TSTP Solution File: ALG012-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG012-1 : TPTP v8.2.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.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 May 20 18:21:44 EDT 2024
% Result : Unsatisfiable 1.41s 0.55s
% Output : Refutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 30
% Syntax : Number of formulae : 145 ( 8 unt; 0 def)
% Number of atoms : 605 ( 1 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 937 ( 477 ~; 440 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 21 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 324 ( 324 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1687,plain,
$false,
inference(avatar_sat_refutation,[],[f126,f131,f211,f266,f294,f344,f512,f571,f593,f602,f808,f840,f1019,f1034,f1263,f1376,f1385,f1394,f1492,f1674,f1686]) ).
fof(f1686,plain,
( spl0_9
| spl0_9
| ~ spl0_11
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1684,f1672,f510,f342,f342]) ).
fof(f342,plain,
( spl0_9
<=> ! [X0] : ~ c(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f510,plain,
( spl0_11
<=> ! [X0,X1] :
( d1(f(X0,X1))
| ~ c(X0)
| ~ c(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1672,plain,
( spl0_20
<=> ! [X2,X0] :
( ~ c(X0)
| ~ d1(f(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1684,plain,
( ! [X0,X1] :
( ~ c(X0)
| ~ c(X1) )
| ~ spl0_11
| ~ spl0_20 ),
inference(duplicate_literal_removal,[],[f1675]) ).
fof(f1675,plain,
( ! [X0,X1] :
( ~ c(X0)
| ~ c(X1)
| ~ c(X0) )
| ~ spl0_11
| ~ spl0_20 ),
inference(resolution,[],[f1673,f511]) ).
fof(f511,plain,
( ! [X0,X1] :
( d1(f(X0,X1))
| ~ c(X0)
| ~ c(X1) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f1673,plain,
( ! [X2,X0] :
( ~ d1(f(X2,X0))
| ~ c(X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f1672]) ).
fof(f1674,plain,
( spl0_14
| spl0_20
| ~ spl0_13
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f1670,f1374,f591,f1672,f806]) ).
fof(f806,plain,
( spl0_14
<=> ! [X2] : ~ d1(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f591,plain,
( spl0_13
<=> ! [X2,X0] :
( ~ c(X0)
| ~ d1(X2)
| ~ c(f(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1374,plain,
( spl0_18
<=> ! [X0,X1] :
( ~ c(f(X0,X1))
| ~ d2(X0)
| ~ c(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1670,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ d1(X1)
| ~ d1(f(X2,X0)) )
| ~ spl0_13
| ~ spl0_18 ),
inference(subsumption_resolution,[],[f1669,f41]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ d1(f(X2,X0))
| ~ c(f(X1,X2))
| ~ d1(X1)
| ~ c(X0) ),
inference(resolution,[],[f29,f10]) ).
fof(f10,axiom,
! [X0,X1] :
( c(f(X0,X1))
| ~ d1(X0)
| ~ d1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_2) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ c(f(X0,f(X1,X2)))
| ~ c(X2)
| ~ c(f(X0,X1)) ),
inference(superposition,[],[f19,f1]) ).
fof(f1,axiom,
! [X2,X0,X1] : f(X0,f(X1,X2)) = f(f(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_is_associative) ).
fof(f19,plain,
! [X0,X1] :
( ~ c(f(X0,X1))
| ~ c(X1)
| ~ c(X0) ),
inference(subsumption_resolution,[],[f18,f3]) ).
fof(f3,axiom,
! [X0] :
( ~ d1(X0)
| ~ c(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_exclusive_c_d1) ).
fof(f18,plain,
! [X0,X1] :
( ~ c(X0)
| d1(f(X0,X1))
| ~ c(X1)
| ~ c(f(X0,X1)) ),
inference(resolution,[],[f9,f4]) ).
fof(f4,axiom,
! [X0] :
( ~ d2(X0)
| ~ c(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_exclusive_c_d2) ).
fof(f9,axiom,
! [X0,X1] :
( d2(f(X0,X1))
| ~ c(X0)
| d1(f(X0,X1))
| ~ c(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).
fof(f1669,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ d1(X1)
| ~ d1(f(X2,X0))
| c(f(X1,X2)) )
| ~ spl0_13
| ~ spl0_18 ),
inference(subsumption_resolution,[],[f1667,f903]) ).
fof(f903,plain,
( ! [X2,X0,X1] :
( ~ d1(f(X1,X2))
| ~ c(X2)
| ~ d1(X0)
| ~ d1(f(X0,X1)) )
| ~ spl0_13 ),
inference(resolution,[],[f838,f10]) ).
fof(f838,plain,
( ! [X2,X0,X1] :
( ~ c(f(X0,f(X1,X2)))
| ~ d1(f(X0,X1))
| ~ c(X2) )
| ~ spl0_13 ),
inference(superposition,[],[f592,f1]) ).
fof(f592,plain,
( ! [X2,X0] :
( ~ c(f(X2,X0))
| ~ d1(X2)
| ~ c(X0) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f591]) ).
fof(f1667,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ d1(X1)
| ~ d1(f(X2,X0))
| d1(f(X1,X2))
| c(f(X1,X2)) )
| ~ spl0_18 ),
inference(resolution,[],[f1617,f2]) ).
fof(f2,axiom,
! [X0] :
( d2(X0)
| d1(X0)
| c(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_union) ).
fof(f1617,plain,
( ! [X2,X0,X1] :
( ~ d2(f(X0,X1))
| ~ c(X2)
| ~ d1(X0)
| ~ d1(f(X1,X2)) )
| ~ spl0_18 ),
inference(resolution,[],[f1417,f10]) ).
fof(f1417,plain,
( ! [X2,X0,X1] :
( ~ c(f(X0,f(X1,X2)))
| ~ d2(f(X0,X1))
| ~ c(X2) )
| ~ spl0_18 ),
inference(superposition,[],[f1375,f1]) ).
fof(f1375,plain,
( ! [X0,X1] :
( ~ c(f(X0,X1))
| ~ d2(X0)
| ~ c(X1) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f1374]) ).
fof(f1492,plain,
( spl0_2
| spl0_19
| ~ spl0_1
| ~ spl0_5
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f1488,f591,f264,f121,f1490,f124]) ).
fof(f124,plain,
( spl0_2
<=> ! [X0] : ~ d2(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1490,plain,
( spl0_19
<=> ! [X2,X0] :
( ~ d1(X0)
| ~ d2(X2)
| ~ c(f(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f121,plain,
( spl0_1
<=> ! [X2,X1] :
( ~ c(X1)
| ~ d2(X2)
| c(f(X1,X2))
| d1(f(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f264,plain,
( spl0_5
<=> ! [X0,X3] :
( ~ c(X0)
| ~ d1(X3)
| ~ d1(f(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1488,plain,
( ! [X2,X0,X1] :
( ~ d1(X0)
| ~ d2(X1)
| ~ c(f(X0,X2))
| ~ d2(X2) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_13 ),
inference(duplicate_literal_removal,[],[f1479]) ).
fof(f1479,plain,
( ! [X2,X0,X1] :
( ~ d1(X0)
| ~ d2(X1)
| ~ c(f(X0,X2))
| ~ d2(X2)
| ~ d2(X1) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_13 ),
inference(resolution,[],[f1408,f11]) ).
fof(f11,axiom,
! [X0,X1] :
( c(f(X0,X1))
| ~ d2(X0)
| ~ d2(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_3) ).
fof(f1408,plain,
( ! [X2,X0,X1] :
( ~ c(f(X1,X2))
| ~ d1(X0)
| ~ d2(X2)
| ~ c(f(X0,X1)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_13 ),
inference(subsumption_resolution,[],[f1403,f592]) ).
fof(f1403,plain,
( ! [X2,X0,X1] :
( ~ d1(X0)
| ~ c(f(X1,X2))
| c(f(X0,f(X1,X2)))
| ~ d2(X2)
| ~ c(f(X0,X1)) )
| ~ spl0_1
| ~ spl0_5 ),
inference(resolution,[],[f265,f137]) ).
fof(f137,plain,
( ! [X2,X0,X1] :
( d1(f(X0,f(X1,X2)))
| c(f(X0,f(X1,X2)))
| ~ d2(X2)
| ~ c(f(X0,X1)) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f135,f1]) ).
fof(f135,plain,
( ! [X2,X0,X1] :
( d1(f(X0,f(X1,X2)))
| ~ d2(X2)
| c(f(f(X0,X1),X2))
| ~ c(f(X0,X1)) )
| ~ spl0_1 ),
inference(superposition,[],[f122,f1]) ).
fof(f122,plain,
( ! [X2,X1] :
( d1(f(X1,X2))
| ~ d2(X2)
| c(f(X1,X2))
| ~ c(X1) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f265,plain,
( ! [X3,X0] :
( ~ d1(f(X3,X0))
| ~ d1(X3)
| ~ c(X0) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f1394,plain,
( spl0_9
| spl0_9
| ~ spl0_4
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f1387,f510,f261,f342,f342]) ).
fof(f261,plain,
( spl0_4
<=> ! [X2,X1] : ~ d1(f(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1387,plain,
( ! [X0,X1] :
( ~ c(X0)
| ~ c(X1) )
| ~ spl0_4
| ~ spl0_11 ),
inference(resolution,[],[f262,f511]) ).
fof(f262,plain,
( ! [X2,X1] : ~ d1(f(X1,X2))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f1385,plain,
( spl0_9
| spl0_14
| ~ spl0_5
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f1384,f1371,f591,f264,f806,f342]) ).
fof(f1371,plain,
( spl0_17
<=> ! [X2,X3] :
( ~ c(X2)
| ~ d1(X3)
| ~ d2(f(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1384,plain,
( ! [X0,X1] :
( ~ d1(X0)
| ~ c(X1) )
| ~ spl0_5
| ~ spl0_13
| ~ spl0_17 ),
inference(subsumption_resolution,[],[f1383,f592]) ).
fof(f1383,plain,
( ! [X0,X1] :
( ~ d1(X0)
| ~ c(X1)
| c(f(X0,X1)) )
| ~ spl0_5
| ~ spl0_17 ),
inference(subsumption_resolution,[],[f1380,f265]) ).
fof(f1380,plain,
( ! [X0,X1] :
( ~ d1(X0)
| ~ c(X1)
| d1(f(X0,X1))
| c(f(X0,X1)) )
| ~ spl0_17 ),
inference(resolution,[],[f1372,f2]) ).
fof(f1372,plain,
( ! [X2,X3] :
( ~ d2(f(X3,X2))
| ~ d1(X3)
| ~ c(X2) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f1371]) ).
fof(f1376,plain,
( spl0_17
| spl0_18
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f1153,f510,f1374,f1371]) ).
fof(f1153,plain,
( ! [X2,X3,X0,X1] :
( ~ c(f(X0,X1))
| ~ c(X2)
| ~ d1(X3)
| ~ c(X1)
| ~ d2(f(X3,X2))
| ~ d2(X0) )
| ~ spl0_11 ),
inference(resolution,[],[f1050,f22]) ).
fof(f22,plain,
! [X2,X0,X1] :
( c(f(X0,f(X1,X2)))
| ~ d2(f(X0,X1))
| ~ d2(X2) ),
inference(superposition,[],[f11,f1]) ).
fof(f1050,plain,
( ! [X2,X3,X0,X1] :
( ~ c(f(X3,f(X0,X1)))
| ~ c(f(X1,X2))
| ~ c(X0)
| ~ d1(X3)
| ~ c(X2) )
| ~ spl0_11 ),
inference(resolution,[],[f511,f54]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( ~ d1(f(X0,f(X1,X2)))
| ~ c(f(X3,f(X0,X1)))
| ~ d1(X3)
| ~ c(X2) ),
inference(superposition,[],[f41,f1]) ).
fof(f1263,plain,
( spl0_14
| spl0_16
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f1259,f510,f1261,f806]) ).
fof(f1261,plain,
( spl0_16
<=> ! [X2,X0,X3] :
( ~ c(X0)
| ~ c(f(X2,X3))
| ~ d1(f(X3,X0))
| ~ c(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1259,plain,
( ! [X2,X3,X0,X1] :
( ~ c(X0)
| ~ d1(X1)
| ~ c(f(X2,X3))
| ~ c(X2)
| ~ d1(f(X3,X0)) )
| ~ spl0_11 ),
inference(duplicate_literal_removal,[],[f1249]) ).
fof(f1249,plain,
( ! [X2,X3,X0,X1] :
( ~ c(X0)
| ~ d1(X1)
| ~ c(f(X2,X3))
| ~ c(X2)
| ~ d1(f(X3,X0))
| ~ d1(X1) )
| ~ spl0_11 ),
inference(resolution,[],[f1086,f23]) ).
fof(f23,plain,
! [X2,X0,X1] :
( c(f(X0,f(X1,X2)))
| ~ d1(f(X0,X1))
| ~ d1(X2) ),
inference(superposition,[],[f10,f1]) ).
fof(f1086,plain,
( ! [X2,X3,X0,X1] :
( ~ c(f(X1,f(X2,X3)))
| ~ c(X2)
| ~ d1(X3)
| ~ c(f(X0,X1))
| ~ c(X0) )
| ~ spl0_11 ),
inference(resolution,[],[f1055,f93]) ).
fof(f93,plain,
! [X2,X3,X0,X1] :
( ~ d1(f(X0,f(X1,X2)))
| ~ d1(X3)
| ~ c(f(X1,f(X2,X3)))
| ~ c(X0) ),
inference(resolution,[],[f35,f19]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( c(f(X3,f(X0,f(X1,X2))))
| ~ d1(f(X3,f(X0,X1)))
| ~ d1(X2) ),
inference(superposition,[],[f23,f1]) ).
fof(f1055,plain,
( ! [X2,X0,X1] :
( d1(f(X0,f(X1,X2)))
| ~ c(f(X0,X1))
| ~ c(X2) )
| ~ spl0_11 ),
inference(superposition,[],[f511,f1]) ).
fof(f1034,plain,
~ spl0_14,
inference(avatar_contradiction_clause,[],[f1030]) ).
fof(f1030,plain,
( $false
| ~ spl0_14 ),
inference(resolution,[],[f807,f7]) ).
fof(f7,axiom,
d1(a2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_d1_not_empty) ).
fof(f807,plain,
( ! [X2] : ~ d1(X2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f806]) ).
fof(f1019,plain,
( spl0_14
| spl0_15
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f1015,f510,f1017,f806]) ).
fof(f1017,plain,
( spl0_15
<=> ! [X0,X1,X3] :
( ~ c(f(X0,X1))
| ~ d1(X1)
| ~ c(X3)
| ~ c(f(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1015,plain,
( ! [X2,X3,X0,X1] :
( ~ c(f(X0,X1))
| ~ d1(X2)
| ~ c(X3)
| ~ c(f(X3,X0))
| ~ d1(X1) )
| ~ spl0_11 ),
inference(duplicate_literal_removal,[],[f1007]) ).
fof(f1007,plain,
( ! [X2,X3,X0,X1] :
( ~ c(f(X0,X1))
| ~ d1(X2)
| ~ c(X3)
| ~ c(f(X3,X0))
| ~ d1(X1)
| ~ d1(X2) )
| ~ spl0_11 ),
inference(resolution,[],[f820,f10]) ).
fof(f820,plain,
( ! [X2,X3,X0,X1] :
( ~ c(f(X2,X3))
| ~ c(f(X1,X2))
| ~ d1(X3)
| ~ c(X0)
| ~ c(f(X0,X1)) )
| ~ spl0_11 ),
inference(resolution,[],[f511,f49]) ).
fof(f49,plain,
! [X2,X3,X0,X1] :
( ~ d1(f(X0,f(X1,X2)))
| ~ d1(X3)
| ~ c(f(X2,X3))
| ~ c(f(X0,X1)) ),
inference(superposition,[],[f34,f1]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ d1(f(X0,X1))
| ~ d1(X2)
| ~ c(f(X1,X2))
| ~ c(X0) ),
inference(resolution,[],[f23,f19]) ).
fof(f840,plain,
( spl0_8
| spl0_9
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f829,f510,f342,f339]) ).
fof(f339,plain,
( spl0_8
<=> ! [X2,X1] :
( ~ c(X1)
| ~ c(f(X1,X2))
| ~ d1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f829,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ c(X1)
| ~ d1(X2)
| ~ c(f(X1,X2)) )
| ~ spl0_11 ),
inference(duplicate_literal_removal,[],[f810]) ).
fof(f810,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ c(X1)
| ~ d1(X2)
| ~ c(f(X1,X2))
| ~ c(X0) )
| ~ spl0_11 ),
inference(resolution,[],[f511,f34]) ).
fof(f808,plain,
( spl0_14
| spl0_2
| spl0_14
| spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f801,f507,f124,f806,f124,f806]) ).
fof(f507,plain,
( spl0_10
<=> ! [X2,X3] :
( ~ d1(X2)
| ~ d2(X3)
| d1(f(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f801,plain,
( ! [X2,X3,X0,X1] :
( ~ d2(X0)
| ~ d1(X1)
| ~ d2(X3)
| ~ d1(X2) )
| ~ spl0_10 ),
inference(subsumption_resolution,[],[f800,f11]) ).
fof(f800,plain,
( ! [X2,X3,X0,X1] :
( ~ d2(X0)
| ~ d1(X1)
| ~ c(f(X0,X3))
| ~ d2(X3)
| ~ d1(X2) )
| ~ spl0_10 ),
inference(subsumption_resolution,[],[f794,f10]) ).
fof(f794,plain,
( ! [X2,X3,X0,X1] :
( ~ d2(X0)
| ~ d1(X1)
| ~ c(f(X2,X1))
| ~ c(f(X0,X3))
| ~ d2(X3)
| ~ d1(X2) )
| ~ spl0_10 ),
inference(resolution,[],[f613,f508]) ).
fof(f508,plain,
( ! [X2,X3] :
( d1(f(X3,X2))
| ~ d2(X3)
| ~ d1(X2) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f613,plain,
( ! [X2,X3,X0,X1] :
( ~ d1(f(X1,X2))
| ~ d2(X0)
| ~ d1(X3)
| ~ c(f(X2,X3))
| ~ c(f(X0,X1)) )
| ~ spl0_10 ),
inference(resolution,[],[f508,f49]) ).
fof(f602,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f594]) ).
fof(f594,plain,
( $false
| ~ spl0_9 ),
inference(resolution,[],[f343,f6]) ).
fof(f6,axiom,
c(a1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_c_not_empty) ).
fof(f343,plain,
( ! [X0] : ~ c(X0)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f593,plain,
( spl0_9
| spl0_13
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f588,f510,f591,f342]) ).
fof(f588,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ c(X1)
| ~ c(f(X2,X0))
| ~ d1(X2) )
| ~ spl0_11 ),
inference(duplicate_literal_removal,[],[f573]) ).
fof(f573,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ c(X1)
| ~ c(f(X2,X0))
| ~ d1(X2)
| ~ c(X1) )
| ~ spl0_11 ),
inference(resolution,[],[f511,f41]) ).
fof(f571,plain,
( spl0_12
| spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f565,f507,f124,f569]) ).
fof(f569,plain,
( spl0_12
<=> ! [X2,X1] :
( ~ d1(f(X1,X2))
| ~ d1(X1)
| ~ d1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f565,plain,
( ! [X2,X0,X1] :
( ~ d2(X0)
| ~ d1(f(X1,X2))
| ~ d1(X2)
| ~ d1(X1) )
| ~ spl0_10 ),
inference(duplicate_literal_removal,[],[f558]) ).
fof(f558,plain,
( ! [X2,X0,X1] :
( ~ d2(X0)
| ~ d1(f(X1,X2))
| ~ d1(X2)
| ~ d2(X0)
| ~ d1(X1) )
| ~ spl0_10 ),
inference(resolution,[],[f527,f508]) ).
fof(f527,plain,
( ! [X2,X0,X1] :
( ~ d1(f(X2,X0))
| ~ d2(X2)
| ~ d1(f(X0,X1))
| ~ d1(X1) )
| ~ spl0_10 ),
inference(resolution,[],[f523,f23]) ).
fof(f523,plain,
( ! [X0,X1] :
( ~ c(f(X0,X1))
| ~ d1(X1)
| ~ d2(X0) )
| ~ spl0_10 ),
inference(resolution,[],[f508,f3]) ).
fof(f512,plain,
( spl0_10
| spl0_11
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f504,f121,f510,f507]) ).
fof(f504,plain,
( ! [X2,X3,X0,X1] :
( d1(f(X0,X1))
| ~ c(X1)
| ~ c(X0)
| ~ d1(X2)
| d1(f(X3,X2))
| ~ d2(X3) )
| ~ spl0_1 ),
inference(subsumption_resolution,[],[f503,f48]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ c(f(X1,X0))
| ~ d2(X0)
| ~ c(X2)
| d1(f(X2,X1))
| ~ c(X1) ),
inference(duplicate_literal_removal,[],[f45]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ d2(X0)
| ~ c(f(X1,X0))
| ~ c(X2)
| ~ c(X2)
| d1(f(X2,X1))
| ~ c(X1) ),
inference(resolution,[],[f30,f9]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ d2(f(X0,X1))
| ~ d2(X2)
| ~ c(f(X1,X2))
| ~ c(X0) ),
inference(resolution,[],[f22,f19]) ).
fof(f503,plain,
( ! [X2,X3,X0,X1] :
( d1(f(X0,X1))
| ~ c(X1)
| ~ c(X0)
| ~ d1(X2)
| d1(f(X3,X2))
| ~ d2(X3)
| c(f(X1,X3)) )
| ~ spl0_1 ),
inference(duplicate_literal_removal,[],[f500]) ).
fof(f500,plain,
( ! [X2,X3,X0,X1] :
( d1(f(X0,X1))
| ~ c(X1)
| ~ c(X0)
| ~ d1(X2)
| d1(f(X3,X2))
| ~ d2(X3)
| c(f(X1,X3))
| ~ c(X1) )
| ~ spl0_1 ),
inference(resolution,[],[f439,f122]) ).
fof(f439,plain,
! [X2,X3,X0,X1] :
( ~ d1(f(X1,X2))
| d1(f(X0,X1))
| ~ c(X1)
| ~ c(X0)
| ~ d1(X3)
| d1(f(X2,X3)) ),
inference(subsumption_resolution,[],[f437,f34]) ).
fof(f437,plain,
! [X2,X3,X0,X1] :
( ~ c(X0)
| d1(f(X0,X1))
| ~ c(X1)
| ~ d1(f(X1,X2))
| ~ d1(X3)
| d1(f(X2,X3))
| c(f(X2,X3)) ),
inference(resolution,[],[f57,f2]) ).
fof(f57,plain,
! [X2,X3,X0,X1] :
( ~ d2(f(X0,X1))
| ~ c(X2)
| d1(f(X2,X3))
| ~ c(X3)
| ~ d1(f(X3,X0))
| ~ d1(X1) ),
inference(resolution,[],[f48,f23]) ).
fof(f344,plain,
( spl0_8
| spl0_9
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f310,f289,f342,f339]) ).
fof(f289,plain,
( spl0_6
<=> ! [X2,X1] : ~ d2(f(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f310,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ c(X1)
| ~ d1(X2)
| ~ c(f(X1,X2)) )
| ~ spl0_6 ),
inference(duplicate_literal_removal,[],[f302]) ).
fof(f302,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ c(X1)
| ~ d1(X2)
| ~ c(f(X1,X2))
| ~ c(X0) )
| ~ spl0_6 ),
inference(resolution,[],[f295,f34]) ).
fof(f295,plain,
( ! [X0,X1] :
( d1(f(X0,X1))
| ~ c(X0)
| ~ c(X1) )
| ~ spl0_6 ),
inference(resolution,[],[f290,f9]) ).
fof(f290,plain,
( ! [X2,X1] : ~ d2(f(X1,X2))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f294,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f284,f292,f289]) ).
fof(f292,plain,
( spl0_7
<=> ! [X0,X3] :
( ~ c(X0)
| ~ d2(X3)
| ~ d2(f(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f284,plain,
! [X2,X3,X0,X1] :
( ~ c(X0)
| ~ d2(f(X1,X2))
| ~ d2(f(X3,X0))
| ~ d2(X3) ),
inference(duplicate_literal_removal,[],[f277]) ).
fof(f277,plain,
! [X2,X3,X0,X1] :
( ~ c(X0)
| ~ d2(f(X1,X2))
| ~ d2(f(X3,X0))
| ~ d2(f(X1,X2))
| ~ d2(X3) ),
inference(resolution,[],[f104,f22]) ).
fof(f104,plain,
! [X2,X3,X0,X1] :
( ~ c(f(X1,f(X2,X3)))
| ~ c(X0)
| ~ d2(f(X1,X2))
| ~ d2(f(X3,X0)) ),
inference(resolution,[],[f42,f22]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( ~ c(f(X3,f(X0,f(X1,X2))))
| ~ c(X2)
| ~ c(f(X3,f(X0,X1))) ),
inference(superposition,[],[f29,f1]) ).
fof(f266,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f256,f264,f261]) ).
fof(f256,plain,
! [X2,X3,X0,X1] :
( ~ c(X0)
| ~ d1(f(X1,X2))
| ~ d1(f(X3,X0))
| ~ d1(X3) ),
inference(duplicate_literal_removal,[],[f248]) ).
fof(f248,plain,
! [X2,X3,X0,X1] :
( ~ c(X0)
| ~ d1(f(X1,X2))
| ~ d1(f(X3,X0))
| ~ d1(f(X1,X2))
| ~ d1(X3) ),
inference(resolution,[],[f103,f23]) ).
fof(f103,plain,
! [X2,X3,X0,X1] :
( ~ c(f(X1,f(X2,X3)))
| ~ c(X0)
| ~ d1(f(X1,X2))
| ~ d1(f(X3,X0)) ),
inference(resolution,[],[f42,f23]) ).
fof(f211,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f195,f124,f209]) ).
fof(f209,plain,
( spl0_3
<=> ! [X2,X1] :
( ~ c(X1)
| ~ d2(X2)
| c(f(X2,X1))
| d1(f(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f195,plain,
! [X2,X0,X1] :
( ~ d2(X0)
| ~ c(X1)
| d1(f(X2,X1))
| c(f(X2,X1))
| ~ d2(X2) ),
inference(duplicate_literal_removal,[],[f188]) ).
fof(f188,plain,
! [X2,X0,X1] :
( ~ d2(X0)
| ~ c(X1)
| d1(f(X2,X1))
| c(f(X2,X1))
| ~ d2(X0)
| ~ d2(X2) ),
inference(resolution,[],[f51,f11]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ c(f(X0,X1))
| ~ d2(X0)
| ~ c(X2)
| d1(f(X1,X2))
| c(f(X1,X2)) ),
inference(resolution,[],[f40,f2]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ d2(f(X2,X0))
| ~ c(f(X1,X2))
| ~ d2(X1)
| ~ c(X0) ),
inference(resolution,[],[f29,f11]) ).
fof(f131,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f127]) ).
fof(f127,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f125,f8]) ).
fof(f8,axiom,
d2(a3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_d2_not_empty) ).
fof(f125,plain,
( ! [X0] : ~ d2(X0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f126,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f119,f124,f121]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ d2(X0)
| ~ c(X1)
| d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X2) ),
inference(duplicate_literal_removal,[],[f112]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ d2(X0)
| ~ c(X1)
| d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X2)
| ~ d2(X0) ),
inference(resolution,[],[f46,f11]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ c(f(X1,X0))
| ~ d2(X0)
| ~ c(X2)
| d1(f(X2,X1))
| c(f(X2,X1)) ),
inference(resolution,[],[f30,f2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG012-1 : TPTP v8.2.0. Released v2.7.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat May 18 22:38:38 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (14336)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (14343)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.37 % (14342)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (14341)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (14337)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [3]
% 0.21/0.38 TRYING [4]
% 0.21/0.39 % (14339)WARNING: value z3 for option sas not known
% 0.21/0.39 % (14340)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.39 % (14339)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.39 TRYING [5]
% 0.21/0.39 % (14338)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 TRYING [3]
% 0.21/0.39 TRYING [4]
% 0.21/0.40 TRYING [5]
% 0.21/0.41 TRYING [6]
% 0.21/0.42 TRYING [6]
% 0.21/0.48 TRYING [7]
% 0.21/0.48 TRYING [7]
% 1.26/0.55 % (14339)First to succeed.
% 1.26/0.55 % (14339)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14336"
% 1.41/0.55 % (14339)Refutation found. Thanks to Tanya!
% 1.41/0.55 % SZS status Unsatisfiable for theBenchmark
% 1.41/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 1.41/0.55 % (14339)------------------------------
% 1.41/0.55 % (14339)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.41/0.55 % (14339)Termination reason: Refutation
% 1.41/0.55
% 1.41/0.55 % (14339)Memory used [KB]: 1718
% 1.41/0.55 % (14339)Time elapsed: 0.185 s
% 1.41/0.55 % (14339)Instructions burned: 276 (million)
% 1.41/0.55 % (14336)Success in time 0.183 s
%------------------------------------------------------------------------------