%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG271^5 : 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 : n019.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 07:45:18 AM UTC 2026
% Result : Theorem 0.25s 0.36s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 26
% Syntax : Number of formulae : 236 ( 50 unt; 0 typ; 18 def)
% Number of atoms : 1369 ( 555 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 2586 ( 192 ~; 309 |; 106 &;1743 @)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 154 ( 154 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 49 usr; 33 con; 0-4 aty)
% ( 175 !!; 42 ??; 0 @@+; 0 @@-)
% Number of variables : 510 ( 0 sgn 118 !; 4 ?; 510 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cGROUP1: ( 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_INVERSE: ( g > 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_6,type,
cGRP_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_8,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
vAND: $o > $o > $o ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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 ).
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 > 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] :
! [X3: g,X1: 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,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( ( X0 @ X2 @ X3 )
= X1 )
& ( ( X0 @ X3 @ X2 )
= X1 ) ) )
= cGRP_INVERSE ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_INVERSE_def) ).
thf(f3,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(f4,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(f5,axiom,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( ( X0 @ X2 @ X1 )
= X2 )
& ( ( X0 @ X1 @ X2 )
= X2 ) ) )
= cGRP_UNIT ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_UNIT_def) ).
thf(f6,axiom,
( cGROUP1
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_UNIT @ X0 @ X1 )
& ( cGRP_INVERSE @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP1_def) ).
thf(f7,axiom,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X1 ) ) )
= cGROUP3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP3_def) ).
thf(f8,conjecture,
! [X0: g > g > g,X1: g] :
( ( cGROUP3 @ X0 @ X1 )
<=> ( cGROUP1 @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQUIV_01_03) ).
thf(f9,negated_conjecture,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP3 @ X0 @ X1 )
<=> ( cGROUP1 @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f10,plain,
( cGRP_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f11,plain,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X1 ) ) )
= cGROUP3 ),
inference(rectify,[],[f7]) ).
thf(f12,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 )
& ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP3 @ X0 @ X1 )
<=> ( cGROUP1 @ X0 @ X1 ) ),
inference(rectify,[],[f9]) ).
thf(f14,plain,
~ ! [X1: g,X0: g > g > g] :
( ( cGROUP1 @ X0 @ X1 )
= ( cGROUP3 @ X0 @ X1 ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( cGROUP1
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_UNIT @ X0 @ X1 )
& ( cGRP_INVERSE @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_INVERSE @ Y0 @ Y1 )
& ( cGRP_UNIT @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ X2 @ ( X0 @ X3 @ X1 ) )
= ( X0 @ ( X0 @ X2 @ X3 ) @ X1 ) ) )
= cGRP_ASSOC ),
inference(rectify,[],[f1]) ).
thf(f18,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ ( Y0 @ Y1 @ Y3 ) )
= ( Y0 @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,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(f20,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f21,plain,
( cGRP_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( ( Y0 @ Y3 @ Y2 )
= Y1 )
& ( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f22,plain,
? [X0: g > g > g,X1: g] :
( ( cGROUP1 @ X0 @ X1 )
!= ( cGROUP3 @ X0 @ X1 ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f23,plain,
( ( cGROUP3 @ sK0 @ sK1 )
!= ( cGROUP1 @ sK0 @ sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f22]) ).
thf(f24,plain,
( ( cGROUP3 @ sK0 @ sK1 )
!= ( cGROUP1 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f25,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ ( Y0 @ Y1 @ Y3 ) )
= ( Y0 @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f26,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 )
& ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
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,[],[f20]) ).
thf(f28,plain,
( cGRP_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( ( Y0 @ Y3 @ Y2 )
= Y1 )
& ( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f29,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f30,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_INVERSE @ Y0 @ Y1 )
& ( cGRP_UNIT @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f31,plain,
( cGRP_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f34,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ ( Y2 @ Y3 @ Y5 ) )
= ( Y2 @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y5 @ Y4 )
= Y3 )
& ( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f30,f25,f28,f31]) ).
thf(f35,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ ( Y2 @ Y3 @ Y5 ) )
= ( Y2 @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f26,f29,f27,f25]) ).
thf(f36,plain,
( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ ( Y2 @ Y3 @ Y5 ) )
= ( Y2 @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
@ Y0 ) )
@ sK0
@ sK1 )
!= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ ( Y2 @ Y3 @ Y5 ) )
= ( Y2 @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y5 @ Y4 )
= Y3 )
& ( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f24,f35,f34]) ).
thf(f37,definition,
( sF2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ ( Y2 @ Y3 @ Y5 ) )
= ( Y2 @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
@ Y0 ) )
@ sK0
@ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f38,plain,
( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ ( Y2 @ Y3 @ Y5 ) )
= ( Y2 @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
@ Y0 ) )
@ sK0
@ sK1 )
= sF2 ),
inference(reorient_equations,[],[f37]) ).
thf(f39,definition,
( sF3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ ( Y2 @ Y3 @ Y5 ) )
= ( Y2 @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y5 @ Y4 )
= Y3 )
& ( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f40,plain,
( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ ( Y2 @ Y3 @ Y5 ) )
= ( Y2 @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y5 @ Y4 )
= Y3 )
& ( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 )
= sF3 ),
inference(reorient_equations,[],[f39]) ).
thf(f41,plain,
sF3 != sF2,
inference(definition_folding,[],[f36,f40,f38]) ).
thf(f42,plain,
( ( $false = sF2 )
| ( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ ( Y2 @ Y3 @ Y5 ) )
= ( Y2 @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
@ Y0 ) )
@ sK0
@ sK1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f38]) ).
thf(f43,plain,
( ( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ ( Y2 @ Y3 @ Y5 ) )
= ( Y2 @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
@ Y0 ) )
@ sK0
@ sK1 )
= $false )
| ( $true = sF2 ) ),
inference(iff_proxy_clausification,[],[f38]) ).
thf(f44,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
= $false )
| ( $true = sF2 ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
= $false )
| ( $true = sF2 )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f46,plain,
( ( $true = sF2 )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
= $false )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) )
@ sK4 )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( $true = sF2 ) ),
inference(and_proxy_clausification,[],[f46]) ).
thf(f48,plain,
( ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ sK5 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( $true = sF2 )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f47]) ).
thf(f49,plain,
( ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ sK5 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK6 ) )
| ( $true = sF2 )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f48]) ).
thf(f50,plain,
( ( ( ( sK0 @ sK5 @ sK1 )
= sK5 )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ sK4 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ sK4 ) @ Y1 ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK6 @ Y0 )
= sK1 ) ) )
| ( $true = sF2 ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
( ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $true = sF2 )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ sK4 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ sK4 ) @ Y1 ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK6 @ Y0 )
= sK1 ) ) ) ),
inference(equality_proxy_clausification,[],[f50]) ).
thf(f52,plain,
( ( $true = sF2 )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ sK4 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ sK4 ) @ Y1 ) ) )
@ sK7 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK6 @ Y0 )
= sK1 ) ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X1: g] :
( ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ sK4 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ sK4 ) @ Y1 ) ) )
@ sK7 ) )
| ( $true = sF2 )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK6 @ Y0 )
= sK1 )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X1: g] :
( ( $false
= ( ( sK0 @ sK6 @ X1 )
= sK1 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $true = sF2 )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK7 @ ( sK0 @ sK4 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK7 @ sK4 ) @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK7 @ ( sK0 @ sK4 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK7 @ sK4 ) @ Y0 ) ) ) )
| ( sK1
!= ( sK0 @ sK6 @ X1 ) )
| ( $true = sF2 )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X1: g] :
( ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $true = sF2 )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK7 @ ( sK0 @ sK4 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK7 @ sK4 ) @ Y0 ) )
@ sK8 ) )
| ( sK1
!= ( sK0 @ sK6 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X1: g] :
( ( $false
= ( ( sK0 @ sK7 @ ( sK0 @ sK4 @ sK8 ) )
= ( sK0 @ ( sK0 @ sK7 @ sK4 ) @ sK8 ) ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $true = sF2 )
| ( sK1
!= ( sK0 @ sK6 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X1: g] :
( ( sK1
!= ( sK0 @ sK6 @ X1 ) )
| ( $true = sF2 )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( ( sK0 @ sK7 @ ( sK0 @ sK4 @ sK8 ) )
!= ( sK0 @ ( sK0 @ sK7 @ sK4 ) @ sK8 ) ) ),
inference(equality_proxy_clausification,[],[f57]) ).
thf(f59,plain,
( ( $false = sF2 )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f60,plain,
( ( $false = sF2 )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f59]) ).
thf(f61,plain,
( ( $false = sF2 )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f59]) ).
thf(f62,plain,
( ( $false = sF2 )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f61]) ).
thf(f63,plain,
( ( $false = sF2 )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f61]) ).
thf(f64,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ X1 )
= $true )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X1: g] :
( ( $false = sF2 )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X1 @ Y0 )
= sK1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X1: g] :
( ( $false = sF2 )
| ( ( ^ [Y0: g] :
( ( sK0 @ X1 @ Y0 )
= sK1 )
@ ( sK9 @ X1 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X1: g] :
( ( $true
= ( ( sK0 @ X1 @ ( sK9 @ X1 ) )
= sK1 ) )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X1: g] :
( ( sK1
= ( sK0 @ X1 @ ( sK9 @ X1 ) ) )
| ( $false = sF2 ) ),
inference(equality_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ X1 )
= $true )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f62]) ).
thf(f70,plain,
! [X1: g] :
( ( $false = sF2 )
| ( ( ( sK0 @ X1 @ sK1 )
= X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
! [X1: g] :
( ( ( sK0 @ X1 @ sK1 )
= X1 )
| ( $false = sF2 ) ),
inference(equality_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X1: g] :
( ( $false = sF2 )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f60]) ).
thf(f73,plain,
! [X1: g] :
( ( $false = sF2 )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ X1 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ X1 ) @ Y1 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X2: g,X1: g] :
( ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ X1 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ X1 ) @ Y1 ) ) )
@ X2 )
= $true )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X2: g,X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ X2 @ ( sK0 @ X1 @ Y0 ) )
= ( sK0 @ ( sK0 @ X2 @ X1 ) @ Y0 ) ) )
= $true )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f76,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ^ [Y0: g] :
( ( sK0 @ X2 @ ( sK0 @ X1 @ Y0 ) )
= ( sK0 @ ( sK0 @ X2 @ X1 ) @ Y0 ) )
@ X3 )
= $true )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ( sK0 @ X2 @ ( sK0 @ X1 @ X3 ) )
= ( sK0 @ ( sK0 @ X2 @ X1 ) @ X3 ) )
= $true )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
! [X2: g,X3: g,X1: g] :
( ( $false = sF2 )
| ( ( sK0 @ ( sK0 @ X2 @ X1 ) @ X3 )
= ( sK0 @ X2 @ ( sK0 @ X1 @ X3 ) ) ) ),
inference(equality_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( ( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ ( Y2 @ Y3 @ Y5 ) )
= ( Y2 @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y5 @ Y4 )
= Y3 )
& ( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 )
= $true )
| ( $false = sF3 ) ),
inference(iff_proxy_clausification,[],[f40]) ).
thf(f80,plain,
( ( sF3 = $true )
| ( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ ( Y2 @ Y3 @ Y5 ) )
= ( Y2 @ ( Y2 @ Y4 @ Y3 ) @ Y5 ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y5 @ Y4 )
= Y3 )
& ( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 )
= $false ) ),
inference(iff_proxy_clausification,[],[f40]) ).
thf(f81,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y1 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
= $false )
| ( sF3 = $true ) ),
inference(beta-eta_normalization,[],[f80]) ).
thf(f82,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( sF3 = $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y1 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f81]) ).
thf(f83,plain,
( ( ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ sK10 )
= $false )
| ( sF3 = $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y1 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
= $false )
| ( sF3 = $true )
| ( ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ sK10 )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y1 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f83]) ).
thf(f85,plain,
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) )
@ sK11 ) )
| ( sF3 = $true )
| ( ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ sK10 )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y1 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f84]) ).
thf(f86,plain,
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) )
@ sK11 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y1 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
@ sK12 ) )
| ( ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ sK10 )
= $false )
| ( sF3 = $true ) ),
inference(sigma_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( ( sF3 = $true )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ Y0 @ sK12 )
= sK1 )
& ( ( sK0 @ sK12 @ Y0 )
= sK1 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ sK11 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ sK11 ) @ Y1 ) ) ) )
= $false )
| ( ( ( ( sK0 @ sK1 @ sK10 )
= sK10 )
& ( ( sK0 @ sK10 @ sK1 )
= sK10 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f88,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( ( ( sK0 @ Y0 @ sK12 )
= sK1 )
& ( ( sK0 @ sK12 @ Y0 )
= sK1 ) )
@ X1 )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ sK11 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ sK11 ) @ Y1 ) ) ) )
= $false )
| ( sF3 = $true )
| ( ( ( ( sK0 @ sK1 @ sK10 )
= sK10 )
& ( ( sK0 @ sK10 @ sK1 )
= sK10 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ sK11 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ sK11 ) @ Y1 ) ) )
@ sK13 )
= $false )
| ( ( ^ [Y0: g] :
( ( ( sK0 @ Y0 @ sK12 )
= sK1 )
& ( ( sK0 @ sK12 @ Y0 )
= sK1 ) )
@ X1 )
= $false )
| ( sF3 = $true )
| ( ( ( ( sK0 @ sK1 @ sK10 )
= sK10 )
& ( ( sK0 @ sK10 @ sK1 )
= sK10 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X1: g] :
( ( $false
= ( ( sK0 @ sK1 @ sK10 )
= sK10 ) )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ sK11 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ sK11 ) @ Y1 ) ) )
@ sK13 )
= $false )
| ( $false
= ( ( sK0 @ sK10 @ sK1 )
= sK10 ) )
| ( sF3 = $true )
| ( ( ^ [Y0: g] :
( ( ( sK0 @ Y0 @ sK12 )
= sK1 )
& ( ( sK0 @ sK12 @ Y0 )
= sK1 ) )
@ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( ( ( sK0 @ Y0 @ sK12 )
= sK1 )
& ( ( sK0 @ sK12 @ Y0 )
= sK1 ) )
@ X1 )
= $false )
| ( sK10
!= ( sK0 @ sK1 @ sK10 ) )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ sK11 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ sK11 ) @ Y1 ) ) )
@ sK13 )
= $false )
| ( sF3 = $true )
| ( $false
= ( ( sK0 @ sK10 @ sK1 )
= sK10 ) ) ),
inference(equality_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ sK11 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ sK11 ) @ Y1 ) ) )
@ sK13 )
= $false )
| ( sK10
!= ( sK0 @ sK1 @ sK10 ) )
| ( sK10
!= ( sK0 @ sK10 @ sK1 ) )
| ( ( ^ [Y0: g] :
( ( ( sK0 @ Y0 @ sK12 )
= sK1 )
& ( ( sK0 @ sK12 @ Y0 )
= sK1 ) )
@ X1 )
= $false )
| ( sF3 = $true ) ),
inference(equality_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X1: g] :
( ( sK10
!= ( sK0 @ sK10 @ sK1 ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK13 @ ( sK0 @ sK11 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK13 @ sK11 ) @ Y0 ) ) )
= $false )
| ( $false
= ( ( ( sK0 @ X1 @ sK12 )
= sK1 )
& ( ( sK0 @ sK12 @ X1 )
= sK1 ) ) )
| ( sF3 = $true )
| ( sK10
!= ( sK0 @ sK1 @ sK10 ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X1: g] :
( ( sF3 = $true )
| ( sK10
!= ( sK0 @ sK10 @ sK1 ) )
| ( ( ^ [Y0: g] :
( ( sK0 @ sK13 @ ( sK0 @ sK11 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK13 @ sK11 ) @ Y0 ) )
@ sK14 )
= $false )
| ( $false
= ( ( ( sK0 @ X1 @ sK12 )
= sK1 )
& ( ( sK0 @ sK12 @ X1 )
= sK1 ) ) )
| ( sK10
!= ( sK0 @ sK1 @ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X1: g] :
( ( ( ( sK0 @ X1 @ sK12 )
= sK1 )
= $false )
| ( sF3 = $true )
| ( sK10
!= ( sK0 @ sK10 @ sK1 ) )
| ( $false
= ( ( sK0 @ sK12 @ X1 )
= sK1 ) )
| ( sK10
!= ( sK0 @ sK1 @ sK10 ) )
| ( ( ^ [Y0: g] :
( ( sK0 @ sK13 @ ( sK0 @ sK11 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK13 @ sK11 ) @ Y0 ) )
@ sK14 )
= $false ) ),
inference(and_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X1: g] :
( ( sK10
!= ( sK0 @ sK1 @ sK10 ) )
| ( sK10
!= ( sK0 @ sK10 @ sK1 ) )
| ( sF3 = $true )
| ( $false
= ( ( sK0 @ sK12 @ X1 )
= sK1 ) )
| ( sK1
!= ( sK0 @ X1 @ sK12 ) )
| ( ( ^ [Y0: g] :
( ( sK0 @ sK13 @ ( sK0 @ sK11 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK13 @ sK11 ) @ Y0 ) )
@ sK14 )
= $false ) ),
inference(equality_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK12 ) )
| ( sK10
!= ( sK0 @ sK1 @ sK10 ) )
| ( sK10
!= ( sK0 @ sK10 @ sK1 ) )
| ( ( ^ [Y0: g] :
( ( sK0 @ sK13 @ ( sK0 @ sK11 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK13 @ sK11 ) @ Y0 ) )
@ sK14 )
= $false )
| ( sF3 = $true )
| ( sK1
!= ( sK0 @ sK12 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X1: g] :
( ( sK10
!= ( sK0 @ sK10 @ sK1 ) )
| ( sK1
!= ( sK0 @ X1 @ sK12 ) )
| ( sF3 = $true )
| ( sK1
!= ( sK0 @ sK12 @ X1 ) )
| ( $false
= ( ( sK0 @ sK13 @ ( sK0 @ sK11 @ sK14 ) )
= ( sK0 @ ( sK0 @ sK13 @ sK11 ) @ sK14 ) ) )
| ( sK10
!= ( sK0 @ sK1 @ sK10 ) ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
! [X1: g] :
( ( sK10
!= ( sK0 @ sK1 @ sK10 ) )
| ( ( sK0 @ ( sK0 @ sK13 @ sK11 ) @ sK14 )
!= ( sK0 @ sK13 @ ( sK0 @ sK11 @ sK14 ) ) )
| ( sK10
!= ( sK0 @ sK10 @ sK1 ) )
| ( sF3 = $true )
| ( sK1
!= ( sK0 @ X1 @ sK12 ) )
| ( sK1
!= ( sK0 @ sK12 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f98]) ).
thf(f100,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y1 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
= $true )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f101,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
= $true )
| ( $false = sF3 ) ),
inference(and_proxy_clausification,[],[f100]) ).
thf(f102,plain,
( ( $false = sF3 )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y1 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f100]) ).
thf(f103,plain,
( ( $false = sF3 )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y1 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f102]) ).
thf(f104,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
= $true )
| ( $false = sF3 ) ),
inference(and_proxy_clausification,[],[f102]) ).
thf(f105,plain,
! [X1: g] :
( ( $false = sF3 )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y1 @ ( sK0 @ Y0 @ Y2 ) )
= ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ Y2 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ X1 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ X1 ) @ Y1 ) ) ) )
= $true )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
! [X2: g,X1: g] :
( ( $false = sF3 )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ ( sK0 @ X1 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ X1 ) @ Y1 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X2: g,X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ X2 @ ( sK0 @ X1 @ Y0 ) )
= ( sK0 @ ( sK0 @ X2 @ X1 ) @ Y0 ) ) )
= $true )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
! [X2: g,X3: g,X1: g] :
( ( $false = sF3 )
| ( ( ^ [Y0: g] :
( ( sK0 @ X2 @ ( sK0 @ X1 @ Y0 ) )
= ( sK0 @ ( sK0 @ X2 @ X1 ) @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f108]) ).
thf(f110,plain,
! [X2: g,X3: g,X1: g] :
( ( $false = sF3 )
| ( ( ( sK0 @ X2 @ ( sK0 @ X1 @ X3 ) )
= ( sK0 @ ( sK0 @ X2 @ X1 ) @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f111,plain,
! [X2: g,X3: g,X1: g] :
( ( $false = sF3 )
| ( ( sK0 @ ( sK0 @ X2 @ X1 ) @ X3 )
= ( sK0 @ X2 @ ( sK0 @ X1 @ X3 ) ) ) ),
inference(equality_proxy_clausification,[],[f110]) ).
thf(f112,plain,
! [X1: g] :
( ( $false = sF3 )
| ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y1 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f103]) ).
thf(f113,plain,
! [X1: g] :
( ( $false = sF3 )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ Y0 @ X1 )
= sK1 )
& ( ( sK0 @ X1 @ Y0 )
= sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( ( ( sK0 @ Y0 @ X1 )
= sK1 )
& ( ( sK0 @ X1 @ Y0 )
= sK1 ) )
@ ( sK15 @ X1 ) )
= $true )
| ( $false = sF3 ) ),
inference(sigma_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X1: g] :
( ( ( ( ( sK0 @ ( sK15 @ X1 ) @ X1 )
= sK1 )
& ( ( sK0 @ X1 @ ( sK15 @ X1 ) )
= sK1 ) )
= $true )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
! [X1: g] :
( ( $false = sF3 )
| ( ( ( sK0 @ X1 @ ( sK15 @ X1 ) )
= sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f115]) ).
thf(f119,plain,
! [X1: g] :
( ( $false = sF3 )
| ( sK1
= ( sK0 @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f116]) ).
thf(f120,plain,
! [X1: g] :
( ( $false = sF3 )
| ( ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f101]) ).
thf(f121,plain,
! [X1: g] :
( ( ( ( ( sK0 @ sK1 @ X1 )
= X1 )
& ( ( sK0 @ X1 @ sK1 )
= X1 ) )
= $true )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
! [X1: g] :
( ( $false = sF3 )
| ( ( ( sK0 @ X1 @ sK1 )
= X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f121]) ).
thf(f125,plain,
! [X1: g] :
( ( ( sK0 @ X1 @ sK1 )
= X1 )
| ( $false = sF3 ) ),
inference(equality_proxy_clausification,[],[f122]) ).
thf(f126,plain,
( ( sF3 = $true )
| ( $true = sF2 ) ),
inference(xor_proxy_clausification,[],[f41]) ).
thf(f127,plain,
( ( $false = sF3 )
| ( $false = sF2 ) ),
inference(xor_proxy_clausification,[],[f41]) ).
thf(f129,definition,
( spl16_1
<=> ! [X1: g] :
( sK1
!= ( sK0 @ sK6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
thf(f130,plain,
( ! [X1: g] :
( sK1
!= ( sK0 @ sK6 @ X1 ) )
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f129]) ).
thf(f132,definition,
( spl16_2
<=> ( sK5
= ( sK0 @ sK5 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
thf(f134,plain,
( ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| spl16_2 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f136,definition,
( spl16_3
<=> ( ( sK0 @ sK7 @ ( sK0 @ sK4 @ sK8 ) )
= ( sK0 @ ( sK0 @ sK7 @ sK4 ) @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
thf(f138,plain,
( ( ( sK0 @ sK7 @ ( sK0 @ sK4 @ sK8 ) )
!= ( sK0 @ ( sK0 @ sK7 @ sK4 ) @ sK8 ) )
| spl16_3 ),
inference(avatar_component_clause,[],[f136]) ).
thf(f140,definition,
( spl16_4
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
thf(f142,plain,
( ( $true = sF2 )
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f140]) ).
thf(f143,plain,
( spl16_1
| ~ spl16_2
| ~ spl16_3
| spl16_4 ),
inference(avatar_split_clause,[],[f58,f140,f136,f132,f129]) ).
thf(f145,definition,
( spl16_5
<=> ( $false = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition]) ).
thf(f147,plain,
( ( $false = sF2 )
| ~ spl16_5 ),
inference(avatar_component_clause,[],[f145]) ).
thf(f149,definition,
( spl16_6
<=> ! [X1: g] :
( sK1
= ( sK0 @ X1 @ ( sK9 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
thf(f150,plain,
( ! [X1: g] :
( sK1
= ( sK0 @ X1 @ ( sK9 @ X1 ) ) )
| ~ spl16_6 ),
inference(avatar_component_clause,[],[f149]) ).
thf(f151,plain,
( spl16_5
| spl16_6 ),
inference(avatar_split_clause,[],[f68,f149,f145]) ).
thf(f153,definition,
( spl16_7
<=> ! [X1: g] :
( ( sK0 @ X1 @ sK1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl16_7])],[avatar_definition]) ).
thf(f154,plain,
( ! [X1: g] :
( ( sK0 @ X1 @ sK1 )
= X1 )
| ~ spl16_7 ),
inference(avatar_component_clause,[],[f153]) ).
thf(f155,plain,
( spl16_7
| spl16_5 ),
inference(avatar_split_clause,[],[f71,f145,f153]) ).
thf(f157,definition,
( spl16_8
<=> ! [X2: g,X1: g,X3: g] :
( ( sK0 @ ( sK0 @ X2 @ X1 ) @ X3 )
= ( sK0 @ X2 @ ( sK0 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_8])],[avatar_definition]) ).
thf(f158,plain,
( ! [X2: g,X3: g,X1: g] :
( ( sK0 @ ( sK0 @ X2 @ X1 ) @ X3 )
= ( sK0 @ X2 @ ( sK0 @ X1 @ X3 ) ) )
| ~ spl16_8 ),
inference(avatar_component_clause,[],[f157]) ).
thf(f159,plain,
( spl16_5
| spl16_8 ),
inference(avatar_split_clause,[],[f78,f157,f145]) ).
thf(f161,definition,
( spl16_9
<=> ( sK10
= ( sK0 @ sK1 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_9])],[avatar_definition]) ).
thf(f163,plain,
( ( sK10
!= ( sK0 @ sK1 @ sK10 ) )
| spl16_9 ),
inference(avatar_component_clause,[],[f161]) ).
thf(f165,definition,
( spl16_10
<=> ! [X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK12 ) )
| ( sK1
!= ( sK0 @ sK12 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition]) ).
thf(f166,plain,
( ! [X1: g] :
( ( sK1
!= ( sK0 @ sK12 @ X1 ) )
| ( sK1
!= ( sK0 @ X1 @ sK12 ) ) )
| ~ spl16_10 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f168,definition,
( spl16_11
<=> ( sK10
= ( sK0 @ sK10 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_11])],[avatar_definition]) ).
thf(f170,plain,
( ( sK10
!= ( sK0 @ sK10 @ sK1 ) )
| spl16_11 ),
inference(avatar_component_clause,[],[f168]) ).
thf(f172,definition,
( spl16_12
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl16_12])],[avatar_definition]) ).
thf(f174,plain,
( ( sF3 = $true )
| ~ spl16_12 ),
inference(avatar_component_clause,[],[f172]) ).
thf(f176,definition,
( spl16_13
<=> ( ( sK0 @ ( sK0 @ sK13 @ sK11 ) @ sK14 )
= ( sK0 @ sK13 @ ( sK0 @ sK11 @ sK14 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_13])],[avatar_definition]) ).
thf(f178,plain,
( ( ( sK0 @ ( sK0 @ sK13 @ sK11 ) @ sK14 )
!= ( sK0 @ sK13 @ ( sK0 @ sK11 @ sK14 ) ) )
| spl16_13 ),
inference(avatar_component_clause,[],[f176]) ).
thf(f179,plain,
( ~ spl16_9
| spl16_10
| ~ spl16_11
| spl16_12
| ~ spl16_13 ),
inference(avatar_split_clause,[],[f99,f176,f172,f168,f165,f161]) ).
thf(f181,definition,
( spl16_14
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl16_14])],[avatar_definition]) ).
thf(f183,plain,
( ( $false = sF3 )
| ~ spl16_14 ),
inference(avatar_component_clause,[],[f181]) ).
thf(f184,plain,
( spl16_8
| spl16_14 ),
inference(avatar_split_clause,[],[f111,f181,f157]) ).
thf(f190,definition,
( spl16_16
<=> ! [X1: g] :
( sK1
= ( sK0 @ X1 @ ( sK15 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_16])],[avatar_definition]) ).
thf(f191,plain,
( ! [X1: g] :
( sK1
= ( sK0 @ X1 @ ( sK15 @ X1 ) ) )
| ~ spl16_16 ),
inference(avatar_component_clause,[],[f190]) ).
thf(f192,plain,
( spl16_14
| spl16_16 ),
inference(avatar_split_clause,[],[f119,f190,f181]) ).
thf(f194,definition,
( spl16_17
<=> ! [X1: g] :
( ( sK0 @ sK1 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl16_17])],[avatar_definition]) ).
thf(f195,plain,
( ! [X1: g] :
( ( sK0 @ sK1 @ X1 )
= X1 )
| ~ spl16_17 ),
inference(avatar_component_clause,[],[f194]) ).
thf(f197,plain,
( spl16_14
| spl16_7 ),
inference(avatar_split_clause,[],[f125,f153,f181]) ).
thf(f198,plain,
( spl16_5
| spl16_14 ),
inference(avatar_split_clause,[],[f127,f181,f145]) ).
thf(f199,plain,
( spl16_12
| spl16_4 ),
inference(avatar_split_clause,[],[f126,f140,f172]) ).
thf(f207,plain,
( ( $false = $true )
| ~ spl16_4
| ~ spl16_5 ),
inference(forward_demodulation,[],[f147,f142]) ).
thf(f208,plain,
( $false
| ~ spl16_4
| ~ spl16_5 ),
inference(trivial_inequality_removal,[],[f207]) ).
thf(f209,plain,
( ~ spl16_4
| ~ spl16_5 ),
inference(avatar_contradiction_clause,[],[f208]) ).
thf(f213,plain,
( ( sK10 != sK10 )
| ~ spl16_7
| spl16_11 ),
inference(constrained_superposition,[],[f170,f154]) ).
thf(f214,plain,
( $false
| ~ spl16_7
| spl16_11 ),
inference(trivial_inequality_removal,[],[f213]) ).
thf(f215,plain,
( ~ spl16_7
| spl16_11 ),
inference(avatar_contradiction_clause,[],[f214]) ).
thf(f216,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X0 @ X1 )
= ( sK0 @ X0 @ ( sK0 @ sK1 @ X1 ) ) )
| ~ spl16_7
| ~ spl16_8 ),
inference(constrained_superposition,[],[f158,f154]) ).
thf(f217,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X0 @ ( sK0 @ ( sK9 @ X0 ) @ X1 ) )
= ( sK0 @ sK1 @ X1 ) )
| ~ spl16_6
| ~ spl16_8 ),
inference(constrained_superposition,[],[f158,f150]) ).
thf(f240,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ ( sK9 @ ( sK9 @ X0 ) ) )
= ( sK0 @ X0 @ sK1 ) )
| ~ spl16_6
| ~ spl16_8 ),
inference(constrained_superposition,[],[f217,f150]) ).
thf(f254,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ ( sK9 @ ( sK9 @ X0 ) ) )
= X0 )
| ~ spl16_6
| ~ spl16_7
| ~ spl16_8 ),
inference(forward_demodulation,[],[f240,f154]) ).
thf(f256,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X1 @ X0 )
= ( sK0 @ X1 @ ( sK9 @ ( sK9 @ X0 ) ) ) )
| ~ spl16_6
| ~ spl16_7
| ~ spl16_8 ),
inference(constrained_superposition,[],[f216,f254]) ).
thf(f263,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ X0 )
= X0 )
| ~ spl16_6
| ~ spl16_7
| ~ spl16_8 ),
inference(constrained_superposition,[],[f254,f256]) ).
thf(f271,plain,
( spl16_17
| ~ spl16_6
| ~ spl16_7
| ~ spl16_8 ),
inference(avatar_split_clause,[],[f263,f157,f153,f149,f194]) ).
thf(f273,plain,
( $false
| spl16_2
| ~ spl16_7 ),
inference(forward_subsumption_resolution,[],[f134,f154]) ).
thf(f274,plain,
( spl16_2
| ~ spl16_7 ),
inference(avatar_contradiction_clause,[],[f273]) ).
thf(f275,plain,
( ( $false = $true )
| ~ spl16_12
| ~ spl16_14 ),
inference(forward_demodulation,[],[f174,f183]) ).
thf(f276,plain,
( $false
| ~ spl16_12
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f275]) ).
thf(f277,plain,
( ~ spl16_12
| ~ spl16_14 ),
inference(avatar_contradiction_clause,[],[f276]) ).
thf(f286,plain,
( ( sK10 != sK10 )
| spl16_9
| ~ spl16_17 ),
inference(constrained_superposition,[],[f163,f195]) ).
thf(f288,plain,
( $false
| spl16_9
| ~ spl16_17 ),
inference(trivial_inequality_removal,[],[f286]) ).
thf(f289,plain,
( spl16_9
| ~ spl16_17 ),
inference(avatar_contradiction_clause,[],[f288]) ).
thf(f298,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X0 @ ( sK0 @ ( sK9 @ X0 ) @ X1 ) )
= ( sK0 @ sK1 @ X1 ) )
| ~ spl16_6
| ~ spl16_8 ),
inference(constrained_superposition,[],[f158,f150]) ).
thf(f306,plain,
( ( ( sK0 @ sK7 @ ( sK0 @ sK4 @ sK8 ) )
!= ( sK0 @ sK7 @ ( sK0 @ sK4 @ sK8 ) ) )
| spl16_3
| ~ spl16_8 ),
inference(constrained_superposition,[],[f138,f158]) ).
thf(f310,plain,
( $false
| spl16_3
| ~ spl16_8 ),
inference(trivial_inequality_removal,[],[f306]) ).
thf(f311,plain,
( spl16_3
| ~ spl16_8 ),
inference(avatar_contradiction_clause,[],[f310]) ).
thf(f312,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X0 @ ( sK0 @ ( sK9 @ X0 ) @ X1 ) )
= X1 )
| ~ spl16_6
| ~ spl16_8
| ~ spl16_17 ),
inference(forward_demodulation,[],[f298,f195]) ).
thf(f319,plain,
( ( sK1 != sK1 )
| ~ spl16_1
| ~ spl16_16 ),
inference(constrained_superposition,[],[f130,f191]) ).
thf(f322,plain,
( $false
| ~ spl16_1
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f319]) ).
thf(f323,plain,
( ~ spl16_1
| ~ spl16_16 ),
inference(avatar_contradiction_clause,[],[f322]) ).
thf(f324,plain,
( $false
| ~ spl16_8
| spl16_13 ),
inference(forward_subsumption_resolution,[],[f178,f158]) ).
thf(f325,plain,
( ~ spl16_8
| spl16_13 ),
inference(avatar_contradiction_clause,[],[f324]) ).
thf(f334,plain,
( ( sK1
!= ( sK0 @ ( sK9 @ sK12 ) @ sK12 ) )
| ( sK1 != sK1 )
| ~ spl16_6
| ~ spl16_10 ),
inference(constrained_superposition,[],[f166,f150]) ).
thf(f336,plain,
( ( sK1
!= ( sK0 @ ( sK9 @ sK12 ) @ sK12 ) )
| ~ spl16_6
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f334]) ).
thf(f345,plain,
( ! [X0: g] :
( ( sK9 @ ( sK9 @ X0 ) )
= ( sK0 @ X0 @ sK1 ) )
| ~ spl16_6
| ~ spl16_8
| ~ spl16_17 ),
inference(constrained_superposition,[],[f312,f150]) ).
thf(f356,plain,
( ! [X0: g] :
( ( sK9 @ ( sK9 @ X0 ) )
= X0 )
| ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_17 ),
inference(forward_demodulation,[],[f345,f154]) ).
thf(f366,plain,
( ! [X0: g] :
( sK1
= ( sK0 @ ( sK9 @ X0 ) @ X0 ) )
| ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_17 ),
inference(constrained_superposition,[],[f150,f356]) ).
thf(f387,plain,
( ( sK1 != sK1 )
| ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_10
| ~ spl16_17 ),
inference(constrained_superposition,[],[f336,f366]) ).
thf(f390,plain,
( $false
| ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_10
| ~ spl16_17 ),
inference(trivial_inequality_removal,[],[f387]) ).
thf(f391,plain,
( ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_10
| ~ spl16_17 ),
inference(avatar_contradiction_clause,[],[f390]) ).
cnf(s1,plain,
( spl16_1
| ~ spl16_2
| ~ spl16_3
| spl16_4 ),
inference(sat_conversion,[],[f143]) ).
cnf(s2,plain,
( spl16_5
| spl16_6 ),
inference(sat_conversion,[],[f151]) ).
cnf(s3,plain,
( spl16_5
| spl16_7 ),
inference(sat_conversion,[],[f155]) ).
cnf(s4,plain,
( spl16_5
| spl16_8 ),
inference(sat_conversion,[],[f159]) ).
cnf(s5,plain,
( ~ spl16_9
| spl16_10
| ~ spl16_11
| spl16_12
| ~ spl16_13 ),
inference(sat_conversion,[],[f179]) ).
cnf(s6,plain,
( spl16_8
| spl16_14 ),
inference(sat_conversion,[],[f184]) ).
cnf(s8,plain,
( spl16_14
| spl16_16 ),
inference(sat_conversion,[],[f192]) ).
cnf(s10,plain,
( spl16_7
| spl16_14 ),
inference(sat_conversion,[],[f197]) ).
cnf(s11,plain,
( spl16_5
| spl16_14 ),
inference(sat_conversion,[],[f198]) ).
cnf(s12,plain,
( spl16_4
| spl16_12 ),
inference(sat_conversion,[],[f199]) ).
cnf(s13,plain,
( ~ spl16_4
| ~ spl16_5 ),
inference(sat_conversion,[],[f209]) ).
cnf(s14,plain,
( ~ spl16_7
| spl16_11 ),
inference(sat_conversion,[],[f215]) ).
cnf(s15,plain,
( ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| spl16_17 ),
inference(sat_conversion,[],[f271]) ).
cnf(s17,plain,
( spl16_2
| ~ spl16_7 ),
inference(sat_conversion,[],[f274]) ).
cnf(s18,plain,
( ~ spl16_12
| ~ spl16_14 ),
inference(sat_conversion,[],[f277]) ).
cnf(s20,plain,
( spl16_9
| ~ spl16_17 ),
inference(sat_conversion,[],[f289]) ).
cnf(s21,plain,
( spl16_3
| ~ spl16_8 ),
inference(sat_conversion,[],[f311]) ).
cnf(s23,plain,
( ~ spl16_1
| ~ spl16_16 ),
inference(sat_conversion,[],[f323]) ).
cnf(s24,plain,
( ~ spl16_8
| spl16_13 ),
inference(sat_conversion,[],[f325]) ).
cnf(s28,plain,
( ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_10
| ~ spl16_17 ),
inference(sat_conversion,[],[f391]) ).
cnf(s29,plain,
spl16_7,
inference(rat,[],[s12,s13,s18,s3,s10]) ).
cnf(s30,plain,
spl16_2,
inference(rat,[],[s17,s29]) ).
cnf(s31,plain,
spl16_11,
inference(rat,[],[s14,s29]) ).
cnf(s32,plain,
spl16_8,
inference(rat,[],[s12,s13,s18,s4,s6]) ).
cnf(s33,plain,
spl16_13,
inference(rat,[],[s24,s32]) ).
cnf(s34,plain,
spl16_3,
inference(rat,[],[s21,s32]) ).
cnf(s35,plain,
spl16_5,
inference(rat,[],[s5,s28,s20,s15,s18,s2,s11,s33,s31,s32,s29]) ).
cnf(s36,plain,
~ spl16_4,
inference(rat,[],[s13,s35]) ).
cnf(s37,plain,
spl16_12,
inference(rat,[],[s12,s36]) ).
cnf(s38,plain,
spl16_1,
inference(rat,[],[s1,s30,s34,s36]) ).
cnf(s39,plain,
~ spl16_14,
inference(rat,[],[s18,s37]) ).
cnf(s40,plain,
~ spl16_16,
inference(rat,[],[s23,s38]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s8,s40,s39]) ).
thf(f393,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG271^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n019.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 17:36:03 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 Running higher-order theorem proving
% 0.10/0.27 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
% 0.25/0.35 % (1129118)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.35 % (1129124)lrs+10_16_si=on:nwc=1.5:random_seed=2249079821:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.35 % (1129129)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.35 % (1129129)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
% 0.25/0.35 % (1129126)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=967260141: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)
% 0.25/0.35 % (1129128)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1849527295:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.35 % (1129125)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3580905718:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.35 % (1129127)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=369233188:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.35 % (1129129)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=1237963837:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.35 % (1129125)Instruction limit reached!
% 0.25/0.35 % (1129125)------------------------------
% 0.25/0.35 % (1129125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (1129125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (1129125)CaDiCaL version: 2.1.3
% 0.25/0.35 % (1129125)Termination reason: Instruction limit
% 0.25/0.35 % (1129125)Termination phase: Saturation
% 0.25/0.35 % (1129125)Time elapsed: 0.003 s
% 0.25/0.35 % (1129125)Peak memory usage: 11 MB
% 0.25/0.35 % (1129125)Instructions burned: 3 (million)
% 0.25/0.35 % (1129124)Instruction limit reached!
% 0.25/0.35 % (1129124)------------------------------
% 0.25/0.35 % (1129124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (1129124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (1129124)CaDiCaL version: 2.1.3
% 0.25/0.35 % (1129124)Termination reason: Instruction limit
% 0.25/0.35 % (1129124)Termination phase: Saturation
% 0.25/0.35 % (1129124)Time elapsed: 0.019 s
% 0.25/0.35 % (1129124)Peak memory usage: 12 MB
% 0.25/0.35 % (1129124)Instructions burned: 18 (million)
% 0.25/0.35 % (1129123)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=767746747:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.35 % (1129129) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1129118-1129129"...
% 0.25/0.35 % (1129127)Instruction limit reached!
% 0.25/0.35 % (1129127)------------------------------
% 0.25/0.35 % (1129127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (1129127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (1129127)CaDiCaL version: 2.1.3
% 0.25/0.36 % (1129127)Termination reason: Instruction limit
% 0.25/0.36 % (1129127)Termination phase: Saturation
% 0.25/0.36 % (1129127)Time elapsed: 0.018 s
% 0.25/0.36 % (1129127)Peak memory usage: 12 MB
% 0.25/0.36 % (1129127)Instructions burned: 26 (million)
% 0.25/0.36 % (1129128) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1129118-1129128"...
% 0.25/0.36 % (1129129)...printing done.
% 0.25/0.36 % (1129128)...printing done.
% 0.25/0.36 % (1129129)Refutation found. Thanks to Tanya!
% 0.25/0.36 % SZS status Theorem for theBenchmark
% 0.25/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.36 % (1129129)------------------------------
% 0.25/0.36 % (1129129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (1129129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (1129129)CaDiCaL version: 2.1.3
% 0.25/0.36 % (1129129)Termination reason: Refutation
% 0.25/0.36 % (1129129)Time elapsed: 0.023 s
% 0.25/0.36 % (1129129)Peak memory usage: 13 MB
% 0.25/0.36 % (1129129)Instructions burned: 35 (million)
% 0.25/0.36 % (1129118)Success in time 0.075 s
% 0.25/0.36 % Vampire exiting
%------------------------------------------------------------------------------