TSTP Solution File: SET183+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET183+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n028.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 12:34:13 EDT 2023
% Result : Theorem 0.16s 0.32s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 10 unt; 0 def)
% Number of atoms : 117 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 42 ~; 47 |; 18 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 83 (; 79 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [B,C,D] :
( ( ~ member(D,intersection(B,C))
| ( member(D,B)
& member(D,C) ) )
& ( member(D,intersection(B,C))
| ~ member(D,B)
| ~ member(D,C) ) ),
inference(NNF_transformation,[status(esa)],[f1]) ).
fof(f11,plain,
( ! [B,C,D] :
( ~ member(D,intersection(B,C))
| ( member(D,B)
& member(D,C) ) )
& ! [B,C,D] :
( member(D,intersection(B,C))
| ~ member(D,B)
| ~ member(D,C) ) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f14,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f15,plain,
! [X0,X1] : subset(intersection(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f16,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f17,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)],[f16]) ).
fof(f18,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)],[f17]) ).
fof(f19,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)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f22,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f23,plain,
! [B,C] :
( ( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f24,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)],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f28,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f37,plain,
? [B,C] :
( subset(B,C)
& intersection(B,C) != B ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f38,plain,
( subset(sk0_2,sk0_3)
& intersection(sk0_2,sk0_3) != sk0_2 ),
inference(skolemization,[status(esa)],[f37]) ).
fof(f39,plain,
subset(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
intersection(sk0_2,sk0_3) != sk0_2,
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f43,plain,
! [X0,X1] : subset(intersection(X0,X1),X1),
inference(paramodulation,[status(thm)],[f28,f15]) ).
fof(f49,plain,
! [X0,X1] :
( X0 = intersection(X1,X0)
| ~ subset(X0,intersection(X1,X0)) ),
inference(resolution,[status(thm)],[f27,f43]) ).
fof(f61,plain,
! [X0,X1] :
( X0 = intersection(X1,X0)
| ~ subset(X0,intersection(X0,X1)) ),
inference(paramodulation,[status(thm)],[f28,f49]) ).
fof(f67,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| member(sk0_0(X1,X0),intersection(X2,X0))
| ~ member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f21,f14]) ).
fof(f68,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| ~ subset(X0,X2)
| member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f21,f20]) ).
fof(f77,plain,
! [X0] :
( subset(sk0_2,X0)
| member(sk0_0(X0,sk0_2),sk0_3) ),
inference(resolution,[status(thm)],[f68,f39]) ).
fof(f122,plain,
! [X0] :
( subset(sk0_2,X0)
| member(sk0_0(X0,sk0_2),intersection(sk0_3,sk0_2))
| subset(sk0_2,X0) ),
inference(resolution,[status(thm)],[f67,f77]) ).
fof(f123,plain,
! [X0] :
( subset(sk0_2,X0)
| member(sk0_0(X0,sk0_2),intersection(sk0_2,sk0_3))
| subset(sk0_2,X0) ),
inference(forward_demodulation,[status(thm)],[f28,f122]) ).
fof(f124,plain,
! [X0] :
( subset(sk0_2,X0)
| member(sk0_0(X0,sk0_2),intersection(sk0_2,sk0_3)) ),
inference(duplicate_literals_removal,[status(esa)],[f123]) ).
fof(f175,plain,
( spl0_3
<=> subset(sk0_2,intersection(sk0_2,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f176,plain,
( subset(sk0_2,intersection(sk0_2,sk0_3))
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( subset(sk0_2,intersection(sk0_2,sk0_3))
| subset(sk0_2,intersection(sk0_2,sk0_3)) ),
inference(resolution,[status(thm)],[f124,f22]) ).
fof(f179,plain,
spl0_3,
inference(split_clause,[status(thm)],[f178,f175]) ).
fof(f184,plain,
( sk0_2 = intersection(sk0_3,sk0_2)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f176,f61]) ).
fof(f185,plain,
( sk0_2 = intersection(sk0_2,sk0_3)
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f28,f184]) ).
fof(f186,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f40]) ).
fof(f187,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f186]) ).
fof(f188,plain,
$false,
inference(sat_refutation,[status(thm)],[f179,f187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SET183+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.31 % Computer : n028.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue May 30 10:33:32 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.31 % Drodi V3.5.1
% 0.16/0.32 % Refutation found
% 0.16/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.33 % Elapsed time: 0.022060 seconds
% 0.16/0.33 % CPU time: 0.039748 seconds
% 0.16/0.33 % Memory used: 14.466 MB
%------------------------------------------------------------------------------