TSTP Solution File: SET624+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET624+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 12:34:51 EDT 2023
% Result : Theorem 1.73s 0.58s
% Output : CNFRefutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 64 ( 1 unt; 0 def)
% Number of atoms : 181 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 196 ( 79 ~; 91 |; 15 &)
% ( 9 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 101 (; 92 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [B,C,D] :
( intersect(B,union(C,D))
<=> ( intersect(B,C)
| intersect(B,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [B,C,D] :
( intersect(B,union(C,D))
<=> ( intersect(B,C)
| intersect(B,D) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [B,C,D] :
( ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) )
& ( member(D,union(B,C))
| ( ~ member(D,B)
& ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f1]) ).
fof(f9,plain,
( ! [B,C,D] :
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) )
& ! [B,C,D] :
( member(D,union(B,C))
| ( ~ member(D,B)
& ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f12,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f13,plain,
! [B,C] :
( ( ~ intersect(B,C)
| ? [D] :
( member(D,B)
& member(D,C) ) )
& ( intersect(B,C)
| ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f14,plain,
( ! [B,C] :
( ~ intersect(B,C)
| ? [D] :
( member(D,B)
& member(D,C) ) )
& ! [B,C] :
( intersect(B,C)
| ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f15,plain,
( ! [B,C] :
( ~ intersect(B,C)
| ( member(sk0_0(C,B),B)
& member(sk0_0(C,B),C) ) )
& ! [B,C] :
( intersect(B,C)
| ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ) ),
inference(skolemization,[status(esa)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f18,plain,
! [X0,X1,X2] :
( intersect(X0,X1)
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f20,plain,
! [B,C] :
( ~ intersect(B,C)
| intersect(C,B) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f21,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| intersect(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f29,plain,
? [B,C,D] :
( intersect(B,union(C,D))
<~> ( intersect(B,C)
| intersect(B,D) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f30,plain,
? [B,C,D] :
( ( intersect(B,union(C,D))
| intersect(B,C)
| intersect(B,D) )
& ( ~ intersect(B,union(C,D))
| ( ~ intersect(B,C)
& ~ intersect(B,D) ) ) ),
inference(NNF_transformation,[status(esa)],[f29]) ).
fof(f31,plain,
( ( intersect(sk0_2,union(sk0_3,sk0_4))
| intersect(sk0_2,sk0_3)
| intersect(sk0_2,sk0_4) )
& ( ~ intersect(sk0_2,union(sk0_3,sk0_4))
| ( ~ intersect(sk0_2,sk0_3)
& ~ intersect(sk0_2,sk0_4) ) ) ),
inference(skolemization,[status(esa)],[f30]) ).
fof(f32,plain,
( intersect(sk0_2,union(sk0_3,sk0_4))
| intersect(sk0_2,sk0_3)
| intersect(sk0_2,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
( ~ intersect(sk0_2,union(sk0_3,sk0_4))
| ~ intersect(sk0_2,sk0_3) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f34,plain,
( ~ intersect(sk0_2,union(sk0_3,sk0_4))
| ~ intersect(sk0_2,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f35,plain,
( spl0_0
<=> intersect(sk0_2,union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f36,plain,
( intersect(sk0_2,union(sk0_3,sk0_4))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f37,plain,
( ~ intersect(sk0_2,union(sk0_3,sk0_4))
| spl0_0 ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,plain,
( spl0_1
<=> intersect(sk0_2,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f41,plain,
( spl0_2
<=> intersect(sk0_2,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f42,plain,
( intersect(sk0_2,sk0_4)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( spl0_0
| spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f32,f35,f38,f41]) ).
fof(f45,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f33,f35,f38]) ).
fof(f46,plain,
( ~ spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f34,f35,f41]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( intersect(X0,union(X1,X2))
| ~ member(X3,X0)
| ~ member(X3,X1) ),
inference(resolution,[status(thm)],[f18,f11]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ intersect(union(X0,X1),X2)
| member(sk0_0(X2,union(X0,X1)),X0)
| member(sk0_0(X2,union(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f16,f10]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ intersect(X0,X1)
| intersect(X2,X1)
| ~ member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f17,f18]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ intersect(union(X0,X1),X2)
| intersect(X1,X2)
| ~ intersect(union(X0,X1),X2)
| member(sk0_0(X2,union(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f74,f67]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ~ intersect(union(X0,X1),X2)
| intersect(X1,X2)
| member(sk0_0(X2,union(X0,X1)),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f93]) ).
fof(f97,plain,
! [X0,X1,X2,X3] :
( ~ intersect(X0,X1)
| intersect(union(X2,X3),X1)
| ~ member(sk0_0(X1,X0),X3) ),
inference(resolution,[status(thm)],[f74,f12]) ).
fof(f172,plain,
! [X0] :
( ~ member(X0,sk0_2)
| ~ member(X0,sk0_3)
| spl0_0 ),
inference(resolution,[status(thm)],[f37,f54]) ).
fof(f178,plain,
! [X0] :
( ~ member(sk0_0(sk0_3,X0),sk0_2)
| ~ intersect(X0,sk0_3)
| spl0_0 ),
inference(resolution,[status(thm)],[f172,f17]) ).
fof(f188,plain,
( ~ intersect(sk0_2,sk0_3)
| ~ intersect(sk0_2,sk0_3)
| spl0_0 ),
inference(resolution,[status(thm)],[f178,f16]) ).
fof(f189,plain,
( ~ spl0_1
| spl0_0 ),
inference(split_clause,[status(thm)],[f188,f38,f35]) ).
fof(f192,plain,
( intersect(union(sk0_3,sk0_4),sk0_2)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f36,f21]) ).
fof(f494,plain,
! [X0,X1,X2] :
( ~ intersect(union(X0,X1),X2)
| intersect(X1,X2)
| ~ intersect(union(X0,X1),X2)
| intersect(X0,X2) ),
inference(resolution,[status(thm)],[f94,f74]) ).
fof(f495,plain,
! [X0,X1,X2] :
( ~ intersect(union(X0,X1),X2)
| intersect(X1,X2)
| intersect(X0,X2) ),
inference(duplicate_literals_removal,[status(esa)],[f494]) ).
fof(f522,plain,
! [X0,X1,X2] :
( ~ intersect(X0,X1)
| intersect(union(X2,X0),X1)
| ~ intersect(X0,X1) ),
inference(resolution,[status(thm)],[f97,f16]) ).
fof(f523,plain,
! [X0,X1,X2] :
( ~ intersect(X0,X1)
| intersect(union(X2,X0),X1) ),
inference(duplicate_literals_removal,[status(esa)],[f522]) ).
fof(f556,plain,
! [X0,X1,X2] :
( ~ intersect(X0,X1)
| intersect(X1,union(X2,X0)) ),
inference(resolution,[status(thm)],[f523,f21]) ).
fof(f793,plain,
( spl0_5
<=> intersect(sk0_4,sk0_2) ),
introduced(split_symbol_definition) ).
fof(f794,plain,
( intersect(sk0_4,sk0_2)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f793]) ).
fof(f865,plain,
( spl0_13
<=> intersect(sk0_3,sk0_2) ),
introduced(split_symbol_definition) ).
fof(f866,plain,
( intersect(sk0_3,sk0_2)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f865]) ).
fof(f868,plain,
( intersect(sk0_4,sk0_2)
| intersect(sk0_3,sk0_2)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f495,f192]) ).
fof(f869,plain,
( spl0_5
| spl0_13
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f868,f793,f865,f35]) ).
fof(f1669,plain,
( intersect(sk0_4,sk0_2)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f42,f21]) ).
fof(f1680,plain,
( ~ intersect(sk0_4,sk0_2)
| spl0_0 ),
inference(resolution,[status(thm)],[f37,f556]) ).
fof(f1681,plain,
( $false
| ~ spl0_2
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f1680,f1669]) ).
fof(f1682,plain,
( ~ spl0_2
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f1681]) ).
fof(f1686,plain,
( intersect(sk0_2,sk0_4)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f794,f21]) ).
fof(f1687,plain,
( spl0_2
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f1686,f41,f793]) ).
fof(f1688,plain,
( intersect(sk0_2,sk0_3)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f866,f21]) ).
fof(f1689,plain,
( spl0_1
| ~ spl0_13 ),
inference(split_clause,[status(thm)],[f1688,f38,f865]) ).
fof(f1690,plain,
$false,
inference(sat_refutation,[status(thm)],[f44,f45,f46,f189,f869,f1682,f1687,f1689]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET624+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n003.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 10:22:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 1.73/0.58 % Refutation found
% 1.73/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.73/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.05/0.60 % Elapsed time: 0.247414 seconds
% 2.05/0.60 % CPU time: 1.818858 seconds
% 2.05/0.60 % Memory used: 68.147 MB
%------------------------------------------------------------------------------