TSTP Solution File: SET929+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 12:35:33 EDT 2023
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 3 unt; 0 def)
% Number of atoms : 107 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 110 ( 43 ~; 45 |; 14 &)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 49 (; 43 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(A,C)
& in(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(A,C)
& in(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(A,C)
& in(B,C) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f21,plain,
! [A,B] :
( ( set_difference(A,B) != empty_set
| subset(A,B) )
& ( set_difference(A,B) = empty_set
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f22,plain,
( ! [A,B] :
( set_difference(A,B) != empty_set
| subset(A,B) )
& ! [A,B] :
( set_difference(A,B) = empty_set
| ~ subset(A,B) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( set_difference(X0,X1) != empty_set
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
! [A,B,C] :
( ( ~ subset(unordered_pair(A,B),C)
| ( in(A,C)
& in(B,C) ) )
& ( subset(unordered_pair(A,B),C)
| ~ in(A,C)
| ~ in(B,C) ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f26,plain,
( ! [A,B,C] :
( ~ subset(unordered_pair(A,B),C)
| ( in(A,C)
& in(B,C) ) )
& ! [A,B,C] :
( subset(unordered_pair(A,B),C)
| ~ in(A,C)
| ~ in(B,C) ) ),
inference(miniscoping,[status(esa)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f29,plain,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X0,X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f30,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<~> ( in(A,C)
& in(B,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f31,plain,
? [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = empty_set
| ( in(A,C)
& in(B,C) ) )
& ( set_difference(unordered_pair(A,B),C) != empty_set
| ~ in(A,C)
| ~ in(B,C) ) ),
inference(NNF_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
( ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = empty_set
| ( in(sk0_2,sk0_4)
& in(sk0_3,sk0_4) ) )
& ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != empty_set
| ~ in(sk0_2,sk0_4)
| ~ in(sk0_3,sk0_4) ) ),
inference(skolemization,[status(esa)],[f31]) ).
fof(f33,plain,
( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = empty_set
| in(sk0_2,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = empty_set
| in(sk0_3,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f35,plain,
( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != empty_set
| ~ in(sk0_2,sk0_4)
| ~ in(sk0_3,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f36,plain,
( spl0_0
<=> set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = empty_set ),
introduced(split_symbol_definition) ).
fof(f37,plain,
( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = empty_set
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f38,plain,
( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != empty_set
| spl0_0 ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,plain,
( spl0_1
<=> in(sk0_2,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f41,plain,
( ~ in(sk0_2,sk0_4)
| spl0_1 ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f33,f36,f39]) ).
fof(f43,plain,
( spl0_2
<=> in(sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f46,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f34,f36,f43]) ).
fof(f47,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f35,f36,f39,f43]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X1,X2) ),
inference(paramodulation,[status(thm)],[f13,f27]) ).
fof(f66,plain,
( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f37,f23]) ).
fof(f77,plain,
( in(sk0_3,sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f66,f49]) ).
fof(f78,plain,
( in(sk0_2,sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f66,f27]) ).
fof(f79,plain,
( $false
| spl0_1
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f78,f41]) ).
fof(f80,plain,
( spl0_1
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f83,plain,
( ~ subset(unordered_pair(sk0_2,sk0_3),sk0_4)
| spl0_0 ),
inference(resolution,[status(thm)],[f38,f24]) ).
fof(f84,plain,
( ~ in(sk0_2,sk0_4)
| ~ in(sk0_3,sk0_4)
| spl0_0 ),
inference(resolution,[status(thm)],[f83,f29]) ).
fof(f85,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_0 ),
inference(split_clause,[status(thm)],[f84,f39,f43,f36]) ).
fof(f86,plain,
( spl0_2
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f77,f43,f36]) ).
fof(f87,plain,
$false,
inference(sat_refutation,[status(thm)],[f42,f46,f47,f80,f85,f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 10:00:17 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 0.12/0.35 % Refutation found
% 0.12/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.36 % Elapsed time: 0.023454 seconds
% 0.18/0.36 % CPU time: 0.032330 seconds
% 0.18/0.36 % Memory used: 14.280 MB
%------------------------------------------------------------------------------