TSTP Solution File: SET881+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 12:35:27 EDT 2023
% Result : Theorem 0.14s 0.53s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 69 ( 46 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 85 ( 33 ~; 32 |; 17 &)
% ( 3 <=>; 0 =>; 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 48 (; 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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(f5,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f13,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)],[f3]) ).
fof(f14,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)],[f13]) ).
fof(f15,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)],[f14]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| in(X3,X0)
| X3 != X1 ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f23,plain,
! [A,B] :
( ( set_difference(singleton(A),B) != empty_set
| in(A,B) )
& ( set_difference(singleton(A),B) = empty_set
| ~ in(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f5]) ).
fof(f24,plain,
( ! [A,B] :
( set_difference(singleton(A),B) != empty_set
| in(A,B) )
& ! [A,B] :
( set_difference(singleton(A),B) = empty_set
| ~ in(A,B) ) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f31,plain,
? [A,B] : set_difference(singleton(A),unordered_pair(A,B)) != empty_set,
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f32,plain,
set_difference(singleton(sk0_3),unordered_pair(sk0_3,sk0_4)) != empty_set,
inference(skolemization,[status(esa)],[f31]) ).
fof(f33,plain,
set_difference(singleton(sk0_3),unordered_pair(sk0_3,sk0_4)) != empty_set,
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f35,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(esa)],[f17]) ).
fof(f43,plain,
~ in(sk0_3,unordered_pair(sk0_3,sk0_4)),
inference(resolution,[status(thm)],[f26,f33]) ).
fof(f44,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f43,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n006.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue May 30 10:12:47 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % Drodi V3.5.1
% 0.14/0.53 % Refutation found
% 0.14/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.53 % Elapsed time: 0.011947 seconds
% 0.14/0.53 % CPU time: 0.010908 seconds
% 0.14/0.53 % Memory used: 3.588 MB
%------------------------------------------------------------------------------