TSTP Solution File: SEV191^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV191^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 16:02:11 EDT 2024
% Result : Theorem 0.21s 0.39s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 85 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 621 ( 362 equ; 0 cnn)
% Maximal formula atoms : 40 ( 7 avg)
% Number of connectives : 1117 ( 155 ~; 229 |; 158 &; 544 @)
% ( 9 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 21 con; 0-3 aty)
% Number of variables : 257 ( 0 ^ 123 !; 134 ?; 257 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cP: a > a > a ).
thf(func_def_2,type,
c0: a ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_7,type,
sK0: a > a > a > $o ).
thf(func_def_8,type,
sK1: a > a > a > $o ).
thf(func_def_9,type,
sK2: a ).
thf(func_def_10,type,
sK3: a ).
thf(func_def_11,type,
sK4: a ).
thf(func_def_12,type,
sK5: a ).
thf(func_def_13,type,
sK6: a ).
thf(func_def_14,type,
sK7: a ).
thf(func_def_15,type,
sK8: a ).
thf(func_def_16,type,
sK9: a ).
thf(func_def_17,type,
sK10: a ).
thf(f175,plain,
$false,
inference(avatar_sat_refutation,[],[f50,f55,f64,f65,f70,f75,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f174]) ).
thf(f174,plain,
( ~ spl11_8
| ~ spl11_1
| ~ spl11_6
| ~ spl11_7
| ~ spl11_9 ),
inference(avatar_split_clause,[],[f173,f77,f67,f61,f39,f72]) ).
thf(f72,plain,
( spl11_8
<=> ( ( cP @ sK10 @ sK8 )
= sK4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_8])]) ).
thf(f39,plain,
( spl11_1
<=> ( $true
= ( sK1 @ sK8 @ sK9 @ sK7 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_1])]) ).
thf(f61,plain,
( spl11_6
<=> ( ( cP @ sK5 @ sK7 )
= sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_6])]) ).
thf(f67,plain,
( spl11_7
<=> ( sK3
= ( cP @ sK6 @ sK9 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_7])]) ).
thf(f77,plain,
( spl11_9
<=> ( $true
= ( sK1 @ sK10 @ sK6 @ sK5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_9])]) ).
thf(f173,plain,
( ( ( cP @ sK10 @ sK8 )
!= sK4 )
| ~ spl11_1
| ~ spl11_6
| ~ spl11_7
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f172,plain,
( ( ( cP @ sK10 @ sK8 )
!= sK4 )
| ( sK2 != sK2 )
| ~ spl11_1
| ~ spl11_6
| ~ spl11_7
| ~ spl11_9 ),
inference(forward_demodulation,[],[f171,f63]) ).
thf(f63,plain,
( ( ( cP @ sK5 @ sK7 )
= sK2 )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f61]) ).
thf(f171,plain,
( ( ( cP @ sK10 @ sK8 )
!= sK4 )
| ( ( cP @ sK5 @ sK7 )
!= sK2 )
| ~ spl11_1
| ~ spl11_7
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f170]) ).
thf(f170,plain,
( ( sK3 != sK3 )
| ( ( cP @ sK5 @ sK7 )
!= sK2 )
| ( ( cP @ sK10 @ sK8 )
!= sK4 )
| ~ spl11_1
| ~ spl11_7
| ~ spl11_9 ),
inference(forward_demodulation,[],[f169,f69]) ).
thf(f69,plain,
( ( sK3
= ( cP @ sK6 @ sK9 ) )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f169,plain,
( ( sK3
!= ( cP @ sK6 @ sK9 ) )
| ( ( cP @ sK10 @ sK8 )
!= sK4 )
| ( ( cP @ sK5 @ sK7 )
!= sK2 )
| ~ spl11_1
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f166]) ).
thf(f166,plain,
( ( ( cP @ sK5 @ sK7 )
!= sK2 )
| ( $true != $true )
| ( ( cP @ sK10 @ sK8 )
!= sK4 )
| ( sK3
!= ( cP @ sK6 @ sK9 ) )
| ~ spl11_1
| ~ spl11_9 ),
inference(superposition,[],[f135,f101]) ).
thf(f101,plain,
( ( ( sK0 @ sK8 @ sK9 @ sK7 )
= $true )
| ~ spl11_1 ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f99,plain,
( ( $true != $true )
| ( ( sK0 @ sK8 @ sK9 @ sK7 )
= $true )
| ~ spl11_1 ),
inference(superposition,[],[f14,f41]) ).
thf(f41,plain,
( ( $true
= ( sK1 @ sK8 @ sK9 @ sK7 ) )
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f14,plain,
! [X18: a,X19: a,X17: a] :
( ( $true
!= ( sK1 @ X17 @ X19 @ X18 ) )
| ( $true
= ( sK0 @ X17 @ X19 @ X18 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
( ( ( sK3 != sK2 )
| ( c0 != sK4 ) )
& ( ( ( sK4 = sK2 )
& ( c0 = sK3 ) )
| ( ( c0 = sK4 )
& ( sK3 = sK2 ) )
| ( ( sK3
= ( cP @ sK6 @ sK9 ) )
& ( ( cP @ sK5 @ sK7 )
= sK2 )
& ( $true
= ( sK1 @ sK10 @ sK6 @ sK5 ) )
& ( $true
= ( sK1 @ sK8 @ sK9 @ sK7 ) )
& ( ( cP @ sK10 @ sK8 )
= sK4 ) ) )
& ! [X11: a,X12: a,X13: a,X14: a,X15: a,X16: a] :
( ( sK4
!= ( cP @ X16 @ X12 ) )
| ( ( cP @ X13 @ X14 )
!= sK2 )
| ( $true
!= ( sK0 @ X16 @ X11 @ X13 ) )
| ( ( cP @ X11 @ X15 )
!= sK3 )
| ( $true
!= ( sK0 @ X12 @ X15 @ X14 ) ) )
& ( ( sK4 != sK2 )
| ( c0 != sK3 ) )
& ! [X17: a,X18: a,X19: a] :
( ( $true
!= ( sK1 @ X17 @ X19 @ X18 ) )
| ( $true
= ( sK0 @ X17 @ X19 @ X18 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10])],[f9,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: a > a > a > $o,X1: a > a > a > $o] :
( ? [X2: a,X3: a,X4: a] :
( ( ( X2 != X3 )
| ( c0 != X4 ) )
& ( ( ( X2 = X4 )
& ( c0 = X3 ) )
| ( ( c0 = X4 )
& ( X2 = X3 ) )
| ? [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
( ( ( cP @ X6 @ X9 )
= X3 )
& ( ( cP @ X5 @ X7 )
= X2 )
& ( $true
= ( X1 @ X10 @ X6 @ X5 ) )
& ( $true
= ( X1 @ X8 @ X9 @ X7 ) )
& ( ( cP @ X10 @ X8 )
= X4 ) ) )
& ! [X11: a,X12: a,X13: a,X14: a,X15: a,X16: a] :
( ( ( cP @ X16 @ X12 )
!= X4 )
| ( ( cP @ X13 @ X14 )
!= X2 )
| ( $true
!= ( X0 @ X16 @ X11 @ X13 ) )
| ( ( cP @ X11 @ X15 )
!= X3 )
| ( ( X0 @ X12 @ X15 @ X14 )
!= $true ) )
& ( ( X2 != X4 )
| ( c0 != X3 ) ) )
& ! [X17: a,X18: a,X19: a] :
( ( $true
!= ( X1 @ X17 @ X19 @ X18 ) )
| ( $true
= ( X0 @ X17 @ X19 @ X18 ) ) ) )
=> ( ? [X4: a,X3: a,X2: a] :
( ( ( X2 != X3 )
| ( c0 != X4 ) )
& ( ( ( X2 = X4 )
& ( c0 = X3 ) )
| ( ( c0 = X4 )
& ( X2 = X3 ) )
| ? [X10: a,X9: a,X8: a,X7: a,X6: a,X5: a] :
( ( ( cP @ X6 @ X9 )
= X3 )
& ( ( cP @ X5 @ X7 )
= X2 )
& ( $true
= ( sK1 @ X10 @ X6 @ X5 ) )
& ( $true
= ( sK1 @ X8 @ X9 @ X7 ) )
& ( ( cP @ X10 @ X8 )
= X4 ) ) )
& ! [X16: a,X15: a,X14: a,X13: a,X12: a,X11: a] :
( ( ( cP @ X16 @ X12 )
!= X4 )
| ( ( cP @ X13 @ X14 )
!= X2 )
| ( $true
!= ( sK0 @ X16 @ X11 @ X13 ) )
| ( ( cP @ X11 @ X15 )
!= X3 )
| ( $true
!= ( sK0 @ X12 @ X15 @ X14 ) ) )
& ( ( X2 != X4 )
| ( c0 != X3 ) ) )
& ! [X19: a,X18: a,X17: a] :
( ( $true
!= ( sK1 @ X17 @ X19 @ X18 ) )
| ( $true
= ( sK0 @ X17 @ X19 @ X18 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
( ? [X4: a,X3: a,X2: a] :
( ( ( X2 != X3 )
| ( c0 != X4 ) )
& ( ( ( X2 = X4 )
& ( c0 = X3 ) )
| ( ( c0 = X4 )
& ( X2 = X3 ) )
| ? [X10: a,X9: a,X8: a,X7: a,X6: a,X5: a] :
( ( ( cP @ X6 @ X9 )
= X3 )
& ( ( cP @ X5 @ X7 )
= X2 )
& ( $true
= ( sK1 @ X10 @ X6 @ X5 ) )
& ( $true
= ( sK1 @ X8 @ X9 @ X7 ) )
& ( ( cP @ X10 @ X8 )
= X4 ) ) )
& ! [X16: a,X15: a,X14: a,X13: a,X12: a,X11: a] :
( ( ( cP @ X16 @ X12 )
!= X4 )
| ( ( cP @ X13 @ X14 )
!= X2 )
| ( $true
!= ( sK0 @ X16 @ X11 @ X13 ) )
| ( ( cP @ X11 @ X15 )
!= X3 )
| ( $true
!= ( sK0 @ X12 @ X15 @ X14 ) ) )
& ( ( X2 != X4 )
| ( c0 != X3 ) ) )
=> ( ( ( sK3 != sK2 )
| ( c0 != sK4 ) )
& ( ( ( sK4 = sK2 )
& ( c0 = sK3 ) )
| ( ( c0 = sK4 )
& ( sK3 = sK2 ) )
| ? [X10: a,X9: a,X8: a,X7: a,X6: a,X5: a] :
( ( ( cP @ X6 @ X9 )
= sK3 )
& ( ( cP @ X5 @ X7 )
= sK2 )
& ( $true
= ( sK1 @ X10 @ X6 @ X5 ) )
& ( $true
= ( sK1 @ X8 @ X9 @ X7 ) )
& ( ( cP @ X10 @ X8 )
= sK4 ) ) )
& ! [X16: a,X15: a,X14: a,X13: a,X12: a,X11: a] :
( ( sK4
!= ( cP @ X16 @ X12 ) )
| ( ( cP @ X13 @ X14 )
!= sK2 )
| ( $true
!= ( sK0 @ X16 @ X11 @ X13 ) )
| ( ( cP @ X11 @ X15 )
!= sK3 )
| ( $true
!= ( sK0 @ X12 @ X15 @ X14 ) ) )
& ( ( sK4 != sK2 )
| ( c0 != sK3 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
( ? [X10: a,X9: a,X8: a,X7: a,X6: a,X5: a] :
( ( ( cP @ X6 @ X9 )
= sK3 )
& ( ( cP @ X5 @ X7 )
= sK2 )
& ( $true
= ( sK1 @ X10 @ X6 @ X5 ) )
& ( $true
= ( sK1 @ X8 @ X9 @ X7 ) )
& ( ( cP @ X10 @ X8 )
= sK4 ) )
=> ( ( sK3
= ( cP @ sK6 @ sK9 ) )
& ( ( cP @ sK5 @ sK7 )
= sK2 )
& ( $true
= ( sK1 @ sK10 @ sK6 @ sK5 ) )
& ( $true
= ( sK1 @ sK8 @ sK9 @ sK7 ) )
& ( ( cP @ sK10 @ sK8 )
= sK4 ) ) ),
introduced(choice_axiom,[]) ).
thf(f9,plain,
? [X0: a > a > a > $o,X1: a > a > a > $o] :
( ? [X2: a,X3: a,X4: a] :
( ( ( X2 != X3 )
| ( c0 != X4 ) )
& ( ( ( X2 = X4 )
& ( c0 = X3 ) )
| ( ( c0 = X4 )
& ( X2 = X3 ) )
| ? [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
( ( ( cP @ X6 @ X9 )
= X3 )
& ( ( cP @ X5 @ X7 )
= X2 )
& ( $true
= ( X1 @ X10 @ X6 @ X5 ) )
& ( $true
= ( X1 @ X8 @ X9 @ X7 ) )
& ( ( cP @ X10 @ X8 )
= X4 ) ) )
& ! [X11: a,X12: a,X13: a,X14: a,X15: a,X16: a] :
( ( ( cP @ X16 @ X12 )
!= X4 )
| ( ( cP @ X13 @ X14 )
!= X2 )
| ( $true
!= ( X0 @ X16 @ X11 @ X13 ) )
| ( ( cP @ X11 @ X15 )
!= X3 )
| ( ( X0 @ X12 @ X15 @ X14 )
!= $true ) )
& ( ( X2 != X4 )
| ( c0 != X3 ) ) )
& ! [X17: a,X18: a,X19: a] :
( ( $true
!= ( X1 @ X17 @ X19 @ X18 ) )
| ( $true
= ( X0 @ X17 @ X19 @ X18 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,plain,
? [X1: a > a > a > $o,X0: a > a > a > $o] :
( ? [X7: a,X6: a,X5: a] :
( ( ( X6 != X7 )
| ( c0 != X5 ) )
& ( ( ( X5 = X7 )
& ( c0 = X6 ) )
| ( ( c0 = X5 )
& ( X6 = X7 ) )
| ? [X12: a,X11: a,X8: a,X10: a,X9: a,X13: a] :
( ( ( cP @ X11 @ X9 )
= X6 )
& ( ( cP @ X12 @ X8 )
= X7 )
& ( $true
= ( X0 @ X13 @ X11 @ X12 ) )
& ( $true
= ( X0 @ X10 @ X9 @ X8 ) )
& ( ( cP @ X13 @ X10 )
= X5 ) ) )
& ! [X19: a,X17: a,X16: a,X18: a,X15: a,X14: a] :
( ( ( cP @ X14 @ X17 )
!= X5 )
| ( ( cP @ X16 @ X18 )
!= X7 )
| ( $true
!= ( X1 @ X14 @ X19 @ X16 ) )
| ( ( cP @ X19 @ X15 )
!= X6 )
| ( $true
!= ( X1 @ X17 @ X15 @ X18 ) ) )
& ( ( X5 != X7 )
| ( c0 != X6 ) ) )
& ! [X4: a,X2: a,X3: a] :
( ( ( X0 @ X4 @ X3 @ X2 )
!= $true )
| ( $true
= ( X1 @ X4 @ X3 @ X2 ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
? [X0: a > a > a > $o,X1: a > a > a > $o] :
( ? [X6: a,X7: a,X5: a] :
( ( ( X5 != X7 )
| ( c0 != X6 ) )
& ( ( X6 != X7 )
| ( c0 != X5 ) )
& ! [X19: a,X17: a,X16: a,X18: a,X15: a,X14: a] :
( ( ( cP @ X14 @ X17 )
!= X5 )
| ( ( cP @ X16 @ X18 )
!= X7 )
| ( $true
!= ( X1 @ X14 @ X19 @ X16 ) )
| ( ( cP @ X19 @ X15 )
!= X6 )
| ( $true
!= ( X1 @ X17 @ X15 @ X18 ) ) )
& ( ( ( X5 = X7 )
& ( c0 = X6 ) )
| ( ( c0 = X5 )
& ( X6 = X7 ) )
| ? [X12: a,X11: a,X8: a,X10: a,X9: a,X13: a] :
( ( ( cP @ X11 @ X9 )
= X6 )
& ( ( cP @ X12 @ X8 )
= X7 )
& ( $true
= ( X0 @ X13 @ X11 @ X12 ) )
& ( $true
= ( X0 @ X10 @ X9 @ X8 ) )
& ( ( cP @ X13 @ X10 )
= X5 ) ) ) )
& ! [X4: a,X2: a,X3: a] :
( ( ( X0 @ X4 @ X3 @ X2 )
!= $true )
| ( $true
= ( X1 @ X4 @ X3 @ X2 ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ! [X0: a > a > a > $o,X1: a > a > a > $o] :
( ! [X2: a,X4: a,X3: a] :
( ( ( X0 @ X4 @ X3 @ X2 )
= $true )
=> ( $true
= ( X1 @ X4 @ X3 @ X2 ) ) )
=> ! [X6: a,X7: a,X5: a] :
( ( ( ( X5 = X7 )
& ( c0 = X6 ) )
| ( ( c0 = X5 )
& ( X6 = X7 ) )
| ? [X12: a,X11: a,X8: a,X10: a,X9: a,X13: a] :
( ( ( cP @ X11 @ X9 )
= X6 )
& ( ( cP @ X12 @ X8 )
= X7 )
& ( $true
= ( X0 @ X13 @ X11 @ X12 ) )
& ( $true
= ( X0 @ X10 @ X9 @ X8 ) )
& ( ( cP @ X13 @ X10 )
= X5 ) ) )
=> ( ( ( X5 = X7 )
& ( c0 = X6 ) )
| ( ( X6 = X7 )
& ( c0 = X5 ) )
| ? [X19: a,X14: a,X17: a,X15: a,X16: a,X18: a] :
( ( $true
= ( X1 @ X17 @ X15 @ X18 ) )
& ( ( cP @ X14 @ X17 )
= X5 )
& ( $true
= ( X1 @ X14 @ X19 @ X16 ) )
& ( ( cP @ X19 @ X15 )
= X6 )
& ( ( cP @ X16 @ X18 )
= X7 ) ) ) ) ),
inference(true_and_false_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ! [X0: a > a > a > $o,X1: a > a > a > $o] :
( ( ! [X2: a,X4: a,X3: a] :
( ( ( X0 @ X4 @ X3 @ X2 )
= $true )
=> ( $true
= ( X1 @ X4 @ X3 @ X2 ) ) )
& $true
& $true )
=> ! [X6: a,X7: a,X5: a] :
( ( ( ( X5 = X7 )
& ( c0 = X6 ) )
| ( ( c0 = X5 )
& ( X6 = X7 ) )
| ? [X12: a,X11: a,X8: a,X10: a,X9: a,X13: a] :
( ( ( cP @ X11 @ X9 )
= X6 )
& ( ( cP @ X12 @ X8 )
= X7 )
& ( $true
= ( X0 @ X13 @ X11 @ X12 ) )
& ( $true
= ( X0 @ X10 @ X9 @ X8 ) )
& ( ( cP @ X13 @ X10 )
= X5 ) ) )
=> ( ( ( X5 = X7 )
& ( c0 = X6 ) )
| ( ( X6 = X7 )
& ( c0 = X5 ) )
| ? [X19: a,X14: a,X17: a,X15: a,X16: a,X18: a] :
( ( $true
= ( X1 @ X17 @ X15 @ X18 ) )
& ( ( cP @ X14 @ X17 )
= X5 )
& ( $true
= ( X1 @ X14 @ X19 @ X16 ) )
& ( ( cP @ X19 @ X15 )
= X6 )
& ( ( cP @ X16 @ X18 )
= X7 ) ) ) ) )
& ( $true
=> $true ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > a > a > $o,X1: a > a > a > $o] :
( ( ! [X2: a,X3: a,X4: a] :
( ( X0 @ X4 @ X3 @ X2 )
=> ( X1 @ X4 @ X3 @ X2 ) )
& $true
& $true )
=> ! [X5: a,X6: a,X7: a] :
( ( ( ( c0 = X5 )
& ( X6 = X7 ) )
| ( ( X5 = X7 )
& ( c0 = X6 ) )
| ? [X8: a,X9: a,X10: a,X11: a,X12: a,X13: a] :
( ( X0 @ X13 @ X11 @ X12 )
& ( ( cP @ X11 @ X9 )
= X6 )
& ( X0 @ X10 @ X9 @ X8 )
& ( ( cP @ X12 @ X8 )
= X7 )
& ( ( cP @ X13 @ X10 )
= X5 ) ) )
=> ( ( ( c0 = X6 )
& ( X5 = X7 ) )
| ( ( c0 = X5 )
& ( X6 = X7 ) )
| ? [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( ( ( cP @ X16 @ X18 )
= X7 )
& ( X1 @ X14 @ X19 @ X16 )
& ( X1 @ X17 @ X15 @ X18 )
& ( ( cP @ X14 @ X17 )
= X5 )
& ( ( cP @ X19 @ X15 )
= X6 ) ) ) ) )
& ( $true
=> $true ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a > a > a > $o,X1: a > a > a > $o] :
( ( ! [X4: a,X3: a,X2: a] :
( ( X0 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) )
& $true
& $true )
=> ! [X2: a,X3: a,X4: a] :
( ( ( ( c0 = X2 )
& ( X3 = X4 ) )
| ( ( X2 = X4 )
& ( c0 = X3 ) )
| ? [X10: a,X8: a,X6: a,X7: a,X9: a,X5: a] :
( ( X0 @ X5 @ X7 @ X9 )
& ( ( cP @ X7 @ X8 )
= X3 )
& ( X0 @ X6 @ X8 @ X10 )
& ( ( cP @ X9 @ X10 )
= X4 )
& ( ( cP @ X5 @ X6 )
= X2 ) ) )
=> ( ( ( c0 = X3 )
& ( X2 = X4 ) )
| ( ( c0 = X2 )
& ( X3 = X4 ) )
| ? [X5: a,X8: a,X9: a,X6: a,X10: a,X7: a] :
( ( ( cP @ X9 @ X10 )
= X4 )
& ( X1 @ X5 @ X7 @ X9 )
& ( X1 @ X6 @ X8 @ X10 )
& ( ( cP @ X5 @ X6 )
= X2 )
& ( ( cP @ X7 @ X8 )
= X3 ) ) ) ) )
& ! [X0: a > a > a > $o] :
( $true
=> $true ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ! [X0: a > a > a > $o,X1: a > a > a > $o] :
( ( ! [X4: a,X3: a,X2: a] :
( ( X0 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) )
& $true
& $true )
=> ! [X2: a,X3: a,X4: a] :
( ( ( ( c0 = X2 )
& ( X3 = X4 ) )
| ( ( X2 = X4 )
& ( c0 = X3 ) )
| ? [X10: a,X8: a,X6: a,X7: a,X9: a,X5: a] :
( ( X0 @ X5 @ X7 @ X9 )
& ( ( cP @ X7 @ X8 )
= X3 )
& ( X0 @ X6 @ X8 @ X10 )
& ( ( cP @ X9 @ X10 )
= X4 )
& ( ( cP @ X5 @ X6 )
= X2 ) ) )
=> ( ( ( c0 = X3 )
& ( X2 = X4 ) )
| ( ( c0 = X2 )
& ( X3 = X4 ) )
| ? [X5: a,X8: a,X9: a,X6: a,X10: a,X7: a] :
( ( ( cP @ X9 @ X10 )
= X4 )
& ( X1 @ X5 @ X7 @ X9 )
& ( X1 @ X6 @ X8 @ X10 )
& ( ( cP @ X5 @ X6 )
= X2 )
& ( ( cP @ X7 @ X8 )
= X3 ) ) ) ) )
& ! [X0: a > a > a > $o] :
( $true
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cS_JOINFN_MONOTONE_pme) ).
thf(f135,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true
!= ( sK0 @ X1 @ X0 @ X2 ) )
| ( sK3
!= ( cP @ sK6 @ X0 ) )
| ( ( cP @ sK10 @ X1 )
!= sK4 )
| ( sK2
!= ( cP @ sK5 @ X2 ) ) )
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f133]) ).
thf(f133,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true
!= ( sK0 @ X1 @ X0 @ X2 ) )
| ( ( cP @ sK10 @ X1 )
!= sK4 )
| ( sK3
!= ( cP @ sK6 @ X0 ) )
| ( sK2
!= ( cP @ sK5 @ X2 ) )
| ( $true != $true ) )
| ~ spl11_9 ),
inference(superposition,[],[f16,f102]) ).
thf(f102,plain,
( ( $true
= ( sK0 @ sK10 @ sK6 @ sK5 ) )
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f100,plain,
( ( $true
= ( sK0 @ sK10 @ sK6 @ sK5 ) )
| ( $true != $true )
| ~ spl11_9 ),
inference(superposition,[],[f14,f79]) ).
thf(f79,plain,
( ( $true
= ( sK1 @ sK10 @ sK6 @ sK5 ) )
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f77]) ).
thf(f16,plain,
! [X11: a,X16: a,X14: a,X15: a,X12: a,X13: a] :
( ( $true
!= ( sK0 @ X16 @ X11 @ X13 ) )
| ( ( cP @ X11 @ X15 )
!= sK3 )
| ( $true
!= ( sK0 @ X12 @ X15 @ X14 ) )
| ( sK4
!= ( cP @ X16 @ X12 ) )
| ( ( cP @ X13 @ X14 )
!= sK2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f95,plain,
( spl11_9
| spl11_4
| spl11_5 ),
inference(avatar_split_clause,[],[f24,f57,f52,f77]) ).
thf(f52,plain,
( spl11_4
<=> ( c0 = sK4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_4])]) ).
thf(f57,plain,
( spl11_5
<=> ( c0 = sK3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_5])]) ).
thf(f24,plain,
( ( $true
= ( sK1 @ sK10 @ sK6 @ sK5 ) )
| ( c0 = sK3 )
| ( c0 = sK4 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f94,plain,
( spl11_5
| spl11_8
| spl11_3 ),
inference(avatar_split_clause,[],[f17,f47,f72,f57]) ).
thf(f47,plain,
( spl11_3
<=> ( sK3 = sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_3])]) ).
thf(f17,plain,
( ( c0 = sK3 )
| ( sK3 = sK2 )
| ( ( cP @ sK10 @ sK8 )
= sK4 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f93,plain,
( spl11_8
| spl11_5
| spl11_4 ),
inference(avatar_split_clause,[],[f22,f52,f57,f72]) ).
thf(f22,plain,
( ( c0 = sK3 )
| ( c0 = sK4 )
| ( ( cP @ sK10 @ sK8 )
= sK4 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f92,plain,
( spl11_2
| spl11_9
| spl11_3 ),
inference(avatar_split_clause,[],[f29,f47,f77,f43]) ).
thf(f43,plain,
( spl11_2
<=> ( sK4 = sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).
thf(f29,plain,
( ( sK3 = sK2 )
| ( sK4 = sK2 )
| ( $true
= ( sK1 @ sK10 @ sK6 @ sK5 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f91,plain,
( spl11_3
| spl11_8
| spl11_2 ),
inference(avatar_split_clause,[],[f27,f43,f72,f47]) ).
thf(f27,plain,
( ( ( cP @ sK10 @ sK8 )
= sK4 )
| ( sK4 = sK2 )
| ( sK3 = sK2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f90,plain,
( spl11_1
| spl11_2
| spl11_4 ),
inference(avatar_split_clause,[],[f33,f52,f43,f39]) ).
thf(f33,plain,
( ( $true
= ( sK1 @ sK8 @ sK9 @ sK7 ) )
| ( sK4 = sK2 )
| ( c0 = sK4 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f89,plain,
( spl11_3
| spl11_5
| spl11_9 ),
inference(avatar_split_clause,[],[f19,f77,f57,f47]) ).
thf(f19,plain,
( ( sK3 = sK2 )
| ( $true
= ( sK1 @ sK10 @ sK6 @ sK5 ) )
| ( c0 = sK3 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f88,plain,
( spl11_3
| spl11_6
| spl11_2 ),
inference(avatar_split_clause,[],[f30,f43,f61,f47]) ).
thf(f30,plain,
( ( ( cP @ sK5 @ sK7 )
= sK2 )
| ( sK3 = sK2 )
| ( sK4 = sK2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f87,plain,
( spl11_3
| spl11_5
| spl11_7 ),
inference(avatar_split_clause,[],[f21,f67,f57,f47]) ).
thf(f21,plain,
( ( c0 = sK3 )
| ( sK3
= ( cP @ sK6 @ sK9 ) )
| ( sK3 = sK2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f86,plain,
( spl11_4
| spl11_7
| spl11_2 ),
inference(avatar_split_clause,[],[f36,f43,f67,f52]) ).
thf(f36,plain,
( ( c0 = sK4 )
| ( sK3
= ( cP @ sK6 @ sK9 ) )
| ( sK4 = sK2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f85,plain,
( spl11_7
| spl11_2
| spl11_3 ),
inference(avatar_split_clause,[],[f31,f47,f43,f67]) ).
thf(f31,plain,
( ( sK3 = sK2 )
| ( sK3
= ( cP @ sK6 @ sK9 ) )
| ( sK4 = sK2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f84,plain,
( spl11_6
| spl11_4
| spl11_2 ),
inference(avatar_split_clause,[],[f35,f43,f52,f61]) ).
thf(f35,plain,
( ( sK4 = sK2 )
| ( ( cP @ sK5 @ sK7 )
= sK2 )
| ( c0 = sK4 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f83,plain,
( ~ spl11_2
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f15,f57,f43]) ).
thf(f15,plain,
( ( c0 != sK3 )
| ( sK4 != sK2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f82,plain,
( spl11_5
| spl11_4
| spl11_1 ),
inference(avatar_split_clause,[],[f23,f39,f52,f57]) ).
thf(f23,plain,
( ( c0 = sK4 )
| ( c0 = sK3 )
| ( $true
= ( sK1 @ sK8 @ sK9 @ sK7 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f81,plain,
( spl11_6
| spl11_3
| spl11_5 ),
inference(avatar_split_clause,[],[f20,f57,f47,f61]) ).
thf(f20,plain,
( ( ( cP @ sK5 @ sK7 )
= sK2 )
| ( c0 = sK3 )
| ( sK3 = sK2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f80,plain,
( spl11_2
| spl11_4
| spl11_9 ),
inference(avatar_split_clause,[],[f34,f77,f52,f43]) ).
thf(f34,plain,
( ( sK4 = sK2 )
| ( c0 = sK4 )
| ( $true
= ( sK1 @ sK10 @ sK6 @ sK5 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f75,plain,
( spl11_2
| spl11_8
| spl11_4 ),
inference(avatar_split_clause,[],[f32,f52,f72,f43]) ).
thf(f32,plain,
( ( c0 = sK4 )
| ( sK4 = sK2 )
| ( ( cP @ sK10 @ sK8 )
= sK4 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f70,plain,
( spl11_7
| spl11_5
| spl11_4 ),
inference(avatar_split_clause,[],[f26,f52,f57,f67]) ).
thf(f26,plain,
( ( c0 = sK3 )
| ( c0 = sK4 )
| ( sK3
= ( cP @ sK6 @ sK9 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f65,plain,
( spl11_3
| spl11_1
| spl11_5 ),
inference(avatar_split_clause,[],[f18,f57,f39,f47]) ).
thf(f18,plain,
( ( sK3 = sK2 )
| ( c0 = sK3 )
| ( $true
= ( sK1 @ sK8 @ sK9 @ sK7 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f64,plain,
( spl11_5
| spl11_6
| spl11_4 ),
inference(avatar_split_clause,[],[f25,f52,f61,f57]) ).
thf(f25,plain,
( ( c0 = sK3 )
| ( c0 = sK4 )
| ( ( cP @ sK5 @ sK7 )
= sK2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f55,plain,
( ~ spl11_4
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f37,f47,f52]) ).
thf(f37,plain,
( ( sK3 != sK2 )
| ( c0 != sK4 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f50,plain,
( spl11_1
| spl11_2
| spl11_3 ),
inference(avatar_split_clause,[],[f28,f47,f43,f39]) ).
thf(f28,plain,
( ( $true
= ( sK1 @ sK8 @ sK9 @ sK7 ) )
| ( sK3 = sK2 )
| ( sK4 = sK2 ) ),
inference(cnf_transformation,[],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV191^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n022.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 : Fri Jun 21 19:12:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.35 Running higher-order theorem proving
% 0.12/0.35 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.21/0.37 % (27514)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.37 % (27515)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.37 % (27516)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.21/0.37 % (27517)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (27518)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (27520)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.37 % (27519)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.21/0.37 % (27517)Instruction limit reached!
% 0.21/0.37 % (27517)------------------------------
% 0.21/0.37 % (27517)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.37 % (27517)Termination reason: Unknown
% 0.21/0.37 % (27517)Termination phase: Preprocessing 3
% 0.21/0.37
% 0.21/0.37 % (27517)Memory used [KB]: 1023
% 0.21/0.37 % (27517)Time elapsed: 0.004 s
% 0.21/0.37 % (27517)Instructions burned: 2 (million)
% 0.21/0.37 % (27517)------------------------------
% 0.21/0.37 % (27517)------------------------------
% 0.21/0.37 % (27518)Instruction limit reached!
% 0.21/0.37 % (27518)------------------------------
% 0.21/0.37 % (27518)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.37 % (27518)Termination reason: Unknown
% 0.21/0.37 % (27518)Termination phase: Property scanning
% 0.21/0.37
% 0.21/0.37 % (27518)Memory used [KB]: 1023
% 0.21/0.37 % (27518)Time elapsed: 0.004 s
% 0.21/0.37 % (27518)Instructions burned: 3 (million)
% 0.21/0.37 % (27518)------------------------------
% 0.21/0.37 % (27518)------------------------------
% 0.21/0.38 % (27515)Instruction limit reached!
% 0.21/0.38 % (27515)------------------------------
% 0.21/0.38 % (27515)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (27515)Termination reason: Unknown
% 0.21/0.38 % (27515)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (27515)Memory used [KB]: 5500
% 0.21/0.38 % (27515)Time elapsed: 0.005 s
% 0.21/0.38 % (27515)Instructions burned: 5 (million)
% 0.21/0.38 % (27515)------------------------------
% 0.21/0.38 % (27515)------------------------------
% 0.21/0.38 % (27516)First to succeed.
% 0.21/0.39 % (27520)Also succeeded, but the first one will report.
% 0.21/0.39 % (27516)Refutation found. Thanks to Tanya!
% 0.21/0.39 % SZS status Theorem for theBenchmark
% 0.21/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39 % (27516)------------------------------
% 0.21/0.39 % (27516)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.39 % (27516)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (27516)Memory used [KB]: 5628
% 0.21/0.39 % (27516)Time elapsed: 0.015 s
% 0.21/0.39 % (27516)Instructions burned: 10 (million)
% 0.21/0.39 % (27516)------------------------------
% 0.21/0.39 % (27516)------------------------------
% 0.21/0.39 % (27513)Success in time 0.029 s
%------------------------------------------------------------------------------