%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG274^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 07:45:29 AM UTC 2026
% Result : Theorem 0.92s 0.37s
% Output : Refutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 19
% Syntax : Number of formulae : 221 ( 33 unt; 0 typ; 12 def)
% Number of atoms : 1471 ( 605 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 3475 ( 282 ~; 369 |; 86 &;2389 @)
% ( 16 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 49 usr; 25 con; 0-4 aty)
% ( 223 !!; 109 ??; 0 @@+; 0 @@-)
% Number of variables : 768 ( 0 sgn 287 !; 15 ?; 768 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cGROUP3: ( g > g > g ) > g > $o ).
thf(func_def_1,type,
cGROUP4: ( g > g > g ) > $o ).
thf(func_def_2,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(func_def_3,type,
cGRP_DIVISORS: ( g > g > g ) > $o ).
thf(func_def_4,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_5,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
vAND: $o > $o > $o ).
thf(func_def_15,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_18,type,
sK0: g > g > g ).
thf(func_def_19,type,
sK1: g ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(func_def_21,type,
sK2: g > g ).
thf(func_def_22,type,
sK3: g > g > g ).
thf(func_def_23,type,
sK4: g > g > g ).
thf(func_def_24,type,
sK5: g > g > g ).
thf(func_def_25,type,
sK6: g > g > g ).
thf(func_def_26,type,
sK7: g > g ).
thf(func_def_27,type,
sK8: g > g > g ).
thf(func_def_28,type,
sK9: g > g > g ).
thf(func_def_29,type,
sK10: g ).
thf(func_def_30,type,
sK11: g > g ).
thf(func_def_31,type,
sK12: g ).
thf(func_def_32,type,
sK13: g > g ).
thf(func_def_33,type,
sK14: g ).
thf(func_def_34,type,
sK15: g ).
thf(func_def_35,type,
sK16: g ).
thf(func_def_36,type,
sK17: g ).
thf(func_def_37,type,
sK18: g ).
thf(func_def_38,type,
sK19: g ).
thf(f1,axiom,
( cGRP_ASSOC
= ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_ASSOC_def) ).
thf(f2,axiom,
( cGRP_DIVISORS
= ( ^ [X0: g > g > g] :
! [X1: g,X2: g] :
( ? [X4: g] :
( ( X0 @ X4 @ X1 )
= X2 )
& ? [X3: g] :
( ( X0 @ X1 @ X3 )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_DIVISORS_def) ).
thf(f3,axiom,
( cGRP_RIGHT_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X2 @ X3 )
= X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_RIGHT_INVERSE_def) ).
thf(f4,axiom,
( cGRP_RIGHT_UNIT
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_RIGHT_UNIT_def) ).
thf(f5,axiom,
( cGROUP3
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGROUP3_def) ).
thf(f6,axiom,
( cGROUP4
= ( ^ [X0: g > g > g] :
( ( cGRP_DIVISORS @ X0 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGROUP4_def) ).
thf(f7,conjecture,
! [X0: g > g > g] :
( ? [X1: g] : ( cGROUP3 @ X0 @ X1 )
<=> ( cGROUP4 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEQUIV_03_04) ).
thf(f8,negated_conjecture,
~ ! [X0: g > g > g] :
( ? [X1: g] : ( cGROUP3 @ X0 @ X1 )
<=> ( cGROUP4 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ Y3 @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f10,plain,
( cGRP_DIVISORS
= ( ^ [X0: g > g > g] :
! [X1: g,X2: g] :
( ? [X3: g] :
( ( X0 @ X3 @ X1 )
= X2 )
& ? [X4: g] :
( ( X0 @ X1 @ X4 )
= X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
( cGRP_DIVISORS
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f13,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f14,plain,
( cGROUP3
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f15,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( cGROUP4
= ( ^ [X0: g > g > g] :
( ( cGRP_DIVISORS @ X0 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f17,plain,
( cGROUP4
= ( ^ [Y0: g > g > g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_DIVISORS @ Y0 ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
~ ! [X0: g > g > g] :
( ? [X1: g] : ( cGROUP3 @ X0 @ X1 )
<=> ( cGROUP4 @ X0 ) ),
inference(rectify,[],[f8]) ).
thf(f19,plain,
~ ! [X0: g > g > g] :
( ? [X1: g] :
( ( cGROUP3 @ X0 @ X1 )
= $true )
<=> ( ( cGROUP4 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
? [X0: g > g > g] :
( ? [X1: g] :
( ( cGROUP3 @ X0 @ X1 )
= $true )
<~> ( ( cGROUP4 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f21,plain,
? [X0: g > g > g] :
( ( ( ( cGROUP4 @ X0 )
!= $true )
| ! [X1: g] :
( ( cGROUP3 @ X0 @ X1 )
!= $true ) )
& ( ( ( cGROUP4 @ X0 )
= $true )
| ? [X1: g] :
( ( cGROUP3 @ X0 @ X1 )
= $true ) ) ),
inference(nnf_transformation,[],[f20]) ).
thf(f22,plain,
? [X0: g > g > g] :
( ( ( ( cGROUP4 @ X0 )
!= $true )
| ! [X1: g] :
( ( cGROUP3 @ X0 @ X1 )
!= $true ) )
& ( ( ( cGROUP4 @ X0 )
= $true )
| ? [X2: g] :
( $true
= ( cGROUP3 @ X0 @ X2 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f23,plain,
( ( ( $true
!= ( cGROUP4 @ sK0 ) )
| ! [X1: g] :
( $true
!= ( cGROUP3 @ sK0 @ X1 ) ) )
& ( ( $true
= ( cGROUP4 @ sK0 ) )
| ( $true
= ( cGROUP3 @ sK0 @ sK1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1)],[f22]) ).
thf(f24,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ Y3 @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f25,plain,
( cGRP_DIVISORS
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f26,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f27,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f28,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f29,plain,
( cGROUP4
= ( ^ [Y0: g > g > g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_DIVISORS @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f30,plain,
( ( $true
= ( cGROUP4 @ sK0 ) )
| ( $true
= ( cGROUP3 @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f31,plain,
! [X1: g] :
( ( $true
!= ( cGROUP4 @ sK0 ) )
| ( $true
!= ( cGROUP3 @ sK0 @ X1 ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f34,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f28,f24,f27,f26]) ).
thf(f35,plain,
( cGROUP4
= ( ^ [Y0: g > g > g] :
( ( ^ [Y1: g > g > g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y1 @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ Y4 @ ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y1: g > g > g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( ?? @ g
@ ^ [Y4: g] :
( ( Y1 @ Y3 @ Y4 )
= Y2 ) )
& ( ?? @ g
@ ^ [Y4: g] :
( ( Y1 @ Y4 @ Y3 )
= Y2 ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f29,f24,f25]) ).
thf(f36,plain,
! [X1: g] :
( ( $true
!= ( ^ [Y0: g > g > g] :
( ( ^ [Y1: g > g > g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y1 @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ Y4 @ ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y1: g > g > g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( ?? @ g
@ ^ [Y4: g] :
( ( Y1 @ Y3 @ Y4 )
= Y2 ) )
& ( ?? @ g
@ ^ [Y4: g] :
( ( Y1 @ Y4 @ Y3 )
= Y2 ) ) ) ) )
@ Y0 ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ X1 ) ) ),
inference(definition_unfolding,[],[f31,f35,f34]) ).
thf(f37,plain,
( ( $true
= ( ^ [Y0: g > g > g] :
( ( ^ [Y1: g > g > g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y1 @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ Y4 @ ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y1: g > g > g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( ?? @ g
@ ^ [Y4: g] :
( ( Y1 @ Y3 @ Y4 )
= Y2 ) )
& ( ?? @ g
@ ^ [Y4: g] :
( ( Y1 @ Y4 @ Y3 )
= Y2 ) ) ) ) )
@ Y0 ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f30,f35,f34]) ).
thf(f38,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f40,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f41,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f43,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f41]) ).
thf(f45,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f46,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: g,X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X1 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X1 ) ) ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X2 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X1 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X1 ) ) ) )
@ X3 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X2 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X2 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X1 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X1 ) ) ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X2 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X2 ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X3 ) @ X1 )
= ( sK0 @ Y0 @ ( sK0 @ X3 @ X1 ) ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X4 ) @ X2 )
= ( sK0 @ Y0 @ ( sK0 @ X4 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
! [X2: g,X3: g,X1: g,X4: g,X5: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X3 ) @ X1 )
= ( sK0 @ Y0 @ ( sK0 @ X3 @ X1 ) ) )
@ X5 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X4 ) @ X2 )
= ( sK0 @ Y0 @ ( sK0 @ X4 @ X2 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X3 ) @ X1 )
= ( sK0 @ Y0 @ ( sK0 @ X3 @ X1 ) ) )
@ X5 ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X4 ) @ X2 )
= ( sK0 @ Y0 @ ( sK0 @ X4 @ X2 ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( $true
= ( ( sK0 @ ( sK0 @ X5 @ X3 ) @ X1 )
= ( sK0 @ X5 @ ( sK0 @ X3 @ X1 ) ) ) )
| ( $true
= ( ( sK0 @ ( sK0 @ X6 @ X4 ) @ X2 )
= ( sK0 @ X6 @ ( sK0 @ X4 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( ( sK0 @ ( sK0 @ X5 @ X3 ) @ X1 )
= ( sK0 @ X5 @ ( sK0 @ X3 @ X1 ) ) )
| ( $true
= ( ( sK0 @ ( sK0 @ X6 @ X4 ) @ X2 )
= ( sK0 @ X6 @ ( sK0 @ X4 @ X2 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( ( sK0 @ ( sK0 @ X5 @ X3 ) @ X1 )
= ( sK0 @ X5 @ ( sK0 @ X3 @ X1 ) ) )
| ( ( sK0 @ ( sK0 @ X6 @ X4 ) @ X2 )
= ( sK0 @ X6 @ ( sK0 @ X4 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f54]) ).
thf(f73,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f74,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f76,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f75]) ).
thf(f95,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f76]) ).
thf(f96,plain,
! [X2: g,X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= X1 ) ) ) ) )
| ( $true
= ( ( sK0 @ X2 @ sK1 )
= X2 ) ) ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= X1 ) ) )
@ X3 ) )
| ( $true
= ( ( sK0 @ X2 @ sK1 )
= X2 ) ) ),
inference(pi_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= X1 ) ) )
@ X3 ) )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f97]) ).
thf(f99,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X3 @ Y0 )
= X1 ) )
& ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X3 )
= X1 ) ) ) )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(beta-eta_normalization,[],[f98]) ).
thf(f100,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X3 )
= X1 ) ) )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(and_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X3 @ Y0 )
= X1 ) ) )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(and_proxy_clausification,[],[f99]) ).
thf(f102,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ X3 @ Y0 )
= X1 )
@ ( sK5 @ X3 @ X1 ) ) )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(sigma_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ( sK0 @ X3 @ ( sK5 @ X3 @ X1 ) )
= X1 ) )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK0 @ X3 @ ( sK5 @ X3 @ X1 ) )
= X1 )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ X3 )
= X1 )
@ ( sK6 @ X3 @ X1 ) ) )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(sigma_proxy_clausification,[],[f100]) ).
thf(f106,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ( sK0 @ ( sK6 @ X3 @ X1 ) @ X3 )
= X1 ) )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK0 @ ( sK6 @ X3 @ X1 ) @ X3 )
= X1 )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f74]) ).
thf(f109,plain,
! [X2: g,X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= X1 ) ) ) ) )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f110,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= X1 ) ) )
@ X3 ) )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 ) ) ) ),
inference(pi_proxy_clausification,[],[f109]) ).
thf(f111,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= X1 ) ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 )
@ ( sK7 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f110]) ).
thf(f112,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X3 @ Y0 )
= X1 ) )
& ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X3 )
= X1 ) ) ) )
| ( $true
= ( ( sK0 @ X2 @ ( sK7 @ X2 ) )
= sK1 ) ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f113,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X3 )
= X1 ) ) )
| ( $true
= ( ( sK0 @ X2 @ ( sK7 @ X2 ) )
= sK1 ) ) ),
inference(and_proxy_clausification,[],[f112]) ).
thf(f114,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X3 @ Y0 )
= X1 ) ) )
| ( $true
= ( ( sK0 @ X2 @ ( sK7 @ X2 ) )
= sK1 ) ) ),
inference(and_proxy_clausification,[],[f112]) ).
thf(f115,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ X3 @ Y0 )
= X1 )
@ ( sK8 @ X3 @ X1 ) ) )
| ( $true
= ( ( sK0 @ X2 @ ( sK7 @ X2 ) )
= sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ X3 @ Y0 )
= X1 )
@ ( sK8 @ X3 @ X1 ) ) )
| ( sK1
= ( sK0 @ X2 @ ( sK7 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ( sK0 @ X3 @ ( sK8 @ X3 @ X1 ) )
= X1 ) )
| ( sK1
= ( sK0 @ X2 @ ( sK7 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK0 @ X3 @ ( sK8 @ X3 @ X1 ) )
= X1 )
| ( sK1
= ( sK0 @ X2 @ ( sK7 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ X3 )
= X1 )
@ ( sK9 @ X3 @ X1 ) ) )
| ( $true
= ( ( sK0 @ X2 @ ( sK7 @ X2 ) )
= sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f113]) ).
thf(f120,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ X3 )
= X1 )
@ ( sK9 @ X3 @ X1 ) ) )
| ( sK1
= ( sK0 @ X2 @ ( sK7 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ( sK0 @ ( sK9 @ X3 @ X1 ) @ X3 )
= X1 ) )
| ( sK1
= ( sK0 @ X2 @ ( sK7 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK0 @ ( sK9 @ X3 @ X1 ) @ X3 )
= X1 )
| ( sK1
= ( sK0 @ X2 @ ( sK7 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X1: g] :
( ( $true
!= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) ) ) ) )
| ( $true
!= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f124,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) ) ) )
| ( $true
!= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X1: g] :
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) )
@ sK10 ) )
| ( $true
!= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X1: g] :
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) )
@ sK10 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X1: g] :
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) )
@ sK10 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) )
@ ( sK11 @ X1 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X1: g] :
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) )
@ sK10 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) )
@ ( sK11 @ X1 ) ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ sK12 ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X1: g] :
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) )
@ sK10 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) )
@ ( sK11 @ X1 ) ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ sK12 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= Y0 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X1: g] :
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) )
@ sK10 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) )
@ ( sK11 @ X1 ) ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ sK12 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= Y0 )
@ ( sK13 @ X1 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f129]) ).
thf(f131,plain,
! [X1: g] :
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ Y2 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK0 @ Y2 @ Y1 )
= Y0 ) ) ) )
@ sK10 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= X1 ) )
@ ( sK11 @ X1 ) ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ sK12 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= Y0 )
@ ( sK13 @ X1 ) ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ sK14 ) ) ),
inference(sigma_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK10 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK10 ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK11 @ X1 ) @ Y0 )
= X1 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK12 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK12 ) ) ) ) ) )
| ( $false
= ( ( sK0 @ ( sK13 @ X1 ) @ X1 )
= ( sK13 @ X1 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK14 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK14 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f133,plain,
! [X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK10 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK10 ) ) )
@ sK15 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK11 @ X1 ) @ Y0 )
= X1 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK12 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK12 ) ) ) ) ) )
| ( $false
= ( ( sK0 @ ( sK13 @ X1 ) @ X1 )
= ( sK13 @ X1 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK14 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK14 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK10 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK10 ) ) )
@ sK15 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK11 @ X1 ) @ Y0 )
= X1 )
@ X2 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK12 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK12 ) ) ) ) ) )
| ( $false
= ( ( sK0 @ ( sK13 @ X1 ) @ X1 )
= ( sK13 @ X1 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK14 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK14 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK10 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK10 ) ) )
@ sK15 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK11 @ X1 ) @ Y0 )
= X1 )
@ X2 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK12 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK12 ) ) ) )
@ sK16 ) )
| ( $false
= ( ( sK0 @ ( sK13 @ X1 ) @ X1 )
= ( sK13 @ X1 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK14 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK14 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f134]) ).
thf(f136,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK10 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK10 ) ) )
@ sK15 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK11 @ X1 ) @ Y0 )
= X1 )
@ X2 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK12 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK12 ) ) ) )
@ sK16 ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK14 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK14 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK10 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK10 ) ) )
@ sK15 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK11 @ X1 ) @ Y0 )
= X1 )
@ X2 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK12 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK12 ) ) ) )
@ sK16 ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK14 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK14 ) ) ) )
@ sK17 ) ) ),
inference(sigma_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK15 @ Y0 )
= sK10 ) )
& ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK15 )
= sK10 ) ) ) )
| ( $false
= ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
= X1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK16 ) @ sK12 )
= ( sK0 @ Y0 @ ( sK0 @ sK16 @ sK12 ) ) ) ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK17 ) @ sK14 )
= ( sK0 @ Y0 @ ( sK0 @ sK17 @ sK14 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
! [X2: g,X1: g] :
( ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK15 )
= sK10 ) ) )
| ( $false
= ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
= X1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK16 ) @ sK12 )
= ( sK0 @ Y0 @ ( sK0 @ sK16 @ sK12 ) ) ) ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK17 ) @ sK14 )
= ( sK0 @ Y0 @ ( sK0 @ sK17 @ sK14 ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK15 @ Y0 )
= sK10 ) ) ) ),
inference(and_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: g,X3: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK15 )
= sK10 )
@ X3 ) )
| ( $false
= ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
= X1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK16 ) @ sK12 )
= ( sK0 @ Y0 @ ( sK0 @ sK16 @ sK12 ) ) ) ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK17 ) @ sK14 )
= ( sK0 @ Y0 @ ( sK0 @ sK17 @ sK14 ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK15 @ Y0 )
= sK10 ) ) ) ),
inference(pi_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: g,X3: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK15 )
= sK10 )
@ X3 ) )
| ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
!= X1 )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK16 ) @ sK12 )
= ( sK0 @ Y0 @ ( sK0 @ sK16 @ sK12 ) ) ) ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK17 ) @ sK14 )
= ( sK0 @ Y0 @ ( sK0 @ sK17 @ sK14 ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK15 @ Y0 )
= sK10 ) ) ) ),
inference(equality_proxy_clausification,[],[f140]) ).
thf(f142,plain,
! [X2: g,X3: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK15 )
= sK10 )
@ X3 ) )
| ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
!= X1 )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK16 ) @ sK12 )
= ( sK0 @ Y0 @ ( sK0 @ sK16 @ sK12 ) ) )
@ sK18 ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK17 ) @ sK14 )
= ( sK0 @ Y0 @ ( sK0 @ sK17 @ sK14 ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK15 @ Y0 )
= sK10 ) ) ) ),
inference(sigma_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: g,X3: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK15 )
= sK10 )
@ X3 ) )
| ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
!= X1 )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK16 ) @ sK12 )
= ( sK0 @ Y0 @ ( sK0 @ sK16 @ sK12 ) ) )
@ sK18 ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK17 ) @ sK14 )
= ( sK0 @ Y0 @ ( sK0 @ sK17 @ sK14 ) ) )
@ sK19 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK15 @ Y0 )
= sK10 ) ) ) ),
inference(sigma_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK15 )
= sK10 )
@ X3 ) )
| ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
!= X1 )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK16 ) @ sK12 )
= ( sK0 @ Y0 @ ( sK0 @ sK16 @ sK12 ) ) )
@ sK18 ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK17 ) @ sK14 )
= ( sK0 @ Y0 @ ( sK0 @ sK17 @ sK14 ) ) )
@ sK19 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK15 @ Y0 )
= sK10 )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( $false
= ( ( sK0 @ X3 @ sK15 )
= sK10 ) )
| ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
!= X1 )
| ( $false
= ( ( sK0 @ ( sK0 @ sK18 @ sK16 ) @ sK12 )
= ( sK0 @ sK18 @ ( sK0 @ sK16 @ sK12 ) ) ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $false
= ( ( sK0 @ ( sK0 @ sK19 @ sK17 ) @ sK14 )
= ( sK0 @ sK19 @ ( sK0 @ sK17 @ sK14 ) ) ) )
| ( $false
= ( ( sK0 @ sK15 @ X4 )
= sK10 ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( sK10
!= ( sK0 @ X3 @ sK15 ) )
| ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
!= X1 )
| ( $false
= ( ( sK0 @ ( sK0 @ sK18 @ sK16 ) @ sK12 )
= ( sK0 @ sK18 @ ( sK0 @ sK16 @ sK12 ) ) ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $false
= ( ( sK0 @ ( sK0 @ sK19 @ sK17 ) @ sK14 )
= ( sK0 @ sK19 @ ( sK0 @ sK17 @ sK14 ) ) ) )
| ( $false
= ( ( sK0 @ sK15 @ X4 )
= sK10 ) ) ),
inference(equality_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( sK10
!= ( sK0 @ X3 @ sK15 ) )
| ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
!= X1 )
| ( ( sK0 @ ( sK0 @ sK18 @ sK16 ) @ sK12 )
!= ( sK0 @ sK18 @ ( sK0 @ sK16 @ sK12 ) ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $false
= ( ( sK0 @ ( sK0 @ sK19 @ sK17 ) @ sK14 )
= ( sK0 @ sK19 @ ( sK0 @ sK17 @ sK14 ) ) ) )
| ( $false
= ( ( sK0 @ sK15 @ X4 )
= sK10 ) ) ),
inference(equality_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( sK10
!= ( sK0 @ X3 @ sK15 ) )
| ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
!= X1 )
| ( ( sK0 @ ( sK0 @ sK18 @ sK16 ) @ sK12 )
!= ( sK0 @ sK18 @ ( sK0 @ sK16 @ sK12 ) ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( ( sK0 @ ( sK0 @ sK19 @ sK17 ) @ sK14 )
!= ( sK0 @ sK19 @ ( sK0 @ sK17 @ sK14 ) ) )
| ( $false
= ( ( sK0 @ sK15 @ X4 )
= sK10 ) ) ),
inference(equality_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( sK10
!= ( sK0 @ X3 @ sK15 ) )
| ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
!= X1 )
| ( ( sK0 @ ( sK0 @ sK18 @ sK16 ) @ sK12 )
!= ( sK0 @ sK18 @ ( sK0 @ sK16 @ sK12 ) ) )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( ( sK0 @ ( sK0 @ sK19 @ sK17 ) @ sK14 )
!= ( sK0 @ sK19 @ ( sK0 @ sK17 @ sK14 ) ) )
| ( sK10
!= ( sK0 @ sK15 @ X4 ) ) ),
inference(equality_proxy_clausification,[],[f148]) ).
thf(f151,definition,
( spl20_1
<=> ! [X6: g,X2: g,X4: g] :
( ( sK0 @ ( sK0 @ X6 @ X4 ) @ X2 )
= ( sK0 @ X6 @ ( sK0 @ X4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
thf(f152,plain,
( ! [X2: g,X6: g,X4: g] :
( ( sK0 @ ( sK0 @ X6 @ X4 ) @ X2 )
= ( sK0 @ X6 @ ( sK0 @ X4 @ X2 ) ) )
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f151]) ).
thf(f153,plain,
( spl20_1
| spl20_1 ),
inference(avatar_split_clause,[],[f55,f151,f151]) ).
thf(f155,definition,
( spl20_2
<=> ! [X2: g] :
( ( sK0 @ X2 @ sK1 )
= X2 ) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
thf(f156,plain,
( ! [X2: g] :
( ( sK0 @ X2 @ sK1 )
= X2 )
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f155]) ).
thf(f171,definition,
( spl20_6
<=> ! [X1: g,X3: g] :
( ( sK0 @ X3 @ ( sK5 @ X3 @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl20_6])],[avatar_definition]) ).
thf(f172,plain,
( ! [X3: g,X1: g] :
( ( sK0 @ X3 @ ( sK5 @ X3 @ X1 ) )
= X1 )
| ~ spl20_6 ),
inference(avatar_component_clause,[],[f171]) ).
thf(f173,plain,
( spl20_2
| spl20_6 ),
inference(avatar_split_clause,[],[f104,f171,f155]) ).
thf(f175,definition,
( spl20_7
<=> ! [X1: g,X3: g] :
( ( sK0 @ ( sK6 @ X3 @ X1 ) @ X3 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
thf(f176,plain,
( ! [X3: g,X1: g] :
( ( sK0 @ ( sK6 @ X3 @ X1 ) @ X3 )
= X1 )
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f175]) ).
thf(f177,plain,
( spl20_2
| spl20_7 ),
inference(avatar_split_clause,[],[f107,f175,f155]) ).
thf(f179,definition,
( spl20_8
<=> ! [X2: g] :
( sK1
= ( sK0 @ X2 @ ( sK7 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition]) ).
thf(f180,plain,
( ! [X2: g] :
( sK1
= ( sK0 @ X2 @ ( sK7 @ X2 ) ) )
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f179]) ).
thf(f182,definition,
( spl20_9
<=> ! [X1: g,X3: g] :
( ( sK0 @ X3 @ ( sK8 @ X3 @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl20_9])],[avatar_definition]) ).
thf(f183,plain,
( ! [X3: g,X1: g] :
( ( sK0 @ X3 @ ( sK8 @ X3 @ X1 ) )
= X1 )
| ~ spl20_9 ),
inference(avatar_component_clause,[],[f182]) ).
thf(f184,plain,
( spl20_8
| spl20_9 ),
inference(avatar_split_clause,[],[f118,f182,f179]) ).
thf(f186,definition,
( spl20_10
<=> ! [X1: g,X3: g] :
( ( sK0 @ ( sK9 @ X3 @ X1 ) @ X3 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl20_10])],[avatar_definition]) ).
thf(f187,plain,
( ! [X3: g,X1: g] :
( ( sK0 @ ( sK9 @ X3 @ X1 ) @ X3 )
= X1 )
| ~ spl20_10 ),
inference(avatar_component_clause,[],[f186]) ).
thf(f188,plain,
( spl20_8
| spl20_10 ),
inference(avatar_split_clause,[],[f122,f186,f179]) ).
thf(f190,definition,
( spl20_11
<=> ! [X4: g] :
( sK10
!= ( sK0 @ sK15 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_11])],[avatar_definition]) ).
thf(f191,plain,
( ! [X4: g] :
( sK10
!= ( sK0 @ sK15 @ X4 ) )
| ~ spl20_11 ),
inference(avatar_component_clause,[],[f190]) ).
thf(f193,definition,
( spl20_12
<=> ( ( sK0 @ ( sK0 @ sK19 @ sK17 ) @ sK14 )
= ( sK0 @ sK19 @ ( sK0 @ sK17 @ sK14 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_12])],[avatar_definition]) ).
thf(f195,plain,
( ( ( sK0 @ ( sK0 @ sK19 @ sK17 ) @ sK14 )
!= ( sK0 @ sK19 @ ( sK0 @ sK17 @ sK14 ) ) )
| spl20_12 ),
inference(avatar_component_clause,[],[f193]) ).
thf(f197,definition,
( spl20_13
<=> ( ( sK0 @ ( sK0 @ sK18 @ sK16 ) @ sK12 )
= ( sK0 @ sK18 @ ( sK0 @ sK16 @ sK12 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_13])],[avatar_definition]) ).
thf(f199,plain,
( ( ( sK0 @ ( sK0 @ sK18 @ sK16 ) @ sK12 )
!= ( sK0 @ sK18 @ ( sK0 @ sK16 @ sK12 ) ) )
| spl20_13 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f201,definition,
( spl20_14
<=> ! [X2: g,X1: g] :
( ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
!= X1 )
| ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_14])],[avatar_definition]) ).
thf(f202,plain,
( ! [X2: g,X1: g] :
( ( ( sK13 @ X1 )
!= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( ( sK0 @ ( sK11 @ X1 ) @ X2 )
!= X1 ) )
| ~ spl20_14 ),
inference(avatar_component_clause,[],[f201]) ).
thf(f204,definition,
( spl20_15
<=> ! [X3: g] :
( sK10
!= ( sK0 @ X3 @ sK15 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_15])],[avatar_definition]) ).
thf(f205,plain,
( ! [X3: g] :
( sK10
!= ( sK0 @ X3 @ sK15 ) )
| ~ spl20_15 ),
inference(avatar_component_clause,[],[f204]) ).
thf(f206,plain,
( spl20_11
| ~ spl20_12
| ~ spl20_13
| spl20_14
| spl20_15 ),
inference(avatar_split_clause,[],[f149,f204,f201,f197,f193,f190]) ).
thf(f214,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X0 @ X1 )
= ( sK0 @ X0 @ ( sK0 @ sK1 @ X1 ) ) )
| ~ spl20_1
| ~ spl20_2 ),
inference(constrained_superposition,[],[f152,f156]) ).
thf(f215,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ sK1 @ X1 )
= ( sK0 @ X0 @ ( sK0 @ ( sK7 @ X0 ) @ X1 ) ) )
| ~ spl20_1
| ~ spl20_8 ),
inference(constrained_superposition,[],[f152,f180]) ).
thf(f221,plain,
( ! [X0: g,X1: g] :
( sK10
!= ( sK0 @ X0 @ ( sK0 @ X1 @ sK15 ) ) )
| ~ spl20_1
| ~ spl20_15 ),
inference(constrained_superposition,[],[f205,f152]) ).
thf(f237,plain,
( ! [X0: g] :
( ( sK0 @ X0 @ sK1 )
= ( sK0 @ sK1 @ ( sK7 @ ( sK7 @ X0 ) ) ) )
| ~ spl20_1
| ~ spl20_8 ),
inference(constrained_superposition,[],[f215,f180]) ).
thf(f249,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ ( sK7 @ ( sK7 @ X0 ) ) )
= X0 )
| ~ spl20_1
| ~ spl20_2
| ~ spl20_8 ),
inference(forward_demodulation,[],[f237,f156]) ).
thf(f260,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X1 @ X0 )
= ( sK0 @ X1 @ ( sK7 @ ( sK7 @ X0 ) ) ) )
| ~ spl20_1
| ~ spl20_2
| ~ spl20_8 ),
inference(constrained_superposition,[],[f214,f249]) ).
thf(f261,plain,
( ! [X0: g] :
( sK1
= ( sK0 @ ( sK7 @ X0 ) @ X0 ) )
| ~ spl20_1
| ~ spl20_2
| ~ spl20_8 ),
inference(constrained_superposition,[],[f260,f180]) ).
thf(f263,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ X0 )
= X0 )
| ~ spl20_1
| ~ spl20_2
| ~ spl20_8 ),
inference(constrained_superposition,[],[f260,f249]) ).
thf(f369,plain,
( ! [X0: g] :
( sK10
!= ( sK0 @ X0 @ sK1 ) )
| ~ spl20_1
| ~ spl20_2
| ~ spl20_8
| ~ spl20_15 ),
inference(constrained_superposition,[],[f221,f261]) ).
thf(f373,plain,
( ! [X0: g] : ( sK10 != X0 )
| ~ spl20_1
| ~ spl20_2
| ~ spl20_8
| ~ spl20_15 ),
inference(forward_demodulation,[],[f369,f156]) ).
thf(f380,plain,
( $false
| ~ spl20_1
| ~ spl20_2
| ~ spl20_8
| ~ spl20_15 ),
inference(equality_resolution,[],[f373]) ).
thf(f381,plain,
( ~ spl20_1
| ~ spl20_2
| ~ spl20_8
| ~ spl20_15 ),
inference(avatar_contradiction_clause,[],[f380]) ).
thf(f387,plain,
( ! [X0: g] :
( sK10
!= ( sK0 @ sK1 @ X0 ) )
| ~ spl20_1
| ~ spl20_8
| ~ spl20_11 ),
inference(constrained_superposition,[],[f191,f215]) ).
thf(f389,plain,
( ! [X0: g] : ( sK10 != X0 )
| ~ spl20_1
| ~ spl20_2
| ~ spl20_8
| ~ spl20_11 ),
inference(forward_demodulation,[],[f387,f263]) ).
thf(f390,plain,
( $false
| ~ spl20_1
| ~ spl20_2
| ~ spl20_8
| ~ spl20_11 ),
inference(equality_resolution,[],[f389]) ).
thf(f391,plain,
( ~ spl20_1
| ~ spl20_2
| ~ spl20_8
| ~ spl20_11 ),
inference(avatar_contradiction_clause,[],[f390]) ).
thf(f1025,plain,
( ! [X0: g] :
( ( ( sK13 @ sK1 )
!= ( sK13 @ sK1 ) )
| ( sK1
!= ( sK0 @ ( sK11 @ sK1 ) @ X0 ) ) )
| ~ spl20_2
| ~ spl20_14 ),
inference(constrained_superposition,[],[f202,f156]) ).
thf(f1030,plain,
( ! [X0: g] :
( sK1
!= ( sK0 @ ( sK11 @ sK1 ) @ X0 ) )
| ~ spl20_2
| ~ spl20_14 ),
inference(trivial_inequality_removal,[],[f1025]) ).
thf(f1037,plain,
( ( sK1 != sK1 )
| ~ spl20_2
| ~ spl20_8
| ~ spl20_14 ),
inference(constrained_superposition,[],[f1030,f180]) ).
thf(f1048,plain,
( $false
| ~ spl20_2
| ~ spl20_8
| ~ spl20_14 ),
inference(trivial_inequality_removal,[],[f1037]) ).
thf(f1049,plain,
( ~ spl20_2
| ~ spl20_8
| ~ spl20_14 ),
inference(avatar_contradiction_clause,[],[f1048]) ).
thf(f1051,plain,
( $false
| ~ spl20_1
| spl20_13 ),
inference(forward_subsumption_resolution,[],[f199,f152]) ).
thf(f1052,plain,
( ~ spl20_1
| spl20_13 ),
inference(avatar_contradiction_clause,[],[f1051]) ).
thf(f1053,plain,
( $false
| ~ spl20_1
| spl20_12 ),
inference(forward_subsumption_resolution,[],[f195,f152]) ).
thf(f1054,plain,
( ~ spl20_1
| spl20_12 ),
inference(avatar_contradiction_clause,[],[f1053]) ).
thf(f1059,plain,
( ! [X2: g,X0: g,X1: g] :
( ( sK0 @ X0 @ X2 )
= ( sK0 @ ( sK9 @ X1 @ X0 ) @ ( sK0 @ X1 @ X2 ) ) )
| ~ spl20_1
| ~ spl20_10 ),
inference(constrained_superposition,[],[f152,f187]) ).
thf(f1060,plain,
( ! [X0: g] : ( sK10 != X0 )
| ~ spl20_10
| ~ spl20_15 ),
inference(constrained_superposition,[],[f205,f187]) ).
thf(f1061,plain,
( $false
| ~ spl20_10
| ~ spl20_15 ),
inference(equality_resolution,[],[f1060]) ).
thf(f1062,plain,
( ~ spl20_10
| ~ spl20_15 ),
inference(avatar_contradiction_clause,[],[f1061]) ).
thf(f1066,plain,
( ! [X2: g,X0: g,X1: g] :
( ( sK0 @ X0 @ X2 )
= ( sK0 @ ( sK6 @ X1 @ X0 ) @ ( sK0 @ X1 @ X2 ) ) )
| ~ spl20_1
| ~ spl20_7 ),
inference(constrained_superposition,[],[f152,f176]) ).
thf(f1102,plain,
( ! [X2: g,X0: g,X1: g] :
( ( sK0 @ X1 @ ( sK8 @ X2 @ X0 ) )
= ( sK0 @ ( sK9 @ X2 @ X1 ) @ X0 ) )
| ~ spl20_1
| ~ spl20_9
| ~ spl20_10 ),
inference(constrained_superposition,[],[f1059,f183]) ).
thf(f1262,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X0 @ ( sK8 @ X1 @ X1 ) )
= X0 )
| ~ spl20_1
| ~ spl20_9
| ~ spl20_10 ),
inference(constrained_superposition,[],[f1102,f187]) ).
thf(f1320,plain,
( ! [X0: g,X1: g] :
( ( ( sK13 @ ( sK8 @ X0 @ X0 ) )
!= ( sK13 @ ( sK8 @ X0 @ X0 ) ) )
| ( ( sK8 @ X0 @ X0 )
!= ( sK0 @ ( sK11 @ ( sK8 @ X0 @ X0 ) ) @ X1 ) ) )
| ~ spl20_1
| ~ spl20_9
| ~ spl20_10
| ~ spl20_14 ),
inference(constrained_superposition,[],[f202,f1262]) ).
thf(f1328,plain,
( ! [X0: g,X1: g] :
( ( sK8 @ X0 @ X0 )
!= ( sK0 @ ( sK11 @ ( sK8 @ X0 @ X0 ) ) @ X1 ) )
| ~ spl20_1
| ~ spl20_9
| ~ spl20_10
| ~ spl20_14 ),
inference(trivial_inequality_removal,[],[f1320]) ).
thf(f1436,plain,
( ! [X0: g,X1: g] :
( ( sK8 @ X1 @ X1 )
!= X0 )
| ~ spl20_1
| ~ spl20_9
| ~ spl20_10
| ~ spl20_14 ),
inference(constrained_superposition,[],[f1328,f183]) ).
thf(f1447,plain,
( $false
| ~ spl20_1
| ~ spl20_9
| ~ spl20_10
| ~ spl20_14 ),
inference(equality_resolution,[],[f1436]) ).
thf(f1448,plain,
( ~ spl20_1
| ~ spl20_9
| ~ spl20_10
| ~ spl20_14 ),
inference(avatar_contradiction_clause,[],[f1447]) ).
thf(f1449,plain,
( ! [X0: g] : ( sK10 != X0 )
| ~ spl20_9
| ~ spl20_11 ),
inference(constrained_superposition,[],[f191,f183]) ).
thf(f1450,plain,
( ! [X0: g] : ( sK10 != X0 )
| ~ spl20_6
| ~ spl20_11 ),
inference(constrained_superposition,[],[f191,f172]) ).
thf(f1460,plain,
( $false
| ~ spl20_9
| ~ spl20_11 ),
inference(equality_resolution,[],[f1449]) ).
thf(f1461,plain,
( ~ spl20_9
| ~ spl20_11 ),
inference(avatar_contradiction_clause,[],[f1460]) ).
thf(f1462,plain,
( $false
| ~ spl20_6
| ~ spl20_11 ),
inference(equality_resolution,[],[f1450]) ).
thf(f1463,plain,
( ~ spl20_6
| ~ spl20_11 ),
inference(avatar_contradiction_clause,[],[f1462]) ).
thf(f1465,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X0 @ ( sK7 @ X1 ) )
= ( sK0 @ ( sK6 @ X1 @ X0 ) @ sK1 ) )
| ~ spl20_1
| ~ spl20_7
| ~ spl20_8 ),
inference(constrained_superposition,[],[f1066,f180]) ).
thf(f1549,plain,
( ! [X0: g] :
( ( sK0 @ X0 @ ( sK7 @ sK1 ) )
= X0 )
| ~ spl20_1
| ~ spl20_7
| ~ spl20_8 ),
inference(constrained_superposition,[],[f1465,f176]) ).
thf(f1566,plain,
( ! [X0: g] :
( ( ( sK13 @ ( sK7 @ sK1 ) )
!= ( sK13 @ ( sK7 @ sK1 ) ) )
| ( ( sK7 @ sK1 )
!= ( sK0 @ ( sK11 @ ( sK7 @ sK1 ) ) @ X0 ) ) )
| ~ spl20_1
| ~ spl20_7
| ~ spl20_8
| ~ spl20_14 ),
inference(constrained_superposition,[],[f202,f1549]) ).
thf(f1571,plain,
( ! [X0: g] :
( ( sK7 @ sK1 )
!= ( sK0 @ ( sK11 @ ( sK7 @ sK1 ) ) @ X0 ) )
| ~ spl20_1
| ~ spl20_7
| ~ spl20_8
| ~ spl20_14 ),
inference(trivial_inequality_removal,[],[f1566]) ).
thf(f1611,plain,
( ! [X0: g] :
( ( sK7 @ sK1 )
!= X0 )
| ~ spl20_1
| ~ spl20_6
| ~ spl20_7
| ~ spl20_8
| ~ spl20_14 ),
inference(constrained_superposition,[],[f1571,f172]) ).
thf(f1619,plain,
( $false
| ~ spl20_1
| ~ spl20_6
| ~ spl20_7
| ~ spl20_8
| ~ spl20_14 ),
inference(equality_resolution,[],[f1611]) ).
thf(f1620,plain,
( ~ spl20_1
| ~ spl20_6
| ~ spl20_7
| ~ spl20_8
| ~ spl20_14 ),
inference(avatar_contradiction_clause,[],[f1619]) ).
thf(f1621,plain,
( ! [X0: g] : ( sK10 != X0 )
| ~ spl20_7
| ~ spl20_15 ),
inference(constrained_superposition,[],[f205,f176]) ).
thf(f1624,plain,
( $false
| ~ spl20_7
| ~ spl20_15 ),
inference(equality_resolution,[],[f1621]) ).
thf(f1625,plain,
( ~ spl20_7
| ~ spl20_15 ),
inference(avatar_contradiction_clause,[],[f1624]) ).
cnf(s1,plain,
( spl20_1
| spl20_1 ),
inference(sat_conversion,[],[f153]) ).
cnf(s2,plain,
spl20_1,
inference(rat,[],[s1]) ).
cnf(s7,plain,
( spl20_2
| spl20_6 ),
inference(sat_conversion,[],[f173]) ).
cnf(s8,plain,
( spl20_2
| spl20_7 ),
inference(sat_conversion,[],[f177]) ).
cnf(s9,plain,
( spl20_8
| spl20_9 ),
inference(sat_conversion,[],[f184]) ).
cnf(s10,plain,
( spl20_8
| spl20_10 ),
inference(sat_conversion,[],[f188]) ).
cnf(s11,plain,
( spl20_11
| ~ spl20_12
| ~ spl20_13
| spl20_14
| spl20_15 ),
inference(sat_conversion,[],[f206]) ).
cnf(s12,plain,
( ~ spl20_1
| ~ spl20_2
| ~ spl20_8
| ~ spl20_15 ),
inference(sat_conversion,[],[f381]) ).
cnf(s13,plain,
( ~ spl20_1
| ~ spl20_2
| ~ spl20_8
| ~ spl20_11 ),
inference(sat_conversion,[],[f391]) ).
cnf(s15,plain,
( ~ spl20_2
| ~ spl20_8
| ~ spl20_14 ),
inference(sat_conversion,[],[f1049]) ).
cnf(s16,plain,
( ~ spl20_1
| spl20_13 ),
inference(sat_conversion,[],[f1052]) ).
cnf(s17,plain,
( ~ spl20_1
| spl20_12 ),
inference(sat_conversion,[],[f1054]) ).
cnf(s18,plain,
( ~ spl20_10
| ~ spl20_15 ),
inference(sat_conversion,[],[f1062]) ).
cnf(s19,plain,
( ~ spl20_1
| ~ spl20_9
| ~ spl20_10
| ~ spl20_14 ),
inference(sat_conversion,[],[f1448]) ).
cnf(s20,plain,
( ~ spl20_9
| ~ spl20_11 ),
inference(sat_conversion,[],[f1461]) ).
cnf(s21,plain,
( ~ spl20_6
| ~ spl20_11 ),
inference(sat_conversion,[],[f1463]) ).
cnf(s22,plain,
( ~ spl20_1
| ~ spl20_6
| ~ spl20_7
| ~ spl20_8
| ~ spl20_14 ),
inference(sat_conversion,[],[f1620]) ).
cnf(s23,plain,
( ~ spl20_7
| ~ spl20_15 ),
inference(sat_conversion,[],[f1625]) ).
cnf(s24,plain,
spl20_12,
inference(rat,[],[s17,s2]) ).
cnf(s25,plain,
spl20_13,
inference(rat,[],[s16,s2]) ).
cnf(s26,plain,
( ~ spl20_14
| ~ spl20_7
| ~ spl20_6 ),
inference(rat,[],[s19,s9,s10,s22,s2]) ).
cnf(s27,plain,
spl20_2,
inference(rat,[],[s26,s11,s21,s23,s7,s8,s25,s24]) ).
cnf(s28,plain,
spl20_8,
inference(rat,[],[s11,s19,s20,s18,s9,s10,s25,s24,s2]) ).
cnf(s29,plain,
~ spl20_14,
inference(rat,[],[s15,s27,s28]) ).
cnf(s30,plain,
~ spl20_11,
inference(rat,[],[s13,s27,s2,s28]) ).
cnf(s31,plain,
~ spl20_15,
inference(rat,[],[s12,s27,s2,s28]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s11,s31,s24,s25,s30,s29]) ).
thf(f1626,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG274^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n017.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:31:52 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.92/0.37 % (648721)Will run a generic schedule for satisfiability detection.
% 0.92/0.37 % (648727)% WARNING: option uhcvi not known.
% 0.92/0.37 % (648726)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3179210760_2999 on theBenchmark for (2999ds/0Mi)
% 0.92/0.37 % (648728)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2723776249:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.92/0.37 % (648727)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1468013124:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.92/0.37 % (648730)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1969358508:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.92/0.37 % (648729)dis+10_1_sil=32000:sp=arity:random_seed=376444223:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.92/0.37 % (648727)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.92/0.37 % (648730)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.92/0.37 % (648732)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=676698784:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.92/0.37 % Exception at run slice level% (648727)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.92/0.37
% 0.92/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.92/0.37 % (648731)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3795100034:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.92/0.37 % (648740)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3459119448:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.92/0.37 % Exception at run slice level
% 0.92/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.92/0.37 % (648742)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3464924406:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.92/0.37 % (648732)Instruction limit reached!
% 0.92/0.37 % (648732)------------------------------
% 0.92/0.37 % (648732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.37 % (648732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.37 % (648732)CaDiCaL version: 2.1.3
% 0.92/0.37 % (648732)Termination reason: Instruction limit
% 0.92/0.37 % (648732)Termination phase: Saturation
% 0.92/0.37 % (648732)Time elapsed: 0.047 s
% 0.92/0.37 % (648732)Peak memory usage: 13 MB
% 0.92/0.37 % (648732)Instructions burned: 159 (million)
% 0.92/0.37 % (648729)Instruction limit reached!
% 0.92/0.37 % (648729)------------------------------
% 0.92/0.37 % (648729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.37 % (648729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.37 % (648729)CaDiCaL version: 2.1.3
% 0.92/0.37 % (648729)Termination reason: Instruction limit
% 0.92/0.37 % (648729)Termination phase: Saturation
% 0.92/0.37 % (648729)Time elapsed: 0.052 s
% 0.92/0.37 % (648729)Peak memory usage: 12 MB
% 0.92/0.37 % (648729)Instructions burned: 104 (million)
% 0.92/0.37 % (648730)Instruction limit reached!
% 0.92/0.37 % (648730)------------------------------
% 0.92/0.37 % (648730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.37 % (648730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.37 % (648730)CaDiCaL version: 2.1.3
% 0.92/0.37 % (648730)Termination reason: Instruction limit
% 0.92/0.37 % (648730)Termination phase: Saturation
% 0.92/0.37 % (648730)Time elapsed: 0.060 s
% 0.92/0.37 % (648730)Peak memory usage: 12 MB
% 0.92/0.37 % (648730)Instructions burned: 117 (million)
% 0.92/0.37 % (648744)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=3565501616:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.92/0.37 % (648744)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.92/0.37 % (648744)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.92/0.37 % (648745)ott-21_1_sil=16000:fs=off:random_seed=2817199082:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.92/0.37 % (648731)Instruction limit reached!
% 0.92/0.37 % (648731)------------------------------
% 0.92/0.37 % (648731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.37 % (648731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.37 % (648731)CaDiCaL version: 2.1.3
% 0.92/0.37 % (648731)Termination reason: Instruction limit
% 0.92/0.37 % (648731)Termination phase: Saturation
% 0.92/0.37 % (648731)Time elapsed: 0.076 s
% 0.92/0.37 % (648731)Peak memory usage: 13 MB
% 0.92/0.37 % (648731)Instructions burned: 132 (million)
% 0.92/0.37 % (648746)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2854057508:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.92/0.37 % (648744) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-648721-648744"...
% 0.92/0.37 % (648750)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4267291258:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.92/0.37 % (648744)...printing done.
% 0.92/0.37 % (648744)Refutation found. Thanks to Tanya!
% 0.92/0.37 % SZS status Theorem for theBenchmark
% 0.92/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.92/0.38 % (648744)------------------------------
% 0.92/0.38 % (648744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.38 % (648744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.38 % (648744)CaDiCaL version: 2.1.3
% 0.92/0.38 % (648744)Termination reason: Refutation
% 0.92/0.38 % (648744)Time elapsed: 0.044 s
% 0.92/0.38 % (648744)Peak memory usage: 14 MB
% 0.92/0.38 % (648744)Instructions burned: 162 (million)
% 0.92/0.38 % (648721)Success in time 0.15 s
% 0.92/0.38 % Vampire exiting
%------------------------------------------------------------------------------