%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL603^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 08:15:02 AM UTC 2026
% Result : Theorem 2.35s 0.58s
% Output : Refutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 12
% Syntax : Number of formulae : 125 ( 47 unt; 0 typ; 4 def)
% Number of atoms : 854 ( 198 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 1137 ( 92 ~; 144 |; 26 &; 744 @)
% ( 4 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 133 ( 133 >; 0 *; 0 +; 0 <<)
% Number of symbols : 78 ( 74 usr; 11 con; 0-4 aty)
% ( 63 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 289 ( 0 sgn 120 !; 1 ?; 289 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_21,type,
pair_rel: $i > $i > $i > $i > $o ).
thf(func_def_22,type,
id_rel: ( $i > $o ) > $i > $i > $o ).
thf(func_def_23,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_25,type,
restrict_rel_domain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
rel_diagonal: $i > $i > $o ).
thf(func_def_27,type,
rel_composition: ( $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_28,type,
reflexive: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
irreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
symmetric: ( $i > $i > $o ) > $o ).
thf(func_def_31,type,
transitive: ( $i > $i > $o ) > $o ).
thf(func_def_32,type,
equiv_rel: ( $i > $i > $o ) > $o ).
thf(func_def_33,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_34,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_35,type,
rel_inverse: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_36,type,
equiv_classes: ( $i > $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_37,type,
restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_38,type,
rel_field: ( $i > $i > $o ) > $i > $o ).
thf(func_def_39,type,
well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_40,type,
upwards_well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_45,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_48,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vAND: $o > $o > $o ).
thf(func_def_50,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
vIMP: $o > $o > $o ).
thf(func_def_52,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_54,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_55,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
vIFF: $o > $o > $o ).
thf(func_def_57,type,
sK0: $i > $i > $o ).
thf(func_def_58,type,
sK1: ( $i > $o ) > $i > $i ).
thf(func_def_59,type,
sK2: ( $i > $o ) > $i > $i ).
thf(func_def_65,type,
sK8: ( $i > $i ) > $i ).
thf(func_def_66,type,
sK9: ( $i > $i ) > $i ).
thf(func_def_71,type,
sK14: ( $i > $i ) > $i ).
thf(func_def_72,type,
sK15: ( $i > $i ) > $i ).
thf(func_def_73,type,
sK16: ( $i > $i ) > $i ).
thf(func_def_76,type,
sK19: ( $i > $i ) > $i ).
thf(func_def_77,type,
sK20: ( $i > $i ) > $i ).
thf(func_def_78,type,
sK21: ( $i > $i ) > $i ).
thf(func_def_81,type,
sK24: ( $i > $i ) > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f24,axiom,
( reflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',reflexive) ).
thf(f27,axiom,
( transitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',transitive) ).
thf(f37,conjecture,
! [X0: $i > $i > $o] :
( ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
& ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) )
=> ( ( transitive @ X0 )
& ( reflexive @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f38,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
& ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) )
=> ( ( transitive @ X0 )
& ( reflexive @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f41,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f42,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f44,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f47,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f49,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f50,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f57,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f58,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f79,plain,
( reflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f24]) ).
thf(f80,plain,
( reflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f85,plain,
( transitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f86,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f104,plain,
~ ! [X0: $i > $i > $o] :
( ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
& ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) )
=> ( ( transitive @ X0 )
& ( reflexive @ X0 ) ) ),
inference(rectify,[],[f38]) ).
thf(f105,plain,
~ ! [X0: $i > $i > $o] :
( ! [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
= $true )
& ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true ) )
=> ( ( ( transitive @ X0 )
= $true )
& ( ( reflexive @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f104]) ).
thf(f106,plain,
? [X0: $i > $i > $o] :
( ( ( ( transitive @ X0 )
!= $true )
| ( ( reflexive @ X0 )
!= $true ) )
& ! [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
= $true )
& ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true ) ) ),
inference(ennf_transformation,[],[f105]) ).
thf(f107,plain,
( ( ( $true
!= ( transitive @ sK0 ) )
| ( $true
!= ( reflexive @ sK0 ) ) )
& ! [X1: $i > $o] :
( ( $true
= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X1 ) @ X1 ) ) )
& ( $true
= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X1 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ X1 ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f106]) ).
thf(f110,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f111,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f113,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f115,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f119,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f131,plain,
( reflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f134,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f144,plain,
! [X1: $i > $o] :
( $true
= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X1 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ X1 ) ) ) ) ),
inference(cnf_transformation,[],[f107]) ).
thf(f145,plain,
! [X1: $i > $o] :
( $true
= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X1 ) @ X1 ) ) ),
inference(cnf_transformation,[],[f107]) ).
thf(f146,plain,
( ( $true
!= ( transitive @ sK0 ) )
| ( $true
!= ( reflexive @ sK0 ) ) ),
inference(cnf_transformation,[],[f107]) ).
thf(f149,plain,
( mimpl
= ( ^ [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,[],[f113,f111,f110]) ).
thf(f153,plain,
( ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f146,f134,f131]) ).
thf(f154,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ X1 )
@ X1 ) ) ),
inference(definition_unfolding,[],[f145,f119,f149,f115]) ).
thf(f155,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ X1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ X1 ) ) ) ) ),
inference(definition_unfolding,[],[f144,f119,f149,f115,f115,f115]) ).
thf(f156,plain,
! [X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) )
@ ( sK1 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( ( sK0 @ X2 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) )
| ( $false
= ( ( sK0 @ X2 @ ( sK1 @ X1 @ X2 ) )
=> ( X1 @ ( sK1 @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( ( sK0 @ X2 @ ( sK1 @ X1 @ X2 ) )
=> ( X1 @ ( sK1 @ X1 @ X2 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( X1 @ ( sK1 @ X1 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $true
= ( sK0 @ X2 @ ( sK1 @ X1 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f164]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $true
= ( sK0 @ X2 @ ( sK1 @ X1 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $true
= ( sK0 @ X2 @ ( sK1 @ X1 @ X2 ) ) )
| ( $true
= ( ( sK0 @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $true
= ( sK0 @ X2 @ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( ( X1 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( X1 @ ( sK1 @ X1 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( X1 @ ( sK1 @ X1 @ X2 ) ) )
| ( $true
= ( ( sK0 @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( X1 @ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( ( X1 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f174,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
| ( X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) )
@ ( sK2 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( $false
= ( ( sK0 @ X2 @ ( sK2 @ X1 @ X2 ) )
=> ( X1 @ ( sK2 @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( X1 @ ( sK2 @ X1 @ X2 ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i > $o] :
( ( $true
= ( sK0 @ X2 @ ( sK2 @ X1 @ X2 ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f183,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK3 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) )
@ sK5 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) )
@ sK6 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( $false
= ( ( ( sK0 @ sK6 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f190,plain,
( ( $false
= ( sK0 @ sK6 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( $true
= ( ( sK0 @ sK6 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f189]) ).
thf(f192,plain,
( ( $true
= ( sK0 @ sK5 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( $true
= ( sK0 @ sK6 @ sK5 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f191]) ).
thf(f195,definition,
( spl7_1
<=> ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f197,plain,
( ( $false
= ( sK0 @ sK4 @ sK4 ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f195]) ).
thf(f199,definition,
( spl7_2
<=> ( $true
= ( sK0 @ sK6 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f201,plain,
( ( $true
= ( sK0 @ sK6 @ sK5 ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f202,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f193,f199,f195]) ).
thf(f204,definition,
( spl7_3
<=> ( $true
= ( sK0 @ sK5 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f206,plain,
( ( $true
= ( sK0 @ sK5 @ sK3 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f204]) ).
thf(f207,plain,
( spl7_1
| spl7_3 ),
inference(avatar_split_clause,[],[f192,f204,f195]) ).
thf(f209,definition,
( spl7_4
<=> ( $false
= ( sK0 @ sK6 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f211,plain,
( ( $false
= ( sK0 @ sK6 @ sK3 ) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f209]) ).
thf(f212,plain,
( spl7_1
| spl7_4 ),
inference(avatar_split_clause,[],[f190,f209,f195]) ).
thf(f213,plain,
! [X0: $i] :
( ( sK2
@ ^ [Y0: $i] : ( Y0 != X0 )
@ X0 )
= X0 ),
inference(leibniz_equality_elimination,[],[f180]) ).
thf(f336,plain,
! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ X0 ) )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != X0 )
@ X0 ) ) ),
inference(constrained_superposition,[],[f181,f213]) ).
thf(f343,plain,
! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ X0 ) )
| ( $true
= ( X0 != X0 ) ) ),
inference(beta-eta_normalization,[],[f336]) ).
thf(f344,plain,
! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ X0 ) )
| ( $false
= ( X0 = X0 ) ) ),
inference(not_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ X0 ) )
| ( X0 != X0 ) ),
inference(equality_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X0: $i] :
( $true
= ( sK0 @ X0 @ X0 ) ),
inference(trivial_inequality_removal,[],[f345]) ).
thf(f347,plain,
( ( $false = $true )
| ~ spl7_1 ),
inference(constrained_superposition,[],[f346,f197]) ).
thf(f360,plain,
( $false
| ~ spl7_1 ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f361,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[],[f360]) ).
thf(f522,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false = $true )
| ( $false
= ( X0 @ ( sK1 @ X0 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( ( X0 @ X1 )
= $true ) )
| ~ spl7_2 ),
inference(constrained_superposition,[],[f201,f172]) ).
thf(f657,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK1 @ X0 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( ( X0 @ X1 )
= $true ) )
| ~ spl7_2 ),
inference(trivial_inequality_removal,[],[f522]) ).
thf(f4807,plain,
( ! [X0: $i > $o] :
( ( $false = $true )
| ( $false
= ( X0 @ ( sK1 @ X0 @ sK6 ) ) )
| ( $true
= ( X0 @ sK3 ) ) )
| ~ spl7_2
| ~ spl7_3 ),
inference(constrained_superposition,[],[f206,f657]) ).
thf(f5025,plain,
( ! [X0: $i > $o] :
( ( $false
= ( X0 @ ( sK1 @ X0 @ sK6 ) ) )
| ( $true
= ( X0 @ sK3 ) ) )
| ~ spl7_2
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f4807]) ).
thf(f5314,plain,
( ( sK3
= ( sK1
@ ^ [Y0: $i] : ( Y0 != sK3 )
@ sK6 ) )
| ~ spl7_2
| ~ spl7_3 ),
inference(leibniz_equality_elimination,[],[f5025]) ).
thf(f5720,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ sK6 @ sK3 ) )
| ( $false
= ( sK0 @ sK6 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != sK3 )
@ X1 ) ) )
| ~ spl7_2
| ~ spl7_3 ),
inference(constrained_superposition,[],[f169,f5314]) ).
thf(f5825,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ sK6 @ sK3 ) )
| ( $false
= ( sK0 @ sK6 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( X1 != sK3 ) ) )
| ~ spl7_2
| ~ spl7_3 ),
inference(beta-eta_normalization,[],[f5720]) ).
thf(f5826,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ sK6 @ sK3 ) )
| ( $false
= ( sK0 @ sK6 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( X1 = sK3 ) ) )
| ~ spl7_2
| ~ spl7_3 ),
inference(not_proxy_clausification,[],[f5825]) ).
thf(f5827,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ sK6 @ sK3 ) )
| ( $false
= ( sK0 @ sK6 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( sK3 != X1 ) )
| ~ spl7_2
| ~ spl7_3 ),
inference(equality_proxy_clausification,[],[f5826]) ).
thf(f5828,plain,
( ! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ sK6 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( sK3 != X1 ) )
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(forward_demodulation,[],[f5827,f211]) ).
thf(f5829,plain,
( ! [X0: $i,X1: $i] :
( ( sK3 != X1 )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( sK0 @ sK6 @ X0 ) ) )
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f5828]) ).
thf(f5834,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $false
= ( sK0 @ sK6 @ X0 ) ) )
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(equality_resolution,[],[f5829]) ).
thf(f5906,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK5 @ sK3 ) )
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(constrained_superposition,[],[f201,f5834]) ).
thf(f5985,plain,
( ( $false
= ( sK0 @ sK5 @ sK3 ) )
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f5906]) ).
thf(f6288,plain,
( ( $false = $true )
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(constrained_superposition,[],[f5985,f206]) ).
thf(f6416,plain,
( $false
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f6288]) ).
thf(f6417,plain,
( ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(avatar_contradiction_clause,[],[f6416]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f202]) ).
cnf(s2,plain,
( spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f207]) ).
cnf(s3,plain,
( spl7_1
| spl7_4 ),
inference(sat_conversion,[],[f212]) ).
cnf(s7,plain,
~ spl7_1,
inference(sat_conversion,[],[f361]) ).
cnf(s17,plain,
( ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(sat_conversion,[],[f6417]) ).
cnf(s19,plain,
spl7_4,
inference(rat,[],[s3,s7]) ).
cnf(s20,plain,
spl7_3,
inference(rat,[],[s2,s7]) ).
cnf(s21,plain,
~ spl7_2,
inference(rat,[],[s17,s19,s20]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s1,s21,s7]) ).
thf(f6418,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL603^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n005.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 09:16:17 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 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
% 2.35/0.58 % (1415687)Will run a generic schedule for satisfiability detection.
% 2.35/0.58 % (1415694)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2633445145:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.35/0.58 % (1415693)% WARNING: option uhcvi not known.
% 2.35/0.58 % (1415692)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4115346828_2999 on theBenchmark for (2999ds/0Mi)
% 2.35/0.58 % (1415693)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1519009631:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.35/0.58 % (1415695)dis+10_1_sil=32000:sp=arity:random_seed=3348948511:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.35/0.58 % (1415697)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3673833110:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.35/0.58 % (1415696)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2124905183:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.35/0.58 % (1415698)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2811964791:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.35/0.58 % (1415693)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.35/0.58 % (1415696)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.35/0.58 % Exception at run slice level
% 2.35/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.35/0.58 % (1415693)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.35/0.58 % (1415706)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=119860215:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.35/0.58 % Exception at run slice level
% 2.35/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.35/0.58 % (1415708)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3283896444:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.35/0.58 % (1415695)Instruction limit reached!
% 2.35/0.58 % (1415695)------------------------------
% 2.35/0.58 % (1415695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.58 % (1415695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.58 % (1415695)CaDiCaL version: 2.1.3
% 2.35/0.58 % (1415695)Termination reason: Instruction limit
% 2.35/0.58 % (1415695)Termination phase: Saturation
% 2.35/0.58 % (1415695)Time elapsed: 0.050 s
% 2.35/0.58 % (1415695)Peak memory usage: 12 MB
% 2.35/0.58 % (1415695)Instructions burned: 103 (million)
% 2.35/0.58 % (1415696)Instruction limit reached!
% 2.35/0.58 % (1415696)------------------------------
% 2.35/0.58 % (1415696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.58 % (1415696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.58 % (1415696)CaDiCaL version: 2.1.3
% 2.35/0.58 % (1415696)Termination reason: Instruction limit
% 2.35/0.58 % (1415696)Termination phase: Saturation
% 2.35/0.58 % (1415696)Time elapsed: 0.056 s
% 2.35/0.58 % (1415696)Peak memory usage: 12 MB
% 2.35/0.58 % (1415696)Instructions burned: 117 (million)
% 2.35/0.58 % (1415697)Instruction limit reached!
% 2.35/0.58 % (1415697)------------------------------
% 2.35/0.58 % (1415697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.58 % (1415697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.58 % (1415697)CaDiCaL version: 2.1.3
% 2.35/0.58 % (1415697)Termination reason: Instruction limit
% 2.35/0.58 % (1415697)Termination phase: Saturation
% 2.35/0.58 % (1415697)Time elapsed: 0.066 s
% 2.35/0.58 % (1415697)Peak memory usage: 13 MB
% 2.35/0.58 % (1415697)Instructions burned: 136 (million)
% 2.35/0.58 % (1415710)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=130764903:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.35/0.58 % (1415710)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.35/0.58 % (1415710)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.35/0.58 % (1415711)ott-21_1_sil=16000:fs=off:random_seed=2697154934:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.35/0.58 % (1415698)Instruction limit reached!
% 2.35/0.58 % (1415698)------------------------------
% 2.35/0.58 % (1415698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.58 % (1415698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.58 % (1415698)CaDiCaL version: 2.1.3
% 2.35/0.58 % (1415698)Termination reason: Instruction limit
% 2.35/0.58 % (1415698)Termination phase: Saturation
% 2.35/0.58 % (1415698)Time elapsed: 0.079 s
% 2.35/0.58 % (1415698)Peak memory usage: 13 MB
% 2.35/0.58 % (1415698)Instructions burned: 160 (million)
% 2.35/0.58 % (1415712)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1655163156:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.35/0.58 % (1415715)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=378013848:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.35/0.58 % Exception at run slice level
% 2.35/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.35/0.58 % (1415708)Instruction limit reached!
% 2.35/0.58 % (1415708)------------------------------
% 2.35/0.58 % (1415708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.58 % (1415708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.58 % (1415708)CaDiCaL version: 2.1.3
% 2.35/0.58 % (1415708)Termination reason: Instruction limit
% 2.35/0.58 % (1415708)Termination phase: Saturation
% 2.35/0.58 % (1415708)Time elapsed: 0.065 s
% 2.35/0.58 % (1415708)Peak memory usage: 12 MB
% 2.35/0.58 % (1415708)Instructions burned: 132 (million)
% 2.35/0.58 % (1415718)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=103216431:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.35/0.58 % (1415719)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=888154569:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.35/0.58 % Exception at run slice level
% 2.35/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.35/0.58 % (1415722)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=494601047: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)
% 2.35/0.58 % (1415722)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.35/0.58 % (1415711)Instruction limit reached!
% 2.35/0.58 % (1415711)------------------------------
% 2.35/0.58 % (1415711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.58 % (1415711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.58 % (1415711)CaDiCaL version: 2.1.3
% 2.35/0.58 % (1415711)Termination reason: Instruction limit
% 2.35/0.58 % (1415711)Termination phase: Saturation
% 2.35/0.58 % (1415711)Time elapsed: 0.084 s
% 2.35/0.58 % (1415711)Peak memory usage: 12 MB
% 2.35/0.58 % (1415711)Instructions burned: 181 (million)
% 2.35/0.58 % (1415724)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=51435671:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 2.35/0.58 % (1415724)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.35/0.58 % (1415710) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1415687-1415710"...
% 2.35/0.58 % (1415710)...printing done.
% 2.35/0.58 % (1415710)Refutation found. Thanks to Tanya!
% 2.35/0.58 % SZS status Theorem for theBenchmark
% 2.35/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 2.35/0.58 % (1415710)------------------------------
% 2.35/0.58 % (1415710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.35/0.58 % (1415710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.58 % (1415710)CaDiCaL version: 2.1.3
% 2.35/0.58 % (1415710)Termination reason: Refutation
% 2.35/0.58 % (1415710)Time elapsed: 0.239 s
% 2.35/0.58 % (1415710)Peak memory usage: 15 MB
% 2.35/0.58 % (1415710)Instructions burned: 512 (million)
% 2.35/0.58 % (1415687)Success in time 0.35 s
% 2.35/0.58 % Vampire exiting
%------------------------------------------------------------------------------