TSTP Solution File: SET693+4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET693+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 20:40:12 EDT 2024
% Result : Theorem 0.21s 0.46s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 3 unt; 0 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 158 ( 58 ~; 71 |; 17 &)
% ( 10 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 89 ( 83 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,A)
| member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B] :
( equal_set(A,union(A,B))
<=> subset(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] :
( equal_set(A,union(A,B))
<=> subset(B,A) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( ~ member(X,A)
| member(X,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ( member(sk0_0(B,A),A)
& ~ member(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f21,plain,
! [A,B] :
( ( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ! [A,B] :
( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f24,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f35,plain,
! [X,A,B] :
( ( ~ member(X,union(A,B))
| member(X,A)
| member(X,B) )
& ( member(X,union(A,B))
| ( ~ member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f5]) ).
fof(f36,plain,
( ! [X,A,B] :
( ~ member(X,union(A,B))
| member(X,A)
| member(X,B) )
& ! [X,A,B] :
( member(X,union(A,B))
| ( ~ member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f68,plain,
? [A,B] :
( equal_set(A,union(A,B))
<~> subset(B,A) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
? [A,B] :
( ( equal_set(A,union(A,B))
| subset(B,A) )
& ( ~ equal_set(A,union(A,B))
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f68]) ).
fof(f70,plain,
( ( equal_set(sk0_3,union(sk0_3,sk0_4))
| subset(sk0_4,sk0_3) )
& ( ~ equal_set(sk0_3,union(sk0_3,sk0_4))
| ~ subset(sk0_4,sk0_3) ) ),
inference(skolemization,[status(esa)],[f69]) ).
fof(f71,plain,
( equal_set(sk0_3,union(sk0_3,sk0_4))
| subset(sk0_4,sk0_3) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f72,plain,
( ~ equal_set(sk0_3,union(sk0_3,sk0_4))
| ~ subset(sk0_4,sk0_3) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f73,plain,
( spl0_0
<=> equal_set(sk0_3,union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f74,plain,
( equal_set(sk0_3,union(sk0_3,sk0_4))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( spl0_1
<=> subset(sk0_4,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f77,plain,
( subset(sk0_4,sk0_3)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f71,f73,f76]) ).
fof(f80,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f72,f73,f76]) ).
fof(f87,plain,
! [X0,X1,X2] :
( subset(union(X0,X1),X2)
| member(sk0_0(X2,union(X0,X1)),X0)
| member(sk0_0(X2,union(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f19,f37]) ).
fof(f88,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| member(sk0_0(X1,X0),union(X2,X0)) ),
inference(resolution,[status(thm)],[f19,f39]) ).
fof(f89,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| member(sk0_0(X1,X0),union(X0,X2)) ),
inference(resolution,[status(thm)],[f19,f38]) ).
fof(f142,plain,
! [X0,X1] :
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) ),
inference(resolution,[status(thm)],[f20,f89]) ).
fof(f143,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(duplicate_literals_removal,[status(esa)],[f142]) ).
fof(f154,plain,
! [X0,X1] :
( equal_set(X0,union(X0,X1))
| ~ subset(union(X0,X1),X0) ),
inference(resolution,[status(thm)],[f143,f25]) ).
fof(f216,plain,
! [X0] :
( ~ member(X0,sk0_4)
| member(X0,sk0_3)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f77,f18]) ).
fof(f218,plain,
! [X0,X1] :
( member(sk0_0(X0,union(X1,sk0_4)),sk0_3)
| subset(union(X1,sk0_4),X0)
| member(sk0_0(X0,union(X1,sk0_4)),X1)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f216,f87]) ).
fof(f234,plain,
( subset(union(sk0_3,sk0_4),sk0_3)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f74,f24]) ).
fof(f241,plain,
( spl0_6
<=> subset(sk0_3,union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f243,plain,
( ~ subset(sk0_3,union(sk0_3,sk0_4))
| spl0_6 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f246,plain,
! [X0] :
( ~ member(X0,union(sk0_3,sk0_4))
| member(X0,sk0_3)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f234,f18]) ).
fof(f247,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f243,f143]) ).
fof(f248,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f247]) ).
fof(f272,plain,
( spl0_9
<=> subset(union(sk0_3,sk0_4),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f273,plain,
( subset(union(sk0_3,sk0_4),sk0_3)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f275,plain,
( subset(union(sk0_3,sk0_4),sk0_3)
| subset(union(sk0_3,sk0_4),sk0_3)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f218,f20]) ).
fof(f276,plain,
( spl0_9
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f275,f272,f76]) ).
fof(f308,plain,
( equal_set(sk0_3,union(sk0_3,sk0_4))
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f273,f154]) ).
fof(f309,plain,
( spl0_0
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f308,f73,f272]) ).
fof(f320,plain,
! [X0] :
( member(sk0_0(X0,sk0_4),sk0_3)
| subset(sk0_4,X0)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f246,f88]) ).
fof(f332,plain,
( subset(sk0_4,sk0_3)
| subset(sk0_4,sk0_3)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f320,f20]) ).
fof(f333,plain,
( spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f332,f76,f73]) ).
fof(f337,plain,
$false,
inference(sat_refutation,[status(thm)],[f79,f80,f248,f276,f309,f333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET693+4 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 21:38:05 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.6.0
% 0.21/0.46 % Refutation found
% 0.21/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.48 % Elapsed time: 0.118578 seconds
% 0.21/0.48 % CPU time: 0.808130 seconds
% 0.21/0.48 % Total memory used: 59.836 MB
% 0.21/0.48 % Net memory used: 59.215 MB
%------------------------------------------------------------------------------