TSTP Solution File: SEU120+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU120+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 20:41:03 EDT 2024
% Result : Theorem 0.10s 0.33s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 4 unt; 0 def)
% Number of atoms : 201 ( 26 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 241 ( 102 ~; 85 |; 45 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 134 ( 114 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,lemma,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] :
~ ( in(C,A)
& in(C,B) ) )
& ~ ( ? [C] :
( in(C,A)
& in(C,B) )
& disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) )
& ~ ( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) )
& ~ ( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f18,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f19,plain,
! [A] :
( ( A != empty_set
| ! [B] : ~ in(B,A) )
& ( A = empty_set
| ? [B] : in(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f20,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| ? [B] : in(B,A) ) ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f21,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| in(sk0_0(A),A) ) ),
inference(skolemization,[status(esa)],[f20]) ).
fof(f23,plain,
! [X0] :
( X0 = empty_set
| in(sk0_0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f24,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(f25,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)],[f24]) ).
fof(f26,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)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X0)
| in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f33,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set )
& ( disjoint(A,B)
| set_intersection2(A,B) != empty_set ) ),
inference(NNF_transformation,[status(esa)],[f5]) ).
fof(f34,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set )
& ! [A,B] :
( disjoint(A,B)
| set_intersection2(A,B) != empty_set ) ),
inference(miniscoping,[status(esa)],[f33]) ).
fof(f36,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f44,plain,
! [A,B] :
( ~ disjoint(A,B)
| disjoint(B,A) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f45,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
! [A,B] :
( ( disjoint(A,B)
| ? [C] :
( in(C,A)
& in(C,B) ) )
& ( ! [C] :
( ~ in(C,A)
| ~ in(C,B) )
| ~ disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f47,plain,
( ! [A,B] :
( disjoint(A,B)
| ? [C] :
( in(C,A)
& in(C,B) ) )
& ! [A,B] :
( ! [C] :
( ~ in(C,A)
| ~ in(C,B) )
| ~ disjoint(A,B) ) ),
inference(miniscoping,[status(esa)],[f46]) ).
fof(f48,plain,
( ! [A,B] :
( disjoint(A,B)
| ( in(sk0_4(B,A),A)
& in(sk0_4(B,A),B) ) )
& ! [A,B] :
( ! [C] :
( ~ in(C,A)
| ~ in(C,B) )
| ~ disjoint(A,B) ) ),
inference(skolemization,[status(esa)],[f47]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ disjoint(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f52,plain,
? [A,B] :
( ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) )
| ( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f53,plain,
! [A,B] :
( pd0_0(B,A)
=> ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) ) ),
introduced(predicate_definition,[f52]) ).
fof(f54,plain,
? [A,B] :
( pd0_0(B,A)
| ( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
inference(formula_renaming,[status(thm)],[f52,f53]) ).
fof(f55,plain,
( ? [A,B] : pd0_0(B,A)
| ? [A,B] :
( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
inference(miniscoping,[status(esa)],[f54]) ).
fof(f56,plain,
( pd0_0(sk0_6,sk0_5)
| ( in(sk0_9,set_intersection2(sk0_7,sk0_8))
& disjoint(sk0_7,sk0_8) ) ),
inference(skolemization,[status(esa)],[f55]) ).
fof(f57,plain,
( pd0_0(sk0_6,sk0_5)
| in(sk0_9,set_intersection2(sk0_7,sk0_8)) ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f58,plain,
( pd0_0(sk0_6,sk0_5)
| disjoint(sk0_7,sk0_8) ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f59,plain,
! [A,B] :
( ~ pd0_0(B,A)
| ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f53]) ).
fof(f60,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| ~ disjoint(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1)
| ~ in(X2,set_intersection2(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f62,plain,
( spl0_0
<=> pd0_0(sk0_6,sk0_5) ),
introduced(split_symbol_definition) ).
fof(f63,plain,
( pd0_0(sk0_6,sk0_5)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,plain,
( spl0_1
<=> in(sk0_9,set_intersection2(sk0_7,sk0_8)) ),
introduced(split_symbol_definition) ).
fof(f66,plain,
( in(sk0_9,set_intersection2(sk0_7,sk0_8))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f57,f62,f65]) ).
fof(f69,plain,
( spl0_2
<=> disjoint(sk0_7,sk0_8) ),
introduced(split_symbol_definition) ).
fof(f70,plain,
( disjoint(sk0_7,sk0_8)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f58,f62,f69]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f27]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f28]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(paramodulation,[status(thm)],[f18,f61]) ).
fof(f98,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ pd0_0(X0,X1) ),
inference(resolution,[status(thm)],[f23,f78]) ).
fof(f116,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| disjoint(X0,X1) ),
inference(resolution,[status(thm)],[f98,f36]) ).
fof(f147,plain,
( disjoint(sk0_6,sk0_5)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f63,f116]) ).
fof(f149,plain,
( ~ disjoint(sk0_5,sk0_6)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f63,f60]) ).
fof(f151,plain,
( disjoint(sk0_5,sk0_6)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f147,f45]) ).
fof(f152,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f149]) ).
fof(f153,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f152]) ).
fof(f154,plain,
! [X0] :
( ~ in(X0,sk0_7)
| ~ in(X0,sk0_8)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f70,f51]) ).
fof(f157,plain,
( in(sk0_9,sk0_8)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f66,f75]) ).
fof(f158,plain,
( in(sk0_9,sk0_7)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f66,f74]) ).
fof(f171,plain,
( ~ in(sk0_9,sk0_7)
| ~ spl0_2
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f154,f157]) ).
fof(f172,plain,
( $false
| ~ spl0_2
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f158]) ).
fof(f173,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f174,plain,
$false,
inference(sat_refutation,[status(thm)],[f68,f72,f153,f173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU120+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n002.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 20:03:54 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % Drodi V3.6.0
% 0.10/0.33 % Refutation found
% 0.10/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.34 % Elapsed time: 0.022907 seconds
% 0.10/0.34 % CPU time: 0.026692 seconds
% 0.10/0.34 % Total memory used: 11.204 MB
% 0.10/0.34 % Net memory used: 11.117 MB
%------------------------------------------------------------------------------