TSTP Solution File: SEV044^5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV044^5 : 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 : n025.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 04:14:19 EDT 2024
% Result : Theorem 0.15s 0.35s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 35
% Syntax : Number of formulae : 101 ( 1 unt; 21 typ; 0 def)
% Number of atoms : 1585 ( 249 equ; 0 cnn)
% Maximal formula atoms : 32 ( 19 avg)
% Number of connectives : 494 ( 180 ~; 186 |; 72 &; 0 @)
% ( 7 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 109 ( 108 >; 1 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 11 con; 0-6 aty)
% Number of variables : 228 ( 0 ^ 168 !; 54 ?; 228 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_5,type,
sK0: b > $o ).
thf(func_def_6,type,
sK1: b > a > a > $o ).
thf(func_def_7,type,
sK2: b > a ).
thf(func_def_8,type,
sK3: b > a ).
thf(func_def_9,type,
sK4: b > a ).
thf(func_def_10,type,
sK5: b ).
thf(func_def_11,type,
sK6: b > a ).
thf(func_def_12,type,
sK7: b > a ).
thf(func_def_13,type,
sK8: b ).
thf(func_def_15,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_16,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
vOR: $o > $o > $o ).
thf(func_def_19,type,
vIMP: $o > $o > $o ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f415,plain,
$false,
inference(avatar_sat_refutation,[],[f66,f71,f80,f84,f141,f213,f307,f309,f326,f350,f351,f359,f381,f414]) ).
thf(f414,plain,
( ~ spl9_6
| spl9_4 ),
inference(avatar_split_clause,[],[f20,f78,f138]) ).
thf(f138,plain,
( spl9_6
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK8),vAPP(b,a,sK7,sK8)),vAPP(b,a,sK6,sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
thf(f78,plain,
( spl9_4
<=> ! [X7: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X7),vAPP(b,a,sK2,X7)),vAPP(b,a,sK3,X7)) )
| ( $true != vAPP(b,$o,sK0,X7) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
thf(f20,plain,
! [X7: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X7),vAPP(b,a,sK2,X7)),vAPP(b,a,sK3,X7)) )
| ( $true != vAPP(b,$o,sK0,X7) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK8),vAPP(b,a,sK7,sK8)),vAPP(b,a,sK6,sK8)) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
( ( ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK5),vAPP(b,a,sK2,sK5)),vAPP(b,a,sK4,sK5)) )
& ( $true = vAPP(b,$o,sK0,sK5) )
& ! [X6: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X6),vAPP(b,a,sK3,X6)),vAPP(b,a,sK4,X6)) )
| ( $true != vAPP(b,$o,sK0,X6) ) )
& ! [X7: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X7),vAPP(b,a,sK2,X7)),vAPP(b,a,sK3,X7)) )
| ( $true != vAPP(b,$o,sK0,X7) ) ) )
| ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK8),vAPP(b,a,sK7,sK8)),vAPP(b,a,sK6,sK8)) )
& ( $true = vAPP(b,$o,sK0,sK8) )
& ! [X11: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X11),vAPP(b,a,sK6,X11)),vAPP(b,a,sK7,X11)) )
| ( $true != vAPP(b,$o,sK0,X11) ) ) ) )
& ! [X12: b] :
( ( ! [X13: a,X14: a,X15: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X13),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X14),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X13),X14) ) )
& ! [X16: a,X17: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X17),X16) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X16),X17) ) ) )
| ( $true != vAPP(b,$o,sK0,X12) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f9,f14,f13,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: b > $o,X1: b > a > a > $o] :
( ( ? [X2: b > a,X3: b > a,X4: b > a] :
( ? [X5: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X5),vAPP(b,a,X2,X5)),vAPP(b,a,X4,X5)) )
& ( $true = vAPP(b,$o,X0,X5) ) )
& ! [X6: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X6),vAPP(b,a,X3,X6)),vAPP(b,a,X4,X6)) )
| ( $true != vAPP(b,$o,X0,X6) ) )
& ! [X7: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X7),vAPP(b,a,X2,X7)),vAPP(b,a,X3,X7)) )
| ( $true != vAPP(b,$o,X0,X7) ) ) )
| ? [X8: b > a,X9: b > a] :
( ? [X10: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X10),vAPP(b,a,X9,X10)),vAPP(b,a,X8,X10)) )
& ( $true = vAPP(b,$o,X0,X10) ) )
& ! [X11: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X11),vAPP(b,a,X8,X11)),vAPP(b,a,X9,X11)) )
| ( $true != vAPP(b,$o,X0,X11) ) ) ) )
& ! [X12: b] :
( ( ! [X13: a,X14: a,X15: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),X13),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),X14),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),X13),X14) ) )
& ! [X16: a,X17: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),X17),X16) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),X16),X17) ) ) )
| ( $true != vAPP(b,$o,X0,X12) ) ) )
=> ( ( ? [X4: b > a,X3: b > a,X2: b > a] :
( ? [X5: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X5),vAPP(b,a,X2,X5)),vAPP(b,a,X4,X5)) )
& ( $true = vAPP(b,$o,sK0,X5) ) )
& ! [X6: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X6),vAPP(b,a,X3,X6)),vAPP(b,a,X4,X6)) )
| ( $true != vAPP(b,$o,sK0,X6) ) )
& ! [X7: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X7),vAPP(b,a,X2,X7)),vAPP(b,a,X3,X7)) )
| ( $true != vAPP(b,$o,sK0,X7) ) ) )
| ? [X9: b > a,X8: b > a] :
( ? [X10: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X10),vAPP(b,a,X9,X10)),vAPP(b,a,X8,X10)) )
& ( $true = vAPP(b,$o,sK0,X10) ) )
& ! [X11: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X11),vAPP(b,a,X8,X11)),vAPP(b,a,X9,X11)) )
| ( $true != vAPP(b,$o,sK0,X11) ) ) ) )
& ! [X12: b] :
( ( ! [X15: a,X14: a,X13: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X13),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X14),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X13),X14) ) )
& ! [X17: a,X16: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X17),X16) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X16),X17) ) ) )
| ( $true != vAPP(b,$o,sK0,X12) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
( ? [X4: b > a,X3: b > a,X2: b > a] :
( ? [X5: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X5),vAPP(b,a,X2,X5)),vAPP(b,a,X4,X5)) )
& ( $true = vAPP(b,$o,sK0,X5) ) )
& ! [X6: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X6),vAPP(b,a,X3,X6)),vAPP(b,a,X4,X6)) )
| ( $true != vAPP(b,$o,sK0,X6) ) )
& ! [X7: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X7),vAPP(b,a,X2,X7)),vAPP(b,a,X3,X7)) )
| ( $true != vAPP(b,$o,sK0,X7) ) ) )
=> ( ? [X5: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X5),vAPP(b,a,sK2,X5)),vAPP(b,a,sK4,X5)) )
& ( $true = vAPP(b,$o,sK0,X5) ) )
& ! [X6: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X6),vAPP(b,a,sK3,X6)),vAPP(b,a,sK4,X6)) )
| ( $true != vAPP(b,$o,sK0,X6) ) )
& ! [X7: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X7),vAPP(b,a,sK2,X7)),vAPP(b,a,sK3,X7)) )
| ( $true != vAPP(b,$o,sK0,X7) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
( ? [X5: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X5),vAPP(b,a,sK2,X5)),vAPP(b,a,sK4,X5)) )
& ( $true = vAPP(b,$o,sK0,X5) ) )
=> ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK5),vAPP(b,a,sK2,sK5)),vAPP(b,a,sK4,sK5)) )
& ( $true = vAPP(b,$o,sK0,sK5) ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
( ? [X9: b > a,X8: b > a] :
( ? [X10: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X10),vAPP(b,a,X9,X10)),vAPP(b,a,X8,X10)) )
& ( $true = vAPP(b,$o,sK0,X10) ) )
& ! [X11: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X11),vAPP(b,a,X8,X11)),vAPP(b,a,X9,X11)) )
| ( $true != vAPP(b,$o,sK0,X11) ) ) )
=> ( ? [X10: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X10),vAPP(b,a,sK7,X10)),vAPP(b,a,sK6,X10)) )
& ( $true = vAPP(b,$o,sK0,X10) ) )
& ! [X11: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X11),vAPP(b,a,sK6,X11)),vAPP(b,a,sK7,X11)) )
| ( $true != vAPP(b,$o,sK0,X11) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
( ? [X10: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X10),vAPP(b,a,sK7,X10)),vAPP(b,a,sK6,X10)) )
& ( $true = vAPP(b,$o,sK0,X10) ) )
=> ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK8),vAPP(b,a,sK7,sK8)),vAPP(b,a,sK6,sK8)) )
& ( $true = vAPP(b,$o,sK0,sK8) ) ) ),
introduced(choice_axiom,[]) ).
thf(f9,plain,
? [X0: b > $o,X1: b > a > a > $o] :
( ( ? [X2: b > a,X3: b > a,X4: b > a] :
( ? [X5: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X5),vAPP(b,a,X2,X5)),vAPP(b,a,X4,X5)) )
& ( $true = vAPP(b,$o,X0,X5) ) )
& ! [X6: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X6),vAPP(b,a,X3,X6)),vAPP(b,a,X4,X6)) )
| ( $true != vAPP(b,$o,X0,X6) ) )
& ! [X7: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X7),vAPP(b,a,X2,X7)),vAPP(b,a,X3,X7)) )
| ( $true != vAPP(b,$o,X0,X7) ) ) )
| ? [X8: b > a,X9: b > a] :
( ? [X10: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X10),vAPP(b,a,X9,X10)),vAPP(b,a,X8,X10)) )
& ( $true = vAPP(b,$o,X0,X10) ) )
& ! [X11: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X11),vAPP(b,a,X8,X11)),vAPP(b,a,X9,X11)) )
| ( $true != vAPP(b,$o,X0,X11) ) ) ) )
& ! [X12: b] :
( ( ! [X13: a,X14: a,X15: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),X13),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),X14),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),X13),X14) ) )
& ! [X16: a,X17: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),X17),X16) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),X16),X17) ) ) )
| ( $true != vAPP(b,$o,X0,X12) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,plain,
? [X0: b > $o,X1: b > a > a > $o] :
( ( ? [X8: b > a,X9: b > a,X10: b > a] :
( ? [X13: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X13),vAPP(b,a,X8,X13)),vAPP(b,a,X10,X13)) )
& ( $true = vAPP(b,$o,X0,X13) ) )
& ! [X11: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X11),vAPP(b,a,X9,X11)),vAPP(b,a,X10,X11)) )
| ( $true != vAPP(b,$o,X0,X11) ) )
& ! [X12: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),vAPP(b,a,X8,X12)),vAPP(b,a,X9,X12)) )
| ( $true != vAPP(b,$o,X0,X12) ) ) )
| ? [X14: b > a,X15: b > a] :
( ? [X17: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X17),vAPP(b,a,X15,X17)),vAPP(b,a,X14,X17)) )
& ( $true = vAPP(b,$o,X0,X17) ) )
& ! [X16: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X16),vAPP(b,a,X14,X16)),vAPP(b,a,X15,X16)) )
| ( $true != vAPP(b,$o,X0,X16) ) ) ) )
& ! [X2: b] :
( ( ! [X3: a,X4: a,X5: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X5) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X4),X5) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X4) != $true ) )
& ! [X6: a,X7: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X7),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X6),X7) ) ) )
| ( vAPP(b,$o,X0,X2) != $true ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
? [X0: b > $o,X1: b > a > a > $o] :
( ( ? [X8: b > a,X9: b > a,X10: b > a] :
( ? [X13: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X13),vAPP(b,a,X8,X13)),vAPP(b,a,X10,X13)) )
& ( $true = vAPP(b,$o,X0,X13) ) )
& ! [X11: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X11),vAPP(b,a,X9,X11)),vAPP(b,a,X10,X11)) )
| ( $true != vAPP(b,$o,X0,X11) ) )
& ! [X12: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),vAPP(b,a,X8,X12)),vAPP(b,a,X9,X12)) )
| ( $true != vAPP(b,$o,X0,X12) ) ) )
| ? [X14: b > a,X15: b > a] :
( ? [X17: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X17),vAPP(b,a,X15,X17)),vAPP(b,a,X14,X17)) )
& ( $true = vAPP(b,$o,X0,X17) ) )
& ! [X16: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X16),vAPP(b,a,X14,X16)),vAPP(b,a,X15,X16)) )
| ( $true != vAPP(b,$o,X0,X16) ) ) ) )
& ! [X2: b] :
( ( ! [X3: a,X4: a,X5: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X5) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X4),X5) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X4) != $true ) )
& ! [X6: a,X7: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X7),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X6),X7) ) ) )
| ( vAPP(b,$o,X0,X2) != $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ! [X0: b > $o,X1: b > a > a > $o] :
( ! [X2: b] :
( ( vAPP(b,$o,X0,X2) = $true )
=> ( ! [X3: a,X4: a,X5: a] :
( ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X4),X5) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X4) = $true ) )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X5) = $true ) )
& ! [X6: a,X7: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X6),X7) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X7),X6) ) ) ) )
=> ( ! [X8: b > a,X9: b > a,X10: b > a] :
( ( ! [X11: b] :
( ( $true = vAPP(b,$o,X0,X11) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X11),vAPP(b,a,X9,X11)),vAPP(b,a,X10,X11)) ) )
& ! [X12: b] :
( ( $true = vAPP(b,$o,X0,X12) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),vAPP(b,a,X8,X12)),vAPP(b,a,X9,X12)) ) ) )
=> ! [X13: b] :
( ( $true = vAPP(b,$o,X0,X13) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X13),vAPP(b,a,X8,X13)),vAPP(b,a,X10,X13)) ) ) )
& ! [X14: b > a,X15: b > a] :
( ! [X16: b] :
( ( $true = vAPP(b,$o,X0,X16) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X16),vAPP(b,a,X14,X16)),vAPP(b,a,X15,X16)) ) )
=> ! [X17: b] :
( ( $true = vAPP(b,$o,X0,X17) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X17),vAPP(b,a,X15,X17)),vAPP(b,a,X14,X17)) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ! [X0: b > $o,X1: b > a > a > $o] :
( ! [X2: b] :
( vAPP(b,$o,X0,X2)
=> ( ! [X3: a,X4: a,X5: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X4),X5)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X4) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X5) )
& ! [X6: a,X7: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X6),X7)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X7),X6) ) ) )
=> ( ! [X8: b > a,X9: b > a,X10: b > a] :
( ( ! [X11: b] :
( vAPP(b,$o,X0,X11)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X11),vAPP(b,a,X9,X11)),vAPP(b,a,X10,X11)) )
& ! [X12: b] :
( vAPP(b,$o,X0,X12)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X12),vAPP(b,a,X8,X12)),vAPP(b,a,X9,X12)) ) )
=> ! [X13: b] :
( vAPP(b,$o,X0,X13)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X13),vAPP(b,a,X8,X13)),vAPP(b,a,X10,X13)) ) )
& ! [X14: b > a,X15: b > a] :
( ! [X16: b] :
( vAPP(b,$o,X0,X16)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X16),vAPP(b,a,X14,X16)),vAPP(b,a,X15,X16)) )
=> ! [X17: b] :
( vAPP(b,$o,X0,X17)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X17),vAPP(b,a,X15,X17)),vAPP(b,a,X14,X17)) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: b > $o,X1: b > a > a > $o] :
( ! [X2: b] :
( vAPP(b,$o,X0,X2)
=> ( ! [X3: a,X4: a,X5: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X4),X5)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X4) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X5) )
& ! [X3: a,X4: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X4)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X4),X3) ) ) )
=> ( ! [X2: b > a,X4: b > a,X5: b > a] :
( ( ! [X3: b] :
( vAPP(b,$o,X0,X3)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X3),vAPP(b,a,X4,X3)),vAPP(b,a,X5,X3)) )
& ! [X3: b] :
( vAPP(b,$o,X0,X3)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X3),vAPP(b,a,X2,X3)),vAPP(b,a,X4,X3)) ) )
=> ! [X3: b] :
( vAPP(b,$o,X0,X3)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X3),vAPP(b,a,X2,X3)),vAPP(b,a,X5,X3)) ) )
& ! [X2: b > a,X4: b > a] :
( ! [X3: b] :
( vAPP(b,$o,X0,X3)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X3),vAPP(b,a,X2,X3)),vAPP(b,a,X4,X3)) )
=> ! [X3: b] :
( vAPP(b,$o,X0,X3)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X3),vAPP(b,a,X4,X3)),vAPP(b,a,X2,X3)) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: b > $o,X1: b > a > a > $o] :
( ! [X2: b] :
( vAPP(b,$o,X0,X2)
=> ( ! [X3: a,X4: a,X5: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X4),X5)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X4) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X5) )
& ! [X3: a,X4: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X3),X4)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X2),X4),X3) ) ) )
=> ( ! [X2: b > a,X4: b > a,X5: b > a] :
( ( ! [X3: b] :
( vAPP(b,$o,X0,X3)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X3),vAPP(b,a,X4,X3)),vAPP(b,a,X5,X3)) )
& ! [X3: b] :
( vAPP(b,$o,X0,X3)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X3),vAPP(b,a,X2,X3)),vAPP(b,a,X4,X3)) ) )
=> ! [X3: b] :
( vAPP(b,$o,X0,X3)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X3),vAPP(b,a,X2,X3)),vAPP(b,a,X5,X3)) ) )
& ! [X2: b > a,X4: b > a] :
( ! [X3: b] :
( vAPP(b,$o,X0,X3)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X3),vAPP(b,a,X2,X3)),vAPP(b,a,X4,X3)) )
=> ! [X3: b] :
( vAPP(b,$o,X0,X3)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),X1,X3),vAPP(b,a,X4,X3)),vAPP(b,a,X2,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM506_pme) ).
thf(f381,plain,
( spl9_7
| spl9_2 ),
inference(avatar_split_clause,[],[f24,f63,f211]) ).
thf(f211,plain,
( spl9_7
<=> ! [X11: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X11),vAPP(b,a,sK6,X11)),vAPP(b,a,sK7,X11)) )
| ( $true != vAPP(b,$o,sK0,X11) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
thf(f63,plain,
( spl9_2
<=> ( $true = vAPP(b,$o,sK0,sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
thf(f24,plain,
! [X11: b] :
( ( $true = vAPP(b,$o,sK0,sK5) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X11),vAPP(b,a,sK6,X11)),vAPP(b,a,sK7,X11)) )
| ( $true != vAPP(b,$o,sK0,X11) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f359,plain,
( ~ spl9_6
| spl9_2 ),
inference(avatar_split_clause,[],[f26,f63,f138]) ).
thf(f26,plain,
( ( $true = vAPP(b,$o,sK0,sK5) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK8),vAPP(b,a,sK7,sK8)),vAPP(b,a,sK6,sK8)) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f351,plain,
( ~ spl9_6
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f29,f68,f138]) ).
thf(f68,plain,
( spl9_3
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK5),vAPP(b,a,sK2,sK5)),vAPP(b,a,sK4,sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
thf(f29,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK5),vAPP(b,a,sK2,sK5)),vAPP(b,a,sK4,sK5)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK8),vAPP(b,a,sK7,sK8)),vAPP(b,a,sK6,sK8)) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f350,plain,
( ~ spl9_1
| spl9_6
| ~ spl9_7 ),
inference(avatar_contradiction_clause,[],[f349]) ).
thf(f349,plain,
( $false
| ~ spl9_1
| spl9_6
| ~ spl9_7 ),
inference(trivial_inequality_removal,[],[f346]) ).
thf(f346,plain,
( ( $true != $true )
| ~ spl9_1
| spl9_6
| ~ spl9_7 ),
inference(superposition,[],[f342,f61]) ).
thf(f61,plain,
( ( $true = vAPP(b,$o,sK0,sK8) )
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f59,plain,
( spl9_1
<=> ( $true = vAPP(b,$o,sK0,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
thf(f342,plain,
( ( $true != vAPP(b,$o,sK0,sK8) )
| ~ spl9_1
| spl9_6
| ~ spl9_7 ),
inference(trivial_inequality_removal,[],[f329]) ).
thf(f329,plain,
( ( $true = $false )
| ( $true != vAPP(b,$o,sK0,sK8) )
| ~ spl9_1
| spl9_6
| ~ spl9_7 ),
inference(superposition,[],[f148,f212]) ).
thf(f212,plain,
( ! [X11: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X11),vAPP(b,a,sK6,X11)),vAPP(b,a,sK7,X11)) )
| ( $true != vAPP(b,$o,sK0,X11) ) )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f148,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK8),vAPP(b,a,sK6,sK8)),vAPP(b,a,sK7,sK8)) )
| ~ spl9_1
| spl9_6 ),
inference(trivial_inequality_removal,[],[f147]) ).
thf(f147,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK8),vAPP(b,a,sK6,sK8)),vAPP(b,a,sK7,sK8)) )
| ~ spl9_1
| spl9_6 ),
inference(forward_demodulation,[],[f146,f61]) ).
thf(f146,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK8),vAPP(b,a,sK6,sK8)),vAPP(b,a,sK7,sK8)) )
| ( $true != vAPP(b,$o,sK0,sK8) )
| spl9_6 ),
inference(trivial_inequality_removal,[],[f143]) ).
thf(f143,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK8),vAPP(b,a,sK6,sK8)),vAPP(b,a,sK7,sK8)) )
| ( $true != vAPP(b,$o,sK0,sK8) )
| spl9_6 ),
inference(superposition,[],[f140,f88]) ).
thf(f88,plain,
! [X2: a,X0: b,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X0),X2),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X0),X1),X2) )
| ( $true != vAPP(b,$o,sK0,X0) ) ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f87,plain,
! [X2: a,X0: b,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X0),X2),X1) )
| ( $true != vAPP(b,$o,sK0,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X0),X1),X2) ) ),
inference(superposition,[],[f16,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f16,plain,
! [X16: a,X17: a,X12: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X16),X17) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X17),X16) )
| ( $true != vAPP(b,$o,sK0,X12) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f140,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK8),vAPP(b,a,sK7,sK8)),vAPP(b,a,sK6,sK8)) )
| spl9_6 ),
inference(avatar_component_clause,[],[f138]) ).
thf(f326,plain,
( spl9_7
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f27,f68,f211]) ).
thf(f27,plain,
! [X11: b] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK5),vAPP(b,a,sK2,sK5)),vAPP(b,a,sK4,sK5)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X11),vAPP(b,a,sK6,X11)),vAPP(b,a,sK7,X11)) )
| ( $true != vAPP(b,$o,sK0,X11) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f309,plain,
( spl9_7
| spl9_4 ),
inference(avatar_split_clause,[],[f18,f78,f211]) ).
thf(f18,plain,
! [X11: b,X7: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X7),vAPP(b,a,sK2,X7)),vAPP(b,a,sK3,X7)) )
| ( $true != vAPP(b,$o,sK0,X7) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X11),vAPP(b,a,sK6,X11)),vAPP(b,a,sK7,X11)) )
| ( $true != vAPP(b,$o,sK0,X11) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f307,plain,
( ~ spl9_2
| spl9_3
| ~ spl9_4
| ~ spl9_5 ),
inference(avatar_contradiction_clause,[],[f306]) ).
thf(f306,plain,
( $false
| ~ spl9_2
| spl9_3
| ~ spl9_4
| ~ spl9_5 ),
inference(trivial_inequality_removal,[],[f303]) ).
thf(f303,plain,
( ( $true != $true )
| ~ spl9_2
| spl9_3
| ~ spl9_4
| ~ spl9_5 ),
inference(superposition,[],[f269,f65]) ).
thf(f65,plain,
( ( $true = vAPP(b,$o,sK0,sK5) )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f269,plain,
( ( $true != vAPP(b,$o,sK0,sK5) )
| ~ spl9_2
| spl9_3
| ~ spl9_4
| ~ spl9_5 ),
inference(trivial_inequality_removal,[],[f261]) ).
thf(f261,plain,
( ( $true != $true )
| ( $true != vAPP(b,$o,sK0,sK5) )
| ~ spl9_2
| spl9_3
| ~ spl9_4
| ~ spl9_5 ),
inference(superposition,[],[f258,f79]) ).
thf(f79,plain,
( ! [X7: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X7),vAPP(b,a,sK2,X7)),vAPP(b,a,sK3,X7)) )
| ( $true != vAPP(b,$o,sK0,X7) ) )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f258,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK5),vAPP(b,a,sK2,sK5)),vAPP(b,a,sK3,sK5)) )
| ~ spl9_2
| spl9_3
| ~ spl9_5 ),
inference(trivial_inequality_removal,[],[f257]) ).
thf(f257,plain,
( ( $true != $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK5),vAPP(b,a,sK2,sK5)),vAPP(b,a,sK3,sK5)) )
| ~ spl9_2
| spl9_3
| ~ spl9_5 ),
inference(forward_demodulation,[],[f256,f65]) ).
thf(f256,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK5),vAPP(b,a,sK2,sK5)),vAPP(b,a,sK3,sK5)) )
| ( $true != vAPP(b,$o,sK0,sK5) )
| spl9_3
| ~ spl9_5 ),
inference(trivial_inequality_removal,[],[f241]) ).
thf(f241,plain,
( ( $true = $false )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK5),vAPP(b,a,sK2,sK5)),vAPP(b,a,sK3,sK5)) )
| ( $true != vAPP(b,$o,sK0,sK5) )
| spl9_3
| ~ spl9_5 ),
inference(superposition,[],[f223,f73]) ).
thf(f73,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK5),vAPP(b,a,sK2,sK5)),vAPP(b,a,sK4,sK5)) )
| spl9_3 ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f72,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK5),vAPP(b,a,sK2,sK5)),vAPP(b,a,sK4,sK5)) )
| spl9_3 ),
inference(superposition,[],[f70,f4]) ).
thf(f70,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK5),vAPP(b,a,sK2,sK5)),vAPP(b,a,sK4,sK5)) )
| spl9_3 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f223,plain,
( ! [X0: b,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X0),X1),vAPP(b,a,sK4,X0)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X0),X1),vAPP(b,a,sK3,X0)) )
| ( $true != vAPP(b,$o,sK0,X0) ) )
| ~ spl9_5 ),
inference(trivial_inequality_removal,[],[f222]) ).
thf(f222,plain,
( ! [X0: b,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X0),X1),vAPP(b,a,sK4,X0)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X0),X1),vAPP(b,a,sK3,X0)) )
| ( $true != vAPP(b,$o,sK0,X0) ) )
| ~ spl9_5 ),
inference(duplicate_literal_removal,[],[f215]) ).
thf(f215,plain,
( ! [X0: b,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X0),X1),vAPP(b,a,sK4,X0)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X0),X1),vAPP(b,a,sK3,X0)) )
| ( $true != vAPP(b,$o,sK0,X0) )
| ( $true != vAPP(b,$o,sK0,X0) ) )
| ~ spl9_5 ),
inference(superposition,[],[f17,f83]) ).
thf(f83,plain,
( ! [X6: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X6),vAPP(b,a,sK3,X6)),vAPP(b,a,sK4,X6)) )
| ( $true != vAPP(b,$o,sK0,X6) ) )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f82,plain,
( spl9_5
<=> ! [X6: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X6),vAPP(b,a,sK3,X6)),vAPP(b,a,sK4,X6)) )
| ( $true != vAPP(b,$o,sK0,X6) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
thf(f17,plain,
! [X14: a,X15: a,X12: b,X13: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X14),X15) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X13),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X12),X13),X14) )
| ( $true != vAPP(b,$o,sK0,X12) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f213,plain,
( spl9_7
| spl9_5 ),
inference(avatar_split_clause,[],[f21,f82,f211]) ).
thf(f21,plain,
! [X11: b,X6: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X6),vAPP(b,a,sK3,X6)),vAPP(b,a,sK4,X6)) )
| ( $true != vAPP(b,$o,sK0,X6) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X11),vAPP(b,a,sK6,X11)),vAPP(b,a,sK7,X11)) )
| ( $true != vAPP(b,$o,sK0,X11) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f141,plain,
( ~ spl9_6
| spl9_5 ),
inference(avatar_split_clause,[],[f23,f82,f138]) ).
thf(f23,plain,
! [X6: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X6),vAPP(b,a,sK3,X6)),vAPP(b,a,sK4,X6)) )
| ( $true != vAPP(b,$o,sK0,X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK8),vAPP(b,a,sK7,sK8)),vAPP(b,a,sK6,sK8)) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f84,plain,
( spl9_1
| spl9_5 ),
inference(avatar_split_clause,[],[f22,f82,f59]) ).
thf(f22,plain,
! [X6: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X6),vAPP(b,a,sK3,X6)),vAPP(b,a,sK4,X6)) )
| ( $true != vAPP(b,$o,sK0,X6) )
| ( $true = vAPP(b,$o,sK0,sK8) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f80,plain,
( spl9_1
| spl9_4 ),
inference(avatar_split_clause,[],[f19,f78,f59]) ).
thf(f19,plain,
! [X7: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,X7),vAPP(b,a,sK2,X7)),vAPP(b,a,sK3,X7)) )
| ( $true != vAPP(b,$o,sK0,X7) )
| ( $true = vAPP(b,$o,sK0,sK8) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f71,plain,
( spl9_1
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f28,f68,f59]) ).
thf(f28,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(b,sTfun(a,sTfun(a,$o)),sK1,sK5),vAPP(b,a,sK2,sK5)),vAPP(b,a,sK4,sK5)) )
| ( $true = vAPP(b,$o,sK0,sK8) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f66,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f25,f63,f59]) ).
thf(f25,plain,
( ( $true = vAPP(b,$o,sK0,sK5) )
| ( $true = vAPP(b,$o,sK0,sK8) ) ),
inference(cnf_transformation,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV044^5 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n025.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun May 19 18:26:23 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.15/0.32 % (32297)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.33 % (32298)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.33 % (32299)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.33 % (32300)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)
% 0.15/0.33 % (32302)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.33 % (32303)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.33 % (32301)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.33 % (32304)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)
% 0.15/0.33 % (32301)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.33 % (32300)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.33 % Exception at run slice level% Exception at run slice level
% 0.15/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.33
% 0.15/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.33 % Exception at run slice level
% 0.15/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.34 % Exception at run slice level
% 0.15/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.35 % (32300)First to succeed.
% 0.15/0.35 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.15/0.35 % (32305)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)
% 0.15/0.35 % (32306)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)
% 0.15/0.35 % (32307)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)
% 0.15/0.35 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.15/0.35 % (32308)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)
% 0.15/0.35 % (32306)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.35 % (32307)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.35 % Exception at run slice level
% 0.15/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.35 % Exception at run slice level% (32300)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-32297"
% 0.15/0.35
% 0.15/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.35 % (32300)Refutation found. Thanks to Tanya!
% 0.15/0.35 % SZS status Theorem for theBenchmark
% 0.15/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.35 % (32300)------------------------------
% 0.15/0.35 % (32300)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.35 % (32300)Termination reason: Refutation
% 0.15/0.35
% 0.15/0.35 % (32300)Memory used [KB]: 918
% 0.15/0.35 % (32300)Time elapsed: 0.020 s
% 0.15/0.35 % (32300)Instructions burned: 40 (million)
% 0.15/0.35 % (32297)Success in time 0.022 s
%------------------------------------------------------------------------------