%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG273^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 0.19s 0.33s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 20
% Syntax : Number of formulae : 210 ( 42 unt; 0 typ; 12 def)
% Number of atoms : 1307 ( 533 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 3004 ( 216 ~; 314 |; 70 &;2083 @)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 50 ( 45 usr; 24 con; 0-4 aty)
% ( 243 !!; 63 ??; 0 @@+; 0 @@-)
% Number of variables : 675 ( 0 sgn 195 !; 4 ?; 675 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(func_def_1,type,
cGROUP3: ( g > g > g ) > g > $o ).
thf(func_def_2,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(func_def_3,type,
cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_4,type,
cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_5,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_6,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_8,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
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(f1,axiom,
( cGRP_ASSOC
= ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_ASSOC_def) ).
thf(f2,axiom,
( cGRP_LEFT_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X3 @ X2 )
= X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_LEFT_INVERSE_def) ).
thf(f3,axiom,
( cGRP_LEFT_UNIT
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X1 @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_LEFT_UNIT_def) ).
thf(f4,axiom,
( cGRP_RIGHT_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X2 @ X3 )
= X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_RIGHT_INVERSE_def) ).
thf(f5,axiom,
( cGRP_RIGHT_UNIT
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_RIGHT_UNIT_def) ).
thf(f6,axiom,
( cGROUP2
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_LEFT_INVERSE @ X0 @ X1 )
& ( cGRP_LEFT_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGROUP2_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/sandbox/benchmark/theBenchmark.p',cGROUP3_def) ).
thf(f8,conjecture,
! [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
<=> ( cGROUP3 @ X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEQUIV_02_03) ).
thf(f9,negated_conjecture,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
<=> ( cGROUP3 @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f10,plain,
( cGRP_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_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f12,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f13,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f14,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f15,plain,
( cGROUP2
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_LEFT_INVERSE @ X0 @ X1 )
& ( cGRP_LEFT_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_LEFT_UNIT @ Y0 @ Y1 )
& ( cGRP_LEFT_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] :
( ( cGROUP2 @ X0 @ X1 )
<=> ( cGROUP3 @ X0 @ X1 ) ),
inference(rectify,[],[f9]) ).
thf(f20,plain,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
= ( cGROUP3 @ X0 @ X1 ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
? [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
!= ( cGROUP3 @ X0 @ X1 ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f22,plain,
( ( cGROUP2 @ 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_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f25,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f26,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f27,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f28,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_LEFT_UNIT @ Y0 @ Y1 )
& ( cGRP_LEFT_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,
( ( cGROUP2 @ sK0 @ sK1 )
!= ( cGROUP3 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f33,plain,
( cGROUP2
= ( ^ [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 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f28,f23,f25,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,f27,f26]) ).
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 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( 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 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( 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 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( 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 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( 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 @ 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 ) ) ) ) ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f40,plain,
( ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( 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 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f39]) ).
thf(f41,plain,
( ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( 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 ) ) ) )
| ( $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 @ 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 ) ) ) )
| ( $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 @ Y1 @ Y0 )
= sK1 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK3 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= 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 @ Y1 @ Y0 )
= sK1 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= 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 @ Y1 @ Y0 )
= sK1 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= 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 @ Y1 @ Y0 )
= sK1 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= 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 @ Y1 @ Y0 )
= sK1 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= 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 @ Y1 @ Y0 )
= sK1 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= 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 @ Y0 @ sK2 )
= sK1 ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 ) ) )
| ( $false
= ( ( sK0 @ sK1 @ sK4 )
= 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 @ Y0 @ sK2 )
= sK1 )
@ X1 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 ) ) )
| ( $false
= ( ( sK0 @ sK1 @ sK4 )
= 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 @ Y0 @ sK2 )
= sK1 )
@ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 )
@ X2 ) )
| ( $false
= ( ( sK0 @ sK1 @ sK4 )
= 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 @ Y0 @ sK2 )
= sK1 )
@ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 )
@ X2 ) )
| ( sK4
!= ( sK0 @ 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(equality_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK2 )
= sK1 )
@ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 )
@ X2 ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK6 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK6 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK2 )
= sK1 )
@ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK3 @ Y0 )
= sK1 )
@ X2 ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK6 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK6 ) ) ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( sK0 @ X1 @ sK2 )
= sK1 ) )
| ( $false
= ( ( sK0 @ sK3 @ X2 )
= sK1 ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK7 ) @ sK6 )
= ( sK0 @ Y0 @ ( sK0 @ sK7 @ sK6 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f56,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK3 @ X2 )
= sK1 ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK7 ) @ sK6 )
= ( sK0 @ Y0 @ ( sK0 @ sK7 @ sK6 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK2 ) )
| ( sK1
!= ( sK0 @ sK3 @ X2 ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK7 ) @ sK6 )
= ( sK0 @ Y0 @ ( sK0 @ sK7 @ sK6 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK2 ) )
| ( sK1
!= ( sK0 @ sK3 @ X2 ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK7 ) @ sK6 )
= ( sK0 @ Y0 @ ( sK0 @ sK7 @ sK6 ) ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK2 ) )
| ( sK1
!= ( sK0 @ sK3 @ X2 ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ( sK0 @ ( sK0 @ sK8 @ sK7 ) @ sK6 )
= ( sK0 @ sK8 @ ( sK0 @ sK7 @ sK6 ) ) ) ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK2 ) )
| ( sK1
!= ( sK0 @ sK3 @ X2 ) )
| ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( ( sK0 @ ( sK0 @ sK8 @ sK7 ) @ sK6 )
!= ( sK0 @ sK8 @ ( sK0 @ sK7 @ sK6 ) ) ) ),
inference(equality_proxy_clausification,[],[f59]) ).
thf(f61,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 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( 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(f62,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( 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,[],[f61]) ).
thf(f63,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 ) ) ) )
| ( $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,[],[f61]) ).
thf(f64,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= 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,[],[f63]) ).
thf(f65,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,[],[f63]) ).
thf(f66,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,[],[f65]) ).
thf(f68,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,[],[f66]) ).
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 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f68]) ).
thf(f71,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,[],[f70]) ).
thf(f72,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,[],[f71]) ).
thf(f73,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,[],[f72]) ).
thf(f74,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,[],[f73]) ).
thf(f75,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,[],[f74]) ).
thf(f76,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,[],[f75]) ).
thf(f77,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,[],[f76]) ).
thf(f78,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,[],[f77]) ).
thf(f79,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,[],[f78]) ).
thf(f80,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,[],[f79]) ).
thf(f98,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= 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,[],[f64]) ).
thf(f99,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 )
@ X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= 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,[],[f98]) ).
thf(f101,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 )
@ X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f100]) ).
thf(f111,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 )
@ X1 ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f101]) ).
thf(f112,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) )
| ( $true
= ( ( sK0 @ X2 @ sK1 )
= X2 ) ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f113,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK1 @ X1 )
= X1 )
| ( $true
= ( ( sK0 @ X2 @ sK1 )
= X2 ) ) ),
inference(equality_proxy_clausification,[],[f112]) ).
thf(f114,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK1 @ X1 )
= X1 )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 )
@ X1 ) )
| ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f99]) ).
thf(f116,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f115]) ).
thf(f117,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK1 @ X1 )
= X1 )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 ) ) ) ),
inference(equality_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK1 @ X1 )
= X1 )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 )
@ ( sK10 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK1 @ X1 )
= X1 )
| ( $true
= ( ( sK0 @ X2 @ ( sK10 @ X2 ) )
= sK1 ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK1 @ X1 )
= X1 )
| ( sK1
= ( sK0 @ X2 @ ( sK10 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( 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,[],[f62]) ).
thf(f122,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) )
@ X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( 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 ) ) ) ) ),
inference(and_proxy_clausification,[],[f121]) ).
thf(f124,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) )
@ X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f123]) ).
thf(f135,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f124]) ).
thf(f136,plain,
! [X2: g,X1: g] :
( ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 ) ) )
| ( $true
= ( ( sK0 @ X2 @ sK1 )
= X2 ) ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f137,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 )
@ ( sK12 @ X1 ) ) )
| ( $true
= ( ( sK0 @ X2 @ sK1 )
= X2 ) ) ),
inference(sigma_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 )
@ ( sK12 @ X1 ) ) )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ ( sK12 @ X1 ) @ X1 )
= sK1 ) )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ ( sK12 @ X1 ) @ X1 ) )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f122]) ).
thf(f142,plain,
! [X2: g,X1: g] :
( ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 ) ) )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 )
@ ( sK13 @ X1 ) ) )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 )
@ ( sK13 @ X1 ) ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 )
@ ( sK14 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ ( sK13 @ X1 ) @ X1 )
= sK1 ) )
| ( $true
= ( ( sK0 @ X2 @ ( sK14 @ X2 ) )
= sK1 ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $true
= ( ( sK0 @ X2 @ ( sK14 @ X2 ) )
= sK1 ) ) ),
inference(equality_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( sK1
= ( sK0 @ X2 @ ( sK14 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f146]) ).
thf(f149,definition,
( spl15_1
<=> ( ( sK0 @ ( sK0 @ sK8 @ sK7 ) @ sK6 )
= ( sK0 @ sK8 @ ( sK0 @ sK7 @ sK6 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
thf(f151,plain,
( ( ( sK0 @ ( sK0 @ sK8 @ sK7 ) @ sK6 )
!= ( sK0 @ sK8 @ ( sK0 @ sK7 @ sK6 ) ) )
| spl15_1 ),
inference(avatar_component_clause,[],[f149]) ).
thf(f153,definition,
( spl15_2
<=> ( sK5
= ( sK0 @ sK5 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
thf(f155,plain,
( ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| spl15_2 ),
inference(avatar_component_clause,[],[f153]) ).
thf(f157,definition,
( spl15_3
<=> ( sK4
= ( sK0 @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
thf(f159,plain,
( ( sK4
!= ( sK0 @ sK1 @ sK4 ) )
| spl15_3 ),
inference(avatar_component_clause,[],[f157]) ).
thf(f161,definition,
( spl15_4
<=> ! [X2: g] :
( sK1
!= ( sK0 @ sK3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
thf(f162,plain,
( ! [X2: g] :
( sK1
!= ( sK0 @ sK3 @ X2 ) )
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f161]) ).
thf(f164,definition,
( spl15_5
<=> ! [X1: g] :
( sK1
!= ( sK0 @ X1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
thf(f165,plain,
( ! [X1: g] :
( sK1
!= ( sK0 @ X1 @ sK2 ) )
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f164]) ).
thf(f166,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| spl15_4
| spl15_5 ),
inference(avatar_split_clause,[],[f60,f164,f161,f157,f153,f149]) ).
thf(f168,definition,
( spl15_6
<=> ! [X6: g,X2: g,X4: g] :
( ( sK0 @ ( sK0 @ X6 @ X4 ) @ X2 )
= ( sK0 @ X6 @ ( sK0 @ X4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
thf(f169,plain,
( ! [X2: g,X6: g,X4: g] :
( ( sK0 @ ( sK0 @ X6 @ X4 ) @ X2 )
= ( sK0 @ X6 @ ( sK0 @ X4 @ X2 ) ) )
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f168]) ).
thf(f170,plain,
( spl15_6
| spl15_6 ),
inference(avatar_split_clause,[],[f80,f168,f168]) ).
thf(f172,definition,
( spl15_7
<=> ! [X2: g] :
( ( sK0 @ X2 @ sK1 )
= X2 ) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
thf(f173,plain,
( ! [X2: g] :
( ( sK0 @ X2 @ sK1 )
= X2 )
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f172]) ).
thf(f180,definition,
( spl15_9
<=> ! [X1: g] :
( ( sK0 @ sK1 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl15_9])],[avatar_definition]) ).
thf(f181,plain,
( ! [X1: g] :
( ( sK0 @ sK1 @ X1 )
= X1 )
| ~ spl15_9 ),
inference(avatar_component_clause,[],[f180]) ).
thf(f183,plain,
( spl15_7
| spl15_9 ),
inference(avatar_split_clause,[],[f114,f180,f172]) ).
thf(f185,definition,
( spl15_10
<=> ! [X2: g] :
( sK1
= ( sK0 @ X2 @ ( sK10 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_10])],[avatar_definition]) ).
thf(f186,plain,
( ! [X2: g] :
( sK1
= ( sK0 @ X2 @ ( sK10 @ X2 ) ) )
| ~ spl15_10 ),
inference(avatar_component_clause,[],[f185]) ).
thf(f187,plain,
( spl15_10
| spl15_9 ),
inference(avatar_split_clause,[],[f120,f180,f185]) ).
thf(f193,definition,
( spl15_12
<=> ! [X1: g] :
( sK1
= ( sK0 @ ( sK12 @ X1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_12])],[avatar_definition]) ).
thf(f194,plain,
( ! [X1: g] :
( sK1
= ( sK0 @ ( sK12 @ X1 ) @ X1 ) )
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f193]) ).
thf(f195,plain,
( spl15_7
| spl15_12 ),
inference(avatar_split_clause,[],[f140,f193,f172]) ).
thf(f197,definition,
( spl15_13
<=> ! [X2: g] :
( sK1
= ( sK0 @ X2 @ ( sK14 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_13])],[avatar_definition]) ).
thf(f198,plain,
( ! [X2: g] :
( sK1
= ( sK0 @ X2 @ ( sK14 @ X2 ) ) )
| ~ spl15_13 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f200,definition,
( spl15_14
<=> ! [X1: g] :
( sK1
= ( sK0 @ ( sK13 @ X1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_14])],[avatar_definition]) ).
thf(f201,plain,
( ! [X1: g] :
( sK1
= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ~ spl15_14 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f202,plain,
( spl15_13
| spl15_14 ),
inference(avatar_split_clause,[],[f147,f200,f197]) ).
thf(f213,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X0 @ X1 )
= ( sK0 @ X0 @ ( sK0 @ sK1 @ X1 ) ) )
| ~ spl15_6
| ~ spl15_7 ),
inference(constrained_superposition,[],[f169,f173]) ).
thf(f214,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ sK1 @ X1 )
= ( sK0 @ X0 @ ( sK0 @ ( sK14 @ X0 ) @ X1 ) ) )
| ~ spl15_6
| ~ spl15_13 ),
inference(constrained_superposition,[],[f169,f198]) ).
thf(f221,plain,
( ( ( sK0 @ sK8 @ ( sK0 @ sK7 @ sK6 ) )
!= ( sK0 @ sK8 @ ( sK0 @ sK7 @ sK6 ) ) )
| spl15_1
| ~ spl15_6 ),
inference(constrained_superposition,[],[f151,f169]) ).
thf(f222,plain,
( $false
| spl15_1
| ~ spl15_6 ),
inference(trivial_inequality_removal,[],[f221]) ).
thf(f223,plain,
( spl15_1
| ~ spl15_6 ),
inference(avatar_contradiction_clause,[],[f222]) ).
thf(f225,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X0 @ ( sK0 @ ( sK14 @ X0 ) @ X1 ) )
= X1 )
| ~ spl15_6
| ~ spl15_9
| ~ spl15_13 ),
inference(forward_demodulation,[],[f214,f181]) ).
thf(f227,plain,
( $false
| spl15_2
| ~ spl15_7 ),
inference(forward_subsumption_resolution,[],[f155,f173]) ).
thf(f228,plain,
( spl15_2
| ~ spl15_7 ),
inference(avatar_contradiction_clause,[],[f227]) ).
thf(f229,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ sK1 @ X1 )
= ( sK0 @ ( sK12 @ X0 ) @ ( sK0 @ X0 @ X1 ) ) )
| ~ spl15_6
| ~ spl15_12 ),
inference(constrained_superposition,[],[f169,f194]) ).
thf(f230,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ ( sK12 @ X0 ) @ ( sK0 @ X0 @ X1 ) )
= X1 )
| ~ spl15_6
| ~ spl15_9
| ~ spl15_12 ),
inference(forward_demodulation,[],[f229,f181]) ).
thf(f232,plain,
( ! [X0: g] :
( ( sK0 @ X0 @ sK1 )
= ( sK14 @ ( sK14 @ X0 ) ) )
| ~ spl15_6
| ~ spl15_9
| ~ spl15_13 ),
inference(constrained_superposition,[],[f225,f198]) ).
thf(f247,plain,
( ! [X0: g] :
( ( sK0 @ ( sK12 @ ( sK12 @ X0 ) ) @ sK1 )
= X0 )
| ~ spl15_6
| ~ spl15_9
| ~ spl15_12 ),
inference(constrained_superposition,[],[f230,f194]) ).
thf(f248,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X1 @ X0 )
= ( sK0 @ ( sK12 @ ( sK12 @ X1 ) ) @ X0 ) )
| ~ spl15_6
| ~ spl15_9
| ~ spl15_12 ),
inference(constrained_superposition,[],[f230,f230]) ).
thf(f251,plain,
( ! [X0: g] :
( ( sK0 @ X0 @ sK1 )
= X0 )
| ~ spl15_6
| ~ spl15_9
| ~ spl15_12 ),
inference(forward_demodulation,[],[f247,f248]) ).
thf(f252,plain,
( spl15_7
| ~ spl15_6
| ~ spl15_9
| ~ spl15_12 ),
inference(avatar_split_clause,[],[f251,f193,f180,f168,f172]) ).
thf(f253,plain,
( $false
| spl15_3
| ~ spl15_9 ),
inference(forward_subsumption_resolution,[],[f159,f181]) ).
thf(f254,plain,
( spl15_3
| ~ spl15_9 ),
inference(avatar_contradiction_clause,[],[f253]) ).
thf(f257,plain,
( ( sK1 != sK1 )
| ~ spl15_4
| ~ spl15_13 ),
inference(constrained_superposition,[],[f162,f198]) ).
thf(f259,plain,
( $false
| ~ spl15_4
| ~ spl15_13 ),
inference(trivial_inequality_removal,[],[f257]) ).
thf(f260,plain,
( ~ spl15_4
| ~ spl15_13 ),
inference(avatar_contradiction_clause,[],[f259]) ).
thf(f261,plain,
( ! [X0: g,X1: g] :
( sK1
!= ( sK0 @ X0 @ ( sK0 @ X1 @ sK2 ) ) )
| ~ spl15_5
| ~ spl15_6 ),
inference(constrained_superposition,[],[f165,f169]) ).
thf(f275,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ sK1 @ X1 )
= ( sK0 @ ( sK13 @ X0 ) @ ( sK0 @ X0 @ X1 ) ) )
| ~ spl15_6
| ~ spl15_14 ),
inference(constrained_superposition,[],[f169,f201]) ).
thf(f331,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ sK1 @ X1 )
= ( sK0 @ X0 @ ( sK0 @ ( sK10 @ X0 ) @ X1 ) ) )
| ~ spl15_6
| ~ spl15_10 ),
inference(constrained_superposition,[],[f169,f186]) ).
thf(f389,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ X0 )
= ( sK0 @ ( sK13 @ ( sK13 @ X0 ) ) @ sK1 ) )
| ~ spl15_6
| ~ spl15_14 ),
inference(constrained_superposition,[],[f275,f201]) ).
thf(f403,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ X0 )
= ( sK13 @ ( sK13 @ X0 ) ) )
| ~ spl15_6
| ~ spl15_7
| ~ spl15_14 ),
inference(forward_demodulation,[],[f389,f173]) ).
thf(f419,plain,
( ! [X0: g] :
( ( sK0 @ X0 @ sK1 )
= ( sK0 @ sK1 @ ( sK10 @ ( sK10 @ X0 ) ) ) )
| ~ spl15_6
| ~ spl15_10 ),
inference(constrained_superposition,[],[f331,f186]) ).
thf(f436,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ ( sK10 @ ( sK10 @ X0 ) ) )
= X0 )
| ~ spl15_6
| ~ spl15_7
| ~ spl15_10 ),
inference(forward_demodulation,[],[f419,f173]) ).
thf(f563,plain,
( ! [X0: g] :
( sK1
= ( sK0 @ ( sK0 @ sK1 @ X0 ) @ ( sK13 @ X0 ) ) )
| ~ spl15_6
| ~ spl15_7
| ~ spl15_14 ),
inference(constrained_superposition,[],[f201,f403]) ).
thf(f564,plain,
( ! [X0: g] :
( sK1
= ( sK0 @ sK1 @ ( sK0 @ X0 @ ( sK13 @ X0 ) ) ) )
| ~ spl15_6
| ~ spl15_7
| ~ spl15_14 ),
inference(forward_demodulation,[],[f563,f169]) ).
thf(f600,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X1 @ X0 )
= ( sK0 @ X1 @ ( sK10 @ ( sK10 @ X0 ) ) ) )
| ~ spl15_6
| ~ spl15_7
| ~ spl15_10 ),
inference(constrained_superposition,[],[f213,f436]) ).
thf(f746,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ X0 )
= X0 )
| ~ spl15_6
| ~ spl15_7
| ~ spl15_10 ),
inference(constrained_superposition,[],[f436,f600]) ).
thf(f747,plain,
( spl15_9
| ~ spl15_6
| ~ spl15_7
| ~ spl15_10 ),
inference(avatar_split_clause,[],[f746,f185,f172,f168,f180]) ).
thf(f754,plain,
( ! [X0: g] :
( ( sK14 @ ( sK14 @ X0 ) )
= X0 )
| ~ spl15_6
| ~ spl15_7
| ~ spl15_9
| ~ spl15_13 ),
inference(forward_demodulation,[],[f232,f173]) ).
thf(f822,plain,
( ! [X2: g,X0: g,X1: g] :
( sK1
!= ( sK0 @ X0 @ ( sK0 @ X1 @ ( sK0 @ X2 @ sK2 ) ) ) )
| ~ spl15_5
| ~ spl15_6 ),
inference(constrained_superposition,[],[f261,f169]) ).
thf(f828,plain,
( ! [X0: g] :
( sK1
= ( sK0 @ ( sK14 @ X0 ) @ X0 ) )
| ~ spl15_6
| ~ spl15_7
| ~ spl15_9
| ~ spl15_13 ),
inference(constrained_superposition,[],[f198,f754]) ).
thf(f1138,plain,
( ( sK1 != sK1 )
| ~ spl15_5
| ~ spl15_6
| ~ spl15_7
| ~ spl15_9
| ~ spl15_13 ),
inference(constrained_superposition,[],[f822,f828]) ).
thf(f1153,plain,
( $false
| ~ spl15_5
| ~ spl15_6
| ~ spl15_7
| ~ spl15_9
| ~ spl15_13 ),
inference(trivial_inequality_removal,[],[f1138]) ).
thf(f1154,plain,
( ~ spl15_5
| ~ spl15_6
| ~ spl15_7
| ~ spl15_9
| ~ spl15_13 ),
inference(avatar_contradiction_clause,[],[f1153]) ).
thf(f1185,plain,
( ! [X0: g] :
( sK1
= ( sK0 @ X0 @ ( sK13 @ X0 ) ) )
| ~ spl15_6
| ~ spl15_7
| ~ spl15_9
| ~ spl15_14 ),
inference(forward_demodulation,[],[f564,f181]) ).
thf(f1213,plain,
( ( sK1 != sK1 )
| ~ spl15_5
| ~ spl15_6
| ~ spl15_14 ),
inference(constrained_superposition,[],[f822,f201]) ).
thf(f1224,plain,
( $false
| ~ spl15_5
| ~ spl15_6
| ~ spl15_14 ),
inference(trivial_inequality_removal,[],[f1213]) ).
thf(f1225,plain,
( ~ spl15_5
| ~ spl15_6
| ~ spl15_14 ),
inference(avatar_contradiction_clause,[],[f1224]) ).
thf(f1303,plain,
( ( sK1 != sK1 )
| ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_9
| ~ spl15_14 ),
inference(constrained_superposition,[],[f162,f1185]) ).
thf(f1305,plain,
( $false
| ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_9
| ~ spl15_14 ),
inference(trivial_inequality_removal,[],[f1303]) ).
thf(f1306,plain,
( ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_9
| ~ spl15_14 ),
inference(avatar_contradiction_clause,[],[f1305]) ).
cnf(s1,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| spl15_4
| spl15_5 ),
inference(sat_conversion,[],[f166]) ).
cnf(s2,plain,
( spl15_6
| spl15_6 ),
inference(sat_conversion,[],[f170]) ).
cnf(s3,plain,
spl15_6,
inference(rat,[],[s2]) ).
cnf(s7,plain,
( spl15_7
| spl15_9 ),
inference(sat_conversion,[],[f183]) ).
cnf(s8,plain,
( spl15_9
| spl15_10 ),
inference(sat_conversion,[],[f187]) ).
cnf(s10,plain,
( spl15_7
| spl15_12 ),
inference(sat_conversion,[],[f195]) ).
cnf(s11,plain,
( spl15_13
| spl15_14 ),
inference(sat_conversion,[],[f202]) ).
cnf(s12,plain,
( spl15_1
| ~ spl15_6 ),
inference(sat_conversion,[],[f223]) ).
cnf(s13,plain,
( spl15_2
| ~ spl15_7 ),
inference(sat_conversion,[],[f228]) ).
cnf(s14,plain,
( ~ spl15_6
| spl15_7
| ~ spl15_9
| ~ spl15_12 ),
inference(sat_conversion,[],[f252]) ).
cnf(s15,plain,
( spl15_3
| ~ spl15_9 ),
inference(sat_conversion,[],[f254]) ).
cnf(s16,plain,
( ~ spl15_4
| ~ spl15_13 ),
inference(sat_conversion,[],[f260]) ).
cnf(s22,plain,
( ~ spl15_6
| ~ spl15_7
| spl15_9
| ~ spl15_10 ),
inference(sat_conversion,[],[f747]) ).
cnf(s26,plain,
( ~ spl15_5
| ~ spl15_6
| ~ spl15_7
| ~ spl15_9
| ~ spl15_13 ),
inference(sat_conversion,[],[f1154]) ).
cnf(s33,plain,
( ~ spl15_5
| ~ spl15_6
| ~ spl15_14 ),
inference(sat_conversion,[],[f1225]) ).
cnf(s38,plain,
( ~ spl15_4
| ~ spl15_6
| ~ spl15_7
| ~ spl15_9
| ~ spl15_14 ),
inference(sat_conversion,[],[f1306]) ).
cnf(s39,plain,
spl15_1,
inference(rat,[],[s12,s3]) ).
cnf(s40,plain,
( ~ spl15_2
| ~ spl15_3
| spl15_4
| spl15_5 ),
inference(rat,[],[s1,s39]) ).
cnf(s41,plain,
spl15_7,
inference(rat,[],[s14,s7,s10,s3]) ).
cnf(s42,plain,
spl15_2,
inference(rat,[],[s13,s41]) ).
cnf(s43,plain,
spl15_9,
inference(rat,[],[s22,s8,s3,s41]) ).
cnf(s44,plain,
spl15_3,
inference(rat,[],[s15,s43]) ).
cnf(s45,plain,
~ spl15_5,
inference(rat,[],[s11,s26,s33,s3,s41,s43]) ).
cnf(s46,plain,
spl15_4,
inference(rat,[],[s40,s44,s42,s45]) ).
cnf(s48,plain,
~ spl15_13,
inference(rat,[],[s16,s46]) ).
cnf(s49,plain,
~ spl15_14,
inference(rat,[],[s38,s43,s41,s3,s46]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s11,s49,s48]) ).
thf(f1310,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG273^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.17 % Computer : n020.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 17:37:19 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.33 % (1368398)Will run a generic schedule for satisfiability detection.
% 0.19/0.33 % (1368409)% WARNING: option uhcvi not known.
% 0.19/0.33 % (1368410)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1283470891:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.33 % (1368409)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3629374513:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.33 % (1368408)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2668528173_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.33 % (1368412)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2785565821:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.33 % (1368411)dis+10_1_sil=32000:sp=arity:random_seed=2012120727:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.33 % (1368412)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.33 % (1368409)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.33 % Exception at run slice level% (1368409)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.33
% 0.19/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.33 % (1368413)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2104955159:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.33 % (1368414)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=557168781:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.33 % (1368424)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=247832753:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.33 % Exception at run slice level
% 0.19/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.33 % (1368435)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3969308795:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.33 % (1368413) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1368398-1368413"...
% 0.19/0.33 % (1368412)Instruction limit reached!
% 0.19/0.33 % (1368412)------------------------------
% 0.19/0.33 % (1368412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (1368412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (1368412)CaDiCaL version: 2.1.3
% 0.19/0.33 % (1368412)Termination reason: Instruction limit
% 0.19/0.33 % (1368412)Termination phase: Saturation
% 0.19/0.33 % (1368412)Time elapsed: 0.057 s
% 0.19/0.33 % (1368412)Peak memory usage: 12 MB
% 0.19/0.33 % (1368412)Instructions burned: 117 (million)
% 0.19/0.33 % (1368411)Instruction limit reached!
% 0.19/0.33 % (1368411)------------------------------
% 0.19/0.33 % (1368411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (1368411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (1368411)CaDiCaL version: 2.1.3
% 0.19/0.33 % (1368411)Termination reason: Instruction limit
% 0.19/0.33 % (1368411)Termination phase: Saturation
% 0.19/0.33 % (1368411)Time elapsed: 0.059 s
% 0.19/0.33 % (1368411)Peak memory usage: 12 MB
% 0.19/0.33 % (1368411)Instructions burned: 104 (million)
% 0.19/0.33 % (1368413)...printing done.
% 0.19/0.33 % (1368413)Refutation found. Thanks to Tanya!
% 0.19/0.33 % SZS status Theorem for theBenchmark
% 0.19/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.33 % (1368413)------------------------------
% 0.19/0.33 % (1368413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (1368413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (1368413)CaDiCaL version: 2.1.3
% 0.19/0.33 % (1368413)Termination reason: Refutation
% 0.19/0.33 % (1368413)Time elapsed: 0.059 s
% 0.19/0.33 % (1368413)Peak memory usage: 13 MB
% 0.19/0.33 % (1368413)Instructions burned: 112 (million)
% 0.19/0.33 % (1368398)Success in time 0.11 s
% 0.19/0.33 % Vampire exiting
%------------------------------------------------------------------------------