TSTP Solution File: SET617+3 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET617+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 0.11s 0.33s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 17 unt; 0 def)
% Number of atoms : 47 ( 32 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 11 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] : union(B,empty_set) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] : difference(B,empty_set) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B] : difference(empty_set,B) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [B] :
( symmetric_difference(B,empty_set) = B
& symmetric_difference(empty_set,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [B] :
( symmetric_difference(B,empty_set) = B
& symmetric_difference(empty_set,B) = B ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f16,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f17,plain,
! [X0] : difference(X0,empty_set) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f18,plain,
! [X0] : difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f26,plain,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f47,plain,
? [B] :
( symmetric_difference(B,empty_set) != B
| symmetric_difference(empty_set,B) != B ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f48,plain,
( ? [B] : symmetric_difference(B,empty_set) != B
| ? [B] : symmetric_difference(empty_set,B) != B ),
inference(miniscoping,[status(esa)],[f47]) ).
fof(f49,plain,
( symmetric_difference(sk0_3,empty_set) != sk0_3
| symmetric_difference(empty_set,sk0_4) != sk0_4 ),
inference(skolemization,[status(esa)],[f48]) ).
fof(f50,plain,
( symmetric_difference(sk0_3,empty_set) != sk0_3
| symmetric_difference(empty_set,sk0_4) != sk0_4 ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f51,plain,
( spl0_0
<=> symmetric_difference(sk0_3,empty_set) = sk0_3 ),
introduced(split_symbol_definition) ).
fof(f53,plain,
( symmetric_difference(sk0_3,empty_set) != sk0_3
| spl0_0 ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,plain,
( spl0_1
<=> symmetric_difference(empty_set,sk0_4) = sk0_4 ),
introduced(split_symbol_definition) ).
fof(f56,plain,
( symmetric_difference(empty_set,sk0_4) != sk0_4
| spl0_1 ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f50,f51,f54]) ).
fof(f62,plain,
! [X0] : symmetric_difference(X0,empty_set) = union(difference(X0,empty_set),empty_set),
inference(paramodulation,[status(thm)],[f18,f15]) ).
fof(f63,plain,
! [X0] : symmetric_difference(X0,empty_set) = difference(X0,empty_set),
inference(forward_demodulation,[status(thm)],[f16,f62]) ).
fof(f64,plain,
! [X0] : symmetric_difference(X0,empty_set) = X0,
inference(forward_demodulation,[status(thm)],[f17,f63]) ).
fof(f67,plain,
! [X0] : symmetric_difference(empty_set,X0) = X0,
inference(paramodulation,[status(thm)],[f26,f64]) ).
fof(f110,plain,
( sk0_3 != sk0_3
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f64,f53]) ).
fof(f111,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f110]) ).
fof(f112,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f111]) ).
fof(f113,plain,
( sk0_4 != sk0_4
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f67,f56]) ).
fof(f114,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f113]) ).
fof(f115,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f116,plain,
$false,
inference(sat_refutation,[status(thm)],[f57,f112,f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET617+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n022.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 29 21:30:28 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.6.0
% 0.11/0.33 % Refutation found
% 0.11/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.34 % Elapsed time: 0.019398 seconds
% 0.11/0.34 % CPU time: 0.028141 seconds
% 0.11/0.34 % Total memory used: 12.832 MB
% 0.11/0.34 % Net memory used: 12.750 MB
%------------------------------------------------------------------------------