 % SZS status Theorem for theBenchmark
% 10.19/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 10.19/1.71 % (2490926)------------------------------
% 10.19/1.71 % (2490926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.71 % (2490926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.71 % (2490926)CaDiCaL version: 2.1.3
% 10.19/1.71 % (2490926)Termination reason: Refutation
% 10.19/1.71 % (2490926)Time elapsed: 1.155 s
% 10.19/1.71 % (2490926)Peak memory usage: 22 MB
% 10.19/1.71 % (2490926)Instructions burned: 5089 (million)
% 10.19/1.71 % (2490881)Success in time 1.484 s
% 10.19/1.71 % Vampire exiting
%------------------------------------------------------------------------------