TSTP Solution File: SEV138^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV138^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.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 : Sun May 5 09:43:56 EDT 2024
% Result : Theorem 0.17s 0.39s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 44
% Syntax : Number of formulae : 181 ( 7 unt; 23 typ; 0 def)
% Number of atoms : 2363 ( 467 equ; 0 cnn)
% Maximal formula atoms : 28 ( 14 avg)
% Number of connectives : 663 ( 197 ~; 299 |; 110 &; 0 @)
% ( 11 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 220 ( 219 >; 1 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 16 con; 0-6 aty)
% Number of variables : 284 ( 0 ^ 213 !; 65 ?; 284 :)
% ( 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_4,type,
sP0: ( a > a > $o ) > ( a > $o ) > $o ).
thf(func_def_5,type,
sP1: ( a > a > $o ) > ( a > $o ) > $o ).
thf(func_def_6,type,
sK2: ( a > a > $o ) > ( a > $o ) > a ).
thf(func_def_7,type,
sK3: ( a > a > $o ) > ( a > $o ) > a ).
thf(func_def_8,type,
sK4: ( a > a > $o ) > ( a > $o ) > a ).
thf(func_def_9,type,
sK5: ( a > a > $o ) > ( a > $o ) > a ).
thf(func_def_10,type,
sK6: a > a > $o ).
thf(func_def_11,type,
sK7: a ).
thf(func_def_12,type,
sK8: a ).
thf(func_def_13,type,
sK9: a ).
thf(func_def_14,type,
sK10: a > $o ).
thf(func_def_15,type,
sK11: ( a > $o ) > a ).
thf(func_def_16,type,
sK12: ( a > $o ) > a ).
thf(func_def_18,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_19,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
vOR: $o > $o > $o ).
thf(func_def_22,type,
vIMP: $o > $o > $o ).
thf(func_def_23,type,
vNOT: $o > $o ).
thf(func_def_24,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1877,plain,
$false,
inference(avatar_sat_refutation,[],[f628,f666,f1050,f1353,f1479,f1507,f1508,f1606,f1710,f1739,f1803,f1876]) ).
thf(f1876,plain,
( spl13_19
| ~ spl13_56
| ~ spl13_77 ),
inference(avatar_contradiction_clause,[],[f1875]) ).
thf(f1875,plain,
( $false
| spl13_19
| ~ spl13_56
| ~ spl13_77 ),
inference(trivial_inequality_removal,[],[f1874]) ).
thf(f1874,plain,
( ( $true = $false )
| spl13_19
| ~ spl13_56
| ~ spl13_77 ),
inference(forward_demodulation,[],[f1873,f1014]) ).
thf(f1014,plain,
( ( $false = vAPP(a,$o,sK10,sK8) )
| ~ spl13_56 ),
inference(avatar_component_clause,[],[f1012]) ).
thf(f1012,plain,
( spl13_56
<=> ( $false = vAPP(a,$o,sK10,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_56])]) ).
thf(f1873,plain,
( ( $true = vAPP(a,$o,sK10,sK8) )
| spl13_19
| ~ spl13_77 ),
inference(subsumption_resolution,[],[f1863,f424]) ).
thf(f424,plain,
( ( $false != vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK12,sK10)) )
| spl13_19 ),
inference(avatar_component_clause,[],[f423]) ).
thf(f423,plain,
( spl13_19
<=> ( $false = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK12,sK10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_19])]) ).
thf(f1863,plain,
( ( $false = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK12,sK10)) )
| ( $true = vAPP(a,$o,sK10,sK8) )
| ~ spl13_77 ),
inference(trivial_inequality_removal,[],[f1857]) ).
thf(f1857,plain,
( ( $true = $false )
| ( $false = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK12,sK10)) )
| ( $true = vAPP(a,$o,sK10,sK8) )
| ~ spl13_77 ),
inference(superposition,[],[f88,f1702]) ).
thf(f1702,plain,
( ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,sK6),sK10) )
| ~ spl13_77 ),
inference(avatar_component_clause,[],[f1700]) ).
thf(f1700,plain,
( spl13_77
<=> ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,sK6),sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_77])]) ).
thf(f88,plain,
! [X0: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,sK6),X0) )
| ( $false = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK12,X0)) )
| ( $true = vAPP(a,$o,X0,sK8) ) ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f87,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,sK6),X0) )
| ( $true = vAPP(a,$o,X0,sK8) )
| ( $false = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK12,X0)) ) ),
inference(superposition,[],[f33,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f33,plain,
! [X10: a > $o] :
( ( $true != vAPP(a,$o,X10,vAPP(sTfun(a,$o),a,sK12,X10)) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,sK6),X10) )
| ( $true = vAPP(a,$o,X10,sK8) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f25,plain,
( ( $true != vAPP(a,$o,sK10,sK9) )
& ! [X5: a,X6: a] :
( ( $true = vAPP(a,$o,sK10,X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,X5),X6) )
| ( $true != vAPP(a,$o,sK10,X5) ) )
& ! [X7: a] :
( ( $true = vAPP(a,$o,sK10,X7) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),X7) ) )
& ! [X8: a > $o] :
( ( $true = vAPP(a,$o,X8,sK9) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,sK6),X8) )
| ( ( $true != vAPP(a,$o,X8,vAPP(sTfun(a,$o),a,sK11,X8)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,X8)) ) ) )
& ! [X10: a > $o] :
( ( $true = vAPP(a,$o,X10,sK8) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,sK6),X10) )
| ( ( $true != vAPP(a,$o,X10,vAPP(sTfun(a,$o),a,sK12,X10)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,X10)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11,sK12])],[f20,f24,f23,f22,f21]) ).
thf(f21,plain,
( ? [X0: a > a > $o,X1: a,X2: a,X3: a] :
( ? [X4: a > $o] :
( ( vAPP(a,$o,X4,X3) != $true )
& ! [X5: a,X6: a] :
( ( vAPP(a,$o,X4,X6) = $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X5),X6) )
| ( vAPP(a,$o,X4,X5) != $true ) )
& ! [X7: a] :
( ( vAPP(a,$o,X4,X7) = $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X7) ) ) )
& ! [X8: a > $o] :
( ( $true = vAPP(a,$o,X8,X3) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X0),X8) )
| ? [X9: a] :
( ( $true != vAPP(a,$o,X8,X9) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X2),X9) ) ) )
& ! [X10: a > $o] :
( ( $true = vAPP(a,$o,X10,X2) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X0),X10) )
| ? [X11: a] :
( ( $true != vAPP(a,$o,X10,X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X11) ) ) ) )
=> ( ? [X4: a > $o] :
( ( $true != vAPP(a,$o,X4,sK9) )
& ! [X6: a,X5: a] :
( ( vAPP(a,$o,X4,X6) = $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,X5),X6) )
| ( vAPP(a,$o,X4,X5) != $true ) )
& ! [X7: a] :
( ( vAPP(a,$o,X4,X7) = $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),X7) ) ) )
& ! [X8: a > $o] :
( ( $true = vAPP(a,$o,X8,sK9) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,sK6),X8) )
| ? [X9: a] :
( ( $true != vAPP(a,$o,X8,X9) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),X9) ) ) )
& ! [X10: a > $o] :
( ( $true = vAPP(a,$o,X10,sK8) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,sK6),X10) )
| ? [X11: a] :
( ( $true != vAPP(a,$o,X10,X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),X11) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f22,plain,
( ? [X4: a > $o] :
( ( $true != vAPP(a,$o,X4,sK9) )
& ! [X6: a,X5: a] :
( ( vAPP(a,$o,X4,X6) = $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,X5),X6) )
| ( vAPP(a,$o,X4,X5) != $true ) )
& ! [X7: a] :
( ( vAPP(a,$o,X4,X7) = $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),X7) ) ) )
=> ( ( $true != vAPP(a,$o,sK10,sK9) )
& ! [X6: a,X5: a] :
( ( $true = vAPP(a,$o,sK10,X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,X5),X6) )
| ( $true != vAPP(a,$o,sK10,X5) ) )
& ! [X7: a] :
( ( $true = vAPP(a,$o,sK10,X7) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),X7) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f23,plain,
! [X8: a > $o] :
( ? [X9: a] :
( ( $true != vAPP(a,$o,X8,X9) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),X9) ) )
=> ( ( $true != vAPP(a,$o,X8,vAPP(sTfun(a,$o),a,sK11,X8)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,X8)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f24,plain,
! [X10: a > $o] :
( ? [X11: a] :
( ( $true != vAPP(a,$o,X10,X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),X11) ) )
=> ( ( $true != vAPP(a,$o,X10,vAPP(sTfun(a,$o),a,sK12,X10)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,X10)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f20,plain,
? [X0: a > a > $o,X1: a,X2: a,X3: a] :
( ? [X4: a > $o] :
( ( vAPP(a,$o,X4,X3) != $true )
& ! [X5: a,X6: a] :
( ( vAPP(a,$o,X4,X6) = $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X5),X6) )
| ( vAPP(a,$o,X4,X5) != $true ) )
& ! [X7: a] :
( ( vAPP(a,$o,X4,X7) = $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X7) ) ) )
& ! [X8: a > $o] :
( ( $true = vAPP(a,$o,X8,X3) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X0),X8) )
| ? [X9: a] :
( ( $true != vAPP(a,$o,X8,X9) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X2),X9) ) ) )
& ! [X10: a > $o] :
( ( $true = vAPP(a,$o,X10,X2) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X0),X10) )
| ? [X11: a] :
( ( $true != vAPP(a,$o,X10,X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X11) ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f11,plain,
? [X0: a > a > $o,X1: a,X2: a,X3: a] :
( ? [X12: a > $o] :
( ( $true != vAPP(a,$o,X12,X3) )
& ! [X13: a,X14: a] :
( ( $true = vAPP(a,$o,X12,X14) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X13),X14) )
| ( $true != vAPP(a,$o,X12,X13) ) )
& ! [X15: a] :
( ( $true = vAPP(a,$o,X12,X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X15) ) ) )
& ! [X4: a > $o] :
( ( vAPP(a,$o,X4,X3) = $true )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X0),X4) )
| ? [X7: a] :
( ( vAPP(a,$o,X4,X7) != $true )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X2),X7) ) ) )
& ! [X8: a > $o] :
( ( $true = vAPP(a,$o,X8,X2) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X0),X8) )
| ? [X11: a] :
( ( $true != vAPP(a,$o,X8,X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X11) ) ) ) ),
inference(definition_folding,[],[f8,f10,f9]) ).
thf(f9,plain,
! [X8: a > $o,X0: a > a > $o] :
( ? [X9: a,X10: a] :
( ( $true != vAPP(a,$o,X8,X10) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X9),X10) )
& ( $true = vAPP(a,$o,X8,X9) ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X0),X8) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f10,plain,
! [X4: a > $o,X0: a > a > $o] :
( ? [X5: a,X6: a] :
( ( vAPP(a,$o,X4,X6) != $true )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X5),X6) )
& ( vAPP(a,$o,X4,X5) = $true ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X0),X4) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f8,plain,
? [X0: a > a > $o,X1: a,X2: a,X3: a] :
( ? [X12: a > $o] :
( ( $true != vAPP(a,$o,X12,X3) )
& ! [X13: a,X14: a] :
( ( $true = vAPP(a,$o,X12,X14) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X13),X14) )
| ( $true != vAPP(a,$o,X12,X13) ) )
& ! [X15: a] :
( ( $true = vAPP(a,$o,X12,X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X15) ) ) )
& ! [X4: a > $o] :
( ( vAPP(a,$o,X4,X3) = $true )
| ? [X5: a,X6: a] :
( ( vAPP(a,$o,X4,X6) != $true )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X5),X6) )
& ( vAPP(a,$o,X4,X5) = $true ) )
| ? [X7: a] :
( ( vAPP(a,$o,X4,X7) != $true )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X2),X7) ) ) )
& ! [X8: a > $o] :
( ( $true = vAPP(a,$o,X8,X2) )
| ? [X9: a,X10: a] :
( ( $true != vAPP(a,$o,X8,X10) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X9),X10) )
& ( $true = vAPP(a,$o,X8,X9) ) )
| ? [X11: a] :
( ( $true != vAPP(a,$o,X8,X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X11) ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
? [X0: a > a > $o,X1: a,X2: a,X3: a] :
( ? [X12: a > $o] :
( ( $true != vAPP(a,$o,X12,X3) )
& ! [X13: a,X14: a] :
( ( $true = vAPP(a,$o,X12,X14) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X13),X14) )
| ( $true != vAPP(a,$o,X12,X13) ) )
& ! [X15: a] :
( ( $true = vAPP(a,$o,X12,X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X15) ) ) )
& ! [X4: a > $o] :
( ( vAPP(a,$o,X4,X3) = $true )
| ? [X5: a,X6: a] :
( ( vAPP(a,$o,X4,X6) != $true )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X5),X6) )
& ( vAPP(a,$o,X4,X5) = $true ) )
| ? [X7: a] :
( ( vAPP(a,$o,X4,X7) != $true )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X2),X7) ) ) )
& ! [X8: a > $o] :
( ( $true = vAPP(a,$o,X8,X2) )
| ? [X9: a,X10: a] :
( ( $true != vAPP(a,$o,X8,X10) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X9),X10) )
& ( $true = vAPP(a,$o,X8,X9) ) )
| ? [X11: a] :
( ( $true != vAPP(a,$o,X8,X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X11) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ! [X0: a > a > $o,X1: a,X2: a,X3: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X5),X6) )
& ( vAPP(a,$o,X4,X5) = $true ) )
=> ( vAPP(a,$o,X4,X6) = $true ) )
& ! [X7: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X2),X7) )
=> ( vAPP(a,$o,X4,X7) = $true ) ) )
=> ( vAPP(a,$o,X4,X3) = $true ) )
& ! [X8: a > $o] :
( ( ! [X9: a,X10: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X9),X10) )
& ( $true = vAPP(a,$o,X8,X9) ) )
=> ( $true = vAPP(a,$o,X8,X10) ) )
& ! [X11: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X11) )
=> ( $true = vAPP(a,$o,X8,X11) ) ) )
=> ( $true = vAPP(a,$o,X8,X2) ) ) )
=> ! [X12: a > $o] :
( ( ! [X13: a,X14: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X13),X14) )
& ( $true = vAPP(a,$o,X12,X13) ) )
=> ( $true = vAPP(a,$o,X12,X14) ) )
& ! [X15: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X15) )
=> ( $true = vAPP(a,$o,X12,X15) ) ) )
=> ( $true = vAPP(a,$o,X12,X3) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ! [X0: a > a > $o,X1: a,X2: a,X3: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a,X6: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X5),X6)
& vAPP(a,$o,X4,X5) )
=> vAPP(a,$o,X4,X6) )
& ! [X7: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X2),X7)
=> vAPP(a,$o,X4,X7) ) )
=> vAPP(a,$o,X4,X3) )
& ! [X8: a > $o] :
( ( ! [X9: a,X10: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X9),X10)
& vAPP(a,$o,X8,X9) )
=> vAPP(a,$o,X8,X10) )
& ! [X11: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X11)
=> vAPP(a,$o,X8,X11) ) )
=> vAPP(a,$o,X8,X2) ) )
=> ! [X12: a > $o] :
( ( ! [X13: a,X14: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X13),X14)
& vAPP(a,$o,X12,X13) )
=> vAPP(a,$o,X12,X14) )
& ! [X15: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X15)
=> vAPP(a,$o,X12,X15) ) )
=> vAPP(a,$o,X12,X3) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: a,X2: a,X3: a] :
( ( ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X6),X7)
& vAPP(a,$o,X4,X6) )
=> vAPP(a,$o,X4,X7) )
& ! [X5: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X2),X5)
=> vAPP(a,$o,X4,X5) ) )
=> vAPP(a,$o,X4,X3) )
& ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X6),X7)
& vAPP(a,$o,X4,X6) )
=> vAPP(a,$o,X4,X7) )
& ! [X5: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X5)
=> vAPP(a,$o,X4,X5) ) )
=> vAPP(a,$o,X4,X2) ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X6),X7)
& vAPP(a,$o,X4,X6) )
=> vAPP(a,$o,X4,X7) )
& ! [X5: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X5)
=> vAPP(a,$o,X4,X5) ) )
=> vAPP(a,$o,X4,X3) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X1: a,X2: a,X3: a] :
( ( ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X6),X7)
& vAPP(a,$o,X4,X6) )
=> vAPP(a,$o,X4,X7) )
& ! [X5: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X2),X5)
=> vAPP(a,$o,X4,X5) ) )
=> vAPP(a,$o,X4,X3) )
& ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X6),X7)
& vAPP(a,$o,X4,X6) )
=> vAPP(a,$o,X4,X7) )
& ! [X5: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X5)
=> vAPP(a,$o,X4,X5) ) )
=> vAPP(a,$o,X4,X2) ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X6),X7)
& vAPP(a,$o,X4,X6) )
=> vAPP(a,$o,X4,X7) )
& ! [X5: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X5)
=> vAPP(a,$o,X4,X5) ) )
=> vAPP(a,$o,X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM150_pme) ).
thf(f1803,plain,
( ~ spl13_8
| ~ spl13_72 ),
inference(avatar_contradiction_clause,[],[f1802]) ).
thf(f1802,plain,
( $false
| ~ spl13_8
| ~ spl13_72 ),
inference(trivial_inequality_removal,[],[f1796]) ).
thf(f1796,plain,
( ( $true = $false )
| ~ spl13_8
| ~ spl13_72 ),
inference(backward_demodulation,[],[f1505,f210]) ).
thf(f210,plain,
( ( $false = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f208]) ).
thf(f208,plain,
( spl13_8
<=> ( $false = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK11,sK10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).
thf(f1505,plain,
( ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ~ spl13_72 ),
inference(avatar_component_clause,[],[f1503]) ).
thf(f1503,plain,
( spl13_72
<=> ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK11,sK10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_72])]) ).
thf(f1739,plain,
( spl13_8
| ~ spl13_75 ),
inference(avatar_split_clause,[],[f1738,f1596,f208]) ).
thf(f1596,plain,
( spl13_75
<=> ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,sK6),sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_75])]) ).
thf(f1738,plain,
( ( $false = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ~ spl13_75 ),
inference(trivial_inequality_removal,[],[f1737]) ).
thf(f1737,plain,
( ( $true = $false )
| ( $false = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ~ spl13_75 ),
inference(forward_demodulation,[],[f1724,f68]) ).
thf(f68,plain,
$false = vAPP(a,$o,sK10,sK9),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f67,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,sK10,sK9) ) ),
inference(superposition,[],[f38,f4]) ).
thf(f38,plain,
$true != vAPP(a,$o,sK10,sK9),
inference(cnf_transformation,[],[f25]) ).
thf(f1724,plain,
( ( $false = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ( $true = vAPP(a,$o,sK10,sK9) )
| ~ spl13_75 ),
inference(trivial_inequality_removal,[],[f1712]) ).
thf(f1712,plain,
( ( $true = $false )
| ( $false = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ( $true = vAPP(a,$o,sK10,sK9) )
| ~ spl13_75 ),
inference(superposition,[],[f1598,f117]) ).
thf(f117,plain,
! [X0: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,sK6),X0) )
| ( $false = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK11,X0)) )
| ( $true = vAPP(a,$o,X0,sK9) ) ),
inference(trivial_inequality_removal,[],[f116]) ).
thf(f116,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,sK6),X0) )
| ( $true = vAPP(a,$o,X0,sK9) )
| ( $false = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,sK11,X0)) ) ),
inference(superposition,[],[f35,f4]) ).
thf(f35,plain,
! [X8: a > $o] :
( ( $true != vAPP(a,$o,X8,vAPP(sTfun(a,$o),a,sK11,X8)) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,sK6),X8) )
| ( $true = vAPP(a,$o,X8,sK9) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f1598,plain,
( ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,sK6),sK10) )
| ~ spl13_75 ),
inference(avatar_component_clause,[],[f1596]) ).
thf(f1710,plain,
spl13_77,
inference(avatar_split_clause,[],[f1709,f1700]) ).
thf(f1709,plain,
$false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,sK6),sK10),
inference(subsumption_resolution,[],[f1686,f222]) ).
thf(f222,plain,
! [X0: a > a > $o,X1: a > $o] :
( ( $true != vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,X0),X1)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f221]) ).
thf(f221,plain,
! [X0: a > a > $o,X1: a > $o] :
( ( $true != $true )
| ( $true != vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,X0),X1)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X0),X1) ) ),
inference(superposition,[],[f31,f4]) ).
thf(f31,plain,
! [X0: a > $o,X1: a > a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X1),X0) )
| ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,X1),X0)) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f19,plain,
! [X0: a > $o,X1: a > a > $o] :
( ( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,X1),X0)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,X1),X0)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,X1),X0)) )
& ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,X1),X0)) ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f17,f18]) ).
thf(f18,plain,
! [X0: a > $o,X1: a > a > $o] :
( ? [X2: a,X3: a] :
( ( $true != vAPP(a,$o,X0,X3) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,X2),X3) )
& ( $true = vAPP(a,$o,X0,X2) ) )
=> ( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,X1),X0)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,X1),X0)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,X1),X0)) )
& ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f17,plain,
! [X0: a > $o,X1: a > a > $o] :
( ? [X2: a,X3: a] :
( ( $true != vAPP(a,$o,X0,X3) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,X2),X3) )
& ( $true = vAPP(a,$o,X0,X2) ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X1),X0) ) ),
inference(rectify,[],[f16]) ).
thf(f16,plain,
! [X8: a > $o,X0: a > a > $o] :
( ? [X9: a,X10: a] :
( ( $true != vAPP(a,$o,X8,X10) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X9),X10) )
& ( $true = vAPP(a,$o,X8,X9) ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X0),X8) ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f1686,plain,
( ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,sK6),sK10) )
| ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,sK6),sK10)) ) ),
inference(trivial_inequality_removal,[],[f1685]) ).
thf(f1685,plain,
( ( $true = $false )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,sK6),sK10) )
| ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,sK6),sK10)) ) ),
inference(duplicate_literal_removal,[],[f1664]) ).
thf(f1664,plain,
( ( $true = $false )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,sK6),sK10) )
| ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,sK6),sK10)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,sK6),sK10) ) ),
inference(superposition,[],[f303,f354]) ).
thf(f354,plain,
! [X0: a > a > $o,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,X0),sK10)),X1) )
| ( $true = vAPP(a,$o,sK10,X1) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X0),sK10) ) ),
inference(trivial_inequality_removal,[],[f353]) ).
thf(f353,plain,
! [X0: a > a > $o,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,sK10,X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,X0),sK10)),X1) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X0),sK10) ) ),
inference(superposition,[],[f75,f168]) ).
thf(f168,plain,
! [X0: a > a > $o,X1: a > $o] :
( ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,X0),X1)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f167]) ).
thf(f167,plain,
! [X0: a > a > $o,X1: a > $o] :
( ( $true != $true )
| ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,X0),X1)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X0),X1) ) ),
inference(superposition,[],[f29,f4]) ).
thf(f29,plain,
! [X0: a > $o,X1: a > a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X1),X0) )
| ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,X1),X0)) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f75,plain,
! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,sK10,X0) )
| ( $true = vAPP(a,$o,sK10,X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f74,plain,
! [X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,sK10,X1) )
| ( $true != vAPP(a,$o,sK10,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,X0),X1) ) ),
inference(superposition,[],[f37,f4]) ).
thf(f37,plain,
! [X6: a,X5: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,X5),X6) )
| ( $true = vAPP(a,$o,sK10,X6) )
| ( $true != vAPP(a,$o,sK10,X5) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f303,plain,
! [X0: a > a > $o,X1: a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,X0),X1)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,X0),X1)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f302]) ).
thf(f302,plain,
! [X0: a > a > $o,X1: a > $o] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,X0),X1)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,X0),X1)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X0),X1) ) ),
inference(superposition,[],[f30,f4]) ).
thf(f30,plain,
! [X0: a > $o,X1: a > a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,X1),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,X1),X0)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,X1),X0)) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f1606,plain,
spl13_75,
inference(avatar_split_clause,[],[f1605,f1596]) ).
thf(f1605,plain,
$false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,sK6),sK10),
inference(subsumption_resolution,[],[f1582,f147]) ).
thf(f147,plain,
! [X0: a > a > $o,X1: a > $o] :
( ( $true != vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,X0),X1)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f146]) ).
thf(f146,plain,
! [X0: a > a > $o,X1: a > $o] :
( ( $true != $true )
| ( $true != vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,X0),X1)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X0),X1) ) ),
inference(superposition,[],[f28,f4]) ).
thf(f28,plain,
! [X0: a > $o,X1: a > a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X1),X0) )
| ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,X1),X0)) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
! [X0: a > $o,X1: a > a > $o] :
( ( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,X1),X0)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,X1),X0)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,X1),X0)) )
& ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,X1),X0)) ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f13,f14]) ).
thf(f14,plain,
! [X0: a > $o,X1: a > a > $o] :
( ? [X2: a,X3: a] :
( ( $true != vAPP(a,$o,X0,X3) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,X2),X3) )
& ( $true = vAPP(a,$o,X0,X2) ) )
=> ( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,X1),X0)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,X1),X0)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,X1),X0)) )
& ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
! [X0: a > $o,X1: a > a > $o] :
( ? [X2: a,X3: a] :
( ( $true != vAPP(a,$o,X0,X3) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,X2),X3) )
& ( $true = vAPP(a,$o,X0,X2) ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X1),X0) ) ),
inference(rectify,[],[f12]) ).
thf(f12,plain,
! [X4: a > $o,X0: a > a > $o] :
( ? [X5: a,X6: a] :
( ( vAPP(a,$o,X4,X6) != $true )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X5),X6) )
& ( vAPP(a,$o,X4,X5) = $true ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X0),X4) ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f1582,plain,
( ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,sK6),sK10) )
| ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,sK6),sK10)) ) ),
inference(trivial_inequality_removal,[],[f1581]) ).
thf(f1581,plain,
( ( $true = $false )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,sK6),sK10) )
| ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,sK6),sK10)) ) ),
inference(duplicate_literal_removal,[],[f1560]) ).
thf(f1560,plain,
( ( $true = $false )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,sK6),sK10) )
| ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,sK6),sK10)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,sK6),sK10) ) ),
inference(superposition,[],[f288,f322]) ).
thf(f322,plain,
! [X0: a > a > $o,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,X0),sK10)),X1) )
| ( $true = vAPP(a,$o,sK10,X1) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X0),sK10) ) ),
inference(trivial_inequality_removal,[],[f321]) ).
thf(f321,plain,
! [X0: a > a > $o,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,sK10,X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,X0),sK10)),X1) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X0),sK10) ) ),
inference(superposition,[],[f75,f131]) ).
thf(f131,plain,
! [X0: a > a > $o,X1: a > $o] :
( ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,X0),X1)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f130]) ).
thf(f130,plain,
! [X0: a > a > $o,X1: a > $o] :
( ( $true != $true )
| ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,X0),X1)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X0),X1) ) ),
inference(superposition,[],[f26,f4]) ).
thf(f26,plain,
! [X0: a > $o,X1: a > a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X1),X0) )
| ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,X1),X0)) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f288,plain,
! [X0: a > a > $o,X1: a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,X0),X1)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,X0),X1)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f287]) ).
thf(f287,plain,
! [X0: a > a > $o,X1: a > $o] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,X0),X1)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,X0),X1)) )
| ( $false = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X0),X1) ) ),
inference(superposition,[],[f27,f4]) ).
thf(f27,plain,
! [X0: a > $o,X1: a > a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,X1),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,X1),X0)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,X1),X0)) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f1508,plain,
( ~ spl13_18
| spl13_72
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f1365,f663,f1503,f419]) ).
thf(f419,plain,
( spl13_18
<=> ( $true = vAPP(a,$o,sK10,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_18])]) ).
thf(f663,plain,
( spl13_38
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,sK10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_38])]) ).
thf(f1365,plain,
( ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ( $true != vAPP(a,$o,sK10,sK8) )
| ~ spl13_38 ),
inference(trivial_inequality_removal,[],[f1364]) ).
thf(f1364,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ( $true != vAPP(a,$o,sK10,sK8) )
| ~ spl13_38 ),
inference(superposition,[],[f37,f665]) ).
thf(f665,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ~ spl13_38 ),
inference(avatar_component_clause,[],[f663]) ).
thf(f1507,plain,
( spl13_56
| spl13_72
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f1366,f663,f1503,f1012]) ).
thf(f1366,plain,
( ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ( $false = vAPP(a,$o,sK10,sK8) )
| ~ spl13_38 ),
inference(trivial_inequality_removal,[],[f1363]) ).
thf(f1363,plain,
( ( $true = $false )
| ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ( $false = vAPP(a,$o,sK10,sK8) )
| ~ spl13_38 ),
inference(superposition,[],[f102,f665]) ).
thf(f102,plain,
! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,X0),X1) )
| ( $true = vAPP(a,$o,sK10,X1) )
| ( $false = vAPP(a,$o,sK10,X0) ) ),
inference(trivial_inequality_removal,[],[f101]) ).
thf(f101,plain,
! [X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,sK10,X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,X0),X1) )
| ( $false = vAPP(a,$o,sK10,X0) ) ),
inference(superposition,[],[f75,f4]) ).
thf(f1479,plain,
( ~ spl13_20
| spl13_28
| ~ spl13_56 ),
inference(avatar_contradiction_clause,[],[f1478]) ).
thf(f1478,plain,
( $false
| ~ spl13_20
| spl13_28
| ~ spl13_56 ),
inference(trivial_inequality_removal,[],[f1477]) ).
thf(f1477,plain,
( ( $true = $false )
| ~ spl13_20
| spl13_28
| ~ spl13_56 ),
inference(forward_demodulation,[],[f1476,f1061]) ).
thf(f1061,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,sK10)) )
| spl13_28 ),
inference(trivial_inequality_removal,[],[f1060]) ).
thf(f1060,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,sK10)) )
| spl13_28 ),
inference(superposition,[],[f540,f4]) ).
thf(f540,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,sK10)) )
| spl13_28 ),
inference(avatar_component_clause,[],[f539]) ).
thf(f539,plain,
( spl13_28
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,sK10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_28])]) ).
thf(f1476,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,sK10)) )
| ~ spl13_20
| ~ spl13_56 ),
inference(trivial_inequality_removal,[],[f1475]) ).
thf(f1475,plain,
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,sK10)) )
| ~ spl13_20
| ~ spl13_56 ),
inference(forward_demodulation,[],[f1474,f1014]) ).
thf(f1474,plain,
( ( $true = vAPP(a,$o,sK10,sK8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,sK10)) )
| ~ spl13_20 ),
inference(subsumption_resolution,[],[f1444,f229]) ).
thf(f229,plain,
! [X0: a > $o] :
( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,sK6),X0)) )
| ( $true = vAPP(a,$o,X0,sK8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,X0)) ) ),
inference(trivial_inequality_removal,[],[f226]) ).
thf(f226,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,sK6),X0)) )
| ( $true = vAPP(a,$o,X0,sK8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,X0)) ) ),
inference(superposition,[],[f31,f32]) ).
thf(f32,plain,
! [X10: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP0,sK6),X10) )
| ( $true = vAPP(a,$o,X10,sK8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,X10)) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f1444,plain,
( ( $true = vAPP(a,$o,sK10,sK8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,sK10)) )
| ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,sK6),sK10)) )
| ~ spl13_20 ),
inference(trivial_inequality_removal,[],[f1421]) ).
thf(f1421,plain,
( ( $true = $false )
| ( $true = vAPP(a,$o,sK10,sK8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,sK10)) )
| ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,sK6),sK10)) )
| ~ spl13_20 ),
inference(superposition,[],[f305,f428]) ).
thf(f428,plain,
( ! [X0: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,sK6),sK10)),X0) )
| ( $true = vAPP(a,$o,sK10,X0) ) )
| ~ spl13_20 ),
inference(avatar_component_clause,[],[f427]) ).
thf(f427,plain,
( spl13_20
<=> ! [X0: a] :
( ( $true = vAPP(a,$o,sK10,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,sK6),sK10)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_20])]) ).
thf(f305,plain,
! [X0: a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,sK6),X0)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,sK6),X0)) )
| ( $true = vAPP(a,$o,X0,sK8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,X0)) ) ),
inference(trivial_inequality_removal,[],[f300]) ).
thf(f300,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,sK6),X0)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK5,sK6),X0)) )
| ( $true = vAPP(a,$o,X0,sK8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,X0)) ) ),
inference(superposition,[],[f30,f32]) ).
thf(f1353,plain,
( spl13_38
| ~ spl13_9 ),
inference(avatar_split_clause,[],[f1352,f212,f663]) ).
thf(f212,plain,
( spl13_9
<=> ! [X0: a] :
( ( $true = vAPP(a,$o,sK10,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,sK6),sK10)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).
thf(f1352,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ~ spl13_9 ),
inference(trivial_inequality_removal,[],[f1351]) ).
thf(f1351,plain,
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ~ spl13_9 ),
inference(forward_demodulation,[],[f1350,f68]) ).
thf(f1350,plain,
( ( $true = vAPP(a,$o,sK10,sK9) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ~ spl13_9 ),
inference(subsumption_resolution,[],[f1298,f257]) ).
thf(f257,plain,
! [X0: a > $o] :
( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,sK6),X0)) )
| ( $true = vAPP(a,$o,X0,sK9) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,X0)) ) ),
inference(trivial_inequality_removal,[],[f254]) ).
thf(f254,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,sK6),X0)) )
| ( $true = vAPP(a,$o,X0,sK9) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,X0)) ) ),
inference(superposition,[],[f28,f34]) ).
thf(f34,plain,
! [X8: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),$o),sP1,sK6),X8) )
| ( $true = vAPP(a,$o,X8,sK9) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,X8)) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f1298,plain,
( ( $true = vAPP(a,$o,sK10,sK9) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,sK6),sK10)) )
| ~ spl13_9 ),
inference(trivial_inequality_removal,[],[f1275]) ).
thf(f1275,plain,
( ( $true = $false )
| ( $true = vAPP(a,$o,sK10,sK9) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,sK10)) )
| ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,sK6),sK10)) )
| ~ spl13_9 ),
inference(superposition,[],[f290,f213]) ).
thf(f213,plain,
( ! [X0: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,sK6),sK10)),X0) )
| ( $true = vAPP(a,$o,sK10,X0) ) )
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f212]) ).
thf(f290,plain,
! [X0: a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,sK6),X0)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,sK6),X0)) )
| ( $true = vAPP(a,$o,X0,sK9) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,X0)) ) ),
inference(trivial_inequality_removal,[],[f285]) ).
thf(f285,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,sK6),X0)),vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK3,sK6),X0)) )
| ( $true = vAPP(a,$o,X0,sK9) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,X0)) ) ),
inference(superposition,[],[f27,f34]) ).
thf(f1050,plain,
( ~ spl13_19
| ~ spl13_28 ),
inference(avatar_contradiction_clause,[],[f1049]) ).
thf(f1049,plain,
( $false
| ~ spl13_19
| ~ spl13_28 ),
inference(trivial_inequality_removal,[],[f1048]) ).
thf(f1048,plain,
( ( $true = $false )
| ~ spl13_19
| ~ spl13_28 ),
inference(forward_demodulation,[],[f1036,f425]) ).
thf(f425,plain,
( ( $false = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK12,sK10)) )
| ~ spl13_19 ),
inference(avatar_component_clause,[],[f423]) ).
thf(f1036,plain,
( ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK12,sK10)) )
| ~ spl13_28 ),
inference(trivial_inequality_removal,[],[f1031]) ).
thf(f1031,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,sK10,vAPP(sTfun(a,$o),a,sK12,sK10)) )
| ~ spl13_28 ),
inference(superposition,[],[f36,f541]) ).
thf(f541,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,sK10)) )
| ~ spl13_28 ),
inference(avatar_component_clause,[],[f539]) ).
thf(f36,plain,
! [X7: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),X7) )
| ( $true = vAPP(a,$o,sK10,X7) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f666,plain,
( spl13_38
| spl13_9 ),
inference(avatar_split_clause,[],[f661,f212,f663]) ).
thf(f661,plain,
! [X0: a] :
( ( $true = vAPP(a,$o,sK10,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,sK6),sK10)),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,sK10)) ) ),
inference(trivial_inequality_removal,[],[f660]) ).
thf(f660,plain,
! [X0: a] :
( ( $true = $false )
| ( $true = vAPP(a,$o,sK10,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,sK6),sK10)),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,sK10)) ) ),
inference(forward_demodulation,[],[f639,f68]) ).
thf(f639,plain,
! [X0: a] :
( ( $true = vAPP(a,$o,sK10,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,sK6),sK10)),X0) )
| ( $true = vAPP(a,$o,sK10,sK9) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,sK10)) ) ),
inference(trivial_inequality_removal,[],[f638]) ).
thf(f638,plain,
! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,sK10,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,sK6),sK10)),X0) )
| ( $true = vAPP(a,$o,sK10,sK9) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,sK10)) ) ),
inference(superposition,[],[f75,f256]) ).
thf(f256,plain,
! [X0: a > $o] :
( ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,sK6),X0)) )
| ( $true = vAPP(a,$o,X0,sK9) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,X0)) ) ),
inference(trivial_inequality_removal,[],[f255]) ).
thf(f255,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK2,sK6),X0)) )
| ( $true = vAPP(a,$o,X0,sK9) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK8),vAPP(sTfun(a,$o),a,sK11,X0)) ) ),
inference(superposition,[],[f26,f34]) ).
thf(f628,plain,
( spl13_28
| spl13_18
| spl13_20 ),
inference(avatar_split_clause,[],[f520,f427,f419,f539]) ).
thf(f520,plain,
! [X0: a] :
( ( $true = vAPP(a,$o,sK10,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,sK6),sK10)),X0) )
| ( $true = vAPP(a,$o,sK10,sK8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,sK10)) ) ),
inference(trivial_inequality_removal,[],[f519]) ).
thf(f519,plain,
! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,sK10,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,sK6),sK10)),X0) )
| ( $true = vAPP(a,$o,sK10,sK8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,sK10)) ) ),
inference(superposition,[],[f75,f228]) ).
thf(f228,plain,
! [X0: a > $o] :
( ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,sK6),X0)) )
| ( $true = vAPP(a,$o,X0,sK8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,X0)) ) ),
inference(trivial_inequality_removal,[],[f227]) ).
thf(f227,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,sTfun(a,$o)),sTfun(sTfun(a,$o),a),sK4,sK6),X0)) )
| ( $true = vAPP(a,$o,X0,sK8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK6,sK7),vAPP(sTfun(a,$o),a,sK12,X0)) ) ),
inference(superposition,[],[f29,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SEV138^5 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n013.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri May 3 11:46:04 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (10018)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.33 % (10023)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.33 % (10022)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.11/0.33 % (10021)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.11/0.33 % (10019)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.33 % (10025)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.33 % (10024)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.11/0.33 % (10021)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.33 % (10022)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.33 % Exception at run slice level% Exception at run slice level
% 0.11/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.33
% 0.11/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.33 % Exception at run slice level
% 0.11/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.34 % (10020)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.34 % Exception at run slice level
% 0.11/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.35 % (10028)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_470 on theBenchmark for (470ds/0Mi)
% 0.11/0.35 % (10026)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.35 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.11/0.35 % (10027)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_476 on theBenchmark for (476ds/0Mi)
% 0.11/0.35 % (10028)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.35 % Exception at run slice level
% 0.11/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.35 % Exception at run slice level
% 0.11/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.35 % (10027)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.35 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.11/0.35 % (10029)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_396 on theBenchmark for (396ds/0Mi)
% 0.17/0.36 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.17/0.36 % (10030)dis+11_4:5_nm=4:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_216 on theBenchmark for (216ds/0Mi)
% 0.17/0.39 % (10024)First to succeed.
% 0.17/0.39 % (10021)Also succeeded, but the first one will report.
% 0.17/0.39 % (10027)Also succeeded, but the first one will report.
% 0.17/0.39 % (10024)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10018"
% 0.17/0.39 % (10024)Refutation found. Thanks to Tanya!
% 0.17/0.39 % SZS status Theorem for theBenchmark
% 0.17/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.39 % (10024)------------------------------
% 0.17/0.39 % (10024)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.39 % (10024)Termination reason: Refutation
% 0.17/0.39
% 0.17/0.39 % (10024)Memory used [KB]: 1530
% 0.17/0.39 % (10024)Time elapsed: 0.059 s
% 0.17/0.39 % (10024)Instructions burned: 148 (million)
% 0.17/0.39 % (10018)Success in time 0.07 s
%------------------------------------------------------------------------------