TSTP Solution File: SET914+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET914+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 : Wed May 31 12:35:31 EDT 2023
% Result : Theorem 0.10s 0.37s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 150 ( 58 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 184 ( 68 ~; 69 |; 41 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 106 (; 94 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,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(f7,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [A,B,C] :
~ ( disjoint(unordered_pair(A,B),C)
& in(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [A,B,C] :
~ ( disjoint(unordered_pair(A,B),C)
& in(A,C) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f19,plain,
! [A] :
( ( A != empty_set
| ! [B] : ~ in(B,A) )
& ( A = empty_set
| ? [B] : in(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
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(f22,plain,
! [X0,X1] :
( X0 != empty_set
| ~ in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f24,plain,
! [A,B,C] :
( ( C != unordered_pair(A,B)
| ! [D] :
( ( ~ in(D,C)
| D = A
| D = B )
& ( in(D,C)
| ( D != A
& D != B ) ) ) )
& ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( D != A
& D != B ) )
& ( in(D,C)
| D = A
| D = B ) ) ) ),
inference(NNF_transformation,[status(esa)],[f5]) ).
fof(f25,plain,
( ! [A,B,C] :
( C != unordered_pair(A,B)
| ( ! [D] :
( ~ in(D,C)
| D = A
| D = B )
& ! [D] :
( in(D,C)
| ( D != A
& D != B ) ) ) )
& ! [A,B,C] :
( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( D != A
& D != B ) )
& ( in(D,C)
| D = A
| D = B ) ) ) ),
inference(miniscoping,[status(esa)],[f24]) ).
fof(f26,plain,
( ! [A,B,C] :
( C != unordered_pair(A,B)
| ( ! [D] :
( ~ in(D,C)
| D = A
| D = B )
& ! [D] :
( in(D,C)
| ( D != A
& D != B ) ) ) )
& ! [A,B,C] :
( C = unordered_pair(A,B)
| ( ( ~ in(sk0_1(C,B,A),C)
| ( sk0_1(C,B,A) != A
& sk0_1(C,B,A) != B ) )
& ( in(sk0_1(C,B,A),C)
| sk0_1(C,B,A) = A
| sk0_1(C,B,A) = B ) ) ) ),
inference(skolemization,[status(esa)],[f25]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| in(X3,X0)
| X3 != X1 ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f33,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)],[f6]) ).
fof(f34,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)],[f33]) ).
fof(f35,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_2(C,B,A),C)
| ~ in(sk0_2(C,B,A),A)
| ~ in(sk0_2(C,B,A),B) )
& ( in(sk0_2(C,B,A),C)
| ( in(sk0_2(C,B,A),A)
& in(sk0_2(C,B,A),B) ) ) ) ) ),
inference(skolemization,[status(esa)],[f34]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f42,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)],[f7]) ).
fof(f43,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)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f55,plain,
? [A,B,C] :
( disjoint(unordered_pair(A,B),C)
& in(A,C) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f56,plain,
? [A,C] :
( ? [B] : disjoint(unordered_pair(A,B),C)
& in(A,C) ),
inference(miniscoping,[status(esa)],[f55]) ).
fof(f57,plain,
( disjoint(unordered_pair(sk0_5,sk0_7),sk0_6)
& in(sk0_5,sk0_6) ),
inference(skolemization,[status(esa)],[f56]) ).
fof(f58,plain,
disjoint(unordered_pair(sk0_5,sk0_7),sk0_6),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f59,plain,
in(sk0_5,sk0_6),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f60,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(esa)],[f22]) ).
fof(f62,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(esa)],[f28]) ).
fof(f66,plain,
! [X0,X1,X2] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,X1)
| ~ in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f38]) ).
fof(f71,plain,
set_intersection2(unordered_pair(sk0_5,sk0_7),sk0_6) = empty_set,
inference(resolution,[status(thm)],[f44,f58]) ).
fof(f130,plain,
! [X0,X1,X2] :
( in(X0,set_intersection2(unordered_pair(X0,X1),X2))
| ~ in(X0,X2) ),
inference(resolution,[status(thm)],[f66,f62]) ).
fof(f134,plain,
! [X0] : in(sk0_5,set_intersection2(unordered_pair(sk0_5,X0),sk0_6)),
inference(resolution,[status(thm)],[f130,f59]) ).
fof(f233,plain,
in(sk0_5,empty_set),
inference(paramodulation,[status(thm)],[f71,f134]) ).
fof(f234,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f233,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SET914+1 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.34 % Computer : n015.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8042.1875MB
% 0.10/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Tue May 30 10:31:49 EDT 2023
% 0.10/0.34 % CPUTime :
% 0.10/0.34 % Drodi V3.5.1
% 0.10/0.37 % Refutation found
% 0.10/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.62 % Elapsed time: 0.056324 seconds
% 0.23/0.62 % CPU time: 0.055052 seconds
% 0.23/0.62 % Memory used: 9.480 MB
%------------------------------------------------------------------------------