%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL879^1 : 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 : n010.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 33.84s 5.12s
% Output : Refutation 33.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 17
% Syntax : Number of formulae : 270 ( 33 unt; 0 typ; 10 def)
% Number of atoms : 2648 ( 542 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 3335 ( 584 ~; 795 |; 14 &;1787 @)
% ( 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 : 246 ( 246 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 77 usr; 25 con; 0-4 aty)
% ( 133 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 624 ( 0 sgn 286 !; 14 ?; 624 :)
% 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 > $i ).
thf(func_def_68,type,
sK21: $i > $i ).
thf(func_def_69,type,
sK22: $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 @ ( mbox @ X0 @ X2 ) @ ( mbox @ X1 @ ( mbox @ X0 @ X2 ) ) ) ) )
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( ( X0 @ X4 @ X5 )
& ( X1 @ X3 @ X4 ) )
=> ( X0 @ X3 @ 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 @ ( mbox @ X0 @ X2 ) @ ( mbox @ X1 @ ( mbox @ X0 @ X2 ) ) ) ) )
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( ( X0 @ X4 @ X5 )
& ( X1 @ X3 @ X4 ) )
=> ( X0 @ X3 @ 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 @ ( mbox @ X0 @ X2 ) @ ( mbox @ X1 @ ( mbox @ X0 @ X2 ) ) ) ) )
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( ( X0 @ X4 @ X5 )
& ( X1 @ X3 @ X4 ) )
=> ( X0 @ X3 @ X5 ) ) ),
inference(rectify,[],[f33]) ).
thf(f86,plain,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ ( mbox @ X0 @ Y0 ) ) ) ) ) )
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( ( ( X0 @ X4 @ X5 )
= $true )
& ( ( X1 @ X3 @ X4 )
= $true ) )
=> ( ( X0 @ X3 @ 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 @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ ( mbox @ X0 @ Y0 ) ) ) ) ) )
<=> ! [X2: $i,X3: $i,X4: $i] :
( ( ( ( X0 @ X3 @ X4 )
= $true )
& ( $true
= ( X1 @ X2 @ X3 ) ) )
=> ( ( X0 @ X2 @ X4 )
= $true ) ) ),
inference(rectify,[],[f86]) ).
thf(f88,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ ( mbox @ X0 @ Y0 ) ) ) ) ) )
<~> ! [X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X2 @ X4 )
= $true )
| ( ( X0 @ X3 @ 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 @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ ( mbox @ X0 @ Y0 ) ) ) ) ) )
<~> ! [X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X2 @ X4 )
= $true )
| ( ( X0 @ X3 @ 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 @ X2 @ X4 )
!= $true )
& ( ( X0 @ X3 @ X4 )
= $true )
& ( $true
= ( X1 @ X2 @ X3 ) ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) )
& ( ! [X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X2 @ X4 )
= $true )
| ( ( X0 @ X3 @ X4 )
!= $true )
| ( $true
!= ( X1 @ X2 @ X3 ) ) )
| ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ ( 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 @ X2 @ X4 )
!= $true )
& ( ( X0 @ X3 @ X4 )
= $true )
& ( $true
= ( X1 @ X2 @ X3 ) ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( $true
= ( X0 @ X5 @ X7 ) )
| ( $true
!= ( X0 @ X6 @ X7 ) )
| ( $true
!= ( X1 @ X5 @ X6 ) ) )
| ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) ) ),
inference(rectify,[],[f90]) ).
thf(f92,plain,
( ( ( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
& ( $true
= ( sK0 @ sK3 @ sK4 ) )
& ( $true
= ( sK1 @ sK2 @ sK3 ) ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK1 @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) ) )
| ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK1 @ ( 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 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK1 @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f125,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK1 @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f126,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK1 @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f127,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK1 @ ( 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 @ 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 > $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 > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f127,f120,f103,f131,f108,f108,f108]) ).
thf(f140,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 > $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 > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f126,f120,f103,f131,f108,f108,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 > $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 > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f125,f120,f103,f131,f108,f108,f108]) ).
thf(f142,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ 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 > $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 > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f124,f120,f103,f131,f108,f108,f108]) ).
thf(f143,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ 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 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ 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 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ 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 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ 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 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ 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 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ 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 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ 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 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ 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 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK1 @ X8 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X9 @ Y1 ) ) ) )
@ X10 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X8 @ Y0 )
| ( X9 @ Y0 ) )
@ ( sK5 @ X8 @ X9 ) ) ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ~ ( sK1 @ X8 @ X10 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( sK0 @ X8 @ ( sK5 @ X8 @ X9 ) )
| ( X9 @ ( sK5 @ X8 @ X9 ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) ) ) )
| ( $false
= ( ~ ( sK0 @ X8 @ ( sK5 @ X8 @ X9 ) )
| ( X9 @ ( sK5 @ X8 @ X9 ) ) ) )
| ( $true
= ( ~ ( sK1 @ X8 @ X10 ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) )
@ X11 ) )
| ( $false
= ( ~ ( sK0 @ X8 @ ( sK5 @ X8 @ X9 ) )
| ( X9 @ ( sK5 @ X8 @ X9 ) ) ) )
| ( $true
= ( ~ ( sK1 @ X8 @ X10 ) ) ) ),
inference(pi_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) )
@ X11 ) )
| ( $false
= ( X9 @ ( sK5 @ X8 @ X9 ) ) )
| ( $true
= ( ~ ( sK1 @ X8 @ X10 ) ) ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) )
@ X11 ) )
| ( $false
= ( ~ ( sK0 @ X8 @ ( sK5 @ X8 @ X9 ) ) ) )
| ( $true
= ( ~ ( sK1 @ X8 @ X10 ) ) ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f157,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) )
@ X11 ) )
| ( $true
= ( sK0 @ X8 @ ( sK5 @ X8 @ X9 ) ) )
| ( $true
= ( ~ ( sK1 @ X8 @ X10 ) ) ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) )
@ X11 ) )
| ( $true
= ( sK0 @ X8 @ ( sK5 @ X8 @ X9 ) ) )
| ( $false
= ( sK1 @ X8 @ X10 ) ) ),
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 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ~ ( sK0 @ X10 @ X11 )
| ( X9 @ X11 ) ) )
| ( $true
= ( sK0 @ X8 @ ( sK5 @ X8 @ X9 ) ) )
| ( $false
= ( sK1 @ X8 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( X9 @ X11 ) )
| ( $true
= ( sK0 @ X8 @ ( sK5 @ X8 @ X9 ) ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $true
= ( ~ ( sK0 @ X10 @ X11 ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( X9 @ X11 ) )
| ( $true
= ( sK0 @ X8 @ ( sK5 @ X8 @ X9 ) ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $false
= ( sK0 @ X10 @ X11 ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X10 @ Y0 )
| ( X9 @ Y0 ) )
@ X11 ) )
| ( $false
= ( X9 @ ( sK5 @ X8 @ X9 ) ) )
| ( $false
= ( sK1 @ X8 @ X10 ) ) ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f163,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( ~ ( sK0 @ X10 @ X11 )
| ( X9 @ X11 ) ) )
| ( $false
= ( X9 @ ( sK5 @ X8 @ X9 ) ) )
| ( $false
= ( sK1 @ X8 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( X9 @ X11 ) )
| ( $false
= ( X9 @ ( sK5 @ X8 @ X9 ) ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $true
= ( ~ ( sK0 @ X10 @ X11 ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i > $o,X7: $i,X5: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( X9 @ X11 ) )
| ( $false
= ( X9 @ ( sK5 @ X8 @ X9 ) ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $false
= ( sK0 @ X10 @ X11 ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,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(f167,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,[],[f166]) ).
thf(f168,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,[],[f167]) ).
thf(f169,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,[],[f168]) ).
thf(f170,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,[],[f169]) ).
thf(f171,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ sK6 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK7 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK6 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK6 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK6 @ Y0 )
| ( sK7 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK6 @ X1 )
| ( sK7 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( sK7 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK6 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( sK7 @ X1 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) ) ),
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 ) ) ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f179,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK6 @ sK8 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK8 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK8 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK6 @ sK8 ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK6 @ sK8 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK8 @ Y0 )
| ( sK7 @ Y0 ) )
@ sK9 ) ) ),
inference(sigma_proxy_clausification,[],[f180]) ).
thf(f184,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK8 @ sK9 )
| ( sK7 @ sK9 ) ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( sK7 @ sK9 ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK8 @ sK9 ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f187,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK8 @ sK9 ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,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,[],[f140]) ).
thf(f189,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 ) ) ) ) ) ) )
@ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( $true
= ( sK0 @ sK3 @ 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 @ sK3 @ 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 @ sK3 @ 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 @ sK3 @ 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 @ sK3 @ sK4 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK10 @ Y0 )
| ( sK11 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f195,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK10 @ Y0 )
| ( sK11 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK10 @ Y0 )
| ( sK11 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( ~ ( sK0 @ sK10 @ X1 )
| ( sK11 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK11 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK10 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK11 @ X1 ) )
| ( $false
= ( sK0 @ sK10 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK1 @ sK10 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK11 @ Y1 ) ) ) )
@ sK12 ) ) ),
inference(sigma_proxy_clausification,[],[f193]) ).
thf(f201,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ~ ( sK1 @ sK10 @ sK12 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK12 @ Y0 )
| ( sK11 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f200]) ).
thf(f202,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK12 @ Y0 )
| ( sK11 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f203,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ~ ( sK1 @ sK10 @ sK12 ) ) ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f204,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK1 @ sK10 @ sK12 ) ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK12 @ Y0 )
| ( sK11 @ Y0 ) )
@ sK13 ) ) ),
inference(sigma_proxy_clausification,[],[f202]) ).
thf(f206,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK12 @ sK13 )
| ( sK11 @ sK13 ) ) ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( sK11 @ sK13 ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK12 @ sK13 ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f209,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK0 @ sK12 @ sK13 ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,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,[],[f139]) ).
thf(f211,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 ) ) ) ) ) ) )
@ sK14 ) ) ),
inference(sigma_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( $true
!= ( sK0 @ sK2 @ 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,[],[f211]) ).
thf(f213,plain,
( ( $true
!= ( sK0 @ sK2 @ 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,[],[f212]) ).
thf(f214,plain,
( ( $true
!= ( sK0 @ sK2 @ 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,[],[f213]) ).
thf(f215,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ sK14 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK15 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK14 @ Y0 )
| ( sK15 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f214]) ).
thf(f217,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK14 @ Y0 )
| ( sK15 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK14 @ Y0 )
| ( sK15 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X1: $i] :
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( ~ ( sK0 @ sK14 @ X1 )
| ( sK15 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
! [X1: $i] :
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( sK15 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK14 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X1: $i] :
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( sK15 @ X1 ) )
| ( $false
= ( sK0 @ sK14 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK1 @ sK14 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK15 @ Y1 ) ) ) )
@ sK16 ) ) ),
inference(sigma_proxy_clausification,[],[f215]) ).
thf(f223,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ~ ( sK1 @ sK14 @ sK16 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK16 @ Y0 )
| ( sK15 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK16 @ Y0 )
| ( sK15 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ~ ( sK1 @ sK14 @ sK16 ) ) ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f226,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( sK1 @ sK14 @ sK16 ) ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK16 @ Y0 )
| ( sK15 @ Y0 ) )
@ sK17 ) ) ),
inference(sigma_proxy_clausification,[],[f224]) ).
thf(f228,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK16 @ sK17 )
| ( sK15 @ sK17 ) ) ) ),
inference(beta-eta_normalization,[],[f227]) ).
thf(f229,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( sK15 @ sK17 ) ) ),
inference(or_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( ~ ( sK0 @ sK16 @ sK17 ) ) ) ),
inference(or_proxy_clausification,[],[f228]) ).
thf(f231,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( sK0 @ sK16 @ sK17 ) ) ),
inference(not_proxy_clausification,[],[f230]) ).
thf(f233,definition,
( spl18_1
<=> ( $false
= ( sK7 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
thf(f235,plain,
( ( $false
= ( sK7 @ sK9 ) )
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f237,definition,
( spl18_2
<=> ( $true
= ( sK1 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
thf(f238,plain,
( ( $true
!= ( sK1 @ sK2 @ sK3 ) )
| spl18_2 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f239,plain,
( ( $true
= ( sK1 @ sK2 @ sK3 ) )
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f240,plain,
( spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f185,f237,f233]) ).
thf(f242,definition,
( spl18_3
<=> ( $false
= ( sK11 @ sK13 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
thf(f244,plain,
( ( $false
= ( sK11 @ sK13 ) )
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f242]) ).
thf(f246,definition,
( spl18_4
<=> ( $true
= ( sK0 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).
thf(f247,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| spl18_4 ),
inference(avatar_component_clause,[],[f246]) ).
thf(f248,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f246]) ).
thf(f249,plain,
( spl18_3
| spl18_4 ),
inference(avatar_split_clause,[],[f207,f246,f242]) ).
thf(f251,definition,
( spl18_5
<=> ( $false
= ( sK15 @ sK17 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
thf(f253,plain,
( ( $false
= ( sK15 @ sK17 ) )
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f251]) ).
thf(f255,definition,
( spl18_6
<=> ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
thf(f256,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f257,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| spl18_6 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f258,plain,
( spl18_5
| ~ spl18_6 ),
inference(avatar_split_clause,[],[f229,f255,f251]) ).
thf(f260,definition,
( spl18_7
<=> ( $true
= ( sK1 @ sK10 @ sK12 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_7])],[avatar_definition]) ).
thf(f262,plain,
( ( $true
= ( sK1 @ sK10 @ sK12 ) )
| ~ spl18_7 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f263,plain,
( spl18_7
| spl18_4 ),
inference(avatar_split_clause,[],[f204,f246,f260]) ).
thf(f282,definition,
( spl18_8
<=> ! [X10: $i,X11: $i,X9: $i > $o,X8: $i] :
( ( $true
= ( X9 @ X11 ) )
| ( $false
= ( sK0 @ X10 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $false
= ( X9 @ ( sK5 @ X8 @ X9 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_8])],[avatar_definition]) ).
thf(f283,plain,
( ! [X10: $i,X11: $i,X8: $i,X9: $i > $o] :
( ( $true
= ( X9 @ X11 ) )
| ( $false
= ( sK0 @ X10 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $false
= ( X9 @ ( sK5 @ X8 @ X9 ) ) ) )
| ~ spl18_8 ),
inference(avatar_component_clause,[],[f282]) ).
thf(f285,definition,
( spl18_9
<=> ! [X6: $i,X5: $i,X7: $i] :
( ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_9])],[avatar_definition]) ).
thf(f286,plain,
( ! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( sK1 @ X5 @ X6 ) )
| ( $true
= ( sK0 @ X5 @ X7 ) )
| ( $true
!= ( sK0 @ X6 @ X7 ) ) )
| ~ spl18_9 ),
inference(avatar_component_clause,[],[f285]) ).
thf(f287,plain,
( spl18_8
| spl18_9 ),
inference(avatar_split_clause,[],[f165,f285,f282]) ).
thf(f315,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK1 @ X2 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( sK11
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( sK5 @ X2
@ ^ [Y0: $i] :
( sK11
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) )
| ( sK13 != X0 ) )
| ~ spl18_3
| ~ spl18_8 ),
inference(constrained_superposition,[],[f244,f283]) ).
thf(f387,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK1 @ X2 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( sK11
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( sK5 @ X2
@ ^ [Y0: $i] :
( sK11
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) )
| ( sK13 != X0 ) )
| ~ spl18_3
| ~ spl18_8 ),
inference(trivial_inequality_removal,[],[f315]) ).
thf(f388,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( sK13 != X0 )
| ( $false
= ( sK1 @ X2 @ X1 ) )
| ( $false
= ( sK11 @ ( sK5 @ X2 @ sK11 ) ) )
| ( $false
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl18_3
| ~ spl18_8 ),
inference(beta-eta_normalization,[],[f387]) ).
thf(f444,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK1 @ X0 @ X1 ) )
| ( $false
= ( sK11 @ ( sK5 @ X0 @ sK11 ) ) )
| ( $false
= ( sK0 @ X1 @ sK13 ) ) )
| ~ spl18_3
| ~ spl18_8 ),
inference(equality_resolution,[],[f388]) ).
thf(f1186,plain,
( ( $true
= ( sK0 @ sK12 @ sK13 ) )
| spl18_4 ),
inference(forward_subsumption_resolution,[],[f209,f247]) ).
thf(f1203,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK1 @ X0 @ sK12 ) )
| ( $false
= ( sK11 @ ( sK5 @ X0 @ sK11 ) ) ) )
| ~ spl18_3
| spl18_4
| ~ spl18_8 ),
inference(constrained_superposition,[],[f444,f1186]) ).
thf(f1220,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 @ sK12 ) )
| ( $false
= ( sK11 @ ( sK5 @ X0 @ sK11 ) ) ) )
| ~ spl18_3
| spl18_4
| ~ spl18_8 ),
inference(trivial_inequality_removal,[],[f1203]) ).
thf(f1240,plain,
( ! [X1: $i] :
( ( $true
= ( sK11 @ X1 ) )
| ( $false
= ( sK0 @ sK10 @ X1 ) ) )
| spl18_4 ),
inference(forward_subsumption_resolution,[],[f199,f247]) ).
thf(f1245,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK10 @ sK13 ) )
| ~ spl18_3
| spl18_4 ),
inference(constrained_superposition,[],[f244,f1240]) ).
thf(f1259,plain,
( ( $false
= ( sK0 @ sK10 @ sK13 ) )
| ~ spl18_3
| spl18_4 ),
inference(trivial_inequality_removal,[],[f1245]) ).
thf(f1304,plain,
( ( $true = $false )
| ( $false
= ( sK11 @ ( sK5 @ sK10 @ sK11 ) ) )
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8 ),
inference(constrained_superposition,[],[f262,f1220]) ).
thf(f1343,plain,
( ( $false
= ( sK11 @ ( sK5 @ sK10 @ sK11 ) ) )
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8 ),
inference(trivial_inequality_removal,[],[f1304]) ).
thf(f1365,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK10 @ ( sK5 @ sK10 @ sK11 ) ) )
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8 ),
inference(constrained_superposition,[],[f1240,f1343]) ).
thf(f1385,plain,
( ( $false
= ( sK0 @ sK10 @ ( sK5 @ sK10 @ sK11 ) ) )
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8 ),
inference(trivial_inequality_removal,[],[f1365]) ).
thf(f1429,plain,
( ( $true
!= ( sK0 @ sK3 @ sK4 ) )
| ~ spl18_2
| spl18_6
| ~ spl18_9 ),
inference(unit_resulting_resolution,[],[f286,f257,f239]) ).
thf(f1430,plain,
( ( $true
= ( sK0 @ sK10 @ sK13 ) )
| spl18_4
| ~ spl18_7
| ~ spl18_9 ),
inference(unit_resulting_resolution,[],[f286,f1186,f262]) ).
thf(f1437,plain,
( ( $true = $false )
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_9 ),
inference(forward_demodulation,[],[f1430,f1259]) ).
thf(f1438,plain,
( $false
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f1437]) ).
thf(f1439,plain,
( ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_9 ),
inference(avatar_contradiction_clause,[],[f1438]) ).
thf(f1494,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( sK5 @ X0
@ ^ [Y0: $i] : ( Y0 != X1 ) )
= X1 )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK1 @ X0 @ X2 ) ) )
| ~ spl18_8 ),
inference(leibniz_equality_elimination,[],[f283]) ).
thf(f3307,definition,
( spl18_14
<=> ! [X10: $i,X11: $i,X9: $i > $o,X8: $i] :
( ( $true
= ( X9 @ X11 ) )
| ( $false
= ( sK0 @ X10 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $true
= ( sK0 @ X8 @ ( sK5 @ X8 @ X9 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_14])],[avatar_definition]) ).
thf(f3308,plain,
( ! [X10: $i,X11: $i,X8: $i,X9: $i > $o] :
( ( $true
= ( X9 @ X11 ) )
| ( $false
= ( sK0 @ X10 @ X11 ) )
| ( $false
= ( sK1 @ X8 @ X10 ) )
| ( $true
= ( sK0 @ X8 @ ( sK5 @ X8 @ X9 ) ) ) )
| ~ spl18_14 ),
inference(avatar_component_clause,[],[f3307]) ).
thf(f3309,plain,
( spl18_14
| spl18_9 ),
inference(avatar_split_clause,[],[f161,f285,f3307]) ).
thf(f3455,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( sK11 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK1 @ sK10 @ X1 ) ) )
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f1385,f3308]) ).
thf(f3528,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK11 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK1 @ sK10 @ X1 ) ) )
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f3455]) ).
thf(f3842,plain,
( ( $true = $false )
| ( $true
= ( sK11 @ sK13 ) )
| ( $false
= ( sK1 @ sK10 @ sK12 ) )
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f1186,f3528]) ).
thf(f3905,plain,
( ( $true
= ( sK11 @ sK13 ) )
| ( $false
= ( sK1 @ sK10 @ sK12 ) )
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f3842]) ).
thf(f3959,plain,
( ( $true = $false )
| ( $false
= ( sK1 @ sK10 @ sK12 ) )
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8
| ~ spl18_14 ),
inference(forward_demodulation,[],[f3905,f244]) ).
thf(f3960,plain,
( ( $false
= ( sK1 @ sK10 @ sK12 ) )
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f3959]) ).
thf(f3963,plain,
( ( $true = $false )
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f3960,f262]) ).
thf(f4023,plain,
( $false
| ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f3963]) ).
thf(f4024,plain,
( ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8
| ~ spl18_14 ),
inference(avatar_contradiction_clause,[],[f4023]) ).
thf(f4411,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != X0 )
@ X2 ) )
| ( $false
= ( sK0 @ X3 @ X2 ) )
| ( $false
= ( sK1 @ X1 @ X3 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) )
| ( $false
= ( sK1 @ X1 @ X4 ) ) )
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f3308,f1494]) ).
thf(f4448,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $true
= ( X2 != X0 ) )
| ( $false
= ( sK0 @ X3 @ X2 ) )
| ( $false
= ( sK1 @ X1 @ X3 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) )
| ( $false
= ( sK1 @ X1 @ X4 ) ) )
| ~ spl18_8
| ~ spl18_14 ),
inference(beta-eta_normalization,[],[f4411]) ).
thf(f4449,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( X2 = X0 ) )
| ( $false
= ( sK0 @ X3 @ X2 ) )
| ( $false
= ( sK1 @ X1 @ X3 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) )
| ( $false
= ( sK1 @ X1 @ X4 ) ) )
| ~ spl18_8
| ~ spl18_14 ),
inference(not_proxy_clausification,[],[f4448]) ).
thf(f4450,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X3 @ X2 ) )
| ( $false
= ( sK1 @ X1 @ X3 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) )
| ( $false
= ( sK1 @ X1 @ X4 ) )
| ( X0 != X2 ) )
| ~ spl18_8
| ~ spl18_14 ),
inference(equality_proxy_clausification,[],[f4449]) ).
thf(f5519,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( sK1 @ X2 @ X0 ) )
| ( $false
= ( sK1 @ X2 @ X0 ) )
| ( X1 != X1 ) )
| ~ spl18_8
| ~ spl18_14 ),
inference(equality_factoring,[],[f4450]) ).
thf(f5522,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( sK1 @ X2 @ X0 ) )
| ( X1 != X1 ) )
| ~ spl18_8
| ~ spl18_14 ),
inference(duplicate_literal_removal,[],[f5519]) ).
thf(f5523,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( sK1 @ X2 @ X0 ) ) )
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f5522]) ).
thf(f5731,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( sK0 @ X0 @ sK4 ) )
| ( $false
= ( sK1 @ X0 @ sK3 ) ) )
| ~ spl18_4
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f248,f5523]) ).
thf(f5773,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ sK4 ) )
| ( $false
= ( sK1 @ X0 @ sK3 ) ) )
| ~ spl18_4
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f5731]) ).
thf(f5846,plain,
( ( ( sK1 @ sK2 @ sK3 )
= $false )
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(unit_resulting_resolution,[],[f5773,f257]) ).
thf(f5999,plain,
( ( $true = $false )
| ~ spl18_2
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f5846,f239]) ).
thf(f6056,plain,
( $false
| ~ spl18_2
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f5999]) ).
thf(f6057,plain,
( ~ spl18_2
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(avatar_contradiction_clause,[],[f6056]) ).
thf(f6059,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK6 @ sK8 ) )
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(forward_demodulation,[],[f182,f5846]) ).
thf(f6060,plain,
( ( $true
= ( sK1 @ sK6 @ sK8 ) )
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f6059]) ).
thf(f6061,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK8 @ sK9 ) )
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(forward_demodulation,[],[f187,f5846]) ).
thf(f6062,plain,
( ( $true
= ( sK0 @ sK8 @ sK9 ) )
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f6061]) ).
thf(f6063,plain,
( ! [X1: $i] :
( ( $true = $false )
| ( $true
= ( sK7 @ X1 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) ) )
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(forward_demodulation,[],[f177,f5846]) ).
thf(f6064,plain,
( ! [X1: $i] :
( ( $true
= ( sK7 @ X1 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) ) )
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f6063]) ).
thf(f6190,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( sK0 @ X0 @ sK9 ) )
| ( $false
= ( sK1 @ X0 @ sK8 ) ) )
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f5523,f6062]) ).
thf(f6191,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ sK9 ) )
| ( $false
= ( sK1 @ X0 @ sK8 ) ) )
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f6190]) ).
thf(f6246,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK6 @ sK9 ) )
| ~ spl18_1
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f235,f6064]) ).
thf(f6247,plain,
( ( $false
= ( sK0 @ sK6 @ sK9 ) )
| ~ spl18_1
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f6246]) ).
thf(f6939,plain,
( ( $true = $false )
| ( $false
= ( sK1 @ sK6 @ sK8 ) )
| ~ spl18_1
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f6247,f6191]) ).
thf(f6976,plain,
( ( $false
= ( sK1 @ sK6 @ sK8 ) )
| ~ spl18_1
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f6939]) ).
thf(f7055,plain,
( ( $true = $false )
| ~ spl18_1
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f6976,f6060]) ).
thf(f7097,plain,
( $false
| ~ spl18_1
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f7055]) ).
thf(f7098,plain,
( ~ spl18_1
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(avatar_contradiction_clause,[],[f7097]) ).
thf(f7321,plain,
( ( $true
= ( sK1 @ sK6 @ sK8 ) )
| spl18_2 ),
inference(forward_subsumption_resolution,[],[f182,f238]) ).
thf(f7371,plain,
( ( $true
= ( sK1 @ sK14 @ sK16 ) )
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f226,f256]) ).
thf(f7421,plain,
( ( $true
= ( sK0 @ sK8 @ sK9 ) )
| spl18_2 ),
inference(forward_subsumption_resolution,[],[f187,f238]) ).
thf(f7519,plain,
( ( $true
= ( sK0 @ sK16 @ sK17 ) )
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f231,f256]) ).
thf(f7563,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( sK0 @ X0 @ sK17 ) )
| ( $false
= ( sK1 @ X0 @ sK16 ) ) )
| ~ spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f5523,f7519]) ).
thf(f7564,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ sK17 ) )
| ( $false
= ( sK1 @ X0 @ sK16 ) ) )
| ~ spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f7563]) ).
thf(f8107,plain,
( ! [X1: $i] :
( ( $true
= ( sK7 @ X1 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) ) )
| spl18_2 ),
inference(forward_subsumption_resolution,[],[f177,f238]) ).
thf(f8120,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK6 @ sK9 ) )
| ~ spl18_1
| spl18_2 ),
inference(constrained_superposition,[],[f235,f8107]) ).
thf(f8121,plain,
( ( $false
= ( sK0 @ sK6 @ sK9 ) )
| ~ spl18_1
| spl18_2 ),
inference(trivial_inequality_removal,[],[f8120]) ).
thf(f8314,plain,
( ! [X1: $i] :
( ( $true
= ( sK15 @ X1 ) )
| ( $false
= ( sK0 @ sK14 @ X1 ) ) )
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f221,f256]) ).
thf(f8327,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK14 @ sK17 ) )
| ~ spl18_5
| ~ spl18_6 ),
inference(constrained_superposition,[],[f253,f8314]) ).
thf(f8328,plain,
( ( $false
= ( sK0 @ sK14 @ sK17 ) )
| ~ spl18_5
| ~ spl18_6 ),
inference(trivial_inequality_removal,[],[f8327]) ).
thf(f8372,plain,
( ( $true = $false )
| ( $false
= ( sK1 @ sK14 @ sK16 ) )
| ~ spl18_5
| ~ spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f7564,f8328]) ).
thf(f8373,plain,
( ( $false
= ( sK1 @ sK14 @ sK16 ) )
| ~ spl18_5
| ~ spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f8372]) ).
thf(f8418,plain,
( ( $true = $false )
| ~ spl18_5
| ~ spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f8373,f7371]) ).
thf(f8460,plain,
( $false
| ~ spl18_5
| ~ spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f8418]) ).
thf(f8461,plain,
( ~ spl18_5
| ~ spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(avatar_contradiction_clause,[],[f8460]) ).
thf(f8605,plain,
( ( $true
= ( sK0 @ sK14 @ sK17 ) )
| ~ spl18_6
| ~ spl18_9 ),
inference(unit_resulting_resolution,[],[f286,f7519,f7371]) ).
thf(f8633,plain,
( ( $true = $false )
| ~ spl18_5
| ~ spl18_6
| ~ spl18_9 ),
inference(forward_demodulation,[],[f8605,f8328]) ).
thf(f8634,plain,
( $false
| ~ spl18_5
| ~ spl18_6
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f8633]) ).
thf(f8635,plain,
( ~ spl18_5
| ~ spl18_6
| ~ spl18_9 ),
inference(avatar_contradiction_clause,[],[f8634]) ).
thf(f8636,plain,
( $false
| ~ spl18_2
| ~ spl18_4
| spl18_6
| ~ spl18_9 ),
inference(forward_subsumption_resolution,[],[f1429,f248]) ).
thf(f8637,plain,
( ~ spl18_2
| ~ spl18_4
| spl18_6
| ~ spl18_9 ),
inference(avatar_contradiction_clause,[],[f8636]) ).
thf(f8720,plain,
( ( $true
= ( sK0 @ sK6 @ sK9 ) )
| spl18_2
| ~ spl18_9 ),
inference(unit_resulting_resolution,[],[f286,f7321,f7421]) ).
thf(f8886,plain,
( ( $true = $false )
| ~ spl18_1
| spl18_2
| ~ spl18_9 ),
inference(forward_demodulation,[],[f8720,f8121]) ).
thf(f8887,plain,
( $false
| ~ spl18_1
| spl18_2
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f8886]) ).
thf(f8888,plain,
( ~ spl18_1
| spl18_2
| ~ spl18_9 ),
inference(avatar_contradiction_clause,[],[f8887]) ).
cnf(s1,plain,
( spl18_1
| spl18_2 ),
inference(sat_conversion,[],[f240]) ).
cnf(s2,plain,
( spl18_3
| spl18_4 ),
inference(sat_conversion,[],[f249]) ).
cnf(s3,plain,
( spl18_5
| ~ spl18_6 ),
inference(sat_conversion,[],[f258]) ).
cnf(s4,plain,
( spl18_4
| spl18_7 ),
inference(sat_conversion,[],[f263]) ).
cnf(s5,plain,
( spl18_8
| spl18_9 ),
inference(sat_conversion,[],[f287]) ).
cnf(s8,plain,
( ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_9 ),
inference(sat_conversion,[],[f1439]) ).
cnf(s9,plain,
( spl18_9
| spl18_14 ),
inference(sat_conversion,[],[f3309]) ).
cnf(s11,plain,
( ~ spl18_3
| spl18_4
| ~ spl18_7
| ~ spl18_8
| ~ spl18_14 ),
inference(sat_conversion,[],[f4024]) ).
cnf(s13,plain,
( ~ spl18_2
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(sat_conversion,[],[f6057]) ).
cnf(s15,plain,
( ~ spl18_1
| ~ spl18_4
| spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(sat_conversion,[],[f7098]) ).
cnf(s19,plain,
( ~ spl18_5
| ~ spl18_6
| ~ spl18_8
| ~ spl18_14 ),
inference(sat_conversion,[],[f8461]) ).
cnf(s20,plain,
( ~ spl18_5
| ~ spl18_6
| ~ spl18_9 ),
inference(sat_conversion,[],[f8635]) ).
cnf(s21,plain,
( ~ spl18_2
| ~ spl18_4
| spl18_6
| ~ spl18_9 ),
inference(sat_conversion,[],[f8637]) ).
cnf(s22,plain,
( ~ spl18_1
| spl18_2
| ~ spl18_9 ),
inference(sat_conversion,[],[f8888]) ).
cnf(s23,plain,
( spl18_6
| ~ spl18_4
| ~ spl18_2 ),
inference(rat,[],[s13,s5,s9,s21]) ).
cnf(s24,plain,
( ~ spl18_5
| ~ spl18_6 ),
inference(rat,[],[s19,s5,s9,s20]) ).
cnf(s25,plain,
~ spl18_6,
inference(rat,[],[s24,s3]) ).
cnf(s26,plain,
( ~ spl18_3
| ~ spl18_7
| spl18_4 ),
inference(rat,[],[s11,s5,s9,s8]) ).
cnf(s27,plain,
spl18_4,
inference(rat,[],[s26,s2,s4]) ).
cnf(s28,plain,
~ spl18_2,
inference(rat,[],[s23,s25,s27]) ).
cnf(s29,plain,
spl18_1,
inference(rat,[],[s1,s28]) ).
cnf(s30,plain,
~ spl18_9,
inference(rat,[],[s22,s28,s29]) ).
cnf(s31,plain,
spl18_14,
inference(rat,[],[s9,s30]) ).
cnf(s32,plain,
spl18_8,
inference(rat,[],[s5,s30]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s15,s25,s27,s29,s31,s32]) ).
thf(f8889,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL879^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 % Computer : n010.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 10:23:48 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.28 Running first-order model finding
% 0.09/0.28 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
% 6.94/1.52 % (2667480)Will run a generic schedule for satisfiability detection.
% 6.94/1.52 % (2667486)% WARNING: option uhcvi not known.
% 6.94/1.52 % (2667489)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=861087686:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.94/1.52 % (2667485)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3265756448_2999 on theBenchmark for (2999ds/0Mi)
% 6.94/1.52 % (2667488)dis+10_1_sil=32000:sp=arity:random_seed=4196676552:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.94/1.52 % (2667487)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3840994411:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.94/1.52 % (2667486)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3455438173:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.94/1.52 % (2667490)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1790416569:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.94/1.52 % (2667491)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=189073452:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.94/1.52 % (2667489)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.94/1.52 % (2667486)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.94/1.52 % Exception at run slice level
% 6.94/1.52 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.94/1.52 % (2667486)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.94/1.52 % (2667499)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=540309785:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.94/1.52 % Exception at run slice level
% 6.94/1.52 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.94/1.52 % (2667501)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1744172403:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.94/1.52 % (2667488)Instruction limit reached!
% 6.94/1.52 % (2667488)------------------------------
% 6.94/1.52 % (2667488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.52 % (2667488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.52 % (2667488)CaDiCaL version: 2.1.3
% 6.94/1.52 % (2667488)Termination reason: Instruction limit
% 6.94/1.52 % (2667488)Termination phase: Saturation
% 6.94/1.52 % (2667488)Time elapsed: 0.090 s
% 6.94/1.52 % (2667488)Peak memory usage: 12 MB
% 6.94/1.52 % (2667488)Instructions burned: 104 (million)
% 6.94/1.52 % (2667489)Instruction limit reached!
% 6.94/1.52 % (2667489)------------------------------
% 6.94/1.52 % (2667489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.52 % (2667489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.52 % (2667489)CaDiCaL version: 2.1.3
% 6.94/1.52 % (2667489)Termination reason: Instruction limit
% 6.94/1.52 % (2667489)Termination phase: Saturation
% 6.94/1.52 % (2667489)Time elapsed: 0.097 s
% 6.94/1.52 % (2667489)Peak memory usage: 12 MB
% 6.94/1.52 % (2667489)Instructions burned: 117 (million)
% 6.94/1.52 % (2667490)Instruction limit reached!
% 6.94/1.52 % (2667490)------------------------------
% 6.94/1.52 % (2667490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.52 % (2667490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.52 % (2667490)CaDiCaL version: 2.1.3
% 6.94/1.52 % (2667490)Termination reason: Instruction limit
% 6.94/1.52 % (2667490)Termination phase: Saturation
% 6.94/1.52 % (2667490)Time elapsed: 0.112 s
% 6.94/1.52 % (2667490)Peak memory usage: 13 MB
% 6.94/1.52 % (2667490)Instructions burned: 131 (million)
% 6.94/1.52 % (2667501)Instruction limit reached!
% 6.94/1.52 % (2667501)------------------------------
% 6.94/1.52 % (2667501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.94/1.52 % (2667501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/1.52 % (2667501)CaDiCaL version: 2.1.3
% 6.94/1.52 % (2667501)Termination reason: Instruction limit
% 6.94/1.52 % (2667501)Termination phase: Saturation
% 6.94/1.52 % (2667501)Time elapsed: 0.067 s
% 6.94/1.52 % (2667501)Peak memory usage: 12 MB
% 6.94/1.52 % (2667501)Instructions burned: 131 (million)
% 6.94/1.52 % (2667503)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=3377563643:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 28.32/4.40 % (2667503)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 28.32/4.40 % (2667504)ott-21_1_sil=16000:fs=off:random_seed=206571711:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 28.32/4.40 % (2667503)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 28.32/4.40 % (2667506)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4290147352:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 28.32/4.40 % Exception at run slice level
% 28.32/4.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 28.32/4.40 % (2667505)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2277280436:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 28.32/4.40 % (2667491)Instruction limit reached!
% 28.32/4.40 % (2667491)------------------------------
% 28.32/4.40 % (2667491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.32/4.40 % (2667491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.32/4.40 % (2667491)CaDiCaL version: 2.1.3
% 28.32/4.40 % (2667491)Termination reason: Instruction limit
% 28.32/4.40 % (2667491)Termination phase: Saturation
% 28.32/4.40 % (2667491)Time elapsed: 0.160 s
% 28.32/4.40 % (2667491)Peak memory usage: 13 MB
% 28.32/4.40 % (2667491)Instructions burned: 159 (million)
% 28.32/4.40 % (2667510)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3621348026:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 28.32/4.40 % (2667513)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1396076937:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 28.32/4.40 % Exception at run slice level
% 28.32/4.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 28.32/4.40 % (2667515)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=2258620604:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 28.32/4.40 % (2667515)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 28.32/4.40 % (2667504)Instruction limit reached!
% 28.32/4.40 % (2667504)------------------------------
% 28.32/4.40 % (2667504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.32/4.40 % (2667504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.32/4.40 % (2667504)CaDiCaL version: 2.1.3
% 28.32/4.40 % (2667504)Termination reason: Instruction limit
% 28.32/4.40 % (2667504)Termination phase: Saturation
% 28.32/4.40 % (2667504)Time elapsed: 0.159 s
% 28.32/4.40 % (2667504)Peak memory usage: 13 MB
% 28.32/4.40 % (2667504)Instructions burned: 180 (million)
% 28.32/4.40 % (2667517)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1735370118:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 28.32/4.40 % (2667517)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 28.32/4.40 % (2667505)Instruction limit reached!
% 28.32/4.40 % (2667505)------------------------------
% 28.32/4.40 % (2667505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.32/4.40 % (2667505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.32/4.40 % (2667505)CaDiCaL version: 2.1.3
% 28.32/4.40 % (2667505)Termination reason: Instruction limit
% 28.32/4.40 % (2667505)Termination phase: Saturation
% 28.32/4.40 % (2667505)Time elapsed: 0.426 s
% 28.32/4.40 % (2667505)Peak memory usage: 13 MB
% 28.32/4.40 % (2667505)Instructions burned: 478 (million)
% 28.32/4.40 % (2667519)fmb+10_1_sil=64000:random_seed=1876713925:i=22061:nm=2:gsp=on_2993 on theBenchmark for (2993ds/22061Mi)
% 28.32/4.40 % (2667519)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 28.32/4.40 % Exception at run slice level
% 28.32/4.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 28.32/4.40 % (2667510)Instruction limit reached!
% 28.32/4.40 % (2667510)------------------------------
% 28.32/4.40 % (2667510)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.32/4.40 % (2667510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.84/5.12 % (2667510)CaDiCaL version: 2.1.3
% 33.84/5.12 % (2667510)Termination reason: Instruction limit
% 33.84/5.12 % (2667510)Termination phase: Saturation
% 33.84/5.12 % (2667510)Time elapsed: 0.490 s
% 33.84/5.12 % (2667510)Peak memory usage: 15 MB
% 33.84/5.12 % (2667510)Instructions burned: 1180 (million)
% 33.84/5.12 % (2667522)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1541453201:fmbsr=1.7:i=920_2992 on theBenchmark for (2992ds/920Mi)
% 33.84/5.12 % Exception at run slice level
% 33.84/5.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.84/5.12 % (2667524)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3006692242:i=5131_2992 on theBenchmark for (2992ds/5131Mi)
% 33.84/5.12 % (2667524)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 33.84/5.12 % (2667521)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3990077342:i=9515:nm=5_2993 on theBenchmark for (2993ds/9515Mi)
% 33.84/5.12 % Exception at run slice level
% 33.84/5.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.84/5.12 % (2667503)Instruction limit reached!
% 33.84/5.12 % (2667503)------------------------------
% 33.84/5.12 % (2667503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.84/5.12 % (2667503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.84/5.12 % (2667503)CaDiCaL version: 2.1.3
% 33.84/5.12 % (2667503)Termination reason: Instruction limit
% 33.84/5.12 % (2667503)Termination phase: Saturation
% 33.84/5.12 % (2667503)Time elapsed: 0.588 s
% 33.84/5.12 % (2667503)Peak memory usage: 15 MB
% 33.84/5.12 % (2667503)Instructions burned: 684 (million)
% 33.84/5.12 % (2667527)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=547620783:i=1472:ins=7:fdi=8:gsp=on_2992 on theBenchmark for (2992ds/1472Mi)
% 33.84/5.12 % (2667527)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 33.84/5.12 % (2667527)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 33.84/5.12 % (2667528)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=437276435:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 33.84/5.12 % Exception at run slice level
% 33.84/5.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.84/5.12 % (2667531)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3964186418:fmbsr=2.30978:i=2174_2991 on theBenchmark for (2991ds/2174Mi)
% 33.84/5.12 % Exception at run slice level
% 33.84/5.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.84/5.12 % (2667515)Instruction limit reached!
% 33.84/5.12 % (2667515)------------------------------
% 33.84/5.12 % (2667515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.84/5.12 % (2667515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.84/5.12 % (2667515)CaDiCaL version: 2.1.3
% 33.84/5.12 % (2667515)Termination reason: Instruction limit
% 33.84/5.12 % (2667515)Termination phase: Saturation
% 33.84/5.12 % (2667515)Time elapsed: 0.593 s
% 33.84/5.12 % (2667515)Peak memory usage: 14 MB
% 33.84/5.12 % (2667515)Instructions burned: 692 (million)
% 33.84/5.12 % (2667533)ott-2_1_sil=16000:newcnf=on:random_seed=1284553847:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2991 on theBenchmark for (2991ds/869Mi)
% 33.84/5.12 % (2667533)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 33.84/5.12 % (2667534)ott+10_1_sil=32000:tgt=ground:random_seed=3440817838:i=5114:av=off_2991 on theBenchmark for (2991ds/5114Mi)
% 33.84/5.12 % (2667517)Instruction limit reached!
% 33.84/5.12 % (2667517)------------------------------
% 33.84/5.12 % (2667517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.84/5.12 % (2667517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.84/5.12 % (2667517)CaDiCaL version: 2.1.3
% 33.84/5.12 % (2667517)Termination reason: Instruction limit
% 33.84/5.12 % (2667517)Termination phase: Saturation
% 33.84/5.12 % (2667517)Time elapsed: 0.773 s
% 33.84/5.12 % (2667517)Peak memory usage: 16 MB
% 33.84/5.12 % (2667517)Instructions burned: 879 (million)
% 33.84/5.12 % (2667537)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=310508969:i=54282_2988 on theBenchmark for (2988ds/54282Mi)
% 33.84/5.12 % Exception at run slice level
% 33.84/5.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.84/5.12 % (2667539)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3884758219:i=3512:aac=none_2987 on theBenchmark for (2987ds/3512Mi)
% 33.84/5.12 % (2667539)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 33.84/5.12 % (2667533)Instruction limit reached!
% 33.84/5.12 % (2667533)------------------------------
% 33.84/5.12 % (2667533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.84/5.12 % (2667533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.84/5.12 % (2667533)CaDiCaL version: 2.1.3
% 33.84/5.12 % (2667533)Termination reason: Instruction limit
% 33.84/5.12 % (2667533)Termination phase: Saturation
% 33.84/5.12 % (2667533)Time elapsed: 0.705 s
% 33.84/5.12 % (2667533)Peak memory usage: 16 MB
% 33.84/5.12 % (2667533)Instructions burned: 869 (million)
% 33.84/5.12 % (2667541)dis+21_1_sil=32000:sas=cadical:random_seed=3967343503:i=3773:amm=off_2983 on theBenchmark for (2983ds/3773Mi)
% 33.84/5.12 % (2667527)Instruction limit reached!
% 33.84/5.12 % (2667527)------------------------------
% 33.84/5.12 % (2667527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.84/5.12 % (2667527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.84/5.12 % (2667527)CaDiCaL version: 2.1.3
% 33.84/5.12 % (2667527)Termination reason: Instruction limit
% 33.84/5.12 % (2667527)Termination phase: Saturation
% 33.84/5.12 % (2667527)Time elapsed: 1.291 s
% 33.84/5.12 % (2667527)Peak memory usage: 19 MB
% 33.84/5.12 % (2667527)Instructions burned: 1472 (million)
% 33.84/5.12 % (2667543)ott+11_1_sil=16000:gs=on:random_seed=1875811873:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2979 on theBenchmark for (2979ds/2251Mi)
% 33.84/5.12 % (2667543)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 33.84/5.12 % (2667524)Instruction limit reached!
% 33.84/5.12 % (2667524)------------------------------
% 33.84/5.12 % (2667524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.84/5.12 % (2667524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.84/5.12 % (2667524)CaDiCaL version: 2.1.3
% 33.84/5.12 % (2667524)Termination reason: Instruction limit
% 33.84/5.12 % (2667524)Termination phase: Saturation
% 33.84/5.12 % (2667524)Time elapsed: 2.008 s
% 33.84/5.12 % (2667524)Peak memory usage: 22 MB
% 33.84/5.12 % (2667524)Instructions burned: 5131 (million)
% 33.84/5.12 % (2667545)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=2915416664:fmbsr=1.6:i=67534_2972 on theBenchmark for (2972ds/67534Mi)
% 33.84/5.12 % Exception at run slice level
% 33.84/5.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.84/5.12 % (2667547)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=294402707:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2971 on theBenchmark for (2971ds/4591Mi)
% 33.84/5.12 % (2667543)Instruction limit reached!
% 33.84/5.12 % (2667543)------------------------------
% 33.84/5.12 % (2667543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.84/5.12 % (2667543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.84/5.12 % (2667543)CaDiCaL version: 2.1.3
% 33.84/5.12 % (2667543)Termination reason: Instruction limit
% 33.84/5.12 % (2667543)Termination phase: Saturation
% 33.84/5.12 % (2667543)Time elapsed: 1.794 s
% 33.84/5.12 % (2667543)Peak memory usage: 17 MB
% 33.84/5.12 % (2667543)Instructions burned: 2252 (million)
% 33.84/5.12 % (2667549)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=1119750287:i=29340_2960 on theBenchmark for (2960ds/29340Mi)
% 33.84/5.12 % (2667539)Instruction limit reached!
% 33.84/5.12 % (2667539)------------------------------
% 33.84/5.12 % (2667539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.84/5.12 % (2667539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.84/5.12 % (2667539)CaDiCaL version: 2.1.3
% 33.84/5.12 % (2667539)Termination reason: Instruction limit
% 33.84/5.12 % (2667539)Termination phase: Saturation
% 33.84/5.12 % (2667539)Time elapsed: 2.782 s
% 33.84/5.12 % (2667539)Peak memory usage: 20 MB
% 33.84/5.12 % (2667539)Instructions burned: 3512 (million)
% 33.84/5.12 % (2667551)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=44441314:i=5211_2959 on theBenchmark for (2959ds/5211Mi)
% 33.84/5.12 % (2667547)Instruction limit reached!
% 33.84/5.12 % (2667547)------------------------------
% 33.84/5.12 % (2667547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.84/5.12 % (2667547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.84/5.12 % (2667547)CaDiCaL version: 2.1.3
% 33.84/5.12 % (2667547)Termination reason: Instruction limit
% 33.84/5.12 % (2667547)Termination phase: Saturation
% 33.84/5.12 % (2667547)Time elapsed: 1.451 s
% 33.84/5.12 % (2667547)Peak memory usage: 14 MB
% 33.84/5.12 % (2667547)Instructions burned: 4592 (million)
% 33.84/5.12 % (2667553)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=142945926:i=5497:nm=2_2956 on theBenchmark for (2956ds/5497Mi)
% 33.84/5.12 % Exception at run slice level
% 33.84/5.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.84/5.12 % (2667555)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=421920973:fmbsr=2:i=46332_2956 on theBenchmark for (2956ds/46332Mi)
% 33.84/5.12 % Exception at run slice level
% 33.84/5.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.84/5.12 % (2667557)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=4252423499:i=14071_2955 on theBenchmark for (2955ds/14071Mi)
% 33.84/5.12 % Exception at run slice level
% 33.84/5.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.84/5.12 % (2667559)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4147949236:i=22565:add=on:rawr=on_2954 on theBenchmark for (2954ds/22565Mi)
% 33.84/5.12 % (2667541)Instruction limit reached!
% 33.84/5.12 % (2667541)------------------------------
% 33.84/5.12 % (2667541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.84/5.12 % (2667541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.84/5.12 % (2667541)CaDiCaL version: 2.1.3
% 33.84/5.12 % (2667541)Termination reason: Instruction limit
% 33.84/5.12 % (2667541)Termination phase: Saturation
% 33.84/5.12 % (2667541)Time elapsed: 2.891 s
% 33.84/5.12 % (2667541)Peak memory usage: 19 MB
% 33.84/5.12 % (2667541)Instructions burned: 3774 (million)
% 33.84/5.12 % (2667561)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=2496549466:i=8173:av=off_2954 on theBenchmark for (2954ds/8173Mi)
% 33.84/5.12 % (2667534)Instruction limit reached!
% 33.84/5.12 % (2667534)------------------------------
% 33.84/5.12 % (2667534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.84/5.12 % (2667534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.84/5.12 % (2667534)CaDiCaL version: 2.1.3
% 33.84/5.12 % (2667534)Termination reason: Instruction limit
% 33.84/5.12 % (2667534)Termination phase: Saturation
% 33.84/5.12 % (2667534)Time elapsed: 3.734 s
% 33.84/5.12 % (2667534)Peak memory usage: 20 MB
% 33.84/5.12 % (2667534)Instructions burned: 5115 (million)
% 33.84/5.12 % (2667563)dis+10_16:1_sil=16000:random_seed=1620623141:i=9155:fsr=off_2953 on theBenchmark for (2953ds/9155Mi)
% 33.84/5.12 % (2667549) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2667480-2667549"...
% 33.84/5.12 % (2667549)...printing done.
% 33.84/5.12 % (2667549)Refutation found. Thanks to Tanya!
% 33.84/5.12 % SZS status Theorem for theBenchmark
% 33.84/5.12 % SZS output start Proof for theBenchmark
% See solution above
% 33.84/5.13 % (2667549)------------------------------
% 33.84/5.13 % (2667549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.84/5.13 % (2667549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.84/5.13 % (2667549)CaDiCaL version: 2.1.3
% 33.84/5.13 % (2667549)Termination reason: Refutation
% 33.84/5.13 % (2667549)Time elapsed: 0.835 s
% 33.84/5.13 % (2667549)Peak memory usage: 16 MB
% 33.84/5.13 % (2667549)Instructions burned: 1006 (million)
% 33.84/5.13 % (2667480)Success in time 4.826 s
% 33.84/5.13 % Vampire exiting
%------------------------------------------------------------------------------