TSTP Solution File: SET633+3 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET633+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n001.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 12:34:52 EDT 2023
% Result : Theorem 0.19s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 86 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 80 ( 30 ~; 29 |; 13 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 61 (; 56 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] :
( ( subset(B,C)
& subset(D,C) )
=> subset(union(B,D),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B,C,D] :
( ( subset(difference(B,C),D)
& subset(difference(C,B),D) )
=> subset(symmetric_difference(B,C),D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B,C,D] :
( ( subset(difference(B,C),D)
& subset(difference(C,B),D) )
=> subset(symmetric_difference(B,C),D) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f12,plain,
! [B,C,D] :
( ~ subset(B,C)
| ~ subset(D,C)
| subset(union(B,D),C) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| subset(union(X0,X2),X1) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f19,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f20,plain,
! [B,C] :
( ( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ? [D] :
( member(D,B)
& ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ? [D] :
( member(D,B)
& ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f22,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ( member(sk0_0(C,B),B)
& ~ member(sk0_0(C,B),C) ) ) ),
inference(skolemization,[status(esa)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f27,plain,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f36,plain,
? [B,C,D] :
( subset(difference(B,C),D)
& subset(difference(C,B),D)
& ~ subset(symmetric_difference(B,C),D) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f37,plain,
( subset(difference(sk0_2,sk0_3),sk0_4)
& subset(difference(sk0_3,sk0_2),sk0_4)
& ~ subset(symmetric_difference(sk0_2,sk0_3),sk0_4) ),
inference(skolemization,[status(esa)],[f36]) ).
fof(f38,plain,
subset(difference(sk0_2,sk0_3),sk0_4),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f39,plain,
subset(difference(sk0_3,sk0_2),sk0_4),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f40,plain,
~ subset(symmetric_difference(sk0_2,sk0_3),sk0_4),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f52,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| ~ subset(X0,X2)
| member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f24,f23]) ).
fof(f53,plain,
! [X0] :
( subset(difference(sk0_3,sk0_2),X0)
| member(sk0_0(X0,difference(sk0_3,sk0_2)),sk0_4) ),
inference(resolution,[status(thm)],[f52,f39]) ).
fof(f68,plain,
( spl0_0
<=> subset(difference(sk0_3,sk0_2),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f71,plain,
( subset(difference(sk0_3,sk0_2),sk0_4)
| subset(difference(sk0_3,sk0_2),sk0_4) ),
inference(resolution,[status(thm)],[f25,f53]) ).
fof(f72,plain,
spl0_0,
inference(split_clause,[status(thm)],[f71,f68]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ subset(difference(X0,X1),X2)
| ~ subset(difference(X1,X0),X2)
| subset(symmetric_difference(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f11,f13]) ).
fof(f135,plain,
( spl0_3
<=> subset(symmetric_difference(sk0_3,sk0_2),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f136,plain,
( subset(symmetric_difference(sk0_3,sk0_2),sk0_4)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( ~ subset(difference(sk0_3,sk0_2),sk0_4)
| subset(symmetric_difference(sk0_3,sk0_2),sk0_4) ),
inference(resolution,[status(thm)],[f81,f38]) ).
fof(f139,plain,
( ~ spl0_0
| spl0_3 ),
inference(split_clause,[status(thm)],[f138,f68,f135]) ).
fof(f149,plain,
( subset(symmetric_difference(sk0_2,sk0_3),sk0_4)
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f27,f136]) ).
fof(f150,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f40]) ).
fof(f151,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f150]) ).
fof(f152,plain,
$false,
inference(sat_refutation,[status(thm)],[f72,f139,f151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET633+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 10:42:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.19/0.37 % Refutation found
% 0.19/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.63 % Elapsed time: 0.071373 seconds
% 0.21/0.63 % CPU time: 0.029864 seconds
% 0.21/0.63 % Memory used: 3.687 MB
%------------------------------------------------------------------------------