TSTP Solution File: SET607+3 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET607+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n018.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 Apr 30 20:39:57 EDT 2024
% Result : Theorem 72.85s 9.55s
% Output : CNFRefutation 72.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 10 unt; 0 def)
% Number of atoms : 194 ( 25 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 205 ( 78 ~; 92 |; 23 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 86 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [B,C] : union(B,difference(C,B)) = union(B,C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [B,C] : union(B,difference(C,B)) = union(B,C),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [B,C,D] :
( ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) )
& ( member(D,union(B,C))
| ( ~ member(D,B)
& ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f1]) ).
fof(f11,plain,
( ! [B,C,D] :
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) )
& ! [B,C,D] :
( member(D,union(B,C))
| ( ~ member(D,B)
& ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f15,plain,
! [B,C,D] :
( ( ~ member(D,difference(B,C))
| ( member(D,B)
& ~ member(D,C) ) )
& ( member(D,difference(B,C))
| ~ member(D,B)
| member(D,C) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f16,plain,
( ! [B,C,D] :
( ~ member(D,difference(B,C))
| ( member(D,B)
& ~ member(D,C) ) )
& ! [B,C,D] :
( member(D,difference(B,C))
| ~ member(D,B)
| member(D,C) ) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f19,plain,
! [X0,X1,X2] :
( member(X0,difference(X1,X2))
| ~ member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f20,plain,
! [B,C] :
( ( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f21,plain,
( ! [B,C] :
( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ! [B,C] :
( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( X0 != X1
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f34,plain,
! [B,C] :
( ( B != C
| ! [D] :
( ( ~ member(D,B)
| member(D,C) )
& ( member(D,B)
| ~ member(D,C) ) ) )
& ( B = C
| ? [D] :
( ( ~ member(D,B)
| ~ member(D,C) )
& ( member(D,B)
| member(D,C) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f35,plain,
( ! [B,C] :
( B != C
| ( ! [D] :
( ~ member(D,B)
| member(D,C) )
& ! [D] :
( member(D,B)
| ~ member(D,C) ) ) )
& ! [B,C] :
( B = C
| ? [D] :
( ( ~ member(D,B)
| ~ member(D,C) )
& ( member(D,B)
| member(D,C) ) ) ) ),
inference(miniscoping,[status(esa)],[f34]) ).
fof(f36,plain,
( ! [B,C] :
( B != C
| ( ! [D] :
( ~ member(D,B)
| member(D,C) )
& ! [D] :
( member(D,B)
| ~ member(D,C) ) ) )
& ! [B,C] :
( B = C
| ( ( ~ member(sk0_1(C,B),B)
| ~ member(sk0_1(C,B),C) )
& ( member(sk0_1(C,B),B)
| member(sk0_1(C,B),C) ) ) ) ),
inference(skolemization,[status(esa)],[f35]) ).
fof(f39,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sk0_1(X1,X0),X0)
| ~ member(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f40,plain,
! [X0,X1] :
( X0 = X1
| member(sk0_1(X1,X0),X0)
| member(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f41,plain,
? [B,C] : union(B,difference(C,B)) != union(B,C),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f42,plain,
union(sk0_2,difference(sk0_3,sk0_2)) != union(sk0_2,sk0_3),
inference(skolemization,[status(esa)],[f41]) ).
fof(f43,plain,
union(sk0_2,difference(sk0_3,sk0_2)) != union(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f22]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,union(X1,difference(X2,X3)))
| member(X0,X1)
| member(X0,X2) ),
inference(resolution,[status(thm)],[f12,f17]) ).
fof(f195,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| member(X0,X2)
| member(X0,union(X3,difference(X1,X2))) ),
inference(resolution,[status(thm)],[f19,f14]) ).
fof(f477,plain,
( spl0_8
<=> member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f478,plain,
( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,sk0_3))
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f480,plain,
( spl0_9
<=> member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,difference(sk0_3,sk0_2))) ),
introduced(split_symbol_definition) ).
fof(f481,plain,
( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,difference(sk0_3,sk0_2)))
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f482,plain,
( ~ member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,difference(sk0_3,sk0_2)))
| spl0_9 ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f523,plain,
( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,sk0_3))
| member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,difference(sk0_3,sk0_2))) ),
inference(resolution,[status(thm)],[f40,f43]) ).
fof(f524,plain,
( spl0_8
| spl0_9 ),
inference(split_clause,[status(thm)],[f523,f477,f480]) ).
fof(f801,plain,
( spl0_10
<=> union(sk0_2,sk0_3) = union(sk0_2,difference(sk0_3,sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f802,plain,
( union(sk0_2,sk0_3) = union(sk0_2,difference(sk0_3,sk0_2))
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f801]) ).
fof(f806,plain,
( spl0_11
<=> member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f807,plain,
( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_2)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f806]) ).
fof(f809,plain,
( spl0_12
<=> member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f810,plain,
( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_3)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f809]) ).
fof(f812,plain,
( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_2)
| member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_3)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f478,f12]) ).
fof(f813,plain,
( spl0_11
| spl0_12
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f812,f806,f809,f477]) ).
fof(f855,plain,
! [X0] :
( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,X0))
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f807,f13]) ).
fof(f1029,plain,
( union(sk0_2,sk0_3) = union(sk0_2,difference(sk0_3,sk0_2))
| ~ member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,sk0_3))
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f855,f39]) ).
fof(f1030,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_11 ),
inference(split_clause,[status(thm)],[f1029,f801,f477,f806]) ).
fof(f1031,plain,
( union(sk0_2,sk0_3) = union(sk0_2,difference(sk0_3,sk0_2))
| ~ member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,difference(sk0_3,sk0_2)))
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f855,f39]) ).
fof(f1032,plain,
( spl0_10
| ~ spl0_9
| ~ spl0_11 ),
inference(split_clause,[status(thm)],[f1031,f801,f480,f806]) ).
fof(f1070,plain,
( $false
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f802,f43]) ).
fof(f1071,plain,
~ spl0_10,
inference(contradiction_clause,[status(thm)],[f1070]) ).
fof(f1079,plain,
! [X0] :
( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(X0,sk0_3))
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f810,f14]) ).
fof(f1332,plain,
( union(sk0_2,sk0_3) = union(sk0_2,difference(sk0_3,sk0_2))
| ~ member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,difference(sk0_3,sk0_2)))
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f1079,f39]) ).
fof(f1333,plain,
( spl0_10
| ~ spl0_9
| ~ spl0_12 ),
inference(split_clause,[status(thm)],[f1332,f801,f480,f809]) ).
fof(f9176,plain,
( spl0_69
<=> subset(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,difference(sk0_3,sk0_2))) ),
introduced(split_symbol_definition) ).
fof(f9178,plain,
( ~ subset(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,difference(sk0_3,sk0_2)))
| spl0_69 ),
inference(component_clause,[status(thm)],[f9176]) ).
fof(f9312,plain,
( $false
| spl0_69 ),
inference(forward_subsumption_resolution,[status(thm)],[f9178,f44]) ).
fof(f9313,plain,
spl0_69,
inference(contradiction_clause,[status(thm)],[f9312]) ).
fof(f15197,plain,
( spl0_159
<=> subset(union(sk0_2,sk0_3),union(sk0_2,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f15199,plain,
( ~ subset(union(sk0_2,sk0_3),union(sk0_2,sk0_3))
| spl0_159 ),
inference(component_clause,[status(thm)],[f15197]) ).
fof(f15614,plain,
( $false
| spl0_159 ),
inference(forward_subsumption_resolution,[status(thm)],[f15199,f44]) ).
fof(f15615,plain,
spl0_159,
inference(contradiction_clause,[status(thm)],[f15614]) ).
fof(f24440,plain,
( ~ member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_3)
| member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_2)
| spl0_9 ),
inference(resolution,[status(thm)],[f195,f482]) ).
fof(f24441,plain,
( ~ spl0_12
| spl0_11
| spl0_9 ),
inference(split_clause,[status(thm)],[f24440,f809,f806,f480]) ).
fof(f25264,plain,
( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_2)
| member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_3)
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f481,f74]) ).
fof(f25265,plain,
( spl0_11
| spl0_12
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f25264,f806,f809,f480]) ).
fof(f25378,plain,
$false,
inference(sat_refutation,[status(thm)],[f524,f813,f1030,f1032,f1071,f1333,f9313,f15615,f24441,f25265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET607+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n018.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 : Mon Apr 29 21:52:43 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 72.85/9.55 % Refutation found
% 72.85/9.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 72.85/9.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 73.51/9.67 % Elapsed time: 9.298321 seconds
% 73.51/9.67 % CPU time: 73.504299 seconds
% 73.51/9.67 % Total memory used: 515.743 MB
% 73.51/9.67 % Net memory used: 503.984 MB
%------------------------------------------------------------------------------