%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG273^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 07:45:19 AM UTC 2026
% Result : Theorem 0.35s 0.42s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 25
% Syntax : Number of formulae : 227 ( 48 unt; 0 typ; 17 def)
% Number of atoms : 1243 ( 450 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 2273 ( 188 ~; 294 |; 51 &;1515 @)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 146 ( 146 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 48 usr; 32 con; 0-4 aty)
% ( 168 !!; 39 ??; 0 @@+; 0 @@-)
% Number of variables : 488 ( 0 sgn 118 !; 4 ?; 488 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(func_def_1,type,
cGROUP3: ( g > g > g ) > g > $o ).
thf(func_def_2,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(func_def_3,type,
cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_4,type,
cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_5,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_6,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_8,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db1:
!>[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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_15,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vAND: $o > $o > $o ).
thf(func_def_17,type,
sK0: g > g > g ).
thf(func_def_18,type,
sK1: g ).
thf(func_def_21,type,
sF2: $o ).
thf(func_def_22,type,
sF3: $o ).
thf(func_def_23,type,
sK4: g > g ).
thf(func_def_24,type,
sK5: g ).
thf(func_def_25,type,
sK6: g ).
thf(func_def_26,type,
sK7: g ).
thf(func_def_27,type,
sK8: g ).
thf(func_def_28,type,
sK9: g ).
thf(func_def_29,type,
sK10: g ).
thf(func_def_30,type,
sK11: g ).
thf(func_def_31,type,
sK12: g ).
thf(func_def_32,type,
sK13: g ).
thf(func_def_33,type,
sK14: g ).
thf(func_def_34,type,
sK15: g > g ).
thf(f1,axiom,
( ( ^ [X0: g > g > g] :
! [X1: g,X3: g,X2: g] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) ) )
= cGRP_ASSOC ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_ASSOC_def) ).
thf(f2,axiom,
( cGRP_LEFT_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X3 @ X2 )
= X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_LEFT_INVERSE_def) ).
thf(f3,axiom,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X1 @ X2 )
= X2 ) )
= cGRP_LEFT_UNIT ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_LEFT_UNIT_def) ).
thf(f4,axiom,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X2 @ X3 )
= X1 ) )
= cGRP_RIGHT_INVERSE ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_RIGHT_INVERSE_def) ).
thf(f5,axiom,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) )
= cGRP_RIGHT_UNIT ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_RIGHT_UNIT_def) ).
thf(f6,axiom,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_LEFT_UNIT @ X0 @ X1 )
& ( cGRP_LEFT_INVERSE @ X0 @ X1 ) ) )
= cGROUP2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP2_def) ).
thf(f7,axiom,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) )
= cGROUP3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP3_def) ).
thf(f8,conjecture,
! [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
<=> ( cGROUP3 @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQUIV_02_03) ).
thf(f9,negated_conjecture,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
<=> ( cGROUP3 @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f10,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f11,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f2]) ).
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,[],[f4]) ).
thf(f13,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f14,plain,
( ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ ( X0 @ X1 @ X3 ) @ X2 )
= ( X0 @ X1 @ ( X0 @ X3 @ X2 ) ) ) )
= cGRP_ASSOC ),
inference(rectify,[],[f1]) ).
thf(f15,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y1 ) @ Y2 )
= ( Y0 @ Y3 @ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) )
= cGROUP3 ),
inference(rectify,[],[f7]) ).
thf(f17,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
<=> ( cGROUP3 @ X0 @ X1 ) ),
inference(rectify,[],[f9]) ).
thf(f19,plain,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
= ( cGROUP3 @ X0 @ X1 ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_LEFT_UNIT @ X0 @ X1 )
& ( cGRP_LEFT_INVERSE @ X0 @ X1 ) ) )
= cGROUP2 ),
inference(rectify,[],[f6]) ).
thf(f21,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_LEFT_INVERSE @ Y0 @ Y1 )
& ( cGRP_LEFT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
? [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
!= ( cGROUP3 @ X0 @ X1 ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f23,plain,
( ( cGROUP3 @ sK0 @ sK1 )
!= ( cGROUP2 @ sK0 @ sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f22]) ).
thf(f24,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_LEFT_INVERSE @ Y0 @ Y1 )
& ( cGRP_LEFT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f25,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f26,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f27,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f28,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(f29,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y1 ) @ Y2 )
= ( Y0 @ Y3 @ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f30,plain,
( ( cGROUP3 @ sK0 @ sK1 )
!= ( cGROUP2 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f31,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f34,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y3 @ Y4 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 )
= ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f24,f26,f31,f29]) ).
thf(f35,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 )
= ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
@ 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,[],[f27,f29,f25,f28]) ).
thf(f36,plain,
( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 )
= ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
@ 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 )
!= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y3 @ Y4 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 )
= ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
@ Y0 ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f30,f35,f34]) ).
thf(f37,definition,
( sF2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 )
= ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
@ 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 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f38,plain,
( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 )
= ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
@ 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 )
= sF2 ),
inference(reorient_equations,[],[f37]) ).
thf(f39,definition,
( sF3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y3 @ Y4 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 )
= ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
@ Y0 ) )
@ sK0
@ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f40,plain,
sF3 != sF2,
inference(definition_folding,[],[f36,f39,f38]) ).
thf(f41,plain,
( ( sF3 = $true )
| ( $false
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y3 @ Y4 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 )
= ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
@ Y0 ) )
@ sK0
@ sK1 ) ) ),
inference(iff_proxy_clausification,[],[f39]) ).
thf(f42,plain,
( ( $false = sF3 )
| ( $true
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y3 @ Y4 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 )
= ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
@ Y0 ) )
@ sK0
@ sK1 ) ) ),
inference(iff_proxy_clausification,[],[f39]) ).
thf(f43,plain,
( ( $false = sF3 )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
( ( $false = sF3 )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f45,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) )
= $true )
| ( $false = sF3 ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f46,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
= $true )
| ( $false = sF3 ) ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( ( $false = sF3 )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f48,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) )
@ X1 )
= $true )
| ( $false = sF3 ) ),
inference(pi_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X1: g] :
( ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 ) ) )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X1: g] :
( ( $false = sF3 )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 )
@ ( sK4 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X1: g] :
( ( ( ( sK0 @ ( sK4 @ X1 ) @ X1 )
= sK1 )
= $true )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X1: g] :
( ( ( sK0 @ ( sK4 @ X1 ) @ X1 )
= sK1 )
| ( $false = sF3 ) ),
inference(equality_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X1: g] :
( ( $false = sF3 )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f54,plain,
! [X1: g] :
( ( $false = sF3 )
| ( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
! [X1: g] :
( ( $false = sF3 )
| ( ( sK0 @ sK1 @ X1 )
= X1 ) ),
inference(equality_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X1: g] :
( ( $false = sF3 )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f57,plain,
! [X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ X1 ) @ Y0 )
= ( sK0 @ Y1 @ ( sK0 @ X1 @ Y0 ) ) ) ) ) )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ X1 ) @ Y0 )
= ( sK0 @ Y1 @ ( sK0 @ X1 @ Y0 ) ) ) )
@ X2 ) )
| ( $false = sF3 ) ),
inference(pi_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: g,X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X1 ) @ X2 )
= ( sK0 @ Y0 @ ( sK0 @ X1 @ X2 ) ) ) )
= $true )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X2: g,X3: g,X1: g] :
( ( $false = sF3 )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X1 ) @ X2 )
= ( sK0 @ Y0 @ ( sK0 @ X1 @ X2 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ( sK0 @ ( sK0 @ X3 @ X1 ) @ X2 )
= ( sK0 @ X3 @ ( sK0 @ X1 @ X2 ) ) ) )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK0 @ ( sK0 @ X3 @ X1 ) @ X2 )
= ( sK0 @ X3 @ ( sK0 @ X1 @ X2 ) ) )
| ( $false = sF3 ) ),
inference(equality_proxy_clausification,[],[f61]) ).
thf(f63,plain,
( ( sF3 = $true )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f64,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) ) )
| ( sF3 = $true ) ),
inference(and_proxy_clausification,[],[f63]) ).
thf(f65,plain,
( ( sF3 = $true )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f64]) ).
thf(f66,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) )
@ sK5 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) )
| ( sF3 = $true ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 )
@ sK6 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) )
| ( sF3 = $true )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( ( sF3 = $true )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) )
@ sK7 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 )
@ sK6 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f67]) ).
thf(f69,plain,
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK7 )
= sK1 ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ sK5 ) @ Y0 )
= ( sK0 @ Y1 @ ( sK0 @ sK5 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( sK0 @ sK1 @ sK6 )
= sK6 ) )
| ( sF3 = $true ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X1: g] :
( ( $false
= ( ( sK0 @ sK1 @ sK6 )
= sK6 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ sK5 ) @ Y0 )
= ( sK0 @ Y1 @ ( sK0 @ sK5 @ Y0 ) ) ) ) ) )
| ( ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK7 )
= sK1 )
@ X1 )
= $false )
| ( sF3 = $true ) ),
inference(pi_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ sK5 ) @ Y0 )
= ( sK0 @ Y1 @ ( sK0 @ sK5 @ Y0 ) ) ) ) ) )
| ( ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK7 )
= sK1 )
@ X1 )
= $false )
| ( sF3 = $true )
| ( ( sK0 @ sK1 @ sK6 )
!= sK6 ) ),
inference(equality_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK7 )
= sK1 )
@ X1 )
= $false )
| ( ( sK0 @ sK1 @ sK6 )
!= sK6 )
| ( sF3 = $true )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ sK5 ) @ Y0 )
= ( sK0 @ Y1 @ ( sK0 @ sK5 @ Y0 ) ) ) )
@ sK8 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK5 ) @ sK8 )
= ( sK0 @ Y0 @ ( sK0 @ sK5 @ sK8 ) ) ) )
= $false )
| ( sF3 = $true )
| ( $false
= ( ( sK0 @ X1 @ sK7 )
= sK1 ) )
| ( ( sK0 @ sK1 @ sK6 )
!= sK6 ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X1: g] :
( ( ( sK0 @ sK1 @ sK6 )
!= sK6 )
| ( sF3 = $true )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK5 ) @ sK8 )
= ( sK0 @ Y0 @ ( sK0 @ sK5 @ sK8 ) ) )
@ sK9 ) )
| ( $false
= ( ( sK0 @ X1 @ sK7 )
= sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK5 ) @ sK8 )
= ( sK0 @ Y0 @ ( sK0 @ sK5 @ sK8 ) ) )
@ sK9 ) )
| ( ( sK0 @ X1 @ sK7 )
!= sK1 )
| ( ( sK0 @ sK1 @ sK6 )
!= sK6 )
| ( sF3 = $true ) ),
inference(equality_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X1: g] :
( ( $false
= ( ( sK0 @ ( sK0 @ sK9 @ sK5 ) @ sK8 )
= ( sK0 @ sK9 @ ( sK0 @ sK5 @ sK8 ) ) ) )
| ( ( sK0 @ X1 @ sK7 )
!= sK1 )
| ( ( sK0 @ sK1 @ sK6 )
!= sK6 )
| ( sF3 = $true ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
! [X1: g] :
( ( sF3 = $true )
| ( ( sK0 @ sK1 @ sK6 )
!= sK6 )
| ( ( sK0 @ X1 @ sK7 )
!= sK1 )
| ( ( sK0 @ ( sK0 @ sK9 @ sK5 ) @ sK8 )
!= ( sK0 @ sK9 @ ( sK0 @ sK5 @ sK8 ) ) ) ),
inference(equality_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( ( sF3 = $true )
| ( sF2 = $true ) ),
inference(xor_proxy_clausification,[],[f40]) ).
thf(f79,plain,
( ( $false = sF2 )
| ( $false = sF3 ) ),
inference(xor_proxy_clausification,[],[f40]) ).
thf(f80,plain,
( ( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 )
= ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
@ 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 )
= $true )
| ( $false = sF2 ) ),
inference(iff_proxy_clausification,[],[f38]) ).
thf(f81,plain,
( ( sF2 = $true )
| ( $false
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 )
= ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
@ 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(iff_proxy_clausification,[],[f38]) ).
thf(f82,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
| ( sF2 = $true ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
= $false )
| ( sF2 = $true ) ),
inference(and_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( ( sF2 = $true )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f83]) ).
thf(f85,plain,
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) )
@ sK10 ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
= $false )
| ( sF2 = $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f84]) ).
thf(f86,plain,
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) )
@ sK10 ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $false )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK11 ) )
| ( sF2 = $true ) ),
inference(sigma_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( ( sF2 = $true )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK11 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) )
@ sK10 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ sK12 ) ) ),
inference(sigma_proxy_clausification,[],[f86]) ).
thf(f88,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ sK10 ) @ Y0 )
= ( sK0 @ Y1 @ ( sK0 @ sK10 @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( ( sK0 @ sK12 @ sK1 )
= sK12 ) )
| ( sF2 = $true )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK11 @ Y0 )
= sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ sK10 ) @ Y0 )
= ( sK0 @ Y1 @ ( sK0 @ sK10 @ Y0 ) ) ) )
@ sK13 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK11 @ Y0 )
= sK1 ) ) )
| ( sF2 = $true )
| ( $false
= ( ( sK0 @ sK12 @ sK1 )
= sK12 ) ) ),
inference(sigma_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X1: g] :
( ( sF2 = $true )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ sK10 ) @ Y0 )
= ( sK0 @ Y1 @ ( sK0 @ sK10 @ Y0 ) ) ) )
@ sK13 ) )
| ( $false
= ( ( sK0 @ sK12 @ sK1 )
= sK12 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK11 @ Y0 )
= sK1 )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X1: g] :
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ sK10 ) @ Y0 )
= ( sK0 @ Y1 @ ( sK0 @ sK10 @ Y0 ) ) ) )
@ sK13 ) )
| ( ( sK0 @ sK12 @ sK1 )
!= sK12 )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK11 @ Y0 )
= sK1 )
@ X1 ) )
| ( sF2 = $true ) ),
inference(equality_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X1: g] :
( ( ( sK0 @ sK12 @ sK1 )
!= sK12 )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK10 ) @ sK13 )
= ( sK0 @ Y0 @ ( sK0 @ sK10 @ sK13 ) ) ) )
= $false )
| ( sF2 = $true )
| ( $false
= ( ( sK0 @ sK11 @ X1 )
= sK1 ) ) ),
inference(beta-eta_normalization,[],[f91]) ).
thf(f93,plain,
! [X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK10 ) @ sK13 )
= ( sK0 @ Y0 @ ( sK0 @ sK10 @ sK13 ) ) )
@ sK14 ) )
| ( sF2 = $true )
| ( $false
= ( ( sK0 @ sK11 @ X1 )
= sK1 ) )
| ( ( sK0 @ sK12 @ sK1 )
!= sK12 ) ),
inference(sigma_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X1: g] :
( ( sK1
!= ( sK0 @ sK11 @ X1 ) )
| ( sF2 = $true )
| ( ( sK0 @ sK12 @ sK1 )
!= sK12 )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK10 ) @ sK13 )
= ( sK0 @ Y0 @ ( sK0 @ sK10 @ sK13 ) ) )
@ sK14 ) ) ),
inference(equality_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X1: g] :
( ( sF2 = $true )
| ( $false
= ( ( sK0 @ ( sK0 @ sK14 @ sK10 ) @ sK13 )
= ( sK0 @ sK14 @ ( sK0 @ sK10 @ sK13 ) ) ) )
| ( sK1
!= ( sK0 @ sK11 @ X1 ) )
| ( ( sK0 @ sK12 @ sK1 )
!= sK12 ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
! [X1: g] :
( ( sK1
!= ( sK0 @ sK11 @ X1 ) )
| ( ( sK0 @ sK14 @ ( sK0 @ sK10 @ sK13 ) )
!= ( sK0 @ ( sK0 @ sK14 @ sK10 ) @ sK13 ) )
| ( sF2 = $true )
| ( ( sK0 @ sK12 @ sK1 )
!= sK12 ) ),
inference(equality_proxy_clausification,[],[f95]) ).
thf(f97,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f80]) ).
thf(f98,plain,
( ( $false = sF2 )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f97]) ).
thf(f99,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
= $true )
| ( $false = sF2 ) ),
inference(and_proxy_clausification,[],[f97]) ).
thf(f100,plain,
( ( $false = sF2 )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f99]) ).
thf(f101,plain,
( ( $false = sF2 )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f99]) ).
thf(f102,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y0 ) @ Y1 )
= ( sK0 @ Y2 @ ( sK0 @ Y0 @ Y1 ) ) ) ) )
@ X1 )
= $true )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X1: g] :
( ( $false = sF2 )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ X1 ) @ Y0 )
= ( sK0 @ Y1 @ ( sK0 @ X1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ X1 ) @ Y0 )
= ( sK0 @ Y1 @ ( sK0 @ X1 @ Y0 ) ) ) )
@ X2 ) )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: g,X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X1 ) @ X2 )
= ( sK0 @ Y0 @ ( sK0 @ X1 @ X2 ) ) ) )
= $true )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f106,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X1 ) @ X2 )
= ( sK0 @ Y0 @ ( sK0 @ X1 @ X2 ) ) )
@ X3 ) )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ( sK0 @ ( sK0 @ X3 @ X1 ) @ X2 )
= ( sK0 @ X3 @ ( sK0 @ X1 @ X2 ) ) ) )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f108,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK0 @ ( sK0 @ X3 @ X1 ) @ X2 )
= ( sK0 @ X3 @ ( sK0 @ X1 @ X2 ) ) )
| ( $false = sF2 ) ),
inference(equality_proxy_clausification,[],[f107]) ).
thf(f109,plain,
! [X1: g] :
( ( $false = sF2 )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f100]) ).
thf(f110,plain,
! [X1: g] :
( ( $true
= ( ( sK0 @ X1 @ sK1 )
= X1 ) )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f111,plain,
! [X1: g] :
( ( ( sK0 @ X1 @ sK1 )
= X1 )
| ( $false = sF2 ) ),
inference(equality_proxy_clausification,[],[f110]) ).
thf(f112,plain,
! [X1: g] :
( ( $false = sF2 )
| ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f98]) ).
thf(f113,plain,
! [X1: g] :
( ( $false = sF2 )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X1 @ Y0 )
= sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
! [X1: g] :
( ( $false = sF2 )
| ( ( ^ [Y0: g] :
( ( sK0 @ X1 @ Y0 )
= sK1 )
@ ( sK15 @ X1 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X1: g] :
( ( $false = sF2 )
| ( ( ( sK0 @ X1 @ ( sK15 @ X1 ) )
= sK1 )
= $true ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
! [X1: g] :
( ( $false = sF2 )
| ( sK1
= ( sK0 @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f115]) ).
thf(f118,definition,
( spl16_1
<=> ! [X1: g] :
( ( sK0 @ ( sK4 @ X1 ) @ X1 )
= sK1 ) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
thf(f119,plain,
( ! [X1: g] :
( ( sK0 @ ( sK4 @ X1 ) @ X1 )
= sK1 )
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f118]) ).
thf(f121,definition,
( spl16_2
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
thf(f123,plain,
( ( $false = sF3 )
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f121]) ).
thf(f124,plain,
( spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f52,f121,f118]) ).
thf(f126,definition,
( spl16_3
<=> ! [X1: g] :
( ( sK0 @ sK1 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
thf(f127,plain,
( ! [X1: g] :
( ( sK0 @ sK1 @ X1 )
= X1 )
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f126]) ).
thf(f128,plain,
( spl16_2
| spl16_3 ),
inference(avatar_split_clause,[],[f55,f126,f121]) ).
thf(f130,definition,
( spl16_4
<=> ! [X2: g,X1: g,X3: g] :
( ( sK0 @ ( sK0 @ X3 @ X1 ) @ X2 )
= ( sK0 @ X3 @ ( sK0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
thf(f131,plain,
( ! [X2: g,X3: g,X1: g] :
( ( sK0 @ ( sK0 @ X3 @ X1 ) @ X2 )
= ( sK0 @ X3 @ ( sK0 @ X1 @ X2 ) ) )
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f130]) ).
thf(f132,plain,
( spl16_2
| spl16_4 ),
inference(avatar_split_clause,[],[f62,f130,f121]) ).
thf(f134,definition,
( spl16_5
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition]) ).
thf(f136,plain,
( ( sF3 = $true )
| ~ spl16_5 ),
inference(avatar_component_clause,[],[f134]) ).
thf(f138,definition,
( spl16_6
<=> ( ( sK0 @ ( sK0 @ sK9 @ sK5 ) @ sK8 )
= ( sK0 @ sK9 @ ( sK0 @ sK5 @ sK8 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
thf(f140,plain,
( ( ( sK0 @ ( sK0 @ sK9 @ sK5 ) @ sK8 )
!= ( sK0 @ sK9 @ ( sK0 @ sK5 @ sK8 ) ) )
| spl16_6 ),
inference(avatar_component_clause,[],[f138]) ).
thf(f142,definition,
( spl16_7
<=> ! [X1: g] :
( ( sK0 @ X1 @ sK7 )
!= sK1 ) ),
introduced(definition,[new_symbols(definition,[spl16_7])],[avatar_definition]) ).
thf(f143,plain,
( ! [X1: g] :
( ( sK0 @ X1 @ sK7 )
!= sK1 )
| ~ spl16_7 ),
inference(avatar_component_clause,[],[f142]) ).
thf(f145,definition,
( spl16_8
<=> ( ( sK0 @ sK1 @ sK6 )
= sK6 ) ),
introduced(definition,[new_symbols(definition,[spl16_8])],[avatar_definition]) ).
thf(f147,plain,
( ( ( sK0 @ sK1 @ sK6 )
!= sK6 )
| spl16_8 ),
inference(avatar_component_clause,[],[f145]) ).
thf(f148,plain,
( spl16_5
| ~ spl16_6
| spl16_7
| ~ spl16_8 ),
inference(avatar_split_clause,[],[f77,f145,f142,f138,f134]) ).
thf(f150,definition,
( spl16_9
<=> ( $false = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl16_9])],[avatar_definition]) ).
thf(f152,plain,
( ( $false = sF2 )
| ~ spl16_9 ),
inference(avatar_component_clause,[],[f150]) ).
thf(f153,plain,
( spl16_9
| spl16_2 ),
inference(avatar_split_clause,[],[f79,f121,f150]) ).
thf(f155,definition,
( spl16_10
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition]) ).
thf(f157,plain,
( ( sF2 = $true )
| ~ spl16_10 ),
inference(avatar_component_clause,[],[f155]) ).
thf(f158,plain,
( spl16_10
| spl16_5 ),
inference(avatar_split_clause,[],[f78,f134,f155]) ).
thf(f160,definition,
( spl16_11
<=> ( ( sK0 @ sK12 @ sK1 )
= sK12 ) ),
introduced(definition,[new_symbols(definition,[spl16_11])],[avatar_definition]) ).
thf(f162,plain,
( ( ( sK0 @ sK12 @ sK1 )
!= sK12 )
| spl16_11 ),
inference(avatar_component_clause,[],[f160]) ).
thf(f164,definition,
( spl16_12
<=> ( ( sK0 @ sK14 @ ( sK0 @ sK10 @ sK13 ) )
= ( sK0 @ ( sK0 @ sK14 @ sK10 ) @ sK13 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_12])],[avatar_definition]) ).
thf(f166,plain,
( ( ( sK0 @ sK14 @ ( sK0 @ sK10 @ sK13 ) )
!= ( sK0 @ ( sK0 @ sK14 @ sK10 ) @ sK13 ) )
| spl16_12 ),
inference(avatar_component_clause,[],[f164]) ).
thf(f168,definition,
( spl16_13
<=> ! [X1: g] :
( sK1
!= ( sK0 @ sK11 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_13])],[avatar_definition]) ).
thf(f169,plain,
( ! [X1: g] :
( sK1
!= ( sK0 @ sK11 @ X1 ) )
| ~ spl16_13 ),
inference(avatar_component_clause,[],[f168]) ).
thf(f170,plain,
( ~ spl16_11
| ~ spl16_12
| spl16_10
| spl16_13 ),
inference(avatar_split_clause,[],[f96,f168,f155,f164,f160]) ).
thf(f171,plain,
( spl16_9
| spl16_4 ),
inference(avatar_split_clause,[],[f108,f130,f150]) ).
thf(f173,definition,
( spl16_14
<=> ! [X1: g] :
( ( sK0 @ X1 @ sK1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl16_14])],[avatar_definition]) ).
thf(f174,plain,
( ! [X1: g] :
( ( sK0 @ X1 @ sK1 )
= X1 )
| ~ spl16_14 ),
inference(avatar_component_clause,[],[f173]) ).
thf(f175,plain,
( spl16_9
| spl16_14 ),
inference(avatar_split_clause,[],[f111,f173,f150]) ).
thf(f177,definition,
( spl16_15
<=> ! [X1: g] :
( sK1
= ( sK0 @ X1 @ ( sK15 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_15])],[avatar_definition]) ).
thf(f178,plain,
( ! [X1: g] :
( sK1
= ( sK0 @ X1 @ ( sK15 @ X1 ) ) )
| ~ spl16_15 ),
inference(avatar_component_clause,[],[f177]) ).
thf(f179,plain,
( spl16_15
| spl16_9 ),
inference(avatar_split_clause,[],[f116,f150,f177]) ).
thf(f180,plain,
( ( $false = $true )
| ~ spl16_2
| ~ spl16_5 ),
inference(forward_demodulation,[],[f123,f136]) ).
thf(f181,plain,
( $false
| ~ spl16_2
| ~ spl16_5 ),
inference(trivial_inequality_removal,[],[f180]) ).
thf(f182,plain,
( ~ spl16_2
| ~ spl16_5 ),
inference(avatar_contradiction_clause,[],[f181]) ).
thf(f183,plain,
( ( $false = $true )
| ~ spl16_9
| ~ spl16_10 ),
inference(forward_demodulation,[],[f157,f152]) ).
thf(f184,plain,
( $false
| ~ spl16_9
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f183]) ).
thf(f185,plain,
( ~ spl16_9
| ~ spl16_10 ),
inference(avatar_contradiction_clause,[],[f184]) ).
thf(f200,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X0 @ ( sK0 @ sK1 @ X1 ) )
= ( sK0 @ X0 @ X1 ) )
| ~ spl16_4
| ~ spl16_14 ),
inference(constrained_superposition,[],[f131,f174]) ).
thf(f201,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ sK1 @ X1 )
= ( sK0 @ X0 @ ( sK0 @ ( sK15 @ X0 ) @ X1 ) ) )
| ~ spl16_4
| ~ spl16_15 ),
inference(constrained_superposition,[],[f131,f178]) ).
thf(f205,plain,
( ( ( sK0 @ sK14 @ ( sK0 @ sK10 @ sK13 ) )
!= ( sK0 @ sK14 @ ( sK0 @ sK10 @ sK13 ) ) )
| ~ spl16_4
| spl16_12 ),
inference(constrained_superposition,[],[f166,f131]) ).
thf(f208,plain,
( $false
| ~ spl16_4
| spl16_12 ),
inference(trivial_inequality_removal,[],[f205]) ).
thf(f209,plain,
( ~ spl16_4
| spl16_12 ),
inference(avatar_contradiction_clause,[],[f208]) ).
thf(f227,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ ( sK15 @ ( sK15 @ X0 ) ) )
= ( sK0 @ X0 @ sK1 ) )
| ~ spl16_4
| ~ spl16_15 ),
inference(constrained_superposition,[],[f201,f178]) ).
thf(f240,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ ( sK15 @ ( sK15 @ X0 ) ) )
= X0 )
| ~ spl16_4
| ~ spl16_14
| ~ spl16_15 ),
inference(forward_demodulation,[],[f227,f174]) ).
thf(f243,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X1 @ X0 )
= ( sK0 @ X1 @ ( sK15 @ ( sK15 @ X0 ) ) ) )
| ~ spl16_4
| ~ spl16_14
| ~ spl16_15 ),
inference(constrained_superposition,[],[f200,f240]) ).
thf(f245,plain,
( ! [X0: g] :
( ( sK0 @ ( sK15 @ X0 ) @ X0 )
= sK1 )
| ~ spl16_4
| ~ spl16_14
| ~ spl16_15 ),
inference(constrained_superposition,[],[f243,f178]) ).
thf(f252,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ X0 )
= X0 )
| ~ spl16_4
| ~ spl16_14
| ~ spl16_15 ),
inference(constrained_superposition,[],[f240,f243]) ).
thf(f257,plain,
( spl16_3
| ~ spl16_4
| ~ spl16_14
| ~ spl16_15 ),
inference(avatar_split_clause,[],[f252,f177,f173,f130,f126]) ).
thf(f265,plain,
( ( sK6 != sK6 )
| ~ spl16_3
| spl16_8 ),
inference(constrained_superposition,[],[f147,f127]) ).
thf(f272,plain,
( $false
| ~ spl16_3
| spl16_8 ),
inference(trivial_inequality_removal,[],[f265]) ).
thf(f273,plain,
( ~ spl16_3
| spl16_8 ),
inference(avatar_contradiction_clause,[],[f272]) ).
thf(f278,plain,
( $false
| ~ spl16_4
| spl16_6 ),
inference(forward_subsumption_resolution,[],[f140,f131]) ).
thf(f279,plain,
( ~ spl16_4
| spl16_6 ),
inference(avatar_contradiction_clause,[],[f278]) ).
thf(f308,plain,
( ( sK1 != sK1 )
| ~ spl16_4
| ~ spl16_7
| ~ spl16_14
| ~ spl16_15 ),
inference(constrained_superposition,[],[f143,f245]) ).
thf(f309,plain,
( $false
| ~ spl16_4
| ~ spl16_7
| ~ spl16_14
| ~ spl16_15 ),
inference(trivial_inequality_removal,[],[f308]) ).
thf(f310,plain,
( ~ spl16_4
| ~ spl16_7
| ~ spl16_14
| ~ spl16_15 ),
inference(avatar_contradiction_clause,[],[f309]) ).
thf(f317,plain,
( $false
| spl16_11
| ~ spl16_14 ),
inference(forward_subsumption_resolution,[],[f162,f174]) ).
thf(f318,plain,
( spl16_11
| ~ spl16_14 ),
inference(avatar_contradiction_clause,[],[f317]) ).
thf(f334,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ sK1 @ X1 )
= ( sK0 @ ( sK4 @ X0 ) @ ( sK0 @ X0 @ X1 ) ) )
| ~ spl16_1
| ~ spl16_4 ),
inference(constrained_superposition,[],[f131,f119]) ).
thf(f337,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ ( sK4 @ X0 ) @ ( sK0 @ X0 @ X1 ) )
= X1 )
| ~ spl16_1
| ~ spl16_3
| ~ spl16_4 ),
inference(forward_demodulation,[],[f334,f127]) ).
thf(f344,plain,
( ! [X0: g] :
( ( sK0 @ ( sK4 @ ( sK4 @ X0 ) ) @ sK1 )
= X0 )
| ~ spl16_1
| ~ spl16_3
| ~ spl16_4 ),
inference(constrained_superposition,[],[f337,f119]) ).
thf(f357,plain,
( ! [X0: g] :
( ( sK4 @ ( sK4 @ X0 ) )
= X0 )
| ~ spl16_1
| ~ spl16_3
| ~ spl16_4
| ~ spl16_14 ),
inference(forward_demodulation,[],[f344,f174]) ).
thf(f360,plain,
( ! [X0: g] :
( sK1
= ( sK0 @ X0 @ ( sK4 @ X0 ) ) )
| ~ spl16_1
| ~ spl16_3
| ~ spl16_4
| ~ spl16_14 ),
inference(constrained_superposition,[],[f119,f357]) ).
thf(f370,plain,
( ( sK1 != sK1 )
| ~ spl16_1
| ~ spl16_3
| ~ spl16_4
| ~ spl16_13
| ~ spl16_14 ),
inference(constrained_superposition,[],[f169,f360]) ).
thf(f371,plain,
( $false
| ~ spl16_1
| ~ spl16_3
| ~ spl16_4
| ~ spl16_13
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f370]) ).
thf(f372,plain,
( ~ spl16_1
| ~ spl16_3
| ~ spl16_4
| ~ spl16_13
| ~ spl16_14 ),
inference(avatar_contradiction_clause,[],[f371]) ).
thf(f382,plain,
( ! [X0: g] :
( sK1
= ( sK0 @ ( sK4 @ ( sK4 @ ( sK4 @ X0 ) ) ) @ X0 ) )
| ~ spl16_1
| ~ spl16_3
| ~ spl16_4 ),
inference(constrained_superposition,[],[f337,f344]) ).
thf(f400,plain,
( ! [X0: g] :
( ( sK0 @ ( sK4 @ ( sK4 @ ( sK4 @ ( sK4 @ X0 ) ) ) ) @ sK1 )
= X0 )
| ~ spl16_1
| ~ spl16_3
| ~ spl16_4 ),
inference(constrained_superposition,[],[f337,f382]) ).
thf(f402,plain,
( ! [X0: g] :
( ( sK4 @ ( sK4 @ X0 ) )
= X0 )
| ~ spl16_1
| ~ spl16_3
| ~ spl16_4 ),
inference(forward_demodulation,[],[f400,f344]) ).
thf(f406,plain,
( ! [X0: g] :
( ( sK0 @ X0 @ sK1 )
= X0 )
| ~ spl16_1
| ~ spl16_3
| ~ spl16_4 ),
inference(constrained_superposition,[],[f344,f402]) ).
thf(f413,plain,
( spl16_14
| ~ spl16_1
| ~ spl16_3
| ~ spl16_4 ),
inference(avatar_split_clause,[],[f406,f130,f126,f118,f173]) ).
cnf(s1,plain,
( spl16_1
| spl16_2 ),
inference(sat_conversion,[],[f124]) ).
cnf(s2,plain,
( spl16_2
| spl16_3 ),
inference(sat_conversion,[],[f128]) ).
cnf(s3,plain,
( spl16_2
| spl16_4 ),
inference(sat_conversion,[],[f132]) ).
cnf(s4,plain,
( spl16_5
| ~ spl16_6
| spl16_7
| ~ spl16_8 ),
inference(sat_conversion,[],[f148]) ).
cnf(s5,plain,
( spl16_2
| spl16_9 ),
inference(sat_conversion,[],[f153]) ).
cnf(s6,plain,
( spl16_5
| spl16_10 ),
inference(sat_conversion,[],[f158]) ).
cnf(s7,plain,
( spl16_10
| ~ spl16_11
| ~ spl16_12
| spl16_13 ),
inference(sat_conversion,[],[f170]) ).
cnf(s8,plain,
( spl16_4
| spl16_9 ),
inference(sat_conversion,[],[f171]) ).
cnf(s9,plain,
( spl16_9
| spl16_14 ),
inference(sat_conversion,[],[f175]) ).
cnf(s10,plain,
( spl16_9
| spl16_15 ),
inference(sat_conversion,[],[f179]) ).
cnf(s11,plain,
( ~ spl16_2
| ~ spl16_5 ),
inference(sat_conversion,[],[f182]) ).
cnf(s12,plain,
( ~ spl16_9
| ~ spl16_10 ),
inference(sat_conversion,[],[f185]) ).
cnf(s13,plain,
( ~ spl16_4
| spl16_12 ),
inference(sat_conversion,[],[f209]) ).
cnf(s14,plain,
( spl16_3
| ~ spl16_4
| ~ spl16_14
| ~ spl16_15 ),
inference(sat_conversion,[],[f257]) ).
cnf(s16,plain,
( ~ spl16_3
| spl16_8 ),
inference(sat_conversion,[],[f273]) ).
cnf(s17,plain,
( ~ spl16_4
| spl16_6 ),
inference(sat_conversion,[],[f279]) ).
cnf(s18,plain,
( ~ spl16_4
| ~ spl16_7
| ~ spl16_14
| ~ spl16_15 ),
inference(sat_conversion,[],[f310]) ).
cnf(s19,plain,
( spl16_11
| ~ spl16_14 ),
inference(sat_conversion,[],[f318]) ).
cnf(s21,plain,
( ~ spl16_1
| ~ spl16_3
| ~ spl16_4
| ~ spl16_13
| ~ spl16_14 ),
inference(sat_conversion,[],[f372]) ).
cnf(s22,plain,
( ~ spl16_1
| ~ spl16_3
| ~ spl16_4
| spl16_14 ),
inference(sat_conversion,[],[f413]) ).
cnf(s23,plain,
spl16_5,
inference(rat,[],[s16,s4,s18,s14,s17,s8,s9,s10,s12,s6]) ).
cnf(s24,plain,
~ spl16_2,
inference(rat,[],[s11,s23]) ).
cnf(s25,plain,
spl16_9,
inference(rat,[],[s5,s24]) ).
cnf(s26,plain,
spl16_4,
inference(rat,[],[s3,s24]) ).
cnf(s27,plain,
spl16_3,
inference(rat,[],[s2,s24]) ).
cnf(s28,plain,
spl16_1,
inference(rat,[],[s1,s24]) ).
cnf(s29,plain,
~ spl16_10,
inference(rat,[],[s12,s25]) ).
cnf(s31,plain,
spl16_12,
inference(rat,[],[s13,s26]) ).
cnf(s32,plain,
spl16_14,
inference(rat,[],[s22,s26,s28,s27]) ).
cnf(s33,plain,
~ spl16_13,
inference(rat,[],[s21,s32,s26,s28,s27]) ).
cnf(s35,plain,
~ spl16_11,
inference(rat,[],[s7,s33,s29,s31]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s19,s32,s35]) ).
thf(f414,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG273^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.26 % Computer : n016.cluster.edu
% 0.12/0.26 % Model : x86_64 x86_64
% 0.12/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.26 % Memory : 8046.5625MB
% 0.12/0.26 % OS : Linux 6.8.0-71-generic
% 0.12/0.26 % CPULimit : 300
% 0.12/0.26 % WCLimit : 300
% 0.12/0.26 % DateTime : Tue Sep 29 17:40:50 UTC 2026
% 0.12/0.27 % CPUTime :
% 0.12/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.32 Running higher-order theorem proving
% 0.27/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/0.42 % (670752)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.35/0.42 % (670762)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1306749502:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.35/0.42 % (670760)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3769774298:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.35/0.42 % (670760)Refutation not found, incomplete strategy
% 0.35/0.42 % (670760)------------------------------
% 0.35/0.42 % (670760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.42 % (670760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.42 % (670760)CaDiCaL version: 2.1.3
% 0.35/0.42 % (670760)Termination reason: Refutation not found, incomplete strategy
% 0.35/0.42 % (670760)Time elapsed: 0.003 s
% 0.35/0.42 % (670760)Peak memory usage: 12 MB
% 0.35/0.42 % (670760)Instructions burned: 3 (million)
% 0.35/0.42 % (670760)------------------------------
% 0.35/0.42 % (670760)------------------------------
% 0.35/0.42 % (670764)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.35/0.42 % (670764)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.35/0.42 % (670762)Instruction limit reached!
% 0.35/0.42 % (670762)------------------------------
% 0.35/0.42 % (670762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.42 % (670762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.42 % (670762)CaDiCaL version: 2.1.3
% 0.35/0.42 % (670762)Termination reason: Instruction limit
% 0.35/0.42 % (670762)Termination phase: Saturation
% 0.35/0.42 % (670762)Time elapsed: 0.012 s
% 0.35/0.42 % (670762)Peak memory usage: 11 MB
% 0.35/0.42 % (670762)Instructions burned: 24 (million)
% 0.35/0.42 % (670759)lrs+10_16_si=on:nwc=1.5:random_seed=925755902:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.35/0.42 % (670761)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4235776767:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.35/0.42 % (670763)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3456657847:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.35/0.42 % (670758)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4052149132:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.35/0.42 % (670764)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2686416549:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.35/0.42 % (670768)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=908775982:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.35/0.42 % (670759)Instruction limit reached!
% 0.35/0.42 % (670759)------------------------------
% 0.35/0.42 % (670759)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.42 % (670759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.42 % (670759)CaDiCaL version: 2.1.3
% 0.35/0.42 % (670759)Termination reason: Instruction limit
% 0.35/0.42 % (670759)Termination phase: Saturation
% 0.35/0.42 % (670759)Time elapsed: 0.017 s
% 0.35/0.42 % (670759)Peak memory usage: 12 MB
% 0.35/0.42 % (670759)Instructions burned: 18 (million)
% 0.35/0.42 % (670768)Instruction limit reached!
% 0.35/0.42 % (670768)------------------------------
% 0.35/0.42 % (670768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.42 % (670768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.42 % (670768)CaDiCaL version: 2.1.3
% 0.35/0.42 % (670768)Termination reason: Instruction limit
% 0.35/0.42 % (670768)Termination phase: Saturation
% 0.35/0.42 % (670768)Time elapsed: 0.003 s
% 0.35/0.42 % (670768)Peak memory usage: 12 MB
% 0.35/0.42 % (670768)Instructions burned: 5 (million)
% 0.35/0.42 % (670774)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2388731890:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.35/0.42 % (670774)Instruction limit reached!
% 0.35/0.42 % (670774)------------------------------
% 0.35/0.42 % (670774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.42 % (670774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.42 % (670774)CaDiCaL version: 2.1.3
% 0.35/0.42 % (670774)Termination reason: Instruction limit
% 0.35/0.42 % (670774)Termination phase: Saturation
% 0.35/0.42 % (670774)Time elapsed: 0.003 s
% 0.35/0.42 % (670774)Peak memory usage: 11 MB
% 0.35/0.42 % (670774)Instructions burned: 7 (million)
% 0.35/0.42 % (670764) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-670752-670764"...
% 0.35/0.42 % (670764)...printing done.
% 0.35/0.42 % (670764)Refutation found. Thanks to Tanya!
% 0.35/0.42 % SZS status Theorem for theBenchmark
% 0.35/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.42 % (670764)------------------------------
% 0.35/0.42 % (670764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.42 % (670764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.42 % (670764)CaDiCaL version: 2.1.3
% 0.35/0.42 % (670764)Termination reason: Refutation
% 0.35/0.42 % (670764)Time elapsed: 0.034 s
% 0.35/0.42 % (670764)Peak memory usage: 13 MB
% 0.35/0.42 % (670764)Instructions burned: 35 (million)
% 0.35/0.42 % (670752)Success in time 0.074 s
% 0.35/0.42 % Vampire exiting
%------------------------------------------------------------------------------