%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:29 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 20
% Syntax : Number of formulae : 195 ( 43 unt; 0 typ; 12 def)
% Number of atoms : 1343 ( 616 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 3136 ( 196 ~; 299 |; 134 &;2196 @)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 120 ( 120 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 46 usr; 24 con; 0-4 aty)
% ( 241 !!; 55 ??; 0 @@+; 0 @@-)
% Number of variables : 629 ( 0 sgn 163 !; 4 ?; 629 :)
% 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,
db3:
!>[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,
db2:
!>[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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
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,
vNOT: $o > $o ).
thf(func_def_22,type,
sK2: g ).
thf(func_def_23,type,
sK3: g ).
thf(func_def_24,type,
sK4: g ).
thf(func_def_25,type,
sK5: g ).
thf(func_def_26,type,
sK6: g ).
thf(func_def_27,type,
sK7: g ).
thf(func_def_28,type,
sK8: g ).
thf(func_def_29,type,
sK9: g > g ).
thf(func_def_30,type,
sK10: g > g ).
thf(func_def_31,type,
sK11: g > g ).
thf(func_def_32,type,
sK12: g > g ).
thf(func_def_33,type,
sK13: g > g ).
thf(func_def_34,type,
sK14: g > g ).
thf(func_def_35,type,
sK15: g > g ).
thf(f1,axiom,
( cGRP_ASSOC
= ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_ASSOC_def) ).
thf(f2,axiom,
( cGRP_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( ( X0 @ X3 @ X2 )
= X1 )
& ( ( X0 @ X2 @ X3 )
= X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_INVERSE_def) ).
thf(f3,axiom,
( cGRP_RIGHT_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X2 @ X3 )
= X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_RIGHT_INVERSE_def) ).
thf(f4,axiom,
( cGRP_RIGHT_UNIT
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_RIGHT_UNIT_def) ).
thf(f5,axiom,
( cGRP_UNIT
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( ( X0 @ X2 @ X1 )
= X2 )
& ( ( X0 @ X1 @ X2 )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_UNIT_def) ).
thf(f6,axiom,
( cGROUP1
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_INVERSE @ X0 @ X1 )
& ( cGRP_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP1_def) ).
thf(f7,axiom,
( cGROUP3
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP3_def) ).
thf(f8,conjecture,
! [X0: g > g > g,X1: g] :
( ( cGROUP1 @ X0 @ X1 )
<=> ( cGROUP3 @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQUIV_01_03) ).
thf(f9,negated_conjecture,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP1 @ X0 @ X1 )
<=> ( cGROUP3 @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f10,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ Y3 @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f11,plain,
( cGRP_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( ( Y0 @ Y2 @ Y3 )
= Y1 )
& ( ( 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,[],[f3]) ).
thf(f13,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f14,plain,
( cGRP_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f15,plain,
( cGROUP1
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_INVERSE @ X0 @ X1 )
& ( cGRP_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_UNIT @ Y0 @ Y1 )
& ( cGRP_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( cGROUP3
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f18,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP1 @ X0 @ X1 )
<=> ( cGROUP3 @ X0 @ X1 ) ),
inference(rectify,[],[f9]) ).
thf(f20,plain,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP1 @ X0 @ X1 )
= ( cGROUP3 @ X0 @ X1 ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
? [X0: g > g > g,X1: g] :
( ( cGROUP1 @ X0 @ X1 )
!= ( cGROUP3 @ X0 @ X1 ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f22,plain,
( ( cGROUP1 @ sK0 @ sK1 )
!= ( cGROUP3 @ sK0 @ sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f21]) ).
thf(f23,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ Y3 @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f24,plain,
( cGRP_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( ( Y0 @ Y2 @ Y3 )
= Y1 )
& ( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f25,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(f26,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f27,plain,
( cGRP_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f28,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_UNIT @ Y0 @ Y1 )
& ( cGRP_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f29,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f30,plain,
( ( cGROUP1 @ sK0 @ sK1 )
!= ( cGROUP3 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f33,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y4 @ Y5 )
= Y3 )
& ( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f28,f23,f27,f24]) ).
thf(f34,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f29,f23,f26,f25]) ).
thf(f35,plain,
( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y4 @ Y5 )
= Y3 )
& ( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 )
!= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f30,f33,f34]) ).
thf(f36,plain,
( ( $true
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y4 @ Y5 )
= Y3 )
& ( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $true
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) ) ),
inference(xor_proxy_clausification,[],[f35]) ).
thf(f37,plain,
( ( $false
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y4 @ Y5 )
= Y3 )
& ( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) )
| ( $false
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) ) ),
inference(xor_proxy_clausification,[],[f35]) ).
thf(f38,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f40,plain,
( ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ sK2 ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f39]) ).
thf(f41,plain,
( ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ sK2 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f42,plain,
( ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK3 ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK3 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f44,plain,
( ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ sK4 ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f43]) ).
thf(f45,plain,
( ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ sK4 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f46,plain,
( ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ sK5 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ sK5 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f46]) ).
thf(f48,plain,
( ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ sK5 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ sK6 ) ) ),
inference(duplicate_literal_removal,[],[f47]) ).
thf(f49,plain,
( ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK2 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK2 )
= sK1 ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 ) ) )
| ( $false
= ( ( ( sK0 @ sK1 @ sK4 )
= sK4 )
& ( ( sK0 @ sK4 @ sK1 )
= sK4 ) ) )
| ( $false
= ( ( sK0 @ sK5 @ sK1 )
= sK5 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK6 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK6 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK2 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK2 )
= sK1 ) )
@ X1 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 ) ) )
| ( $false
= ( ( ( sK0 @ sK1 @ sK4 )
= sK4 )
& ( ( sK0 @ sK4 @ sK1 )
= sK4 ) ) )
| ( $false
= ( ( sK0 @ sK5 @ sK1 )
= sK5 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK6 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK6 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK2 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK2 )
= sK1 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 )
@ X2 ) )
| ( $false
= ( ( ( sK0 @ sK1 @ sK4 )
= sK4 )
& ( ( sK0 @ sK4 @ sK1 )
= sK4 ) ) )
| ( $false
= ( ( sK0 @ sK5 @ sK1 )
= sK5 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK6 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK6 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK2 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK2 )
= sK1 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 )
@ X2 ) )
| ( $false
= ( ( sK0 @ sK4 @ sK1 )
= sK4 ) )
| ( $false
= ( ( sK0 @ sK5 @ sK1 )
= sK5 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK6 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK6 ) ) ) ) ) )
| ( $false
= ( ( sK0 @ sK1 @ sK4 )
= sK4 ) ) ),
inference(and_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK2 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK2 )
= sK1 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 )
@ X2 ) )
| ( sK4
!= ( sK0 @ sK4 @ sK1 ) )
| ( $false
= ( ( sK0 @ sK5 @ sK1 )
= sK5 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK6 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK6 ) ) ) ) ) )
| ( $false
= ( ( sK0 @ sK1 @ sK4 )
= sK4 ) ) ),
inference(equality_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK2 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK2 )
= sK1 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 )
@ X2 ) )
| ( sK4
!= ( sK0 @ sK4 @ sK1 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK6 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK6 ) ) ) ) ) )
| ( $false
= ( ( sK0 @ sK1 @ sK4 )
= sK4 ) ) ),
inference(equality_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK2 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK2 )
= sK1 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 )
@ X2 ) )
| ( sK4
!= ( sK0 @ sK4 @ sK1 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK6 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK6 ) ) ) )
@ sK7 ) )
| ( $false
= ( ( sK0 @ sK1 @ sK4 )
= sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK2 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK2 )
= sK1 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 )
@ X2 ) )
| ( sK4
!= ( sK0 @ sK4 @ sK1 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK6 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK6 ) ) ) )
@ sK7 ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) ) ),
inference(equality_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( ( sK0 @ sK2 @ X1 )
= sK1 )
& ( ( sK0 @ X1 @ sK2 )
= sK1 ) ) )
| ( $false
= ( ( sK0 @ sK3 @ X2 )
= sK1 ) )
| ( sK4
!= ( sK0 @ sK4 @ sK1 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK7 ) @ sK6 )
= ( sK0 @ Y0 @ ( sK0 @ sK7 @ sK6 ) ) ) ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( sK0 @ X1 @ sK2 )
= sK1 ) )
| ( $false
= ( ( sK0 @ sK3 @ X2 )
= sK1 ) )
| ( sK4
!= ( sK0 @ sK4 @ sK1 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK7 ) @ sK6 )
= ( sK0 @ Y0 @ ( sK0 @ sK7 @ sK6 ) ) ) ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( ( sK0 @ sK2 @ X1 )
= sK1 ) ) ),
inference(and_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK3 @ X2 )
= sK1 ) )
| ( sK4
!= ( sK0 @ sK4 @ sK1 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK7 ) @ sK6 )
= ( sK0 @ Y0 @ ( sK0 @ sK7 @ sK6 ) ) ) ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( ( sK0 @ sK2 @ X1 )
= sK1 ) ) ),
inference(equality_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK2 ) )
| ( sK1
!= ( sK0 @ sK3 @ X2 ) )
| ( sK4
!= ( sK0 @ sK4 @ sK1 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK7 ) @ sK6 )
= ( sK0 @ Y0 @ ( sK0 @ sK7 @ sK6 ) ) ) ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( ( sK0 @ sK2 @ X1 )
= sK1 ) ) ),
inference(equality_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK2 ) )
| ( sK1
!= ( sK0 @ sK3 @ X2 ) )
| ( sK4
!= ( sK0 @ sK4 @ sK1 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK7 ) @ sK6 )
= ( sK0 @ Y0 @ ( sK0 @ sK7 @ sK6 ) ) )
@ sK8 ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( ( sK0 @ sK2 @ X1 )
= sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK2 ) )
| ( sK1
!= ( sK0 @ sK3 @ X2 ) )
| ( sK4
!= ( sK0 @ sK4 @ sK1 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK7 ) @ sK6 )
= ( sK0 @ Y0 @ ( sK0 @ sK7 @ sK6 ) ) )
@ sK8 ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( sK1
!= ( sK0 @ sK2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK2 ) )
| ( sK1
!= ( sK0 @ sK3 @ X2 ) )
| ( sK4
!= ( sK0 @ sK4 @ sK1 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ( sK0 @ ( sK0 @ sK8 @ sK7 ) @ sK6 )
= ( sK0 @ sK8 @ ( sK0 @ sK7 @ sK6 ) ) ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( sK1
!= ( sK0 @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK2 ) )
| ( sK1
!= ( sK0 @ sK3 @ X2 ) )
| ( sK4
!= ( sK0 @ sK4 @ sK1 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( ( sK0 @ ( sK0 @ sK8 @ sK7 ) @ sK6 )
!= ( sK0 @ sK8 @ ( sK0 @ sK7 @ sK6 ) ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( sK1
!= ( sK0 @ sK2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f63]) ).
thf(f65,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f66,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f68,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f67]) ).
thf(f69,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f67]) ).
thf(f70,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f69]) ).
thf(f72,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f70]) ).
thf(f74,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f75,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X2: g,X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X1 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X1 ) ) ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X2 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X1 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X1 ) ) ) )
@ X3 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X2 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X2 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X1 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X1 ) ) ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X2 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X2 ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X3 ) @ X1 )
= ( sK0 @ Y0 @ ( sK0 @ X3 @ X1 ) ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X4 ) @ X2 )
= ( sK0 @ Y0 @ ( sK0 @ X4 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X2: g,X3: g,X1: g,X4: g,X5: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X3 ) @ X1 )
= ( sK0 @ Y0 @ ( sK0 @ X3 @ X1 ) ) )
@ X5 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X4 ) @ X2 )
= ( sK0 @ Y0 @ ( sK0 @ X4 @ X2 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X3 ) @ X1 )
= ( sK0 @ Y0 @ ( sK0 @ X3 @ X1 ) ) )
@ X5 ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X4 ) @ X2 )
= ( sK0 @ Y0 @ ( sK0 @ X4 @ X2 ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( $true
= ( ( sK0 @ ( sK0 @ X5 @ X3 ) @ X1 )
= ( sK0 @ X5 @ ( sK0 @ X3 @ X1 ) ) ) )
| ( $true
= ( ( sK0 @ ( sK0 @ X6 @ X4 ) @ X2 )
= ( sK0 @ X6 @ ( sK0 @ X4 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( ( sK0 @ ( sK0 @ X5 @ X3 ) @ X1 )
= ( sK0 @ X5 @ ( sK0 @ X3 @ X1 ) ) )
| ( $true
= ( ( sK0 @ ( sK0 @ X6 @ X4 ) @ X2 )
= ( sK0 @ X6 @ ( sK0 @ X4 @ X2 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( ( sK0 @ ( sK0 @ X5 @ X3 ) @ X1 )
= ( sK0 @ X5 @ ( sK0 @ X3 @ X1 ) ) )
| ( ( sK0 @ ( sK0 @ X6 @ X4 ) @ X2 )
= ( sK0 @ X6 @ ( sK0 @ X4 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f83]) ).
thf(f102,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f68]) ).
thf(f104,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f102]) ).
thf(f105,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f104]) ).
thf(f123,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f105]) ).
thf(f124,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( ( sK0 @ sK1 @ X1 )
= X1 )
& ( ( sK0 @ X1 @ sK1 )
= X1 ) ) )
| ( $true
= ( ( sK0 @ X2 @ sK1 )
= X2 ) ) ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f125,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ X1 @ sK1 )
= X1 ) )
| ( $true
= ( ( sK0 @ X2 @ sK1 )
= X2 ) ) ),
inference(and_proxy_clausification,[],[f124]) ).
thf(f129,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ X1 @ sK1 )
= X1 )
| ( $true
= ( ( sK0 @ X2 @ sK1 )
= X2 ) ) ),
inference(equality_proxy_clausification,[],[f125]) ).
thf(f130,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ X1 @ sK1 )
= X1 )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f129]) ).
thf(f143,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f66]) ).
thf(f144,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f143]) ).
thf(f172,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f173,plain,
! [X2: g,X1: g] :
( ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ X1 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ X1 )
= sK1 ) ) ) )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ( sK0 @ X1 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ X1 )
= sK1 ) )
@ ( sK14 @ X1 ) ) )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ( sK0 @ X1 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ X1 )
= sK1 ) )
@ ( sK14 @ X1 ) ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 )
@ ( sK15 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 )
& ( ( sK0 @ ( sK14 @ X1 ) @ X1 )
= sK1 ) ) )
| ( $true
= ( ( sK0 @ X2 @ ( sK15 @ X2 ) )
= sK1 ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ ( sK14 @ X1 ) @ X1 )
= sK1 ) )
| ( $true
= ( ( sK0 @ X2 @ ( sK15 @ X2 ) )
= sK1 ) ) ),
inference(and_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 ) )
| ( $true
= ( ( sK0 @ X2 @ ( sK15 @ X2 ) )
= sK1 ) ) ),
inference(and_proxy_clausification,[],[f176]) ).
thf(f179,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( ( sK0 @ X2 @ ( sK15 @ X2 ) )
= sK1 ) ) ),
inference(equality_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ X1 @ ( sK14 @ X1 ) ) )
| ( sK1
= ( sK0 @ X2 @ ( sK15 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ ( sK14 @ X1 ) @ X1 ) )
| ( $true
= ( ( sK0 @ X2 @ ( sK15 @ X2 ) )
= sK1 ) ) ),
inference(equality_proxy_clausification,[],[f177]) ).
thf(f182,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ ( sK14 @ X1 ) @ X1 ) )
| ( sK1
= ( sK0 @ X2 @ ( sK15 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f181]) ).
thf(f184,definition,
( spl16_1
<=> ( sK4
= ( sK0 @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
thf(f186,plain,
( ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| spl16_1 ),
inference(avatar_component_clause,[],[f184]) ).
thf(f188,definition,
( spl16_2
<=> ( ( sK0 @ ( sK0 @ sK8 @ sK7 ) @ sK6 )
= ( sK0 @ sK8 @ ( sK0 @ sK7 @ sK6 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
thf(f190,plain,
( ( ( sK0 @ ( sK0 @ sK8 @ sK7 ) @ sK6 )
!= ( sK0 @ sK8 @ ( sK0 @ sK7 @ sK6 ) ) )
| spl16_2 ),
inference(avatar_component_clause,[],[f188]) ).
thf(f192,definition,
( spl16_3
<=> ( sK5
= ( sK0 @ sK5 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
thf(f194,plain,
( ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| spl16_3 ),
inference(avatar_component_clause,[],[f192]) ).
thf(f196,definition,
( spl16_4
<=> ( sK4
= ( sK0 @ sK4 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
thf(f198,plain,
( ( sK4
!= ( sK0 @ sK4 @ sK1 ) )
| spl16_4 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f200,definition,
( spl16_5
<=> ! [X2: g] :
( sK1
!= ( sK0 @ sK3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition]) ).
thf(f201,plain,
( ! [X2: g] :
( sK1
!= ( sK0 @ sK3 @ X2 ) )
| ~ spl16_5 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f203,definition,
( spl16_6
<=> ! [X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK2 ) )
| ( sK1
!= ( sK0 @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
thf(f204,plain,
( ! [X1: g] :
( ( sK1
!= ( sK0 @ sK2 @ X1 ) )
| ( sK1
!= ( sK0 @ X1 @ sK2 ) ) )
| ~ spl16_6 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f205,plain,
( ~ spl16_1
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| spl16_5
| spl16_6 ),
inference(avatar_split_clause,[],[f64,f203,f200,f196,f192,f188,f184]) ).
thf(f207,definition,
( spl16_7
<=> ! [X6: g,X2: g,X4: g] :
( ( sK0 @ ( sK0 @ X6 @ X4 ) @ X2 )
= ( sK0 @ X6 @ ( sK0 @ X4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_7])],[avatar_definition]) ).
thf(f208,plain,
( ! [X2: g,X6: g,X4: g] :
( ( sK0 @ ( sK0 @ X6 @ X4 ) @ X2 )
= ( sK0 @ X6 @ ( sK0 @ X4 @ X2 ) ) )
| ~ spl16_7 ),
inference(avatar_component_clause,[],[f207]) ).
thf(f209,plain,
( spl16_7
| spl16_7 ),
inference(avatar_split_clause,[],[f84,f207,f207]) ).
thf(f211,definition,
( spl16_8
<=> ! [X2: g] :
( ( sK0 @ X2 @ sK1 )
= X2 ) ),
introduced(definition,[new_symbols(definition,[spl16_8])],[avatar_definition]) ).
thf(f212,plain,
( ! [X2: g] :
( ( sK0 @ X2 @ sK1 )
= X2 )
| ~ spl16_8 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f219,definition,
( spl16_10
<=> ! [X1: g] :
( ( sK0 @ sK1 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition]) ).
thf(f220,plain,
( ! [X1: g] :
( ( sK0 @ sK1 @ X1 )
= X1 )
| ~ spl16_10 ),
inference(avatar_component_clause,[],[f219]) ).
thf(f224,plain,
( spl16_8
| spl16_8 ),
inference(avatar_split_clause,[],[f130,f211,f211]) ).
thf(f250,definition,
( spl16_17
<=> ! [X2: g] :
( sK1
= ( sK0 @ X2 @ ( sK15 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_17])],[avatar_definition]) ).
thf(f251,plain,
( ! [X2: g] :
( sK1
= ( sK0 @ X2 @ ( sK15 @ X2 ) ) )
| ~ spl16_17 ),
inference(avatar_component_clause,[],[f250]) ).
thf(f253,definition,
( spl16_18
<=> ! [X1: g] :
( sK1
= ( sK0 @ X1 @ ( sK14 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_18])],[avatar_definition]) ).
thf(f254,plain,
( ! [X1: g] :
( sK1
= ( sK0 @ X1 @ ( sK14 @ X1 ) ) )
| ~ spl16_18 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f255,plain,
( spl16_17
| spl16_18 ),
inference(avatar_split_clause,[],[f180,f253,f250]) ).
thf(f257,definition,
( spl16_19
<=> ! [X1: g] :
( sK1
= ( sK0 @ ( sK14 @ X1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_19])],[avatar_definition]) ).
thf(f258,plain,
( ! [X1: g] :
( sK1
= ( sK0 @ ( sK14 @ X1 ) @ X1 ) )
| ~ spl16_19 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f259,plain,
( spl16_17
| spl16_19 ),
inference(avatar_split_clause,[],[f182,f257,f250]) ).
thf(f267,plain,
( $false
| spl16_3
| ~ spl16_8 ),
inference(backward_subsumption_resolution,[],[f194,f212]) ).
thf(f268,plain,
( spl16_3
| ~ spl16_8 ),
inference(avatar_contradiction_clause,[],[f267]) ).
thf(f269,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ sK1 @ X1 )
= ( sK0 @ X0 @ ( sK0 @ ( sK15 @ X0 ) @ X1 ) ) )
| ~ spl16_7
| ~ spl16_17 ),
inference(constrained_superposition,[],[f208,f251]) ).
thf(f272,plain,
( ! [X0: g,X1: g] :
( sK1
= ( sK0 @ X0 @ ( sK0 @ X1 @ ( sK15 @ ( sK0 @ X0 @ X1 ) ) ) ) )
| ~ spl16_7
| ~ spl16_17 ),
inference(constrained_superposition,[],[f208,f251]) ).
thf(f278,plain,
( $false
| spl16_1
| ~ spl16_10 ),
inference(backward_subsumption_resolution,[],[f186,f220]) ).
thf(f282,plain,
( spl16_1
| ~ spl16_10 ),
inference(avatar_contradiction_clause,[],[f278]) ).
thf(f297,plain,
( ! [X0: g] :
( ( sK0 @ X0 @ sK1 )
= ( sK0 @ sK1 @ ( sK15 @ ( sK15 @ X0 ) ) ) )
| ~ spl16_7
| ~ spl16_17 ),
inference(constrained_superposition,[],[f269,f251]) ).
thf(f312,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ ( sK15 @ ( sK15 @ X0 ) ) )
= X0 )
| ~ spl16_7
| ~ spl16_8
| ~ spl16_17 ),
inference(forward_demodulation,[],[f297,f212]) ).
thf(f319,plain,
( ! [X0: g] :
( sK1
= ( sK0 @ X0 @ ( sK0 @ sK1 @ ( sK15 @ X0 ) ) ) )
| ~ spl16_7
| ~ spl16_8
| ~ spl16_17 ),
inference(constrained_superposition,[],[f272,f212]) ).
thf(f453,plain,
( ! [X0: g] :
( sK1
= ( sK0 @ ( sK15 @ X0 ) @ X0 ) )
| ~ spl16_7
| ~ spl16_8
| ~ spl16_17 ),
inference(constrained_superposition,[],[f319,f312]) ).
thf(f462,plain,
( ! [X0: g] :
( ( sK0 @ X0 @ sK1 )
= ( sK0 @ sK1 @ ( sK0 @ sK1 @ ( sK15 @ ( sK15 @ X0 ) ) ) ) )
| ~ spl16_7
| ~ spl16_8
| ~ spl16_17 ),
inference(constrained_superposition,[],[f269,f319]) ).
thf(f466,plain,
( ! [X0: g] :
( ( sK0 @ X0 @ sK1 )
= ( sK0 @ sK1 @ X0 ) )
| ~ spl16_7
| ~ spl16_8
| ~ spl16_17 ),
inference(forward_demodulation,[],[f462,f312]) ).
thf(f473,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ X0 )
= X0 )
| ~ spl16_7
| ~ spl16_8
| ~ spl16_17 ),
inference(forward_demodulation,[],[f466,f212]) ).
thf(f475,plain,
( spl16_10
| ~ spl16_7
| ~ spl16_8
| ~ spl16_17 ),
inference(avatar_split_clause,[],[f473,f250,f211,f207,f219]) ).
thf(f478,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ sK1 @ X1 )
= ( sK0 @ X0 @ ( sK0 @ ( sK14 @ X0 ) @ X1 ) ) )
| ~ spl16_7
| ~ spl16_18 ),
inference(constrained_superposition,[],[f208,f254]) ).
thf(f555,plain,
( ! [X0: g] :
( ( sK0 @ X0 @ sK1 )
= ( sK0 @ sK1 @ X0 ) )
| ~ spl16_7
| ~ spl16_18
| ~ spl16_19 ),
inference(constrained_superposition,[],[f478,f258]) ).
thf(f575,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ X0 )
= X0 )
| ~ spl16_7
| ~ spl16_8
| ~ spl16_18
| ~ spl16_19 ),
inference(forward_demodulation,[],[f555,f212]) ).
thf(f586,plain,
( spl16_10
| ~ spl16_7
| ~ spl16_8
| ~ spl16_18
| ~ spl16_19 ),
inference(avatar_split_clause,[],[f575,f257,f253,f211,f207,f219]) ).
thf(f587,plain,
( $false
| spl16_2
| ~ spl16_7 ),
inference(forward_subsumption_resolution,[],[f190,f208]) ).
thf(f588,plain,
( spl16_2
| ~ spl16_7 ),
inference(avatar_contradiction_clause,[],[f587]) ).
thf(f589,plain,
( $false
| spl16_4
| ~ spl16_8 ),
inference(forward_subsumption_resolution,[],[f198,f212]) ).
thf(f590,plain,
( spl16_4
| ~ spl16_8 ),
inference(avatar_contradiction_clause,[],[f589]) ).
thf(f597,plain,
( ( sK1 != sK1 )
| ( sK1
!= ( sK0 @ ( sK14 @ sK2 ) @ sK2 ) )
| ~ spl16_6
| ~ spl16_18 ),
inference(constrained_superposition,[],[f204,f254]) ).
thf(f607,plain,
( ( sK1
!= ( sK0 @ ( sK14 @ sK2 ) @ sK2 ) )
| ~ spl16_6
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f597]) ).
thf(f623,plain,
( $false
| ~ spl16_6
| ~ spl16_18
| ~ spl16_19 ),
inference(forward_subsumption_resolution,[],[f607,f258]) ).
thf(f624,plain,
( ~ spl16_6
| ~ spl16_18
| ~ spl16_19 ),
inference(avatar_contradiction_clause,[],[f623]) ).
thf(f626,plain,
( ( sK1 != sK1 )
| ~ spl16_5
| ~ spl16_18 ),
inference(constrained_superposition,[],[f201,f254]) ).
thf(f638,plain,
( $false
| ~ spl16_5
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f626]) ).
thf(f639,plain,
( ~ spl16_5
| ~ spl16_18 ),
inference(avatar_contradiction_clause,[],[f638]) ).
thf(f683,plain,
( ( sK1 != sK1 )
| ( sK1
!= ( sK0 @ ( sK15 @ sK2 ) @ sK2 ) )
| ~ spl16_6
| ~ spl16_17 ),
inference(constrained_superposition,[],[f204,f251]) ).
thf(f684,plain,
( ( sK1
!= ( sK0 @ ( sK15 @ sK2 ) @ sK2 ) )
| ~ spl16_6
| ~ spl16_17 ),
inference(trivial_inequality_removal,[],[f683]) ).
thf(f958,plain,
( $false
| ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_17 ),
inference(backward_subsumption_resolution,[],[f684,f453]) ).
thf(f968,plain,
( ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_17 ),
inference(avatar_contradiction_clause,[],[f958]) ).
thf(f974,plain,
( ( sK1 != sK1 )
| ~ spl16_5
| ~ spl16_17 ),
inference(constrained_superposition,[],[f201,f251]) ).
thf(f981,plain,
( $false
| ~ spl16_5
| ~ spl16_17 ),
inference(trivial_inequality_removal,[],[f974]) ).
thf(f982,plain,
( ~ spl16_5
| ~ spl16_17 ),
inference(avatar_contradiction_clause,[],[f981]) ).
cnf(s1,plain,
( ~ spl16_1
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| spl16_5
| spl16_6 ),
inference(sat_conversion,[],[f205]) ).
cnf(s2,plain,
( spl16_7
| spl16_7 ),
inference(sat_conversion,[],[f209]) ).
cnf(s3,plain,
spl16_7,
inference(rat,[],[s2]) ).
cnf(s9,plain,
( spl16_8
| spl16_8 ),
inference(sat_conversion,[],[f224]) ).
cnf(s10,plain,
spl16_8,
inference(rat,[],[s9]) ).
cnf(s17,plain,
( spl16_17
| spl16_18 ),
inference(sat_conversion,[],[f255]) ).
cnf(s18,plain,
( spl16_17
| spl16_19 ),
inference(sat_conversion,[],[f259]) ).
cnf(s19,plain,
( spl16_3
| ~ spl16_8 ),
inference(sat_conversion,[],[f268]) ).
cnf(s20,plain,
( spl16_1
| ~ spl16_10 ),
inference(sat_conversion,[],[f282]) ).
cnf(s22,plain,
( ~ spl16_7
| ~ spl16_8
| spl16_10
| ~ spl16_17 ),
inference(sat_conversion,[],[f475]) ).
cnf(s23,plain,
( ~ spl16_7
| ~ spl16_8
| spl16_10
| ~ spl16_18
| ~ spl16_19 ),
inference(sat_conversion,[],[f586]) ).
cnf(s24,plain,
( spl16_2
| ~ spl16_7 ),
inference(sat_conversion,[],[f588]) ).
cnf(s25,plain,
( spl16_4
| ~ spl16_8 ),
inference(sat_conversion,[],[f590]) ).
cnf(s28,plain,
( ~ spl16_6
| ~ spl16_18
| ~ spl16_19 ),
inference(sat_conversion,[],[f624]) ).
cnf(s31,plain,
( ~ spl16_5
| ~ spl16_18 ),
inference(sat_conversion,[],[f639]) ).
cnf(s41,plain,
( ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_17 ),
inference(sat_conversion,[],[f968]) ).
cnf(s43,plain,
( ~ spl16_5
| ~ spl16_17 ),
inference(sat_conversion,[],[f982]) ).
cnf(s44,plain,
spl16_4,
inference(rat,[],[s25,s10]) ).
cnf(s45,plain,
spl16_3,
inference(rat,[],[s19,s10]) ).
cnf(s46,plain,
spl16_2,
inference(rat,[],[s24,s3]) ).
cnf(s47,plain,
( ~ spl16_1
| spl16_5
| spl16_6 ),
inference(rat,[],[s1,s44,s45,s46]) ).
cnf(s48,plain,
spl16_10,
inference(rat,[],[s23,s17,s18,s22,s10,s3]) ).
cnf(s49,plain,
spl16_1,
inference(rat,[],[s20,s48]) ).
cnf(s50,plain,
~ spl16_6,
inference(rat,[],[s28,s17,s18,s41,s10,s3]) ).
cnf(s51,plain,
spl16_5,
inference(rat,[],[s47,s49,s50]) ).
cnf(s52,plain,
~ spl16_17,
inference(rat,[],[s43,s51]) ).
cnf(s54,plain,
~ spl16_18,
inference(rat,[],[s31,s51]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s17,s54,s52]) ).
thf(f983,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:33:56 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.29 % (3693931)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (3693943)% WARNING: option uhcvi not known.
% 0.20/0.29 % (3693943)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4102038977:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (3693943)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (3693943)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.29 % (3693942)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2334574406_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (3693945)dis+10_1_sil=32000:sp=arity:random_seed=3040715403:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (3693946)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=655052950:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (3693944)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=417209950:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (3693947)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4243380375:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (3693948)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3621075419:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (3693946)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (3693943) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3693931-3693943"...
% 0.20/0.29 % (3693943)...printing done.
% 0.20/0.29 % (3693943)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (3693943)------------------------------
% 0.20/0.29 % (3693943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3693943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3693943)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3693943)Termination reason: Refutation
% 0.20/0.29 % (3693943)Time elapsed: 0.025 s
% 0.20/0.29 % (3693943)Peak memory usage: 13 MB
% 0.20/0.29 % (3693943)Instructions burned: 91 (million)
% 0.20/0.29 % (3693931)Success in time 0.052 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------