TSTP Solution File: SEV104^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV104^5 : 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 : n014.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 04:14:27 EDT 2024
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 29
% Syntax : Number of formulae : 76 ( 3 unt; 20 typ; 0 def)
% Number of atoms : 1069 ( 174 equ; 0 cnn)
% Maximal formula atoms : 18 ( 19 avg)
% Number of connectives : 348 ( 117 ~; 105 |; 89 &; 0 @)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 25 ( 24 >; 1 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 11 con; 0-6 aty)
% Number of variables : 179 ( 0 ^ 152 !; 21 ?; 179 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
cR: a > a > $o ).
thf(func_def_3,type,
z: a ).
thf(func_def_4,type,
f: a > b > $o ).
thf(func_def_5,type,
cS: b > b > $o ).
thf(func_def_9,type,
sK0: b ).
thf(func_def_10,type,
sK1: a ).
thf(func_def_11,type,
sK2: a ).
thf(func_def_12,type,
sK3: a > b ).
thf(func_def_14,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_15,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_16,type,
vAND: $o > $o > $o ).
thf(func_def_17,type,
vOR: $o > $o > $o ).
thf(func_def_18,type,
vIMP: $o > $o > $o ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(func_def_20,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f149,plain,
$false,
inference(avatar_sat_refutation,[],[f64,f71,f74,f79,f108,f113,f120,f148]) ).
thf(f148,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f147]) ).
thf(f147,plain,
( $false
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f146]) ).
thf(f146,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_5 ),
inference(forward_demodulation,[],[f144,f53]) ).
thf(f53,plain,
$false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),sK2),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f52,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),sK2) ) ),
inference(superposition,[],[f23,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f23,plain,
$true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),sK2),
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),sK2) )
& ! [X3: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK2),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X3),sK0) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,sK2),sK0) ) )
& ! [X4: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X4),sK0) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,sK1),sK0) ) )
& ! [X5: a,X6: a,X7: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X5),X6) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X6),X7) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X5),X7) ) )
& ! [X8: a,X9: b,X10: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),cS,X9),X10) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X8),X10) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X8),X9) ) )
& ! [X11: a] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X11),vAPP(a,b,sK3,X11)) )
& ! [X13: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X13),X13) )
& ! [X14: a,X15: a,X16: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X14),X16) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X16),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X14),X15) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12,f11]) ).
thf(f11,plain,
( ? [X0: b,X1: a,X2: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),X2) )
& ! [X3: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X2),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X3),X0) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X2),X0) ) )
& ! [X4: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X4),X0) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X1),X0) ) ) )
=> ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),sK2) )
& ! [X3: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK2),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X3),sK0) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,sK2),sK0) ) )
& ! [X4: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X4),sK0) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,sK1),sK0) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
! [X11: a] :
( ? [X12: b] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X11),X12) )
=> ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X11),vAPP(a,b,sK3,X11)) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
( ? [X0: b,X1: a,X2: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),X2) )
& ! [X3: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X2),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X3),X0) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X2),X0) ) )
& ! [X4: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X4),X0) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X1),X0) ) ) )
& ! [X5: a,X6: a,X7: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X5),X6) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X6),X7) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X5),X7) ) )
& ! [X8: a,X9: b,X10: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),cS,X9),X10) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X8),X10) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X8),X9) ) )
& ! [X11: a] :
? [X12: b] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X11),X12) )
& ! [X13: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X13),X13) )
& ! [X14: a,X15: a,X16: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X14),X16) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X16),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X14),X15) ) ) ),
inference(rectify,[],[f9]) ).
thf(f9,plain,
( ? [X12: b,X13: a,X14: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X13),X14) )
& ! [X15: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X14),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X15),X12) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X14),X12) ) )
& ! [X16: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X13),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X16),X12) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X13),X12) ) ) )
& ! [X4: a,X5: a,X6: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X4),X5) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X5),X6) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X4),X6) ) )
& ! [X7: a,X8: b,X9: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),cS,X8),X9) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X9) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X8) ) )
& ! [X10: a] :
? [X11: b] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X10),X11) )
& ! [X0: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),X0) )
& ! [X1: a,X2: a,X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X3),X2) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),X2) ) ) ),
inference(flattening,[],[f8]) ).
thf(f8,plain,
( ? [X12: b,X13: a,X14: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X13),X14) )
& ! [X15: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X14),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X15),X12) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X14),X12) ) )
& ! [X16: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X13),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X16),X12) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X13),X12) ) ) )
& ! [X4: a,X5: a,X6: b] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X4),X5) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X5),X6) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X4),X6) ) )
& ! [X7: a,X8: b,X9: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),cS,X8),X9) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X9) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X8) ) )
& ! [X10: a] :
? [X11: b] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X10),X11) )
& ! [X0: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),X0) )
& ! [X1: a,X2: a,X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X3),X2) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),X2) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
~ ( ( ! [X0: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),X0) )
& ! [X1: a,X2: a,X3: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X3),X2) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),X2) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),X3) ) ) )
=> ( ( ! [X4: a,X5: a,X6: b] :
( ( ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X5),X6) )
& ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X4),X6) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X4),X5) ) )
& ! [X7: a,X8: b,X9: b] :
( ( ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X9) )
& ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X8) ) )
=> ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),cS,X8),X9) ) )
& ! [X10: a] :
? [X11: b] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X10),X11) ) )
=> ! [X12: b,X13: a,X14: a] :
( ( ! [X15: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X14),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X15),X12) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X14),X12) ) )
& ! [X16: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X13),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X16),X12) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X13),X12) ) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X13),X14) ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),X0) )
& ! [X1: a,X2: a,X3: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X3),X2) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),X2) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),X3) ) ) )
=> ( ( ! [X4: a,X5: a,X6: b] :
( ( ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X5),X6) )
& ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X4),X6) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X4),X5) ) )
& ! [X7: a,X8: b,X9: b] :
( ( ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X9) )
& ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X8) ) )
=> ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),cS,X8),X9) ) )
& ! [X10: a] :
? [X11: b] : ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X10),X11) ) )
=> ! [X12: b,X13: a,X14: a] :
( ( ! [X15: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X14),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X15),X12) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X14),X12) ) )
& ! [X16: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X13),z) )
& ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X16),X12) ) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X13),X12) ) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X13),X14) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),X0)
& ! [X1: a,X2: a,X3: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X3),X2)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),X2) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X1),X3) ) )
=> ( ( ! [X4: a,X5: a,X6: b] :
( ( vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X5),X6)
& vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X4),X6) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X4),X5) )
& ! [X7: a,X8: b,X9: b] :
( ( vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X9)
& vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X8) )
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),cS,X8),X9) )
& ! [X10: a] :
? [X11: b] : vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X10),X11) )
=> ! [X12: b,X13: a,X14: a] :
( ( ! [X15: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X14),z)
& ~ vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X15),X12) )
| vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X14),X12) )
& ! [X16: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X13),z)
& ~ vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X16),X12) )
| vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X13),X12) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X13),X14) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X3),X3)
& ! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X2),X1)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),X1) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),X2) ) )
=> ( ( ! [X7: a,X8: a,X4: b] :
( ( vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X8),X4)
& vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X4) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X7),X8) )
& ! [X3: a,X5: b,X6: b] :
( ( vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X3),X6)
& vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X3),X5) )
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),cS,X5),X6) )
& ! [X3: a] :
? [X4: b] : vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X3),X4) )
=> ! [X4: b,X7: a,X8: a] :
( ( ! [X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X8),z)
& ~ vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X2),X4) )
| vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X8),X4) )
& ! [X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X7),z)
& ~ vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X2),X4) )
| vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X4) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X7),X8) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ! [X3: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X3),X3)
& ! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X2),X1)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),X1) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),X2) ) )
=> ( ( ! [X7: a,X8: a,X4: b] :
( ( vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X8),X4)
& vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X4) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X7),X8) )
& ! [X3: a,X5: b,X6: b] :
( ( vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X3),X6)
& vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X3),X5) )
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),cS,X5),X6) )
& ! [X3: a] :
? [X4: b] : vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X3),X4) )
=> ! [X4: b,X7: a,X8: a] :
( ( ! [X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X8),z)
& ~ vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X2),X4) )
| vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X8),X4) )
& ! [X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X7),z)
& ~ vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X2),X4) )
| vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X7),X4) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X7),X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM552D_pme) ).
thf(f144,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),sK2) )
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f139]) ).
thf(f139,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),sK2) )
| ~ spl4_3
| ~ spl4_5 ),
inference(superposition,[],[f122,f70]) ).
thf(f70,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),z) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f68,plain,
( spl4_3
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),z) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
thf(f122,plain,
( ! [X0: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),z) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),sK2) ) )
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f121,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),sK2) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),z) ) )
| ~ spl4_5 ),
inference(superposition,[],[f14,f119]) ).
thf(f119,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK2),z) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f117,plain,
( spl4_5
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK2),z) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
thf(f14,plain,
! [X16: a,X14: a,X15: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X16),X15) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X14),X16) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X14),X15) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f120,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f22,f117,f76]) ).
thf(f76,plain,
( spl4_4
<=> ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,sK2),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
thf(f22,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK2),z) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,sK2),sK0) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f113,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f112]) ).
thf(f112,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f109,plain,
( ( $true != $true )
| ~ spl4_2
| ~ spl4_4 ),
inference(superposition,[],[f63,f78]) ).
thf(f78,plain,
( ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,sK2),sK0) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f76]) ).
thf(f63,plain,
( ! [X4: a] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X4),sK0) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f62,plain,
( spl4_2
<=> ! [X4: a] : ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X4),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
thf(f108,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f107]) ).
thf(f107,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f106,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_4 ),
inference(forward_demodulation,[],[f105,f53]) ).
thf(f105,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),sK2) )
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f100,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),sK2) )
| ~ spl4_1
| ~ spl4_4 ),
inference(superposition,[],[f97,f60]) ).
thf(f60,plain,
( ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,sK1),sK0) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f58,plain,
( spl4_1
<=> ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,sK1),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
thf(f97,plain,
( ! [X0: a] :
( ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X0),sK0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),sK2) ) )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f94,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X0),sK2) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X0),sK0) ) )
| ~ spl4_4 ),
inference(superposition,[],[f18,f78]) ).
thf(f18,plain,
! [X6: a,X7: b,X5: a] :
( ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X6),X7) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,X5),X6) )
| ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X5),X7) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f79,plain,
( spl4_4
| spl4_2 ),
inference(avatar_split_clause,[],[f21,f62,f76]) ).
thf(f21,plain,
! [X3: a] :
( ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X3),sK0) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,sK2),sK0) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f74,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f73]) ).
thf(f73,plain,
( $false
| ~ spl4_1
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f72,plain,
( ( $true != $true )
| ~ spl4_1
| ~ spl4_2 ),
inference(superposition,[],[f63,f60]) ).
thf(f71,plain,
( spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f20,f68,f58]) ).
thf(f20,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cR,sK1),z) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,sK1),sK0) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f64,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f19,f62,f58]) ).
thf(f19,plain,
! [X4: a] :
( ( $true != vAPP(b,$o,vAPP(a,sTfun(b,$o),f,X4),sK0) )
| ( $true = vAPP(b,$o,vAPP(a,sTfun(b,$o),f,sK1),sK0) ) ),
inference(cnf_transformation,[],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV104^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 19:10:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (28217)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (28219)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.37 % (28223)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.21/0.37 % (28220)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)
% 0.21/0.37 % (28221)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.21/0.37 % (28222)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.21/0.37 % (28220)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.37 % Exception at run slice level
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37 % (28221)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.37 % Exception at run slice level
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.38 % (28220)First to succeed.
% 0.21/0.38 % (28223)Also succeeded, but the first one will report.
% 0.21/0.38 % (28220)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-28217"
% 0.21/0.38 % (28220)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38 % (28220)------------------------------
% 0.21/0.38 % (28220)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38 % (28220)Termination reason: Refutation
% 0.21/0.38
% 0.21/0.38 % (28220)Memory used [KB]: 868
% 0.21/0.38 % (28220)Time elapsed: 0.009 s
% 0.21/0.38 % (28220)Instructions burned: 15 (million)
% 0.21/0.38 % (28217)Success in time 0.02 s
%------------------------------------------------------------------------------