%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL621^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:15:03 AM UTC 2026
% Result : Theorem 6.04s 1.05s
% Output : Refutation 6.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 10
% Syntax : Number of formulae : 155 ( 49 unt; 0 typ; 1 def)
% Number of atoms : 1200 ( 477 equ; 14 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1761 ( 166 ~; 273 |; 59 &;1101 @)
% ( 0 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 275 ( 275 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 45 usr; 8 con; 0-4 aty)
% ( 63 !!; 26 ??; 0 @@+; 0 @@-)
% Number of variables : 667 ( 351 ^; 311 !; 5 ?; 667 :)
% 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_22,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_23,type,
vNOT: $o > $o ).
thf(func_def_24,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vOR: $o > $o > $o ).
thf(func_def_27,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vAND: $o > $o > $o ).
thf(func_def_29,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_30,type,
vIMP: $o > $o > $o ).
thf(func_def_31,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
sK0: $i > $i > $o ).
thf(func_def_34,type,
sK1: $i > $o ).
thf(func_def_35,type,
sK2: $i > $o ).
thf(func_def_36,type,
sF3: $o ).
thf(func_def_37,type,
sK4: ( $i > $o ) > ( $i > $i > $o ) > $i > $i ).
thf(func_def_39,type,
sK6: $i > $i ).
thf(func_def_41,type,
sK8: $i > $i ).
thf(func_def_42,type,
sK9: $i > $i ).
thf(func_def_43,type,
sK10: $i > $i ).
thf(func_def_44,type,
sK11: $i > $i ).
thf(func_def_45,type,
sK12: $i > $i ).
thf(func_def_46,type,
sK13: $i > $i ).
thf(func_def_47,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mand) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f9,axiom,
( mdia
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mdia) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
! [X0: $i > $i > $o,X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k4) ).
thf(f17,conjecture,
! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] : ( mvalid @ ( mimpl @ ( mand @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f18,negated_conjecture,
~ ! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] : ( mvalid @ ( mimpl @ ( mand @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
thf(f21,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f22,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f24,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f26,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f29,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f30,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f31,plain,
( mdia
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f32,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f37,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f38,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f45,plain,
! [X0: $i > $i > $o,X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f46,plain,
! [X0: $i > $i > $o,X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
~ ! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] : ( mvalid @ ( mimpl @ ( mand @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f48,plain,
~ ! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
( ( mvalid @ ( mimpl @ ( mand @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
? [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
( ( mvalid @ ( mimpl @ ( mand @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) )
!= $true ),
inference(ennf_transformation,[],[f48]) ).
thf(f50,plain,
( $true
!= ( mvalid @ ( mimpl @ ( mand @ ( mbox @ sK0 @ ( mdia @ sK0 @ sK1 ) ) @ ( mbox @ sK0 @ sK2 ) ) @ ( mbox @ sK0 @ ( mdia @ sK0 @ ( mand @ sK1 @ sK2 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f49]) ).
thf(f53,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f54,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f55,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f56,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f58,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f59,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f62,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f66,plain,
! [X0: $i > $i > $o,X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f67,plain,
( $true
!= ( mvalid @ ( mimpl @ ( mand @ ( mbox @ sK0 @ ( mdia @ sK0 @ sK1 ) ) @ ( mbox @ sK0 @ sK2 ) ) @ ( mbox @ sK0 @ ( mdia @ sK0 @ ( mand @ sK1 @ sK2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f70,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,[],[f56,f54,f53]) ).
thf(f72,plain,
! [X0: $i > $i > $o,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 ) ) )
@ X0
@ X1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ X0
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ X0
@ X1 ) ) ) ) ),
inference(definition_unfolding,[],[f66,f62,f70,f58,f58,f58]) ).
thf(f73,plain,
( $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 > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [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
@ sK1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ sK2 ) )
@ ( ^ [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
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ sK1
@ sK2 ) ) ) ) ) ),
inference(definition_unfolding,[],[f67,f62,f70,f55,f58,f59,f58,f58,f59,f55]) ).
thf(f74,definition,
( sF3
= ( ^ [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 > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [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
@ sK1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ sK2 ) )
@ ( ^ [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
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ sK1
@ sK2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f75,plain,
( ( ^ [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 > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [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
@ sK1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ sK2 ) )
@ ( ^ [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
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ sK1
@ sK2 ) ) ) ) )
= sF3 ),
inference(reorient_equations,[],[f74]) ).
thf(f76,plain,
$true != sF3,
inference(definition_folding,[],[f73,f75]) ).
thf(f77,plain,
! [X0: $i > $i > $o,X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( X0 @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f78,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( X0 @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i > $o] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( $true
= ( ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( $true
= ( ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( $true
= ( ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) )
@ ( sK4 @ X1 @ X0 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( $true
= ( ( X0 @ X2 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) )
| ( $false
= ( ( X0 @ X2 @ ( sK4 @ X1 @ X0 @ X2 ) )
=> ( X1 @ ( sK4 @ X1 @ X0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( ( X0 @ X2 @ X3 )
= $false )
| ( $false
= ( ( X0 @ X2 @ ( sK4 @ X1 @ X0 @ X2 ) )
=> ( X1 @ ( sK4 @ X1 @ X0 @ X2 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( ( X0 @ X2 @ X3 )
= $false )
| ( $false
= ( X1 @ ( sK4 @ X1 @ X0 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( ( X0 @ X2 @ X3 )
= $false )
| ( $true
= ( X0 @ X2 @ ( sK4 @ X1 @ X0 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o,X4: $i] :
( ( ( X0 @ X2 @ X3 )
= $false )
| ( $true
= ( X0 @ X2 @ ( sK4 @ X1 @ X0 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( X0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o,X4: $i] :
( ( ( X0 @ X2 @ X3 )
= $false )
| ( $true
= ( X0 @ X2 @ ( sK4 @ X1 @ X0 @ X2 ) ) )
| ( $true
= ( ( X0 @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o,X4: $i] :
( ( ( X0 @ X2 @ X3 )
= $false )
| ( $true
= ( X0 @ X2 @ ( sK4 @ X1 @ X0 @ X2 ) ) )
| ( $false
= ( X0 @ X3 @ X4 ) )
| ( $true
= ( X1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o,X4: $i] :
( ( ( X0 @ X2 @ X3 )
= $false )
| ( $false
= ( X1 @ ( sK4 @ X1 @ X0 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( X0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f86]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o,X4: $i] :
( ( ( X0 @ X2 @ X3 )
= $false )
| ( $false
= ( X1 @ ( sK4 @ X1 @ X0 @ X2 ) ) )
| ( $true
= ( ( X0 @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o,X4: $i] :
( ( ( X0 @ X2 @ X3 )
= $false )
| ( $false
= ( X1 @ ( sK4 @ X1 @ X0 @ X2 ) ) )
| ( $false
= ( X0 @ X3 @ X4 ) )
| ( $true
= ( X1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f92]) ).
thf(f95,plain,
( ( $false
= ( ^ [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 > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [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
@ sK1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ sK2 ) )
@ ( ^ [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
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ sK1
@ sK2 ) ) ) ) ) )
| ( $true = sF3 ) ),
inference(iff_proxy_clausification,[],[f75]) ).
thf(f96,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK1 @ Y2 )
& ( sK2 @ Y2 ) ) ) ) ) ) ) )
| ( $true = sF3 ) ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK1 @ Y2 )
& ( sK2 @ Y2 ) ) ) ) ) )
@ sK5 ) )
| ( $true = sF3 ) ),
inference(sigma_proxy_clausification,[],[f96]) ).
thf(f98,plain,
( ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) ) ) )
| ( $true = sF3 ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) ) )
| ( $true = sF3 ) ),
inference(or_proxy_clausification,[],[f98]) ).
thf(f100,plain,
( ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ) ) )
| ( $true = sF3 ) ),
inference(or_proxy_clausification,[],[f98]) ).
thf(f101,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ) )
| ( $true = sF3 ) ),
inference(not_proxy_clausification,[],[f100]) ).
thf(f102,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
| ( $true = sF3 ) ),
inference(and_proxy_clausification,[],[f101]) ).
thf(f103,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 ) ) ) ) ) )
| ( $true = sF3 ) ),
inference(and_proxy_clausification,[],[f101]) ).
thf(f104,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 ) ) ) )
@ X1 ) )
| ( $true = sF3 ) ),
inference(pi_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK5 @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) )
| ( $true = sF3 ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f106,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true = sF3 )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true = sF3 )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( sK1 @ Y0 ) )
@ ( sK6 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true = sF3 )
| ( $true
= ( ( sK0 @ X1 @ ( sK6 @ X1 ) )
& ( sK1 @ ( sK6 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true = sF3 )
| ( $true
= ( sK1 @ ( sK6 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f108]) ).
thf(f110,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true = sF3 )
| ( $true
= ( sK0 @ X1 @ ( sK6 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f108]) ).
thf(f111,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK2 @ Y0 ) )
@ X1 ) )
| ( $true = sF3 ) ),
inference(pi_proxy_clausification,[],[f102]) ).
thf(f112,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK5 @ X1 )
=> ( sK2 @ X1 ) ) )
| ( $true = sF3 ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f113,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true = sF3 )
| ( $true
= ( sK2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f112]) ).
thf(f114,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK1 @ Y1 )
& ( sK2 @ Y1 ) ) ) )
@ sK7 ) )
| ( $true = sF3 ) ),
inference(sigma_proxy_clausification,[],[f99]) ).
thf(f115,plain,
( ( $false
= ( ( sK0 @ sK5 @ sK7 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK7 @ Y0 )
& ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) )
| ( $true = sF3 ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK7 @ Y0 )
& ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( $true = sF3 ) ),
inference(imp_proxy_clausification,[],[f115]) ).
thf(f117,plain,
( ( $true
= ( sK0 @ sK5 @ sK7 ) )
| ( $true = sF3 ) ),
inference(imp_proxy_clausification,[],[f115]) ).
thf(f118,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK7 @ Y0 )
& ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
@ X1 ) )
| ( $true = sF3 ) ),
inference(pi_proxy_clausification,[],[f116]) ).
thf(f119,plain,
! [X1: $i] :
( ( $false
= ( ( sK0 @ sK7 @ X1 )
& ( sK1 @ X1 )
& ( sK2 @ X1 ) ) )
| ( $true = sF3 ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X1: $i] :
( ( $false
= ( ( sK1 @ X1 )
& ( sK2 @ X1 ) ) )
| ( $true = sF3 )
| ( $false
= ( sK0 @ sK7 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( $true = sF3 )
| ( $false
= ( sK0 @ sK7 @ X1 ) )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f120]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) ) ),
inference(forward_subsumption_resolution,[],[f110,f76]) ).
thf(f168,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK1 @ ( sK6 @ X1 ) ) ) ),
inference(forward_subsumption_resolution,[],[f109,f76]) ).
thf(f169,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK2 @ X1 ) ) ),
inference(forward_subsumption_resolution,[],[f113,f76]) ).
thf(f170,plain,
( $true
= ( sK0 @ sK5 @ sK7 ) ),
inference(forward_subsumption_resolution,[],[f117,f76]) ).
thf(f171,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK7 @ X1 ) )
| ( $false
= ( sK2 @ X1 ) )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(forward_subsumption_resolution,[],[f121,f76]) ).
thf(f184,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $i > $o] :
( ( ( sK4
@ ^ [Y0: $i] : ( Y0 != X0 )
@ X1
@ X2 )
= X0 )
| ( $false
= ( X1 @ X2 @ X3 ) )
| ( $false
= ( X1 @ X3 @ X0 ) ) ),
inference(leibniz_equality_elimination,[],[f93]) ).
thf(f442,plain,
( ( $false = $true )
| ( $true
= ( sK2 @ sK7 ) ) ),
inference(constrained_superposition,[],[f170,f169]) ).
thf(f449,plain,
( $true
= ( sK2 @ sK7 ) ),
inference(trivial_inequality_removal,[],[f442]) ).
thf(f466,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ X2
@ X3 ) )
| ( $true
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ X2
@ ( sK4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ X2 ) ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ X3
@ X4 ) )
| ( $true
= ( X1 @ X4 ) ) ),
inference(primitive_instantiation,[],[f90]) ).
thf(f467,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X2
@ X3 ) )
| ( $true
= ( ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X2
@ ( sK4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X2 ) ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X3
@ X4 ) )
| ( $true
= ( X1 @ X4 ) ) ),
inference(primitive_instantiation,[],[f90]) ).
thf(f777,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( X2 != X3 ) )
| ( $true
= ( X2
!= ( sK4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X2 ) ) )
| ( $false
= ( X3 != X4 ) )
| ( $true
= ( X1 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f467]) ).
thf(f778,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $true
= ( X2 = X3 ) )
| ( $true
= ( X2
!= ( sK4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X2 ) ) )
| ( $false
= ( X3 != X4 ) )
| ( $true
= ( X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f777]) ).
thf(f779,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( X2 = X3 )
| ( $true
= ( X2
!= ( sK4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X2 ) ) )
| ( $false
= ( X3 != X4 ) )
| ( $true
= ( X1 @ X4 ) ) ),
inference(equality_proxy_clausification,[],[f778]) ).
thf(f780,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( X2 = X3 )
| ( $false
= ( X2
= ( sK4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X2 ) ) )
| ( $false
= ( X3 != X4 ) )
| ( $true
= ( X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f779]) ).
thf(f781,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( X2 = X3 )
| ( ( sK4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X2 )
!= X2 )
| ( $false
= ( X3 != X4 ) )
| ( $true
= ( X1 @ X4 ) ) ),
inference(equality_proxy_clausification,[],[f780]) ).
thf(f782,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( X2 = X3 )
| ( ( sK4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X2 )
!= X2 )
| ( $true
= ( X3 = X4 ) )
| ( $true
= ( X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f781]) ).
thf(f783,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( ( sK4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X2 )
!= X2 )
| ( X2 = X3 )
| ( X3 = X4 )
| ( $true
= ( X1 @ X4 ) ) ),
inference(equality_proxy_clausification,[],[f782]) ).
thf(f784,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( X2 = X3 ) )
| ( $true
= ( X2
= ( sK4 @ X1 @ (=) @ X2 ) ) )
| ( $false
= ( X3 = X4 ) )
| ( $true
= ( X1 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f466]) ).
thf(f785,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( X2 != X3 )
| ( $true
= ( X2
= ( sK4 @ X1 @ (=) @ X2 ) ) )
| ( $false
= ( X3 = X4 ) )
| ( $true
= ( X1 @ X4 ) ) ),
inference(equality_proxy_clausification,[],[f784]) ).
thf(f786,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( X2 != X3 )
| ( ( sK4 @ X1 @ (=) @ X2 )
= X2 )
| ( $false
= ( X3 = X4 ) )
| ( $true
= ( X1 @ X4 ) ) ),
inference(equality_proxy_clausification,[],[f785]) ).
thf(f787,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( ( sK4 @ X1 @ (=) @ X2 )
= X2 )
| ( $true
= ( X1 @ X4 ) )
| ( X3 != X4 )
| ( X2 != X3 ) ),
inference(equality_proxy_clausification,[],[f786]) ).
thf(f1039,plain,
( ( $false = $true )
| ( $true
= ( sK1 @ ( sK6 @ sK7 ) ) ) ),
inference(constrained_superposition,[],[f170,f168]) ).
thf(f1064,plain,
( $true
= ( sK1 @ ( sK6 @ sK7 ) ) ),
inference(trivial_inequality_removal,[],[f1039]) ).
thf(f2036,plain,
( ( $false = $true )
| ( $false
= ( sK2 @ ( sK6 @ sK7 ) ) )
| ( $false
= ( sK1 @ ( sK6 @ sK7 ) ) )
| ( $false
= ( sK0 @ sK5 @ sK7 ) ) ),
inference(constrained_superposition,[],[f171,f167]) ).
thf(f2082,plain,
( ( $false
= ( sK2 @ ( sK6 @ sK7 ) ) )
| ( $false
= ( sK1 @ ( sK6 @ sK7 ) ) )
| ( $false
= ( sK0 @ sK5 @ sK7 ) ) ),
inference(trivial_inequality_removal,[],[f2036]) ).
thf(f2128,plain,
( ( $false = $true )
| ( $false
= ( sK2 @ ( sK6 @ sK7 ) ) )
| ( $false
= ( sK0 @ sK5 @ sK7 ) ) ),
inference(forward_demodulation,[],[f2082,f1064]) ).
thf(f2129,plain,
( ( $false
= ( sK2 @ ( sK6 @ sK7 ) ) )
| ( $false
= ( sK0 @ sK5 @ sK7 ) ) ),
inference(trivial_inequality_removal,[],[f2128]) ).
thf(f2132,plain,
( ( $false = $true )
| ( $false
= ( sK2 @ ( sK6 @ sK7 ) ) ) ),
inference(forward_demodulation,[],[f2129,f170]) ).
thf(f2133,plain,
( $false
= ( sK2 @ ( sK6 @ sK7 ) ) ),
inference(trivial_inequality_removal,[],[f2132]) ).
thf(f2299,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( ( sK4
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ (=)
@ X1 )
= X1 )
| ( X0 != X2 )
| ( X1 != X2 )
| ( ( sK6 @ sK7 )
!= X0 ) ),
inference(constrained_superposition,[],[f787,f2133]) ).
thf(f2333,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK4
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ (=)
@ X1 )
= X1 )
| ( X0 != X2 )
| ( X1 != X2 )
| ( ( sK6 @ sK7 )
!= X0 ) ),
inference(trivial_inequality_removal,[],[f2299]) ).
thf(f2334,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK6 @ sK7 )
!= X0 )
| ( ( sK4 @ sK2 @ (=) @ X1 )
= X1 )
| ( X1 != X2 )
| ( X0 != X2 ) ),
inference(beta-eta_normalization,[],[f2333]) ).
thf(f4421,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X0 = X1 )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != X0 )
@ X2 ) )
| ( X2 != X3 )
| ( X1 != X3 )
| ( $false
= ( X1 = X4 ) )
| ( $false
= ( X4 = X0 ) ) ),
inference(constrained_superposition,[],[f787,f184]) ).
thf(f4424,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X0 != X1 )
| ( X1 = X2 )
| ( X2 = X3 )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != X0 )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X1
@ X4 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X4
@ X0 ) ) ),
inference(constrained_superposition,[],[f783,f184]) ).
thf(f4689,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X0 != X1 )
| ( X1 = X2 )
| ( X2 = X3 )
| ( $true
= ( X3 != X0 ) )
| ( $false
= ( X1 != X4 ) )
| ( $false
= ( X4 != X0 ) ) ),
inference(beta-eta_normalization,[],[f4424]) ).
thf(f4690,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X0 != X1 )
| ( X1 = X2 )
| ( X2 = X3 )
| ( $false
= ( X3 = X0 ) )
| ( $false
= ( X1 != X4 ) )
| ( $false
= ( X4 != X0 ) ) ),
inference(not_proxy_clausification,[],[f4689]) ).
thf(f4691,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X0 != X1 )
| ( X1 = X2 )
| ( X2 = X3 )
| ( X0 != X3 )
| ( $false
= ( X1 != X4 ) )
| ( $false
= ( X4 != X0 ) ) ),
inference(equality_proxy_clausification,[],[f4690]) ).
thf(f4692,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X0 != X1 )
| ( X1 = X2 )
| ( X2 = X3 )
| ( X0 != X3 )
| ( $true
= ( X1 = X4 ) )
| ( $false
= ( X4 != X0 ) ) ),
inference(not_proxy_clausification,[],[f4691]) ).
thf(f4693,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X0 != X1 )
| ( X1 = X2 )
| ( X2 = X3 )
| ( X0 != X3 )
| ( X1 = X4 )
| ( $false
= ( X4 != X0 ) ) ),
inference(equality_proxy_clausification,[],[f4692]) ).
thf(f4694,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X0 != X1 )
| ( X1 = X2 )
| ( X2 = X3 )
| ( X0 != X3 )
| ( X1 = X4 )
| ( $true
= ( X4 = X0 ) ) ),
inference(not_proxy_clausification,[],[f4693]) ).
thf(f4695,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X1 = X2 )
| ( X2 = X3 )
| ( X1 = X4 )
| ( X0 = X4 )
| ( X0 != X1 )
| ( X0 != X3 ) ),
inference(equality_proxy_clausification,[],[f4694]) ).
thf(f4711,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X0 = X1 )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != X0 )
@ X2 ) )
| ( X2 != X3 )
| ( X1 != X3 )
| ( X1 != X4 )
| ( $false
= ( X4 = X0 ) ) ),
inference(equality_proxy_clausification,[],[f4421]) ).
thf(f4712,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X0 = X1 )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != X0 )
@ X2 ) )
| ( X2 != X3 )
| ( X1 != X3 )
| ( X1 != X4 )
| ( X0 != X4 ) ),
inference(equality_proxy_clausification,[],[f4711]) ).
thf(f4713,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X0 = X1 )
| ( $true
= ( X2 != X0 ) )
| ( X2 != X3 )
| ( X1 != X3 )
| ( X1 != X4 )
| ( X0 != X4 ) ),
inference(beta-eta_normalization,[],[f4712]) ).
thf(f4714,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X0 = X1 )
| ( $false
= ( X2 = X0 ) )
| ( X2 != X3 )
| ( X1 != X3 )
| ( X1 != X4 )
| ( X0 != X4 ) ),
inference(not_proxy_clausification,[],[f4713]) ).
thf(f4715,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( X0 = X1 )
| ( X0 != X2 )
| ( X2 != X3 )
| ( X1 != X3 )
| ( X1 != X4 )
| ( X0 != X4 ) ),
inference(equality_proxy_clausification,[],[f4714]) ).
thf(f6017,plain,
! [X0: $i,X1: $i] :
( ( ( sK6 @ sK7 )
!= X1 )
| ( ( sK4 @ sK2 @ (=) @ X0 )
= X0 )
| ( X0 != X1 ) ),
inference(equality_resolution,[],[f2334]) ).
thf(f7160,plain,
! [X0: $i] :
( ( ( sK6 @ sK7 )
!= X0 )
| ( ( sK4 @ sK2 @ (=) @ X0 )
= X0 ) ),
inference(equality_resolution,[],[f6017]) ).
thf(f8494,plain,
( ( sK6 @ sK7 )
= ( sK4 @ sK2 @ (=) @ ( sK6 @ sK7 ) ) ),
inference(equality_resolution,[],[f7160]) ).
thf(f12194,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X1 != X2 )
| ( X0 = X3 )
| ( X0 = X3 )
| ( X0 = X2 )
| ( X2 != X3 )
| ( X1 != X2 ) ),
inference(equality_factoring,[],[f4695]) ).
thf(f12212,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X1 != X1 )
| ( X0 = X2 )
| ( X2 = X3 )
| ( X0 = X1 )
| ( X0 != X0 )
| ( X0 != X3 ) ),
inference(equality_factoring,[],[f4695]) ).
thf(f12215,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X1 != X2 )
| ( X0 = X3 )
| ( X0 = X2 )
| ( X0 = X3 )
| ( X1 != X3 )
| ( X1 != X2 ) ),
inference(equality_factoring,[],[f4695]) ).
thf(f12219,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X1 != X2 )
| ( X0 = X3 )
| ( X0 = X2 )
| ( X1 != X3 ) ),
inference(duplicate_literal_removal,[],[f12215]) ).
thf(f12221,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X0 = X2 )
| ( X2 = X3 )
| ( X0 = X1 )
| ( X0 != X3 ) ),
inference(trivial_inequality_removal,[],[f12212]) ).
thf(f12232,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X1 != X2 )
| ( X0 = X3 )
| ( X0 = X2 )
| ( X2 != X3 ) ),
inference(duplicate_literal_removal,[],[f12194]) ).
thf(f12241,plain,
! [X2: $i,X3: $i,X0: $i] :
( ( X0 = X3 )
| ( X0 = X2 )
| ( X2 != X3 ) ),
inference(forward_subsumption_resolution,[],[f12232,f12221]) ).
thf(f12639,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( sK6 @ sK7 )
= X0 )
| ( X0 != X1 )
| ( X1 != X2 )
| ( ( sK4 @ sK2 @ (=) @ ( sK6 @ sK7 ) )
!= X2 )
| ( ( sK4 @ sK2 @ (=) @ ( sK6 @ sK7 ) )
!= X3 )
| ( X0 != X3 ) ),
inference(constrained_superposition,[],[f8494,f4715]) ).
thf(f12657,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( sK6 @ sK7 )
!= X2 )
| ( ( sK6 @ sK7 )
= X0 )
| ( X0 != X1 )
| ( X1 != X2 )
| ( ( sK4 @ sK2 @ (=) @ ( sK6 @ sK7 ) )
!= X3 )
| ( X0 != X3 ) ),
inference(forward_demodulation,[],[f12639,f8494]) ).
thf(f12659,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( sK6 @ sK7 )
= X0 )
| ( X0 != X1 )
| ( X1 != X2 )
| ( ( sK4 @ sK2 @ (=) @ ( sK6 @ sK7 ) )
!= X3 )
| ( X0 != X3 ) ),
inference(forward_subsumption_resolution,[],[f12657,f12219]) ).
thf(f12661,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( sK6 @ sK7 )
!= X3 )
| ( ( sK6 @ sK7 )
= X0 )
| ( X0 != X1 )
| ( X1 != X2 )
| ( X0 != X3 ) ),
inference(forward_demodulation,[],[f12659,f8494]) ).
thf(f12663,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( sK6 @ sK7 )
= X0 )
| ( X0 != X1 )
| ( X1 != X2 )
| ( X0 != X3 ) ),
inference(forward_subsumption_resolution,[],[f12661,f12241]) ).
thf(f12689,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( sK2 @ X0 ) )
| ( X0 != X1 )
| ( X1 != X2 )
| ( X0 != X3 ) ),
inference(constrained_superposition,[],[f2133,f12663]) ).
thf(f14419,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( sK7 != X0 )
| ( X0 != X1 )
| ( sK7 != X2 ) ),
inference(constrained_superposition,[],[f449,f12689]) ).
thf(f14420,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( sK7 != X2 )
| ( sK7 != X0 )
| ( X0 != X1 ) ),
inference(trivial_inequality_removal,[],[f14419]) ).
thf(f15735,plain,
! [X0: $i,X1: $i] :
( ( sK7 != X0 )
| ( X0 != X1 ) ),
inference(equality_resolution,[],[f14420]) ).
thf(f15800,plain,
! [X0: $i] : ( sK7 != X0 ),
inference(equality_resolution,[],[f15735]) ).
thf(f16135,plain,
$false,
inference(equality_resolution,[],[f15800]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL621^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 09:26:49 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.13 Running first-order model finding
% 0.09/0.13 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.60/0.57 % (4047524)Will run a generic schedule for satisfiability detection.
% 2.60/0.57 % (4047530)% WARNING: option uhcvi not known.
% 2.60/0.57 % (4047530)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2520938591:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.60/0.57 % (4047533)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1133284434:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.60/0.57 % (4047531)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=692227403:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.60/0.57 % (4047529)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1337106734_2999 on theBenchmark for (2999ds/0Mi)
% 2.60/0.57 % (4047530)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.60/0.57 % Exception at run slice level
% 2.60/0.57 User error: % (4047530)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.60/0.57 Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.60/0.57 % (4047533)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.60/0.57 % (4047535)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1410117020:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.60/0.57 % (4047534)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3746010896:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.60/0.57 % (4047532)dis+10_1_sil=32000:sp=arity:random_seed=2290611300:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.60/0.57 % (4047540)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=84376980:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.60/0.57 % Exception at run slice level
% 2.60/0.57 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.60/0.57 % (4047545)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3235519285:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.60/0.57 % (4047535)Instruction limit reached!
% 2.60/0.57 % (4047535)------------------------------
% 2.60/0.57 % (4047535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.60/0.57 % (4047535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/0.57 % (4047535)CaDiCaL version: 2.1.3
% 2.60/0.57 % (4047535)Termination reason: Instruction limit
% 2.60/0.57 % (4047535)Termination phase: Saturation
% 2.60/0.57 % (4047535)Time elapsed: 0.041 s
% 2.60/0.57 % (4047535)Peak memory usage: 13 MB
% 2.60/0.57 % (4047535)Instructions burned: 159 (million)
% 2.60/0.57 % (4047545)Instruction limit reached!
% 2.60/0.57 % (4047545)------------------------------
% 2.60/0.57 % (4047545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.60/0.57 % (4047545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/0.57 % (4047545)CaDiCaL version: 2.1.3
% 2.60/0.57 % (4047545)Termination reason: Instruction limit
% 2.60/0.57 % (4047545)Termination phase: Saturation
% 2.60/0.57 % (4047545)Time elapsed: 0.035 s
% 2.60/0.57 % (4047545)Peak memory usage: 12 MB
% 2.60/0.57 % (4047545)Instructions burned: 134 (million)
% 2.60/0.57 % (4047547)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=1691328491:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.60/0.57 % (4047547)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.60/0.57 % (4047547)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.60/0.57 % (4047533)Instruction limit reached!
% 2.60/0.57 % (4047533)------------------------------
% 2.60/0.57 % (4047533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.60/0.57 % (4047533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/0.57 % (4047533)CaDiCaL version: 2.1.3
% 2.60/0.57 % (4047533)Termination reason: Instruction limit
% 2.60/0.57 % (4047533)Termination phase: Saturation
% 2.60/0.57 % (4047533)Time elapsed: 0.061 s
% 2.60/0.57 % (4047533)Peak memory usage: 12 MB
% 2.60/0.57 % (4047533)Instructions burned: 118 (million)
% 2.60/0.57 % (4047532)Instruction limit reached!
% 2.60/0.57 % (4047532)------------------------------
% 2.60/0.57 % (4047532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.04/1.05 % (4047532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.05 % (4047532)CaDiCaL version: 2.1.3
% 6.04/1.05 % (4047532)Termination reason: Instruction limit
% 6.04/1.05 % (4047532)Termination phase: Saturation
% 6.04/1.05 % (4047532)Time elapsed: 0.053 s
% 6.04/1.05 % (4047532)Peak memory usage: 12 MB
% 6.04/1.05 % (4047532)Instructions burned: 104 (million)
% 6.04/1.05 % (4047534)Instruction limit reached!
% 6.04/1.05 % (4047534)------------------------------
% 6.04/1.05 % (4047534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.04/1.05 % (4047534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.05 % (4047534)CaDiCaL version: 2.1.3
% 6.04/1.05 % (4047534)Termination reason: Instruction limit
% 6.04/1.05 % (4047534)Termination phase: Saturation
% 6.04/1.05 % (4047534)Time elapsed: 0.059 s
% 6.04/1.05 % (4047534)Peak memory usage: 12 MB
% 6.04/1.05 % (4047534)Instructions burned: 133 (million)
% 6.04/1.05 % (4047549)ott-21_1_sil=16000:fs=off:random_seed=858185404:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 6.04/1.05 % (4047550)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3824781116:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 6.04/1.05 % (4047551)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1652915661:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 6.04/1.05 % Exception at run slice level
% 6.04/1.05 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.04/1.05 % (4047552)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=104529916:i=1179_2999 on theBenchmark for (2999ds/1179Mi)
% 6.04/1.05 % (4047556)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1400446902:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 6.04/1.05 % Exception at run slice level
% 6.04/1.05 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.04/1.05 % (4047559)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=3449584202: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)
% 6.04/1.05 % (4047559)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.04/1.05 % (4047549)Instruction limit reached!
% 6.04/1.05 % (4047549)------------------------------
% 6.04/1.05 % (4047549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.04/1.05 % (4047549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.05 % (4047549)CaDiCaL version: 2.1.3
% 6.04/1.05 % (4047549)Termination reason: Instruction limit
% 6.04/1.05 % (4047549)Termination phase: Saturation
% 6.04/1.05 % (4047549)Time elapsed: 0.045 s
% 6.04/1.05 % (4047549)Peak memory usage: 12 MB
% 6.04/1.05 % (4047549)Instructions burned: 182 (million)
% 6.04/1.05 % (4047561)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=896844721:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 6.04/1.05 % (4047561)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.04/1.05 % (4047547)Instruction limit reached!
% 6.04/1.05 % (4047547)------------------------------
% 6.04/1.05 % (4047547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.04/1.05 % (4047547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.05 % (4047547)CaDiCaL version: 2.1.3
% 6.04/1.05 % (4047547)Termination reason: Instruction limit
% 6.04/1.05 % (4047547)Termination phase: Saturation
% 6.04/1.05 % (4047547)Time elapsed: 0.179 s
% 6.04/1.05 % (4047547)Peak memory usage: 15 MB
% 6.04/1.05 % (4047547)Instructions burned: 686 (million)
% 6.04/1.05 % (4047563)fmb+10_1_sil=64000:random_seed=4066119854:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 6.04/1.05 % (4047563)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.04/1.05 % Exception at run slice level
% 6.04/1.05 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.04/1.05 % (4047565)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3623281475:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 6.04/1.05 % Exception at run slice level
% 6.04/1.05 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.04/1.05 % (4047567)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2782686352:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 6.04/1.05 % Exception at run slice level
% 6.04/1.05 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.04/1.05 % (4047569)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2405521420:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 6.04/1.05 % (4047569)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.04/1.05 % (4047550)Instruction limit reached!
% 6.04/1.05 % (4047550)------------------------------
% 6.04/1.05 % (4047550)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.04/1.05 % (4047550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.05 % (4047550)CaDiCaL version: 2.1.3
% 6.04/1.05 % (4047550)Termination reason: Instruction limit
% 6.04/1.05 % (4047550)Termination phase: Saturation
% 6.04/1.05 % (4047550)Time elapsed: 0.217 s
% 6.04/1.05 % (4047550)Peak memory usage: 13 MB
% 6.04/1.05 % (4047550)Instructions burned: 477 (million)
% 6.04/1.05 % (4047571)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2791945627:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 6.04/1.05 % (4047571)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.04/1.05 % (4047571)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.04/1.05 % (4047561)Instruction limit reached!
% 6.04/1.05 % (4047561)------------------------------
% 6.04/1.05 % (4047561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.04/1.05 % (4047561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.05 % (4047561)CaDiCaL version: 2.1.3
% 6.04/1.05 % (4047561)Termination reason: Instruction limit
% 6.04/1.05 % (4047561)Termination phase: Saturation
% 6.04/1.05 % (4047561)Time elapsed: 0.228 s
% 6.04/1.05 % (4047561)Peak memory usage: 15 MB
% 6.04/1.05 % (4047561)Instructions burned: 892 (million)
% 6.04/1.05 % (4047573)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2058044665:i=6324_2996 on theBenchmark for (2996ds/6324Mi)
% 6.04/1.05 % Exception at run slice level
% 6.04/1.05 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.04/1.05 % (4047552)Instruction limit reached!
% 6.04/1.05 % (4047552)------------------------------
% 6.04/1.05 % (4047552)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.04/1.05 % (4047552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.05 % (4047552)CaDiCaL version: 2.1.3
% 6.04/1.05 % (4047552)Termination reason: Instruction limit
% 6.04/1.05 % (4047552)Termination phase: Saturation
% 6.04/1.05 % (4047552)Time elapsed: 0.298 s
% 6.04/1.05 % (4047552)Peak memory usage: 15 MB
% 6.04/1.05 % (4047552)Instructions burned: 1181 (million)
% 6.04/1.05 % (4047575)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1136224186:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 6.04/1.05 % Exception at run slice level
% 6.04/1.05 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.04/1.05 % (4047559)Instruction limit reached!
% 6.04/1.05 % (4047559)------------------------------
% 6.04/1.05 % (4047559)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.04/1.05 % (4047559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.05 % (4047559)CaDiCaL version: 2.1.3
% 6.04/1.05 % (4047559)Termination reason: Instruction limit
% 6.04/1.05 % (4047559)Termination phase: Saturation
% 6.04/1.05 % (4047559)Time elapsed: 0.289 s
% 6.04/1.05 % (4047559)Peak memory usage: 17 MB
% 6.04/1.05 % (4047559)Instructions burned: 692 (million)
% 6.04/1.05 % (4047576)ott-2_1_sil=16000:newcnf=on:random_seed=725074281:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2995 on theBenchmark for (2995ds/869Mi)
% 6.04/1.05 % (4047576)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.04/1.05 % (4047578)ott+10_1_sil=32000:tgt=ground:random_seed=1876603535:i=5114:av=off_2995 on theBenchmark for (2995ds/5114Mi)
% 6.04/1.05 % (4047579)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1041913387:i=54282_2995 on theBenchmark for (2995ds/54282Mi)
% 6.04/1.05 % Exception at run slice level
% 6.04/1.05 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.04/1.05 % (4047583)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2613132504:i=3512:aac=none_2995 on theBenchmark for (2995ds/3512Mi)
% 6.04/1.05 % (4047583)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.04/1.05 % (4047576)Instruction limit reached!
% 6.04/1.05 % (4047576)------------------------------
% 6.04/1.05 % (4047576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.04/1.05 % (4047576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.05 % (4047576)CaDiCaL version: 2.1.3
% 6.04/1.05 % (4047576)Termination reason: Instruction limit
% 6.04/1.05 % (4047576)Termination phase: Saturation
% 6.04/1.05 % (4047576)Time elapsed: 0.248 s
% 6.04/1.05 % (4047576)Peak memory usage: 16 MB
% 6.04/1.05 % (4047576)Instructions burned: 871 (million)
% 6.04/1.05 % (4047585)dis+21_1_sil=32000:sas=cadical:random_seed=3598619694:i=3773:amm=off_2993 on theBenchmark for (2993ds/3773Mi)
% 6.04/1.05 % (4047571)Instruction limit reached!
% 6.04/1.05 % (4047571)------------------------------
% 6.04/1.05 % (4047571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.04/1.05 % (4047571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.05 % (4047571)CaDiCaL version: 2.1.3
% 6.04/1.05 % (4047571)Termination reason: Instruction limit
% 6.04/1.05 % (4047571)Termination phase: Saturation
% 6.04/1.05 % (4047571)Time elapsed: 0.501 s
% 6.04/1.05 % (4047571)Peak memory usage: 20 MB
% 6.04/1.05 % (4047571)Instructions burned: 1475 (million)
% 6.04/1.05 % (4047587)ott+11_1_sil=16000:gs=on:random_seed=2785689733:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2991 on theBenchmark for (2991ds/2251Mi)
% 6.04/1.05 % (4047587)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.04/1.05 % (4047578) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4047524-4047578"...
% 6.04/1.05 % (4047578)...printing done.
% 6.04/1.05 % (4047578)Refutation found. Thanks to Tanya!
% 6.04/1.05 % SZS status Theorem for theBenchmark
% 6.04/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 6.04/1.05 % (4047578)------------------------------
% 6.04/1.05 % (4047578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.04/1.05 % (4047578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.05 % (4047578)CaDiCaL version: 2.1.3
% 6.04/1.05 % (4047578)Termination reason: Refutation
% 6.04/1.05 % (4047578)Time elapsed: 0.479 s
% 6.04/1.05 % (4047578)Peak memory usage: 16 MB
% 6.04/1.05 % (4047578)Instructions burned: 1940 (million)
% 6.04/1.05 % (4047524)Success in time 0.914 s
% 6.04/1.05 % Vampire exiting
%------------------------------------------------------------------------------