TSTP Solution File: SEU129+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU129+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 20:41:06 EDT 2024
% Result : Theorem 0.11s 0.30s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 7 unt; 0 def)
% Number of atoms : 138 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 155 ( 60 ~; 61 |; 25 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 97 ( 87 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f21,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f22,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f21]) ).
fof(f23,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f24,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_0(B,A),A)
& ~ in(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f28,plain,
! [A,B,C] :
( ( C != set_intersection2(A,B)
| ! [D] :
( ( ~ in(D,C)
| ( in(D,A)
& in(D,B) ) )
& ( in(D,C)
| ~ in(D,A)
| ~ in(D,B) ) ) )
& ( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ~ in(D,A)
| ~ in(D,B) )
& ( in(D,C)
| ( in(D,A)
& in(D,B) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f29,plain,
( ! [A,B,C] :
( C != set_intersection2(A,B)
| ( ! [D] :
( ~ in(D,C)
| ( in(D,A)
& in(D,B) ) )
& ! [D] :
( in(D,C)
| ~ in(D,A)
| ~ in(D,B) ) ) )
& ! [A,B,C] :
( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ~ in(D,A)
| ~ in(D,B) )
& ( in(D,C)
| ( in(D,A)
& in(D,B) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f28]) ).
fof(f30,plain,
( ! [A,B,C] :
( C != set_intersection2(A,B)
| ( ! [D] :
( ~ in(D,C)
| ( in(D,A)
& in(D,B) ) )
& ! [D] :
( in(D,C)
| ~ in(D,A)
| ~ in(D,B) ) ) )
& ! [A,B,C] :
( C = set_intersection2(A,B)
| ( ( ~ in(sk0_1(C,B,A),C)
| ~ in(sk0_1(C,B,A),A)
| ~ in(sk0_1(C,B,A),B) )
& ( in(sk0_1(C,B,A),C)
| ( in(sk0_1(C,B,A),A)
& in(sk0_1(C,B,A),B) ) ) ) ) ),
inference(skolemization,[status(esa)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X0)
| in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f46,plain,
? [A,B,C] :
( subset(A,B)
& ~ subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f47,plain,
? [A,B] :
( subset(A,B)
& ? [C] : ~ subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(miniscoping,[status(esa)],[f46]) ).
fof(f48,plain,
( subset(sk0_4,sk0_5)
& ~ subset(set_intersection2(sk0_4,sk0_6),set_intersection2(sk0_5,sk0_6)) ),
inference(skolemization,[status(esa)],[f47]) ).
fof(f49,plain,
subset(sk0_4,sk0_5),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f50,plain,
~ subset(set_intersection2(sk0_4,sk0_6),set_intersection2(sk0_5,sk0_6)),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f31]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f32]) ).
fof(f62,plain,
! [X0,X1,X2] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,X1)
| ~ in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f33]) ).
fof(f63,plain,
! [X0] :
( ~ in(X0,sk0_4)
| in(X0,sk0_5) ),
inference(resolution,[status(thm)],[f25,f49]) ).
fof(f93,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X1),X2)
| in(sk0_0(X2,set_intersection2(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f26,f61]) ).
fof(f94,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X1),X2)
| in(sk0_0(X2,set_intersection2(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f26,f60]) ).
fof(f99,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ in(sk0_0(set_intersection2(X1,X2),X0),X1)
| ~ in(sk0_0(set_intersection2(X1,X2),X0),X2) ),
inference(resolution,[status(thm)],[f27,f62]) ).
fof(f114,plain,
in(sk0_0(set_intersection2(sk0_5,sk0_6),set_intersection2(sk0_4,sk0_6)),sk0_6),
inference(resolution,[status(thm)],[f93,f50]) ).
fof(f124,plain,
in(sk0_0(set_intersection2(sk0_5,sk0_6),set_intersection2(sk0_4,sk0_6)),sk0_4),
inference(resolution,[status(thm)],[f94,f50]) ).
fof(f369,plain,
( spl0_17
<=> in(sk0_0(set_intersection2(sk0_5,sk0_6),set_intersection2(sk0_4,sk0_6)),sk0_5) ),
introduced(split_symbol_definition) ).
fof(f371,plain,
( ~ in(sk0_0(set_intersection2(sk0_5,sk0_6),set_intersection2(sk0_4,sk0_6)),sk0_5)
| spl0_17 ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f372,plain,
( spl0_18
<=> in(sk0_0(set_intersection2(sk0_5,sk0_6),set_intersection2(sk0_4,sk0_6)),sk0_6) ),
introduced(split_symbol_definition) ).
fof(f374,plain,
( ~ in(sk0_0(set_intersection2(sk0_5,sk0_6),set_intersection2(sk0_4,sk0_6)),sk0_6)
| spl0_18 ),
inference(component_clause,[status(thm)],[f372]) ).
fof(f375,plain,
( ~ in(sk0_0(set_intersection2(sk0_5,sk0_6),set_intersection2(sk0_4,sk0_6)),sk0_5)
| ~ in(sk0_0(set_intersection2(sk0_5,sk0_6),set_intersection2(sk0_4,sk0_6)),sk0_6) ),
inference(resolution,[status(thm)],[f99,f50]) ).
fof(f376,plain,
( ~ spl0_17
| ~ spl0_18 ),
inference(split_clause,[status(thm)],[f375,f369,f372]) ).
fof(f390,plain,
( $false
| spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f374,f114]) ).
fof(f391,plain,
spl0_18,
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f392,plain,
( ~ in(sk0_0(set_intersection2(sk0_5,sk0_6),set_intersection2(sk0_4,sk0_6)),sk0_4)
| spl0_17 ),
inference(resolution,[status(thm)],[f371,f63]) ).
fof(f393,plain,
( $false
| spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f392,f124]) ).
fof(f394,plain,
spl0_17,
inference(contradiction_clause,[status(thm)],[f393]) ).
fof(f395,plain,
$false,
inference(sat_refutation,[status(thm)],[f376,f391,f394]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.06 % Problem : SEU129+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.25 % Computer : n010.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Mon Apr 29 19:32:50 EDT 2024
% 0.06/0.26 % CPUTime :
% 0.11/0.26 % Drodi V3.6.0
% 0.11/0.30 % Refutation found
% 0.11/0.30 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.31 % Elapsed time: 0.047559 seconds
% 0.11/0.31 % CPU time: 0.291748 seconds
% 0.11/0.31 % Total memory used: 63.981 MB
% 0.11/0.31 % Net memory used: 63.663 MB
%------------------------------------------------------------------------------