TSTP Solution File: SEV210^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV210^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:15:26 EDT 2024
% Result : Timeout 286.17s 41.27s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 68
% Syntax : Number of formulae : 302 ( 6 unt; 37 typ; 0 def)
% Number of atoms : 5449 ( 967 equ; 0 cnn)
% Maximal formula atoms : 45 ( 20 avg)
% Number of connectives : 1603 ( 441 ~; 792 |; 281 &; 0 @)
% ( 23 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 298 ( 297 >; 1 *; 0 +; 0 <<)
% Number of symbols : 62 ( 59 usr; 30 con; 0-6 aty)
% Number of variables : 590 ( 0 ^ 386 !; 198 ?; 590 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
v: a ).
thf(func_def_2,type,
u: a ).
thf(func_def_3,type,
cP: a > a > a ).
thf(func_def_4,type,
y: a ).
thf(func_def_5,type,
x: a ).
thf(func_def_6,type,
cZ: a ).
thf(func_def_10,type,
sK0: a > a > a > $o ).
thf(func_def_11,type,
sK1: ( a > a > a > $o ) > a ).
thf(func_def_12,type,
sK2: ( a > a > a > $o ) > a ).
thf(func_def_13,type,
sK3: ( a > a > a > $o ) > a ).
thf(func_def_14,type,
sK4: ( a > a > a > $o ) > a ).
thf(func_def_15,type,
sK5: ( a > a > a > $o ) > a ).
thf(func_def_16,type,
sK6: ( a > a > a > $o ) > a ).
thf(func_def_17,type,
sK7: ( a > a > a > $o ) > a ).
thf(func_def_18,type,
sK8: ( a > a > a > $o ) > a ).
thf(func_def_19,type,
sK9: ( a > a > a > $o ) > a ).
thf(func_def_20,type,
sK10: ( a > a > a > $o ) > a ).
thf(func_def_21,type,
sK11: ( a > a > a > $o ) > a ).
thf(func_def_22,type,
sK12: ( a > a > a > $o ) > a ).
thf(func_def_23,type,
sK13: ( a > a > a > $o ) > a ).
thf(func_def_24,type,
sK14: ( a > a > a > $o ) > a ).
thf(func_def_25,type,
sK15: ( a > a > a > $o ) > a ).
thf(func_def_26,type,
sK16: ( a > a > a > $o ) > a ).
thf(func_def_27,type,
sK17: ( a > a > a > $o ) > a ).
thf(func_def_28,type,
sK18: ( a > a > a > $o ) > a ).
thf(func_def_29,type,
sK19: ( a > $o ) > a ).
thf(func_def_30,type,
sK20: ( a > $o ) > a ).
thf(func_def_32,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_33,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_34,type,
vAND: $o > $o > $o ).
thf(func_def_35,type,
vOR: $o > $o > $o ).
thf(func_def_36,type,
vIMP: $o > $o > $o ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f22932,plain,
$false,
inference(avatar_sat_refutation,[],[f246,f268,f1072,f1092,f1106,f1124,f9215,f9668,f9860,f9895,f12435,f12474,f12478,f12966,f13544,f18579,f18846,f18902,f19120,f19431,f19437,f19836,f21121,f21131,f21137,f22706,f22807,f22811,f22815,f22821,f22833,f22854,f22901,f22912]) ).
thf(f22912,plain,
( spl21_19
| spl21_137
| spl21_1990
| ~ spl21_425
| ~ spl21_470 ),
inference(avatar_split_clause,[],[f22911,f5198,f4754,f20986,f1078,f347]) ).
thf(f347,plain,
( spl21_19
<=> ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_19])]) ).
thf(f1078,plain,
( spl21_137
<=> ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_137])]) ).
thf(f20986,plain,
( spl21_1990
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_1990])]) ).
thf(f4754,plain,
( spl21_425
<=> ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_425])]) ).
thf(f5198,plain,
( spl21_470
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_470])]) ).
thf(f22911,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_425
| ~ spl21_470 ),
inference(trivial_inequality_removal,[],[f22910]) ).
thf(f22910,plain,
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_425
| ~ spl21_470 ),
inference(forward_demodulation,[],[f18371,f4755]) ).
thf(f4755,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ~ spl21_425 ),
inference(avatar_component_clause,[],[f4754]) ).
thf(f18371,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_470 ),
inference(superposition,[],[f5199,f35]) ).
thf(f35,plain,
! [X20: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f17,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)) )
& ! [X1: a,X2: a,X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X1),X2),X3) )
| ( ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X5),X7),X9) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X4),X6),X8) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9) != X3 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7) != X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X5) != X1 ) )
& ( ( X1 != X3 )
| ( cZ != X2 ) )
& ( ( X2 != X3 )
| ( cZ != X1 ) ) ) )
& ! [X10: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,y),v),v) )
| ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10)) )
& ( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK5,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK7,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,X10)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK4,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,X10)) )
& ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,X10)) )
& ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK7,X10)) )
& ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK4,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK5,X10)) ) )
| ( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10) )
& ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) ) )
| ( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10) )
& ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) ) ) ) ) )
& ! [X20: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20)) )
& ( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,X20)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,X20)) )
& ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,X20)) )
& ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,X20)) )
& ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,X20)) ) )
| ( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) )
& ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) ) )
| ( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) )
& ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) ) ) ) ) )
& ! [X30: a > $o] :
( ! [X31: a] : ( $true = vAPP(a,$o,X30,X31) )
| ( ( $true != vAPP(a,$o,X30,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,$o),a,sK19,X30)),vAPP(sTfun(a,$o),a,sK20,X30))) )
& ( $true = vAPP(a,$o,X30,vAPP(sTfun(a,$o),a,sK20,X30)) )
& ( $true = vAPP(a,$o,X30,vAPP(sTfun(a,$o),a,sK19,X30)) ) )
| ( $true != vAPP(a,$o,X30,cZ) ) )
& ! [X34: a,X35: a,X36: a,X37: a] :
( ( ( X36 = X37 )
& ( X34 = X35 ) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X34),X36) != vAPP(a,a,vAPP(a,sTfun(a,a),cP,X35),X37) ) )
& ! [X38: a,X39: a] : ( cZ != vAPP(a,a,vAPP(a,sTfun(a,a),cP,X38),X39) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17,sK18,sK19,sK20])],[f10,f16,f15,f14,f13,f12,f11]) ).
thf(f11,plain,
( ? [X0: a > a > a > $o] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)) )
& ! [X1: a,X2: a,X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,X1),X2),X3) )
| ( ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,X5),X7),X9) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,X4),X6),X8) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9) != X3 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7) != X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X5) != X1 ) )
& ( ( X1 != X3 )
| ( cZ != X2 ) )
& ( ( X2 != X3 )
| ( cZ != X1 ) ) ) ) )
=> ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)) )
& ! [X3: a,X2: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X1),X2),X3) )
| ( ! [X9: a,X8: a,X7: a,X6: a,X5: a,X4: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X5),X7),X9) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X4),X6),X8) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9) != X3 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7) != X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X5) != X1 ) )
& ( ( X1 != X3 )
| ( cZ != X2 ) )
& ( ( X2 != X3 )
| ( cZ != X1 ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
! [X10: a > a > a > $o] :
( ? [X11: a,X12: a,X13: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X11),X12),X13) )
& ( ? [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X15),X17),X19) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X14),X16),X18) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X18),X19) = X13 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17) = X12 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X14),X15) = X11 ) )
| ( ( X11 = X13 )
& ( cZ = X12 ) )
| ( ( X12 = X13 )
& ( cZ = X11 ) ) ) )
=> ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10)) )
& ( ? [X19: a,X18: a,X17: a,X16: a,X15: a,X14: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X15),X17),X19) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X14),X16),X18) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X18),X19) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X14),X15) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) ) )
| ( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10) )
& ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) ) )
| ( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10) )
& ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
! [X10: a > a > a > $o] :
( ? [X19: a,X18: a,X17: a,X16: a,X15: a,X14: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X15),X17),X19) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X14),X16),X18) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X18),X19) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X14),X15) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) ) )
=> ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK5,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK7,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,X10)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK4,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,X10)) )
& ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,X10)) )
& ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK7,X10)) )
& ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK4,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK5,X10)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
! [X20: a > a > a > $o] :
( ? [X21: a,X22: a,X23: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X21),X22),X23) )
& ( ? [X24: a,X25: a,X26: a,X27: a,X28: a,X29: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X25),X27),X29) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X24),X26),X28) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X28),X29) = X23 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X26),X27) = X22 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X24),X25) = X21 ) )
| ( ( X21 = X23 )
& ( cZ = X22 ) )
| ( ( X22 = X23 )
& ( cZ = X21 ) ) ) )
=> ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20)) )
& ( ? [X29: a,X28: a,X27: a,X26: a,X25: a,X24: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X25),X27),X29) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X24),X26),X28) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X28),X29) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X26),X27) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X24),X25) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) ) )
| ( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) )
& ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) ) )
| ( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) )
& ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f15,plain,
! [X20: a > a > a > $o] :
( ? [X29: a,X28: a,X27: a,X26: a,X25: a,X24: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X25),X27),X29) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X24),X26),X28) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X28),X29) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X26),X27) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X24),X25) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) ) )
=> ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,X20)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,X20)) )
& ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,X20)) )
& ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,X20)) )
& ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,X20)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f16,plain,
! [X30: a > $o] :
( ? [X32: a,X33: a] :
( ( $true != vAPP(a,$o,X30,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X32),X33)) )
& ( $true = vAPP(a,$o,X30,X33) )
& ( $true = vAPP(a,$o,X30,X32) ) )
=> ( ( $true != vAPP(a,$o,X30,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,$o),a,sK19,X30)),vAPP(sTfun(a,$o),a,sK20,X30))) )
& ( $true = vAPP(a,$o,X30,vAPP(sTfun(a,$o),a,sK20,X30)) )
& ( $true = vAPP(a,$o,X30,vAPP(sTfun(a,$o),a,sK19,X30)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
( ? [X0: a > a > a > $o] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)) )
& ! [X1: a,X2: a,X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,X1),X2),X3) )
| ( ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,X5),X7),X9) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,X4),X6),X8) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9) != X3 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7) != X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X5) != X1 ) )
& ( ( X1 != X3 )
| ( cZ != X2 ) )
& ( ( X2 != X3 )
| ( cZ != X1 ) ) ) ) )
& ! [X10: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,y),v),v) )
| ? [X11: a,X12: a,X13: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X11),X12),X13) )
& ( ? [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X15),X17),X19) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X14),X16),X18) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X18),X19) = X13 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17) = X12 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X14),X15) = X11 ) )
| ( ( X11 = X13 )
& ( cZ = X12 ) )
| ( ( X12 = X13 )
& ( cZ = X11 ) ) ) ) )
& ! [X20: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ? [X21: a,X22: a,X23: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X21),X22),X23) )
& ( ? [X24: a,X25: a,X26: a,X27: a,X28: a,X29: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X25),X27),X29) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X24),X26),X28) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X28),X29) = X23 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X26),X27) = X22 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X24),X25) = X21 ) )
| ( ( X21 = X23 )
& ( cZ = X22 ) )
| ( ( X22 = X23 )
& ( cZ = X21 ) ) ) ) )
& ! [X30: a > $o] :
( ! [X31: a] : ( $true = vAPP(a,$o,X30,X31) )
| ? [X32: a,X33: a] :
( ( $true != vAPP(a,$o,X30,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X32),X33)) )
& ( $true = vAPP(a,$o,X30,X33) )
& ( $true = vAPP(a,$o,X30,X32) ) )
| ( $true != vAPP(a,$o,X30,cZ) ) )
& ! [X34: a,X35: a,X36: a,X37: a] :
( ( ( X36 = X37 )
& ( X34 = X35 ) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X34),X36) != vAPP(a,a,vAPP(a,sTfun(a,a),cP,X35),X37) ) )
& ! [X38: a,X39: a] : ( cZ != vAPP(a,a,vAPP(a,sTfun(a,a),cP,X38),X39) ) ),
inference(rectify,[],[f9]) ).
thf(f9,plain,
( ? [X30: a > a > a > $o] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)) )
& ! [X31: a,X32: a,X33: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X31),X32),X33) )
| ( ! [X34: a,X35: a,X36: a,X37: a,X38: a,X39: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X35),X37),X39) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X34),X36),X38) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X38),X39) != X33 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X36),X37) != X32 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X34),X35) != X31 ) )
& ( ( X31 != X33 )
| ( cZ != X32 ) )
& ( ( X32 != X33 )
| ( cZ != X31 ) ) ) ) )
& ! [X20: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,y),v),v) )
| ? [X21: a,X22: a,X23: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X21),X22),X23) )
& ( ? [X24: a,X25: a,X26: a,X27: a,X28: a,X29: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X25),X27),X29) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X24),X26),X28) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X28),X29) = X23 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X26),X27) = X22 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X24),X25) = X21 ) )
| ( ( X21 = X23 )
& ( cZ = X22 ) )
| ( ( X22 = X23 )
& ( cZ = X21 ) ) ) ) )
& ! [X10: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,x),u),u) )
| ? [X11: a,X12: a,X13: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X11),X12),X13) )
& ( ? [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X15),X17),X19) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X14),X16),X18) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X18),X19) = X13 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17) = X12 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X14),X15) = X11 ) )
| ( ( X11 = X13 )
& ( cZ = X12 ) )
| ( ( X12 = X13 )
& ( cZ = X11 ) ) ) ) )
& ! [X0: a > $o] :
( ! [X3: a] : ( $true = vAPP(a,$o,X0,X3) )
| ? [X1: a,X2: a] :
( ( $true != vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X2)) )
& ( $true = vAPP(a,$o,X0,X2) )
& ( $true = vAPP(a,$o,X0,X1) ) )
| ( $true != vAPP(a,$o,X0,cZ) ) )
& ! [X4: a,X5: a,X6: a,X7: a] :
( ( ( X6 = X7 )
& ( X4 = X5 ) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X6) != vAPP(a,a,vAPP(a,sTfun(a,a),cP,X5),X7) ) )
& ! [X8: a,X9: a] : ( cZ != vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9) ) ),
inference(flattening,[],[f8]) ).
thf(f8,plain,
( ? [X30: a > a > a > $o] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)) )
& ! [X31: a,X32: a,X33: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X31),X32),X33) )
| ( ! [X34: a,X35: a,X36: a,X37: a,X38: a,X39: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X35),X37),X39) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X34),X36),X38) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X38),X39) != X33 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X36),X37) != X32 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X34),X35) != X31 ) )
& ( ( X31 != X33 )
| ( cZ != X32 ) )
& ( ( X32 != X33 )
| ( cZ != X31 ) ) ) ) )
& ! [X20: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,y),v),v) )
| ? [X21: a,X22: a,X23: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X21),X22),X23) )
& ( ? [X24: a,X25: a,X26: a,X27: a,X28: a,X29: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X25),X27),X29) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X24),X26),X28) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X28),X29) = X23 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X26),X27) = X22 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X24),X25) = X21 ) )
| ( ( X21 = X23 )
& ( cZ = X22 ) )
| ( ( X22 = X23 )
& ( cZ = X21 ) ) ) ) )
& ! [X10: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,x),u),u) )
| ? [X11: a,X12: a,X13: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X11),X12),X13) )
& ( ? [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X15),X17),X19) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X14),X16),X18) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X18),X19) = X13 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17) = X12 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X14),X15) = X11 ) )
| ( ( X11 = X13 )
& ( cZ = X12 ) )
| ( ( X12 = X13 )
& ( cZ = X11 ) ) ) ) )
& ! [X0: a > $o] :
( ! [X3: a] : ( $true = vAPP(a,$o,X0,X3) )
| ? [X1: a,X2: a] :
( ( $true != vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X2)) )
& ( $true = vAPP(a,$o,X0,X2) )
& ( $true = vAPP(a,$o,X0,X1) ) )
| ( $true != vAPP(a,$o,X0,cZ) ) )
& ! [X4: a,X5: a,X6: a,X7: a] :
( ( ( X6 = X7 )
& ( X4 = X5 ) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X6) != vAPP(a,a,vAPP(a,sTfun(a,a),cP,X5),X7) ) )
& ! [X8: a,X9: a] : ( cZ != vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
~ ( ( ! [X0: a > $o] :
( ( ! [X1: a,X2: a] :
( ( ( $true = vAPP(a,$o,X0,X2) )
& ( $true = vAPP(a,$o,X0,X1) ) )
=> ( $true = vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X2)) ) )
& ( $true = vAPP(a,$o,X0,cZ) ) )
=> ! [X3: a] : ( $true = vAPP(a,$o,X0,X3) ) )
& ! [X4: a,X5: a,X6: a,X7: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X6) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,X5),X7) )
=> ( ( X6 = X7 )
& ( X4 = X5 ) ) )
& ! [X8: a,X9: a] : ( cZ != vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9) ) )
=> ( ! [X10: a > a > a > $o] :
( ! [X11: a,X12: a,X13: a] :
( ( ? [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X15),X17),X19) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X14),X16),X18) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X18),X19) = X13 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17) = X12 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X14),X15) = X11 ) )
| ( ( X11 = X13 )
& ( cZ = X12 ) )
| ( ( X12 = X13 )
& ( cZ = X11 ) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X11),X12),X13) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,x),u),u) ) )
=> ( ! [X20: a > a > a > $o] :
( ! [X21: a,X22: a,X23: a] :
( ( ? [X24: a,X25: a,X26: a,X27: a,X28: a,X29: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X25),X27),X29) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X24),X26),X28) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X28),X29) = X23 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X26),X27) = X22 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X24),X25) = X21 ) )
| ( ( X21 = X23 )
& ( cZ = X22 ) )
| ( ( X22 = X23 )
& ( cZ = X21 ) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X21),X22),X23) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,y),v),v) ) )
=> ! [X30: a > a > a > $o] :
( ! [X31: a,X32: a,X33: a] :
( ( ? [X34: a,X35: a,X36: a,X37: a,X38: a,X39: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X35),X37),X39) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X34),X36),X38) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X38),X39) = X33 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X36),X37) = X32 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X34),X35) = X31 ) )
| ( ( X31 = X33 )
& ( cZ = X32 ) )
| ( ( X32 = X33 )
& ( cZ = X31 ) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X31),X32),X33) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)) ) ) ) ) ),
inference(true_and_false_elimination,[],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: a > $o] :
( ( ! [X1: a,X2: a] :
( ( ( $true = vAPP(a,$o,X0,X2) )
& ( $true = vAPP(a,$o,X0,X1) ) )
=> ( $true = vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X2)) ) )
& ( $true = vAPP(a,$o,X0,cZ) ) )
=> ! [X3: a] : ( $true = vAPP(a,$o,X0,X3) ) )
& ! [X4: a,X5: a,X6: a,X7: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X6) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,X5),X7) )
=> ( ( X6 = X7 )
& ( X4 = X5 ) ) )
& ! [X8: a,X9: a] : ( cZ != vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9) ) )
=> ( ! [X10: a > a > a > $o] :
( ( ! [X11: a,X12: a,X13: a] :
( ( ? [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X15),X17),X19) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X14),X16),X18) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X18),X19) = X13 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17) = X12 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X14),X15) = X11 ) )
| ( ( X11 = X13 )
& ( cZ = X12 ) )
| ( ( X12 = X13 )
& ( cZ = X11 ) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X11),X12),X13) ) )
& $true )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,x),u),u) ) )
=> ( ! [X20: a > a > a > $o] :
( ( ! [X21: a,X22: a,X23: a] :
( ( ? [X24: a,X25: a,X26: a,X27: a,X28: a,X29: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X25),X27),X29) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X24),X26),X28) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X28),X29) = X23 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X26),X27) = X22 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X24),X25) = X21 ) )
| ( ( X21 = X23 )
& ( cZ = X22 ) )
| ( ( X22 = X23 )
& ( cZ = X21 ) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X21),X22),X23) ) )
& $true )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,y),v),v) ) )
=> ! [X30: a > a > a > $o] :
( ( ! [X31: a,X32: a,X33: a] :
( ( ? [X34: a,X35: a,X36: a,X37: a,X38: a,X39: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X35),X37),X39) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X34),X36),X38) )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X38),X39) = X33 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X36),X37) = X32 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X34),X35) = X31 ) )
| ( ( X31 = X33 )
& ( cZ = X32 ) )
| ( ( X32 = X33 )
& ( cZ = X31 ) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X31),X32),X33) ) )
& $true )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: a > $o] :
( ( ! [X1: a,X2: a] :
( ( vAPP(a,$o,X0,X2)
& vAPP(a,$o,X0,X1) )
=> vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X2)) )
& vAPP(a,$o,X0,cZ) )
=> ! [X3: a] : vAPP(a,$o,X0,X3) )
& ! [X4: a,X5: a,X6: a,X7: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X6) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,X5),X7) )
=> ( ( X6 = X7 )
& ( X4 = X5 ) ) )
& ! [X8: a,X9: a] : ( cZ != vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9) ) )
=> ( ! [X10: a > a > a > $o] :
( ( ! [X11: a,X12: a,X13: a] :
( ( ? [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X15),X17),X19)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X14),X16),X18)
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X18),X19) = X13 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17) = X12 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X14),X15) = X11 ) )
| ( ( X11 = X13 )
& ( cZ = X12 ) )
| ( ( X12 = X13 )
& ( cZ = X11 ) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,X11),X12),X13) )
& $true )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,x),u),u) )
=> ( ! [X20: a > a > a > $o] :
( ( ! [X21: a,X22: a,X23: a] :
( ( ? [X24: a,X25: a,X26: a,X27: a,X28: a,X29: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X25),X27),X29)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X24),X26),X28)
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X28),X29) = X23 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X26),X27) = X22 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X24),X25) = X21 ) )
| ( ( X21 = X23 )
& ( cZ = X22 ) )
| ( ( X22 = X23 )
& ( cZ = X21 ) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,X21),X22),X23) )
& $true )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,y),v),v) )
=> ! [X30: a > a > a > $o] :
( ( ! [X31: a,X32: a,X33: a] :
( ( ? [X34: a,X35: a,X36: a,X37: a,X38: a,X39: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X35),X37),X39)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X34),X36),X38)
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X38),X39) = X33 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X36),X37) = X32 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X34),X35) = X31 ) )
| ( ( X31 = X33 )
& ( cZ = X32 ) )
| ( ( X32 = X33 )
& ( cZ = X31 ) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,X31),X32),X33) )
& $true )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X30,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X4: a > $o] :
( ( ! [X0: a,X1: a] :
( ( vAPP(a,$o,X4,X1)
& vAPP(a,$o,X4,X0) )
=> vAPP(a,$o,X4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)) )
& vAPP(a,$o,X4,cZ) )
=> ! [X0: a] : vAPP(a,$o,X4,X0) )
& ! [X0: a,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X3) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) )
& ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1) != cZ ) )
=> ( ! [X5: a > a > a > $o] :
( ( ! [X6: a,X7: a,X8: a] :
( ( ? [X9: a,X10: a,X11: a,X12: a,X13: a,X14: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X10),X12),X14)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X9),X11),X13)
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X13),X14) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X11),X12) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X9),X10) = X6 ) )
| ( ( X6 = X8 )
& ( cZ = X7 ) )
| ( ( X7 = X8 )
& ( cZ = X6 ) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X6),X7),X8) )
& $true )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,x),u),u) )
=> ( ! [X5: a > a > a > $o] :
( ( ! [X6: a,X7: a,X8: a] :
( ( ? [X9: a,X10: a,X11: a,X12: a,X13: a,X14: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X10),X12),X14)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X9),X11),X13)
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X13),X14) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X11),X12) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X9),X10) = X6 ) )
| ( ( X6 = X8 )
& ( cZ = X7 ) )
| ( ( X7 = X8 )
& ( cZ = X6 ) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X6),X7),X8) )
& $true )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,y),v),v) )
=> ! [X5: a > a > a > $o] :
( ( ! [X6: a,X7: a,X8: a] :
( ( ? [X9: a,X10: a,X11: a,X12: a,X13: a,X14: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X10),X12),X14)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X9),X11),X13)
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X13),X14) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X11),X12) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X9),X10) = X6 ) )
| ( ( X6 = X8 )
& ( cZ = X7 ) )
| ( ( X7 = X8 )
& ( cZ = X6 ) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X6),X7),X8) )
& $true )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ! [X4: a > $o] :
( ( ! [X0: a,X1: a] :
( ( vAPP(a,$o,X4,X1)
& vAPP(a,$o,X4,X0) )
=> vAPP(a,$o,X4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)) )
& vAPP(a,$o,X4,cZ) )
=> ! [X0: a] : vAPP(a,$o,X4,X0) )
& ! [X0: a,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X3) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) )
& ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1) != cZ ) )
=> ( ! [X5: a > a > a > $o] :
( ( ! [X6: a,X7: a,X8: a] :
( ( ? [X9: a,X10: a,X11: a,X12: a,X13: a,X14: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X10),X12),X14)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X9),X11),X13)
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X13),X14) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X11),X12) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X9),X10) = X6 ) )
| ( ( X6 = X8 )
& ( cZ = X7 ) )
| ( ( X7 = X8 )
& ( cZ = X6 ) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X6),X7),X8) )
& $true )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,x),u),u) )
=> ( ! [X5: a > a > a > $o] :
( ( ! [X6: a,X7: a,X8: a] :
( ( ? [X9: a,X10: a,X11: a,X12: a,X13: a,X14: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X10),X12),X14)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X9),X11),X13)
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X13),X14) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X11),X12) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X9),X10) = X6 ) )
| ( ( X6 = X8 )
& ( cZ = X7 ) )
| ( ( X7 = X8 )
& ( cZ = X6 ) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X6),X7),X8) )
& $true )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,y),v),v) )
=> ! [X5: a > a > a > $o] :
( ( ! [X6: a,X7: a,X8: a] :
( ( ? [X9: a,X10: a,X11: a,X12: a,X13: a,X14: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X10),X12),X14)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X9),X11),X13)
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X13),X14) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X11),X12) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X9),X10) = X6 ) )
| ( ( X6 = X8 )
& ( cZ = X7 ) )
| ( ( X7 = X8 )
& ( cZ = X6 ) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,X6),X7),X8) )
& $true )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_LEM1E_pme) ).
thf(f5199,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ~ spl21_470 ),
inference(avatar_component_clause,[],[f5198]) ).
thf(f22901,plain,
( spl21_1990
| spl21_9
| spl21_10
| ~ spl21_425
| ~ spl21_470 ),
inference(avatar_split_clause,[],[f22900,f5198,f4754,f238,f235,f20986]) ).
thf(f235,plain,
( spl21_9
<=> ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_9])]) ).
thf(f238,plain,
( spl21_10
<=> ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_10])]) ).
thf(f22900,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| spl21_9
| spl21_10
| ~ spl21_425
| ~ spl21_470 ),
inference(trivial_inequality_removal,[],[f22899]) ).
thf(f22899,plain,
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| spl21_9
| spl21_10
| ~ spl21_425
| ~ spl21_470 ),
inference(forward_demodulation,[],[f22898,f4755]) ).
thf(f22898,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| spl21_9
| spl21_10
| ~ spl21_470 ),
inference(subsumption_resolution,[],[f22897,f8117]) ).
thf(f8117,plain,
( ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) )
| spl21_9 ),
inference(avatar_component_clause,[],[f235]) ).
thf(f22897,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) )
| spl21_10
| ~ spl21_470 ),
inference(subsumption_resolution,[],[f18374,f9894]) ).
thf(f9894,plain,
( ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| spl21_10 ),
inference(avatar_component_clause,[],[f238]) ).
thf(f18374,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) )
| ~ spl21_470 ),
inference(superposition,[],[f5199,f32]) ).
thf(f32,plain,
! [X20: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f22854,plain,
( spl21_470
| spl21_9
| spl21_10
| ~ spl21_163
| ~ spl21_425 ),
inference(avatar_split_clause,[],[f22853,f4754,f2490,f238,f235,f5198]) ).
thf(f2490,plain,
( spl21_163
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,sK0)),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_163])]) ).
thf(f22853,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| spl21_9
| spl21_10
| ~ spl21_163
| ~ spl21_425 ),
inference(trivial_inequality_removal,[],[f22852]) ).
thf(f22852,plain,
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| spl21_9
| spl21_10
| ~ spl21_163
| ~ spl21_425 ),
inference(forward_demodulation,[],[f19299,f4755]) ).
thf(f19299,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| spl21_9
| spl21_10
| ~ spl21_163 ),
inference(subsumption_resolution,[],[f19298,f8117]) ).
thf(f19298,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) )
| spl21_10
| ~ spl21_163 ),
inference(subsumption_resolution,[],[f5184,f9894]) ).
thf(f5184,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) )
| ~ spl21_163 ),
inference(trivial_inequality_removal,[],[f5166]) ).
thf(f5166,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) )
| ~ spl21_163 ),
inference(superposition,[],[f2491,f40]) ).
thf(f40,plain,
! [X20: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f2491,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,sK0)),X0),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X1)) ) )
| ~ spl21_163 ),
inference(avatar_component_clause,[],[f2490]) ).
thf(f22833,plain,
( spl21_19
| spl21_137
| spl21_470
| ~ spl21_163
| ~ spl21_425 ),
inference(avatar_split_clause,[],[f22832,f4754,f2490,f5198,f1078,f347]) ).
thf(f22832,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_163
| ~ spl21_425 ),
inference(trivial_inequality_removal,[],[f22831]) ).
thf(f22831,plain,
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_163
| ~ spl21_425 ),
inference(forward_demodulation,[],[f5187,f4755]) ).
thf(f5187,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_163 ),
inference(trivial_inequality_removal,[],[f5163]) ).
thf(f5163,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_163 ),
inference(superposition,[],[f2491,f43]) ).
thf(f43,plain,
! [X20: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f22821,plain,
( spl21_19
| spl21_137
| spl21_163
| ~ spl21_12
| ~ spl21_425 ),
inference(avatar_split_clause,[],[f22820,f4754,f244,f2490,f1078,f347]) ).
thf(f244,plain,
( spl21_12
<=> ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_12])]) ).
thf(f22820,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,sK0)),X0),X1) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) ) )
| ~ spl21_12
| ~ spl21_425 ),
inference(trivial_inequality_removal,[],[f22819]) ).
thf(f22819,plain,
( ! [X0: a,X1: a] :
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,sK0)),X0),X1) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) ) )
| ~ spl21_12
| ~ spl21_425 ),
inference(forward_demodulation,[],[f22510,f4755]) ).
thf(f22510,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,sK0)),X0),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) ) )
| ~ spl21_12 ),
inference(superposition,[],[f245,f27]) ).
thf(f27,plain,
! [X20: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f245,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) ) )
| ~ spl21_12 ),
inference(avatar_component_clause,[],[f244]) ).
thf(f22815,plain,
( spl21_9
| spl21_163
| spl21_10
| ~ spl21_12
| ~ spl21_425 ),
inference(avatar_split_clause,[],[f22814,f4754,f244,f238,f2490,f235]) ).
thf(f22814,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,sK0)),X0),X1) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) ) )
| spl21_10
| ~ spl21_12
| ~ spl21_425 ),
inference(trivial_inequality_removal,[],[f22813]) ).
thf(f22813,plain,
( ! [X0: a,X1: a] :
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,sK0)),X0),X1) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) ) )
| spl21_10
| ~ spl21_12
| ~ spl21_425 ),
inference(forward_demodulation,[],[f22812,f4755]) ).
thf(f22812,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,sK0)),X0),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) ) )
| spl21_10
| ~ spl21_12 ),
inference(subsumption_resolution,[],[f22513,f9894]) ).
thf(f22513,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,sK0)),X0),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) ) )
| ~ spl21_12 ),
inference(superposition,[],[f245,f24]) ).
thf(f24,plain,
! [X20: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f22811,plain,
( spl21_19
| spl21_163
| spl21_10
| ~ spl21_12
| ~ spl21_425 ),
inference(avatar_split_clause,[],[f22810,f4754,f244,f238,f2490,f347]) ).
thf(f22810,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,sK0)),X0),X1) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) ) )
| spl21_10
| ~ spl21_12
| ~ spl21_425 ),
inference(trivial_inequality_removal,[],[f22809]) ).
thf(f22809,plain,
( ! [X0: a,X1: a] :
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,sK0)),X0),X1) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) ) )
| spl21_10
| ~ spl21_12
| ~ spl21_425 ),
inference(forward_demodulation,[],[f22808,f4755]) ).
thf(f22808,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,sK0)),X0),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) ) )
| spl21_10
| ~ spl21_12 ),
inference(subsumption_resolution,[],[f22512,f9894]) ).
thf(f22512,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,sK0)),X0),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) ) )
| ~ spl21_12 ),
inference(superposition,[],[f245,f25]) ).
thf(f25,plain,
! [X20: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f22807,plain,
( spl21_19
| spl21_470
| spl21_10
| ~ spl21_163
| ~ spl21_425 ),
inference(avatar_split_clause,[],[f22806,f4754,f2490,f238,f5198,f347]) ).
thf(f22806,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| spl21_10
| ~ spl21_163
| ~ spl21_425 ),
inference(trivial_inequality_removal,[],[f22805]) ).
thf(f22805,plain,
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| spl21_10
| ~ spl21_163
| ~ spl21_425 ),
inference(forward_demodulation,[],[f22804,f4755]) ).
thf(f22804,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| spl21_10
| ~ spl21_163 ),
inference(subsumption_resolution,[],[f21562,f9894]) ).
thf(f21562,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_163 ),
inference(trivial_inequality_removal,[],[f5165]) ).
thf(f5165,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,sK0))) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_163 ),
inference(superposition,[],[f2491,f41]) ).
thf(f41,plain,
! [X20: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK14,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f22706,plain,
( spl21_19
| ~ spl21_9
| spl21_10
| ~ spl21_425 ),
inference(avatar_split_clause,[],[f22705,f4754,f238,f235,f347]) ).
thf(f22705,plain,
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_9
| spl21_10
| ~ spl21_425 ),
inference(subsumption_resolution,[],[f22685,f9894]) ).
thf(f22685,plain,
( ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_9
| ~ spl21_425 ),
inference(trivial_inequality_removal,[],[f22684]) ).
thf(f22684,plain,
( ( $true = $false )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_9
| ~ spl21_425 ),
inference(forward_demodulation,[],[f21841,f4755]) ).
thf(f21841,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_9 ),
inference(trivial_inequality_removal,[],[f21676]) ).
thf(f21676,plain,
( ( cZ != cZ )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_9 ),
inference(superposition,[],[f275,f236]) ).
thf(f236,plain,
( ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) )
| ~ spl21_9 ),
inference(avatar_component_clause,[],[f235]) ).
thf(f275,plain,
! [X0: a > a > a > $o] :
( ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X0) ) ),
inference(superposition,[],[f18,f25]) ).
thf(f18,plain,
! [X38: a,X39: a] : ( cZ != vAPP(a,a,vAPP(a,sTfun(a,a),cP,X38),X39) ),
inference(cnf_transformation,[],[f17]) ).
thf(f21137,plain,
( spl21_9
| spl21_10
| ~ spl21_425
| ~ spl21_1990 ),
inference(avatar_contradiction_clause,[],[f21136]) ).
thf(f21136,plain,
( $false
| spl21_9
| spl21_10
| ~ spl21_425
| ~ spl21_1990 ),
inference(trivial_inequality_removal,[],[f21135]) ).
thf(f21135,plain,
( ( $true = $false )
| spl21_9
| spl21_10
| ~ spl21_425
| ~ spl21_1990 ),
inference(forward_demodulation,[],[f21134,f4755]) ).
thf(f21134,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| spl21_9
| spl21_10
| ~ spl21_1990 ),
inference(subsumption_resolution,[],[f21133,f44]) ).
thf(f44,plain,
! [X20: a > a > a > $o] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f21133,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| spl21_9
| spl21_10
| ~ spl21_1990 ),
inference(subsumption_resolution,[],[f21132,f8117]) ).
thf(f21132,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) )
| spl21_10
| ~ spl21_1990 ),
inference(subsumption_resolution,[],[f21101,f9894]) ).
thf(f21101,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) )
| ~ spl21_1990 ),
inference(superposition,[],[f20987,f28]) ).
thf(f28,plain,
! [X20: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f20987,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,sK0))),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| ~ spl21_1990 ),
inference(avatar_component_clause,[],[f20986]) ).
thf(f21131,plain,
( spl21_19
| spl21_10
| ~ spl21_425
| ~ spl21_1990 ),
inference(avatar_split_clause,[],[f21130,f20986,f4754,f238,f347]) ).
thf(f21130,plain,
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| spl21_10
| ~ spl21_425
| ~ spl21_1990 ),
inference(trivial_inequality_removal,[],[f21129]) ).
thf(f21129,plain,
( ( $true = $false )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| spl21_10
| ~ spl21_425
| ~ spl21_1990 ),
inference(forward_demodulation,[],[f21128,f4755]) ).
thf(f21128,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| spl21_10
| ~ spl21_1990 ),
inference(subsumption_resolution,[],[f21127,f44]) ).
thf(f21127,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| spl21_10
| ~ spl21_1990 ),
inference(subsumption_resolution,[],[f21100,f9894]) ).
thf(f21100,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_1990 ),
inference(superposition,[],[f20987,f29]) ).
thf(f29,plain,
! [X20: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f21121,plain,
( spl21_19
| spl21_137
| ~ spl21_425
| ~ spl21_1990 ),
inference(avatar_split_clause,[],[f21120,f20986,f4754,f1078,f347]) ).
thf(f21120,plain,
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_425
| ~ spl21_1990 ),
inference(trivial_inequality_removal,[],[f21119]) ).
thf(f21119,plain,
( ( $true = $false )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_425
| ~ spl21_1990 ),
inference(forward_demodulation,[],[f21118,f4755]) ).
thf(f21118,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_1990 ),
inference(subsumption_resolution,[],[f21098,f44]) ).
thf(f21098,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_1990 ),
inference(superposition,[],[f20987,f31]) ).
thf(f31,plain,
! [X20: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK16,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f19836,plain,
( ~ spl21_16
| ~ spl21_834 ),
inference(avatar_contradiction_clause,[],[f19835]) ).
thf(f19835,plain,
( $false
| ~ spl21_16
| ~ spl21_834 ),
inference(trivial_inequality_removal,[],[f19834]) ).
thf(f19834,plain,
( ( $true = $false )
| ~ spl21_16
| ~ spl21_834 ),
inference(forward_demodulation,[],[f264,f9212]) ).
thf(f9212,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_834 ),
inference(avatar_component_clause,[],[f9211]) ).
thf(f9211,plain,
( spl21_834
<=> ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_834])]) ).
thf(f264,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_16 ),
inference(avatar_component_clause,[],[f263]) ).
thf(f263,plain,
( spl21_16
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_16])]) ).
thf(f19437,plain,
( spl21_20
| spl21_820
| ~ spl21_14
| ~ spl21_834 ),
inference(avatar_split_clause,[],[f19436,f9211,f257,f9009,f359]) ).
thf(f359,plain,
( spl21_20
<=> ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_20])]) ).
thf(f9009,plain,
( spl21_820
<=> ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_820])]) ).
thf(f257,plain,
( spl21_14
<=> ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_14])]) ).
thf(f19436,plain,
( ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ~ spl21_14
| ~ spl21_834 ),
inference(trivial_inequality_removal,[],[f19435]) ).
thf(f19435,plain,
( ( $true = $false )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ~ spl21_14
| ~ spl21_834 ),
inference(forward_demodulation,[],[f1252,f9212]) ).
thf(f1252,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ~ spl21_14 ),
inference(trivial_inequality_removal,[],[f1251]) ).
thf(f1251,plain,
( ( cZ != cZ )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ~ spl21_14 ),
inference(superposition,[],[f395,f258]) ).
thf(f258,plain,
( ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) )
| ~ spl21_14 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f395,plain,
! [X0: a > a > a > $o] :
( ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X0) ) ),
inference(inner_rewriting,[],[f394]) ).
thf(f394,plain,
! [X0: a > a > a > $o] :
( ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,y),v),v) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X0) ) ),
inference(superposition,[],[f18,f48]) ).
thf(f48,plain,
! [X10: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK4,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK5,X10)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,y),v),v) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f19431,plain,
( spl21_20
| spl21_15
| ~ spl21_14
| ~ spl21_834 ),
inference(avatar_split_clause,[],[f19430,f9211,f257,f260,f359]) ).
thf(f260,plain,
( spl21_15
<=> ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_15])]) ).
thf(f19430,plain,
( ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ~ spl21_14
| ~ spl21_834 ),
inference(trivial_inequality_removal,[],[f19429]) ).
thf(f19429,plain,
( ( $true = $false )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ~ spl21_14
| ~ spl21_834 ),
inference(forward_demodulation,[],[f1247,f9212]) ).
thf(f1247,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ~ spl21_14 ),
inference(trivial_inequality_removal,[],[f1246]) ).
thf(f1246,plain,
( ( cZ != cZ )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ~ spl21_14 ),
inference(superposition,[],[f309,f258]) ).
thf(f309,plain,
! [X0: a > a > a > $o] :
( ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X0) ) ),
inference(superposition,[],[f18,f46]) ).
thf(f46,plain,
! [X10: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK4,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK5,X10)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f19120,plain,
( ~ spl21_14
| spl21_16
| ~ spl21_20 ),
inference(avatar_contradiction_clause,[],[f19119]) ).
thf(f19119,plain,
( $false
| ~ spl21_14
| spl21_16
| ~ spl21_20 ),
inference(subsumption_resolution,[],[f19118,f76]) ).
thf(f76,plain,
! [X3: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,cZ),X3),X3) ),
inference(equality_resolution,[],[f75]) ).
thf(f75,plain,
! [X3: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X1),X3),X3) )
| ( cZ != X1 ) ),
inference(equality_resolution,[],[f66]) ).
thf(f66,plain,
! [X2: a,X3: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X1),X2),X3) )
| ( X2 != X3 )
| ( cZ != X1 ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f19118,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,cZ),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)) )
| ~ spl21_14
| spl21_16
| ~ spl21_20 ),
inference(forward_demodulation,[],[f19117,f258]) ).
thf(f19117,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)) )
| spl21_16
| ~ spl21_20 ),
inference(subsumption_resolution,[],[f18993,f9862]) ).
thf(f9862,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| spl21_16 ),
inference(avatar_component_clause,[],[f263]) ).
thf(f18993,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_20 ),
inference(superposition,[],[f65,f360]) ).
thf(f360,plain,
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ~ spl21_20 ),
inference(avatar_component_clause,[],[f359]) ).
thf(f65,plain,
! [X10: a > a > a > $o] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,y),v),v) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f18902,plain,
( spl21_16
| ~ spl21_1851 ),
inference(avatar_contradiction_clause,[],[f18901]) ).
thf(f18901,plain,
( $false
| spl21_16
| ~ spl21_1851 ),
inference(subsumption_resolution,[],[f18886,f9862]) ).
thf(f18886,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_1851 ),
inference(trivial_inequality_removal,[],[f18885]) ).
thf(f18885,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_1851 ),
inference(superposition,[],[f65,f18839]) ).
thf(f18839,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0)) )
| ~ spl21_1851 ),
inference(avatar_component_clause,[],[f18838]) ).
thf(f18838,plain,
( spl21_1851
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_1851])]) ).
thf(f18846,plain,
( spl21_14
| spl21_15
| spl21_1851
| spl21_16
| ~ spl21_1816 ),
inference(avatar_split_clause,[],[f18845,f18571,f263,f18838,f260,f257]) ).
thf(f18571,plain,
( spl21_1816
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_1816])]) ).
thf(f18845,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0)) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) )
| spl21_16
| ~ spl21_1816 ),
inference(subsumption_resolution,[],[f18819,f9862]) ).
thf(f18819,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) )
| ~ spl21_1816 ),
inference(superposition,[],[f18572,f53]) ).
thf(f53,plain,
! [X10: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,X10)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f18572,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,sK0))) )
| ~ spl21_1816 ),
inference(avatar_component_clause,[],[f18571]) ).
thf(f18579,plain,
( spl21_14
| spl21_15
| spl21_1816
| spl21_16
| ~ spl21_1183 ),
inference(avatar_split_clause,[],[f18578,f13536,f263,f18571,f260,f257]) ).
thf(f13536,plain,
( spl21_1183
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK7,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_1183])]) ).
thf(f18578,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,sK0))) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) )
| spl21_16
| ~ spl21_1183 ),
inference(subsumption_resolution,[],[f18548,f9862]) ).
thf(f18548,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,sK0))) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) )
| ~ spl21_1183 ),
inference(superposition,[],[f13537,f49]) ).
thf(f49,plain,
! [X10: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK7,X10)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f13537,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK7,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,sK0))) )
| ~ spl21_1183 ),
inference(avatar_component_clause,[],[f13536]) ).
thf(f13544,plain,
( spl21_14
| spl21_15
| spl21_1183
| spl21_16
| ~ spl21_1122 ),
inference(avatar_split_clause,[],[f13543,f12958,f263,f13536,f260,f257]) ).
thf(f12958,plain,
( spl21_1122
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK5,sK0)),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_1122])]) ).
thf(f13543,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK7,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,sK0))) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) )
| spl21_16
| ~ spl21_1122 ),
inference(subsumption_resolution,[],[f13515,f9862]) ).
thf(f13515,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK7,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,sK0))) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) )
| ~ spl21_1122 ),
inference(trivial_inequality_removal,[],[f13497]) ).
thf(f13497,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK7,sK0))),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,sK0))) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) )
| ~ spl21_1122 ),
inference(superposition,[],[f12959,f61]) ).
thf(f61,plain,
! [X10: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK5,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK7,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK9,X10)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f12959,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK5,sK0)),X0),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),X1)) ) )
| ~ spl21_1122 ),
inference(avatar_component_clause,[],[f12958]) ).
thf(f12966,plain,
( spl21_14
| spl21_15
| spl21_1122
| spl21_16
| ~ spl21_17 ),
inference(avatar_split_clause,[],[f12965,f266,f263,f12958,f260,f257]) ).
thf(f266,plain,
( spl21_17
<=> ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK4,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,sK0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_17])]) ).
thf(f12965,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK5,sK0)),X0),X1) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) ) )
| spl21_16
| ~ spl21_17 ),
inference(subsumption_resolution,[],[f12931,f9862]) ).
thf(f12931,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK5,sK0)),X0),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) ) )
| ~ spl21_17 ),
inference(superposition,[],[f267,f45]) ).
thf(f45,plain,
! [X10: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK4,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK5,X10)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f267,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK4,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,sK0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) ) )
| ~ spl21_17 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f12478,plain,
( ~ spl21_11
| ~ spl21_425 ),
inference(avatar_contradiction_clause,[],[f12477]) ).
thf(f12477,plain,
( $false
| ~ spl21_11
| ~ spl21_425 ),
inference(trivial_inequality_removal,[],[f12476]) ).
thf(f12476,plain,
( ( $true = $false )
| ~ spl21_11
| ~ spl21_425 ),
inference(forward_demodulation,[],[f242,f4755]) ).
thf(f242,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ~ spl21_11 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f241,plain,
( spl21_11
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_11])]) ).
thf(f12474,plain,
( ~ spl21_16
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f12420,f1070,f263]) ).
thf(f1070,plain,
( spl21_135
<=> ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_135])]) ).
thf(f12420,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_135 ),
inference(trivial_inequality_removal,[],[f9491]) ).
thf(f9491,plain,
( ( $true = $false )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_135 ),
inference(superposition,[],[f1071,f186]) ).
thf(f186,plain,
$false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),
inference(trivial_inequality_removal,[],[f185]) ).
thf(f185,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)) ) ),
inference(superposition,[],[f69,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f69,plain,
$true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),y)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),v)),
inference(cnf_transformation,[],[f17]) ).
thf(f1071,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) ) )
| ~ spl21_135 ),
inference(avatar_component_clause,[],[f1070]) ).
thf(f12435,plain,
( spl21_14
| spl21_22
| spl21_16
| ~ spl21_15 ),
inference(avatar_split_clause,[],[f1249,f260,f263,f421,f257]) ).
thf(f421,plain,
( spl21_22
<=> ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_22])]) ).
thf(f1249,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) )
| ~ spl21_15 ),
inference(trivial_inequality_removal,[],[f1248]) ).
thf(f1248,plain,
( ( cZ != cZ )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) )
| ~ spl21_15 ),
inference(superposition,[],[f329,f261]) ).
thf(f261,plain,
( ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ~ spl21_15 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f329,plain,
! [X0: a > a > a > $o] :
( ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,y),v),v) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X0) ) ),
inference(superposition,[],[f18,f51]) ).
thf(f51,plain,
! [X10: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK7,X10)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,y),v),v) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,X10) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f9895,plain,
( ~ spl21_10
| spl21_9
| ~ spl21_19
| ~ spl21_425 ),
inference(avatar_split_clause,[],[f9893,f4754,f347,f235,f238]) ).
thf(f9893,plain,
( ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| spl21_9
| ~ spl21_19
| ~ spl21_425 ),
inference(trivial_inequality_removal,[],[f9892]) ).
thf(f9892,plain,
( ( $true = $false )
| ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| spl21_9
| ~ spl21_19
| ~ spl21_425 ),
inference(forward_demodulation,[],[f9891,f4755]) ).
thf(f9891,plain,
( ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| spl21_9
| ~ spl21_19 ),
inference(subsumption_resolution,[],[f1224,f8117]) ).
thf(f1224,plain,
( ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) )
| ~ spl21_19 ),
inference(superposition,[],[f304,f348]) ).
thf(f348,plain,
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_19 ),
inference(avatar_component_clause,[],[f347]) ).
thf(f304,plain,
! [X0: a > a > a > $o] :
( ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X0) ) ),
inference(duplicate_literal_removal,[],[f303]) ).
thf(f303,plain,
! [X0: a > a > a > $o] :
( ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X0) ) ),
inference(inner_rewriting,[],[f302]) ).
thf(f302,plain,
! [X0: a > a > a > $o] :
( ( cZ != vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X0,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X0) ) ),
inference(superposition,[],[f18,f34]) ).
thf(f34,plain,
! [X20: a > a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK18,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f9860,plain,
( spl21_16
| ~ spl21_15
| ~ spl21_22 ),
inference(avatar_split_clause,[],[f9831,f421,f260,f263]) ).
thf(f9831,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_15
| ~ spl21_22 ),
inference(subsumption_resolution,[],[f9830,f74]) ).
thf(f74,plain,
! [X3: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X3),cZ),X3) ),
inference(equality_resolution,[],[f73]) ).
thf(f73,plain,
! [X2: a,X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X3),X2),X3) )
| ( cZ != X2 ) ),
inference(equality_resolution,[],[f67]) ).
thf(f67,plain,
! [X2: a,X3: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X1),X2),X3) )
| ( X1 != X3 )
| ( cZ != X2 ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f9830,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),cZ),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_15
| ~ spl21_22 ),
inference(forward_demodulation,[],[f9784,f261]) ).
thf(f9784,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_22 ),
inference(superposition,[],[f65,f422]) ).
thf(f422,plain,
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ~ spl21_22 ),
inference(avatar_component_clause,[],[f421]) ).
thf(f9668,plain,
( ~ spl21_14
| ~ spl21_15
| ~ spl21_820
| ~ spl21_834 ),
inference(avatar_contradiction_clause,[],[f9667]) ).
thf(f9667,plain,
( $false
| ~ spl21_14
| ~ spl21_15
| ~ spl21_820
| ~ spl21_834 ),
inference(trivial_inequality_removal,[],[f9666]) ).
thf(f9666,plain,
( ( $true = $false )
| ~ spl21_14
| ~ spl21_15
| ~ spl21_820
| ~ spl21_834 ),
inference(forward_demodulation,[],[f9665,f9212]) ).
thf(f9665,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_14
| ~ spl21_15
| ~ spl21_820 ),
inference(subsumption_resolution,[],[f9664,f76]) ).
thf(f9664,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,cZ),cZ),cZ) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_14
| ~ spl21_15
| ~ spl21_820 ),
inference(forward_demodulation,[],[f9663,f258]) ).
thf(f9663,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),cZ),cZ) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_15
| ~ spl21_820 ),
inference(forward_demodulation,[],[f9598,f261]) ).
thf(f9598,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0)),cZ) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ~ spl21_820 ),
inference(superposition,[],[f65,f9010]) ).
thf(f9010,plain,
( ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK3,sK0) )
| ~ spl21_820 ),
inference(avatar_component_clause,[],[f9009]) ).
thf(f9215,plain,
( spl21_834
| spl21_425 ),
inference(avatar_split_clause,[],[f5045,f4754,f9211]) ).
thf(f5045,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) ) ),
inference(trivial_inequality_removal,[],[f5024]) ).
thf(f5024,plain,
( ( $true = $false )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) ) ),
inference(superposition,[],[f1794,f186]) ).
thf(f1794,plain,
! [X2: a,X3: a,X0: a,X1: a,X4: a,X5: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X5),X2)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X3),X4),X5) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) ) ),
inference(trivial_inequality_removal,[],[f1793]) ).
thf(f1793,plain,
! [X2: a,X3: a,X0: a,X1: a,X4: a,X5: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X5),X2)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X3),X4),X5) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) ) ),
inference(superposition,[],[f229,f4]) ).
thf(f229,plain,
! [X2: a,X3: a,X0: a,X1: a,X4: a,X5: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X3),X4),X5) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X4)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),X5)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) ) ),
inference(trivial_inequality_removal,[],[f228]) ).
thf(f228,plain,
! [X2: a,X3: a,X0: a,X1: a,X4: a,X5: a] :
( ( $true != $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X3),X4),X5) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X4)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),X5)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) ) ),
inference(superposition,[],[f72,f4]) ).
thf(f72,plain,
! [X8: a,X6: a,X9: a,X7: a,X4: a,X5: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X4),X6),X8) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X5),X7),X9) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X5)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9)) ) ),
inference(equality_resolution,[],[f71]) ).
thf(f71,plain,
! [X1: a,X8: a,X6: a,X9: a,X7: a,X4: a,X5: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X1),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X5),X7),X9) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X4),X6),X8) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X5) != X1 ) ),
inference(equality_resolution,[],[f70]) ).
thf(f70,plain,
! [X2: a,X1: a,X8: a,X6: a,X9: a,X7: a,X4: a,X5: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X5),X7),X9) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X4),X6),X8) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7) != X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X5) != X1 ) ),
inference(equality_resolution,[],[f68]) ).
thf(f68,plain,
! [X2: a,X3: a,X1: a,X8: a,X6: a,X9: a,X7: a,X4: a,X5: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X1),X2),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X5),X7),X9) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X4),X6),X8) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9) != X3 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7) != X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X5) != X1 ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f1124,plain,
( spl21_11
| ~ spl21_10
| ~ spl21_137 ),
inference(avatar_split_clause,[],[f1123,f1078,f238,f241]) ).
thf(f1123,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ~ spl21_10
| ~ spl21_137 ),
inference(subsumption_resolution,[],[f1122,f74]) ).
thf(f1122,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),cZ),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ~ spl21_10
| ~ spl21_137 ),
inference(forward_demodulation,[],[f1118,f239]) ).
thf(f239,plain,
( ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ~ spl21_10 ),
inference(avatar_component_clause,[],[f238]) ).
thf(f1118,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ~ spl21_137 ),
inference(superposition,[],[f44,f1079]) ).
thf(f1079,plain,
( ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ~ spl21_137 ),
inference(avatar_component_clause,[],[f1078]) ).
thf(f1106,plain,
( spl21_11
| ~ spl21_9
| ~ spl21_19 ),
inference(avatar_split_clause,[],[f1105,f347,f235,f241]) ).
thf(f1105,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ~ spl21_9
| ~ spl21_19 ),
inference(subsumption_resolution,[],[f1104,f76]) ).
thf(f1104,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,cZ),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ~ spl21_9
| ~ spl21_19 ),
inference(forward_demodulation,[],[f1103,f236]) ).
thf(f1103,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ~ spl21_19 ),
inference(superposition,[],[f44,f348]) ).
thf(f1092,plain,
( spl21_19
| spl21_137
| spl21_11
| spl21_12 ),
inference(avatar_split_clause,[],[f409,f244,f241,f1078,f347]) ).
thf(f409,plain,
! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X2)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) ) ),
inference(trivial_inequality_removal,[],[f408]) ).
thf(f408,plain,
! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X2)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,sK0) ) ),
inference(superposition,[],[f72,f39]) ).
thf(f39,plain,
! [X20: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) )
| ( vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK12,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f1072,plain,
( spl21_135
| ~ spl21_11 ),
inference(avatar_split_clause,[],[f1068,f241,f1070]) ).
thf(f1068,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),X2)) ) )
| ~ spl21_11 ),
inference(trivial_inequality_removal,[],[f1067]) ).
thf(f1067,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,x),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,u),X2)) ) )
| ~ spl21_11 ),
inference(superposition,[],[f72,f242]) ).
thf(f268,plain,
( spl21_14
| spl21_15
| spl21_16
| spl21_17 ),
inference(avatar_split_clause,[],[f255,f266,f263,f260,f257]) ).
thf(f255,plain,
! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK4,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,sK0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),X2)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) ) ),
inference(trivial_inequality_removal,[],[f254]) ).
thf(f254,plain,
! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK4,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,sK0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,sK0)),X2)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,sK0) ) ),
inference(superposition,[],[f72,f57]) ).
thf(f57,plain,
! [X10: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK4,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK6,X10)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK8,X10)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X10,y),v),v) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK2,X10) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK1,X10) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f246,plain,
( spl21_9
| spl21_10
| spl21_11
| spl21_12 ),
inference(avatar_split_clause,[],[f233,f244,f241,f238,f235]) ).
thf(f233,plain,
! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X2)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) ) ),
inference(trivial_inequality_removal,[],[f232]) ).
thf(f232,plain,
! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,X0),X1),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,sK0)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,sK0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,sK0)),X2)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),sK0,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,sK0) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,sK0) ) ),
inference(superposition,[],[f72,f36]) ).
thf(f36,plain,
! [X20: a > a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK13,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK15,X20)),vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK17,X20)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),X20,x),u),u) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK11,X20) )
| ( cZ = vAPP(sTfun(a,sTfun(a,sTfun(a,$o))),a,sK10,X20) ) ),
inference(cnf_transformation,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV210^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 18:57:07 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (4816)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (4817)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % (4822)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.19/0.38 % (4819)WARNING: value z3 for option sas not known
% 0.19/0.38 % (4819)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.19/0.38 % (4821)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.19/0.39 % (4818)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.39 % (4823)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.19/0.39 % (4824)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.19/0.39 % (4823)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.39 % Exception at run slice level
% 0.19/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.39 % (4824)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.39 % Exception at run slice level
% 0.19/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.39 % (4820)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.40 % Exception at run slice level
% 0.19/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.40 % (4825)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.19/0.41 % (4825)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.41 % (4826)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.19/0.41 % (4827)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 248.81/35.91 % (4827)Time limit reached!
% 248.81/35.91 % (4827)------------------------------
% 248.81/35.91 % (4827)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 248.81/35.91 % (4827)Termination reason: Time limit
% 248.81/35.91 % (4827)Termination phase: Saturation
% 248.81/35.91
% 248.81/35.91 % (4827)Memory used [KB]: 209928
% 248.81/35.91 % (4827)Time elapsed: 35.500 s
% 248.81/35.91 % (4827)Instructions burned: 99359 (million)
% 248.81/35.91 % (4827)------------------------------
% 248.81/35.91 % (4827)------------------------------
% 248.94/35.96 % (5472)WARNING: value z3 for option sas not known
% 248.94/35.96 % (5472)ott-11_10:1_aac=none:add=off:afr=on:amm=off:anc=all_dependent:bd=off:fsd=off:fde=none:gsp=on:irw=on:lma=on:nm=64:nwc=1.2:nicw=on:sas=z3:sp=occurrence_186 on theBenchmark for (186ds/0Mi)
% 248.94/35.96 % (5472)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 257.78/37.21 % (4826)Time limit reached!
% 257.78/37.21 % (4826)------------------------------
% 257.78/37.21 % (4826)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 257.78/37.21 % (4826)Termination reason: Time limit
% 257.78/37.21 % (4826)Termination phase: Saturation
% 257.78/37.21
% 257.78/37.21 % (4826)Memory used [KB]: 60212
% 257.78/37.21 % (4826)Time elapsed: 36.800 s
% 257.78/37.21 % (4826)Instructions burned: 139797 (million)
% 257.78/37.21 % (4826)------------------------------
% 257.78/37.21 % (4826)------------------------------
% 257.78/37.23 % (5473)dis-3_1_acc=on:anc=none:bd=preordered:fsd=off:fsr=off:fde=none:gs=on:gsem=on:lcm=predicate:lma=on:msp=off:nm=4:nicw=on:sims=off:sp=weighted_frequency:urr=ec_only_180 on theBenchmark for (180ds/0Mi)
% 268.07/38.70 % (4825)Time limit reached!
% 268.07/38.70 % (4825)------------------------------
% 268.07/38.70 % (4825)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 268.07/38.70 % (4825)Termination reason: Time limit
% 268.07/38.70 % (4825)Termination phase: Saturation
% 268.07/38.70
% 268.07/38.70 % (4825)Memory used [KB]: 239479
% 268.07/38.70 % (4825)Time elapsed: 38.300 s
% 268.07/38.70 % (4825)Instructions burned: 126982 (million)
% 268.07/38.70 % (4825)------------------------------
% 268.07/38.70 % (4825)------------------------------
% 268.60/38.76 % (5474)dis-3_6_add=off:afr=on:amm=off:anc=none:bd=off:bs=on:bsr=on:bce=on:fsd=off:fde=none:gsp=on:gs=on:gsaa=full_model:gsem=off:sims=off:sac=on:sp=reverse_frequency_90 on theBenchmark for (90ds/0Mi)
% 268.60/38.76 % (5474)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 286.17/41.27 % (5472)First to succeed.
% 286.17/41.29 % (5472)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4816"
% 286.17/41.29 % (5472)Refutation found. Thanks to Tanya!
% 286.17/41.29 % SZS status Theorem for theBenchmark
% 286.17/41.29 % SZS output start Proof for theBenchmark
% See solution above
% 286.17/41.30 % (5472)------------------------------
% 286.17/41.30 % (5472)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 286.17/41.30 % (5472)Termination reason: Refutation
% 286.17/41.30
% 286.17/41.30 % (5472)Memory used [KB]: 10817
% 286.17/41.30 % (5472)Time elapsed: 5.321 s
% 286.17/41.30 % (5472)Instructions burned: 20418 (million)
% 286.17/41.30 % (4816)Success in time 40.928 s
%------------------------------------------------------------------------------