TSTP Solution File: SET616+3 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET616+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 20:39:59 EDT 2024
% Result : Theorem 0.15s 0.35s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 7 unt; 0 def)
% Number of atoms : 118 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 121 ( 47 ~; 46 |; 18 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 69 ( 65 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B,C] :
( difference(B,C) = difference(C,B)
=> B = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C] :
( difference(B,C) = difference(C,B)
=> B = C ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f14,plain,
! [B,C,D] :
( ( ~ member(D,difference(B,C))
| ( member(D,B)
& ~ member(D,C) ) )
& ( member(D,difference(B,C))
| ~ member(D,B)
| member(D,C) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f15,plain,
( ! [B,C,D] :
( ~ member(D,difference(B,C))
| ( member(D,B)
& ~ member(D,C) ) )
& ! [B,C,D] :
( member(D,difference(B,C))
| ~ member(D,B)
| member(D,C) ) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X0,difference(X1,X2))
| ~ member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f19,plain,
! [B,C] :
( ( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f20,plain,
( ! [B,C] :
( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ! [B,C] :
( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f23,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f31,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f32,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)],[f31]) ).
fof(f33,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)],[f32]) ).
fof(f34,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ( member(sk0_2(C,B),B)
& ~ member(sk0_2(C,B),C) ) ) ),
inference(skolemization,[status(esa)],[f33]) ).
fof(f36,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_2(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f37,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_2(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f39,plain,
? [B,C] :
( difference(B,C) = difference(C,B)
& B != C ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f40,plain,
( difference(sk0_3,sk0_4) = difference(sk0_4,sk0_3)
& sk0_3 != sk0_4 ),
inference(skolemization,[status(esa)],[f39]) ).
fof(f41,plain,
difference(sk0_3,sk0_4) = difference(sk0_4,sk0_3),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f42,plain,
sk0_3 != sk0_4,
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f45,plain,
! [X0] :
( ~ member(X0,difference(sk0_3,sk0_4))
| member(X0,sk0_4) ),
inference(paramodulation,[status(thm)],[f41,f16]) ).
fof(f46,plain,
! [X0] : ~ member(X0,difference(sk0_3,sk0_4)),
inference(backward_subsumption_resolution,[status(thm)],[f45,f17]) ).
fof(f49,plain,
! [X0] :
( ~ member(X0,sk0_3)
| member(X0,sk0_4) ),
inference(resolution,[status(thm)],[f18,f46]) ).
fof(f50,plain,
! [X0] :
( member(X0,difference(sk0_3,sk0_4))
| ~ member(X0,sk0_4)
| member(X0,sk0_3) ),
inference(paramodulation,[status(thm)],[f41,f18]) ).
fof(f51,plain,
! [X0] :
( ~ member(X0,sk0_4)
| member(X0,sk0_3) ),
inference(forward_subsumption_resolution,[status(thm)],[f50,f46]) ).
fof(f52,plain,
! [X0] :
( subset(sk0_4,X0)
| member(sk0_2(X0,sk0_4),sk0_3) ),
inference(resolution,[status(thm)],[f36,f51]) ).
fof(f53,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_2(X0,sk0_3),sk0_4) ),
inference(resolution,[status(thm)],[f36,f49]) ).
fof(f237,plain,
( spl0_0
<=> subset(sk0_4,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f238,plain,
( subset(sk0_4,sk0_3)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,plain,
( subset(sk0_4,sk0_3)
| subset(sk0_4,sk0_3) ),
inference(resolution,[status(thm)],[f52,f37]) ).
fof(f241,plain,
spl0_0,
inference(split_clause,[status(thm)],[f240,f237]) ).
fof(f244,plain,
( spl0_1
<=> sk0_3 = sk0_4 ),
introduced(split_symbol_definition) ).
fof(f245,plain,
( sk0_3 = sk0_4
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( spl0_2
<=> subset(sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f250,plain,
( sk0_3 = sk0_4
| ~ subset(sk0_3,sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f238,f23]) ).
fof(f251,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f250,f244,f247,f237]) ).
fof(f252,plain,
( subset(sk0_3,sk0_4)
| subset(sk0_3,sk0_4) ),
inference(resolution,[status(thm)],[f53,f37]) ).
fof(f253,plain,
spl0_2,
inference(split_clause,[status(thm)],[f252,f247]) ).
fof(f255,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f245,f42]) ).
fof(f256,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f255]) ).
fof(f257,plain,
$false,
inference(sat_refutation,[status(thm)],[f241,f251,f253,f256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET616+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.15/0.34 % Computer : n011.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon Apr 29 21:52:31 EDT 2024
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % Drodi V3.6.0
% 0.15/0.35 % Refutation found
% 0.15/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.37 % Elapsed time: 0.022109 seconds
% 0.15/0.37 % CPU time: 0.045819 seconds
% 0.15/0.37 % Total memory used: 13.147 MB
% 0.15/0.37 % Net memory used: 13.104 MB
%------------------------------------------------------------------------------