TSTP Solution File: SET878+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET878+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%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 : Tue Apr 30 20:40:37 EDT 2024
% Result : Theorem 0.10s 0.34s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 67 ( 46 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 79 ( 31 ~; 30 |; 15 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 50 ( 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f14,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f15,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)],[f4]) ).
fof(f16,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)],[f15]) ).
fof(f17,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_0(C,B,A),C)
| ( sk0_0(C,B,A) != A
& sk0_0(C,B,A) != B ) )
& ( in(sk0_0(C,B,A),C)
| sk0_0(C,B,A) = A
| sk0_0(C,B,A) = B ) ) ) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| in(X3,X0)
| X3 != X1 ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f26,plain,
! [A,B] :
( ~ in(A,B)
| set_intersection2(B,singleton(A)) = singleton(A) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f27,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_intersection2(X1,singleton(X0)) = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f32,plain,
? [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) != singleton(A),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f33,plain,
set_intersection2(singleton(sk0_3),unordered_pair(sk0_3,sk0_4)) != singleton(sk0_3),
inference(skolemization,[status(esa)],[f32]) ).
fof(f34,plain,
set_intersection2(singleton(sk0_3),unordered_pair(sk0_3,sk0_4)) != singleton(sk0_3),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f36,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(esa)],[f19]) ).
fof(f44,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_intersection2(singleton(X0),X1) = singleton(X0) ),
inference(paramodulation,[status(thm)],[f14,f27]) ).
fof(f46,plain,
~ in(sk0_3,unordered_pair(sk0_3,sk0_4)),
inference(resolution,[status(thm)],[f44,f34]) ).
fof(f47,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f46,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET878+1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n023.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 21:44:55 EDT 2024
% 0.10/0.33 % CPUTime :
% 0.10/0.33 % Drodi V3.6.0
% 0.10/0.34 % Refutation found
% 0.10/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.35 % Elapsed time: 0.015238 seconds
% 0.10/0.35 % CPU time: 0.019001 seconds
% 0.10/0.35 % Total memory used: 10.891 MB
% 0.10/0.35 % Net memory used: 10.777 MB
%------------------------------------------------------------------------------