TSTP Solution File: SEV218^5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV218^5 : 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 : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:15:27 EDT 2024
% Result : Theorem 0.12s 0.38s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 35
% Syntax : Number of formulae : 108 ( 4 unt; 20 typ; 0 def)
% Number of atoms : 1059 ( 195 equ; 0 cnn)
% Maximal formula atoms : 11 ( 12 avg)
% Number of connectives : 292 ( 81 ~; 118 |; 62 &; 0 @)
% ( 10 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 41 ( 40 >; 1 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 16 con; 0-6 aty)
% Number of variables : 156 ( 0 ^ 97 !; 53 ?; 156 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cQ: a > a > $o ).
thf(func_def_5,type,
sP0: $o ).
thf(func_def_6,type,
sK1: a ).
thf(func_def_7,type,
sK2: a ).
thf(func_def_8,type,
sK3: a ).
thf(func_def_9,type,
sK4: a ).
thf(func_def_10,type,
sK5: a ).
thf(func_def_11,type,
sK6: a ).
thf(func_def_12,type,
sK7: a > a > $o ).
thf(func_def_13,type,
sK8: a > a ).
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(f609,plain,
$false,
inference(avatar_sat_refutation,[],[f39,f44,f49,f58,f63,f131,f371,f608]) ).
thf(f608,plain,
( spl9_2
| ~ spl9_3
| ~ spl9_4 ),
inference(avatar_contradiction_clause,[],[f607]) ).
thf(f607,plain,
( $false
| spl9_2
| ~ spl9_3
| ~ spl9_4 ),
inference(trivial_inequality_removal,[],[f596]) ).
thf(f596,plain,
( ( $true = $false )
| spl9_2
| ~ spl9_3
| ~ spl9_4 ),
inference(backward_demodulation,[],[f48,f563]) ).
thf(f563,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) )
| spl9_2
| ~ spl9_3 ),
inference(trivial_inequality_removal,[],[f562]) ).
thf(f562,plain,
( ( $true = $false )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) )
| spl9_2
| ~ spl9_3 ),
inference(superposition,[],[f125,f540]) ).
thf(f540,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK1),sK2) )
| spl9_2
| ~ spl9_3 ),
inference(trivial_inequality_removal,[],[f539]) ).
thf(f539,plain,
( ( $true = $false )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK1),sK2) )
| spl9_2
| ~ spl9_3 ),
inference(superposition,[],[f492,f389]) ).
thf(f389,plain,
( ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),sK3) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),sK2) ) )
| ~ spl9_3 ),
inference(trivial_inequality_removal,[],[f388]) ).
thf(f388,plain,
( ! [X0: a] :
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),sK3) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),sK2) ) )
| ~ spl9_3 ),
inference(superposition,[],[f123,f43]) ).
thf(f43,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK2),sK3) )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f41,plain,
( spl9_3
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK2),sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
thf(f123,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X2) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f122]) ).
thf(f122,plain,
! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X2) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
inference(superposition,[],[f30,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f30,plain,
! [X6: a,X4: a,X5: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X5) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X6) ) ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
! [X6: a,X4: a,X5: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X5) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f20,plain,
( ( ( $true = sP0 )
| ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) ) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X4) )
& ! [X5: a] :
( ! [X6: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X5) ) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),vAPP(a,a,sK8,X4)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f15,f19,f18,f17,f16]) ).
thf(f16,plain,
( ? [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X0) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) ) )
=> ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) ) ) ),
introduced(choice_axiom,[]) ).
thf(f17,plain,
( ? [X2: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X2) )
=> ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) ) ),
introduced(choice_axiom,[]) ).
thf(f18,plain,
( ? [X3: a > a > $o] :
! [X4: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X4) )
& ! [X5: a] :
( ! [X6: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) = vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X5) ) )
& ? [X7: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X7) ) )
=> ! [X4: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X4) )
& ! [X5: a] :
( ! [X6: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X5) ) )
& ? [X7: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X7) ) ) ),
introduced(choice_axiom,[]) ).
thf(f19,plain,
! [X4: a] :
( ? [X7: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X7) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),vAPP(a,a,sK8,X4)) ) ),
introduced(choice_axiom,[]) ).
thf(f15,plain,
( ( ( $true = sP0 )
| ? [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X0) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) ) )
| ? [X2: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X2) ) )
& ? [X3: a > a > $o] :
! [X4: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X4) )
& ! [X5: a] :
( ! [X6: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) = vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X5) ) )
& ? [X7: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X3,X4),X7) ) ) ),
inference(rectify,[],[f10]) ).
thf(f10,plain,
( ( ( $true = sP0 )
| ? [X8: a,X9: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X9),X8) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X8),X9) ) )
| ? [X10: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X10),X10) ) )
& ? [X0: a > a > $o] :
! [X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1) = $true )
& ! [X2: a] :
( ! [X3: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3) = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X3) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) != $true ) )
& ? [X4: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4) = $true ) ) ),
inference(definition_folding,[],[f8,f9]) ).
thf(f9,plain,
( ? [X5: a,X6: a,X7: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X7) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X6),X7) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) ) )
| ( $true != sP0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f8,plain,
( ( ? [X5: a,X6: a,X7: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X7) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X6),X7) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) ) )
| ? [X8: a,X9: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X9),X8) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X8),X9) ) )
| ? [X10: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X10),X10) ) )
& ? [X0: a > a > $o] :
! [X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1) = $true )
& ! [X2: a] :
( ! [X3: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3) = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X3) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) != $true ) )
& ? [X4: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4) = $true ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
( ( ? [X5: a,X6: a,X7: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X7) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X6),X7) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) ) )
| ? [X8: a,X9: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X9),X8) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X8),X9) ) )
| ? [X10: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X10),X10) ) )
& ? [X0: a > a > $o] :
! [X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1) = $true )
& ! [X2: a] :
( ! [X3: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3) = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X3) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) != $true ) )
& ? [X4: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4) = $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ( ? [X0: a > a > $o] :
! [X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1) = $true )
& ! [X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) = $true )
=> ! [X3: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3) = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X3) ) )
& ? [X4: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4) = $true ) )
=> ( ! [X5: a,X6: a,X7: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X6),X7) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X7) ) )
& ! [X8: a,X9: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X8),X9) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X9),X8) ) )
& ! [X10: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X10),X10) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ? [X0: a > a > $o] :
! [X1: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1)
& ! [X2: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2)
=> ! [X3: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3)
<=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X2),X3) ) )
& ? [X4: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4) )
=> ( ! [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X6),X7)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X7) )
& ! [X8: a,X9: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X8),X9)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X9),X8) )
& ! [X10: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X10),X10) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X0: a > a > $o] :
! [X1: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1)
& ! [X3: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3)
=> ! [X4: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4)
<=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X3),X4) ) )
& ? [X2: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) )
=> ( ! [X1: a,X4: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X4),X2)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X4) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) )
& ! [X1: a,X4: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X4)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X4),X1) )
& ! [X1: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X1) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ? [X0: a > a > $o] :
! [X1: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X1)
& ! [X3: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X3)
=> ! [X4: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X4)
<=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X3),X4) ) )
& ? [X2: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,X1),X2) )
=> ( ! [X1: a,X4: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X4),X2)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X4) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) )
& ! [X1: a,X4: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X4)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X4),X1) )
& ! [X1: a] : vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM559A_pme) ).
thf(f492,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK1),sK3) )
| spl9_2 ),
inference(trivial_inequality_removal,[],[f489]) ).
thf(f489,plain,
( ( $true = $false )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK1),sK3) )
| spl9_2 ),
inference(superposition,[],[f190,f437]) ).
thf(f437,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK3),sK1) )
| spl9_2 ),
inference(trivial_inequality_removal,[],[f436]) ).
thf(f436,plain,
( ( $true = $false )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK3),sK1) )
| spl9_2 ),
inference(superposition,[],[f125,f386]) ).
thf(f386,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK3),sK1) )
| spl9_2 ),
inference(trivial_inequality_removal,[],[f380]) ).
thf(f380,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK3),sK1) )
| spl9_2 ),
inference(superposition,[],[f38,f190]) ).
thf(f38,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK3) )
| spl9_2 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f36,plain,
( spl9_2
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
thf(f190,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f171]) ).
thf(f171,plain,
! [X0: a,X1: a] :
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
inference(superposition,[],[f26,f105]) ).
thf(f105,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) = $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X2) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f104,plain,
! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) = $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X2) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
inference(superposition,[],[f29,f4]) ).
thf(f29,plain,
! [X6: a,X4: a,X5: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X5) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X6) ) ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f26,plain,
! [X4: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X4),X4) ),
inference(cnf_transformation,[],[f20]) ).
thf(f125,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f119]) ).
thf(f119,plain,
! [X0: a,X1: a] :
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
inference(superposition,[],[f30,f26]) ).
thf(f48,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f46,plain,
( spl9_4
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
thf(f371,plain,
( spl9_6
| ~ spl9_7 ),
inference(avatar_contradiction_clause,[],[f370]) ).
thf(f370,plain,
( $false
| spl9_6
| ~ spl9_7 ),
inference(trivial_inequality_removal,[],[f359]) ).
thf(f359,plain,
( ( $true = $false )
| spl9_6
| ~ spl9_7 ),
inference(backward_demodulation,[],[f62,f326]) ).
thf(f326,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) )
| spl9_6 ),
inference(trivial_inequality_removal,[],[f325]) ).
thf(f325,plain,
( ( $true = $false )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) )
| spl9_6 ),
inference(superposition,[],[f125,f307]) ).
thf(f307,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK4),sK5) )
| spl9_6 ),
inference(trivial_inequality_removal,[],[f294]) ).
thf(f294,plain,
( ( $true = $false )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,sK4),sK5) )
| spl9_6 ),
inference(superposition,[],[f133,f190]) ).
thf(f133,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) )
| spl9_6 ),
inference(trivial_inequality_removal,[],[f132]) ).
thf(f132,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) )
| spl9_6 ),
inference(superposition,[],[f57,f4]) ).
thf(f57,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) )
| spl9_6 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f55,plain,
( spl9_6
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
thf(f62,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f60,plain,
( spl9_7
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
thf(f131,plain,
spl9_5,
inference(avatar_contradiction_clause,[],[f130]) ).
thf(f130,plain,
( $false
| spl9_5 ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f126,plain,
( ( $true = $false )
| spl9_5 ),
inference(superposition,[],[f115,f98]) ).
thf(f98,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) )
| spl9_5 ),
inference(trivial_inequality_removal,[],[f97]) ).
thf(f97,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) )
| spl9_5 ),
inference(superposition,[],[f53,f4]) ).
thf(f53,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) )
| spl9_5 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f51,plain,
( spl9_5
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
thf(f115,plain,
! [X0: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X0) ),
inference(trivial_inequality_removal,[],[f111]) ).
thf(f111,plain,
! [X0: a] :
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X0) ) ),
inference(superposition,[],[f26,f107]) ).
thf(f107,plain,
! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f102]) ).
thf(f102,plain,
! [X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK7,X0),X1) ) ),
inference(superposition,[],[f29,f26]) ).
thf(f63,plain,
( ~ spl9_5
| spl9_7
| spl9_1 ),
inference(avatar_split_clause,[],[f27,f32,f60,f51]) ).
thf(f32,plain,
( spl9_1
<=> ( $true = sP0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
thf(f27,plain,
( ( $true = sP0 )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK4),sK5) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f58,plain,
( ~ spl9_5
| ~ spl9_6
| spl9_1 ),
inference(avatar_split_clause,[],[f28,f32,f55,f51]) ).
thf(f28,plain,
( ( $true = sP0 )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK5),sK4) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK6),sK6) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f49,plain,
( ~ spl9_1
| spl9_4 ),
inference(avatar_split_clause,[],[f21,f46,f32]) ).
thf(f21,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
( ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK3) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK2),sK3) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) ) )
| ( $true != sP0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: a,X1: a,X2: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X2) )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) = $true )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) ) )
=> ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK3) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK2),sK3) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK2) ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
( ? [X0: a,X1: a,X2: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X2) )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X1),X2) = $true )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X0),X1) ) )
| ( $true != sP0 ) ),
inference(rectify,[],[f11]) ).
thf(f11,plain,
( ? [X5: a,X6: a,X7: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X7) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X6),X7) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,X5),X6) ) )
| ( $true != sP0 ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f44,plain,
( ~ spl9_1
| spl9_3 ),
inference(avatar_split_clause,[],[f22,f41,f32]) ).
thf(f22,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK2),sK3) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f39,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f23,f36,f32]) ).
thf(f23,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cQ,sK1),sK3) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV218^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun May 19 18:51:07 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % (26856)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35 % (26862)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.12/0.35 % (26860)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.12/0.35 % (26863)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)
% 0.12/0.35 % (26858)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.35 % (26860)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.35 % Exception at run slice level
% 0.12/0.35 % Exception at run slice level
% 0.12/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.35 % (26857)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.12/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.36 % Exception at run slice level
% 0.12/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.36 % Exception at run slice level
% 0.12/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.36 % (26859)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)
% 0.12/0.36 % (26859)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.37 % (26861)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.12/0.37 % (26864)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)
% 0.12/0.37 % (26866)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)
% 0.12/0.37 % Exception at run slice level
% 0.12/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.12/0.37 % (26866)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.37 % Exception at run slice level
% 0.12/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37 % (26865)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)
% 0.12/0.37 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.12/0.37 % (26862)First to succeed.
% 0.12/0.37 % (26867)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)
% 0.12/0.37 % (26865)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.37 % (26862)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26856"
% 0.12/0.38 % (26862)Refutation found. Thanks to Tanya!
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.38 % (26862)------------------------------
% 0.12/0.38 % (26862)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.38 % (26862)Termination reason: Refutation
% 0.12/0.38
% 0.12/0.38 % (26862)Memory used [KB]: 916
% 0.12/0.38 % (26862)Time elapsed: 0.022 s
% 0.12/0.38 % (26862)Instructions burned: 44 (million)
% 0.12/0.38 % (26856)Success in time 0.035 s
%------------------------------------------------------------------------------