TSTP Solution File: SET592+3 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET592+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 20:39:54 EDT 2024
% Result : Theorem 0.09s 0.29s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 10 unt; 0 def)
% Number of atoms : 150 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 153 ( 60 ~; 55 |; 27 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 73 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( subset(B,empty_set)
=> B = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
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,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [B,C,D] :
( ( subset(B,C)
& subset(B,D)
& intersection(C,D) = empty_set )
=> B = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [B,C,D] :
( ( subset(B,C)
& subset(B,D)
& intersection(C,D) = empty_set )
=> B = empty_set ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [B] :
( ~ subset(B,empty_set)
| B = empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f14,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f17,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f18,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)],[f4]) ).
fof(f19,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)],[f18]) ).
fof(f22,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f23,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f24,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)],[f23]) ).
fof(f25,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)],[f24]) ).
fof(f26,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)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f35,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f37,plain,
! [B] :
( ( ~ empty(B)
| ! [C] : ~ member(C,B) )
& ( empty(B)
| ? [C] : member(C,B) ) ),
inference(NNF_transformation,[status(esa)],[f9]) ).
fof(f38,plain,
( ! [B] :
( ~ empty(B)
| ! [C] : ~ member(C,B) )
& ! [B] :
( empty(B)
| ? [C] : member(C,B) ) ),
inference(miniscoping,[status(esa)],[f37]) ).
fof(f39,plain,
( ! [B] :
( ~ empty(B)
| ! [C] : ~ member(C,B) )
& ! [B] :
( empty(B)
| member(sk0_1(B),B) ) ),
inference(skolemization,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ member(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f41,plain,
! [X0] :
( empty(X0)
| member(sk0_1(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f49,plain,
? [B,C,D] :
( subset(B,C)
& subset(B,D)
& intersection(C,D) = empty_set
& B != empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f50,plain,
? [B] :
( ? [C,D] :
( subset(B,C)
& subset(B,D)
& intersection(C,D) = empty_set )
& B != empty_set ),
inference(miniscoping,[status(esa)],[f49]) ).
fof(f51,plain,
( subset(sk0_3,sk0_4)
& subset(sk0_3,sk0_5)
& intersection(sk0_4,sk0_5) = empty_set
& sk0_3 != empty_set ),
inference(skolemization,[status(esa)],[f50]) ).
fof(f52,plain,
subset(sk0_3,sk0_4),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f53,plain,
subset(sk0_3,sk0_5),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f54,plain,
intersection(sk0_4,sk0_5) = empty_set,
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f55,plain,
sk0_3 != empty_set,
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f80,plain,
! [X0] :
( ~ member(X0,sk0_3)
| member(X0,sk0_5) ),
inference(resolution,[status(thm)],[f27,f53]) ).
fof(f81,plain,
! [X0] :
( ~ member(X0,sk0_3)
| member(X0,sk0_4) ),
inference(resolution,[status(thm)],[f27,f52]) ).
fof(f89,plain,
( spl0_4
<=> member(sk0_1(sk0_3),sk0_5) ),
introduced(split_symbol_definition) ).
fof(f90,plain,
( member(sk0_1(sk0_3),sk0_5)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( spl0_5
<=> empty(sk0_3) ),
introduced(split_symbol_definition) ).
fof(f93,plain,
( empty(sk0_3)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,plain,
( member(sk0_1(sk0_3),sk0_5)
| empty(sk0_3) ),
inference(resolution,[status(thm)],[f80,f41]) ).
fof(f96,plain,
( spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f95,f89,f92]) ).
fof(f97,plain,
( spl0_6
<=> member(sk0_1(sk0_3),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f98,plain,
( member(sk0_1(sk0_3),sk0_4)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( member(sk0_1(sk0_3),sk0_4)
| empty(sk0_3) ),
inference(resolution,[status(thm)],[f81,f41]) ).
fof(f101,plain,
( spl0_6
| spl0_5 ),
inference(split_clause,[status(thm)],[f100,f97,f92]) ).
fof(f107,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f28,f40]) ).
fof(f197,plain,
! [X0] :
( subset(sk0_3,X0)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f93,f107]) ).
fof(f198,plain,
( sk0_3 = empty_set
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f197,f14]) ).
fof(f199,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f55]) ).
fof(f200,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f199]) ).
fof(f203,plain,
! [X0] :
( member(sk0_1(sk0_3),intersection(sk0_5,X0))
| ~ member(sk0_1(sk0_3),X0)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f90,f22]) ).
fof(f221,plain,
( member(sk0_1(sk0_3),intersection(sk0_5,sk0_4))
| ~ spl0_4
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f203,f98]) ).
fof(f222,plain,
( member(sk0_1(sk0_3),intersection(sk0_4,sk0_5))
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f35,f221]) ).
fof(f223,plain,
( member(sk0_1(sk0_3),empty_set)
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f54,f222]) ).
fof(f224,plain,
( $false
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f223,f17]) ).
fof(f225,plain,
( ~ spl0_4
| ~ spl0_6 ),
inference(contradiction_clause,[status(thm)],[f224]) ).
fof(f226,plain,
$false,
inference(sat_refutation,[status(thm)],[f96,f101,f200,f225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : SET592+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Mon Apr 29 21:43:05 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % Drodi V3.6.0
% 0.09/0.29 % Refutation found
% 0.09/0.29 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.30 % Elapsed time: 0.013977 seconds
% 0.09/0.30 % CPU time: 0.028291 seconds
% 0.09/0.30 % Total memory used: 13.018 MB
% 0.09/0.30 % Net memory used: 12.933 MB
%------------------------------------------------------------------------------