TSTP Solution File: SEU230+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU230+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 12:36:22 EDT 2023
% Result : Theorem 0.20s 0.39s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 101 ( 34 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 121 ( 45 ~; 48 |; 24 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 71 (; 66 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A] : in(A,succ(A)),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f50,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f51,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f52,plain,
! [A,B] :
( ( B != singleton(A)
| ! [C] :
( ( ~ in(C,B)
| C = A )
& ( in(C,B)
| C != A ) ) )
& ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f53,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(miniscoping,[status(esa)],[f52]) ).
fof(f54,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ( ( ~ in(sk0_0(B,A),B)
| sk0_0(B,A) != A )
& ( in(sk0_0(B,A),B)
| sk0_0(B,A) = A ) ) ) ),
inference(skolemization,[status(esa)],[f53]) ).
fof(f56,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| in(X2,X0)
| X2 != X1 ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f59,plain,
! [A,B,C] :
( ( C != set_union2(A,B)
| ! [D] :
( ( ~ in(D,C)
| in(D,A)
| in(D,B) )
& ( in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) ) ) )
& ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) )
& ( in(D,C)
| in(D,A)
| in(D,B) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f60,plain,
( ! [A,B,C] :
( C != set_union2(A,B)
| ( ! [D] :
( ~ in(D,C)
| in(D,A)
| in(D,B) )
& ! [D] :
( in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) ) ) )
& ! [A,B,C] :
( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) )
& ( in(D,C)
| in(D,A)
| in(D,B) ) ) ) ),
inference(miniscoping,[status(esa)],[f59]) ).
fof(f61,plain,
( ! [A,B,C] :
( C != set_union2(A,B)
| ( ! [D] :
( ~ in(D,C)
| in(D,A)
| in(D,B) )
& ! [D] :
( in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) ) ) )
& ! [A,B,C] :
( C = set_union2(A,B)
| ( ( ~ in(sk0_1(C,B,A),C)
| ( ~ in(sk0_1(C,B,A),A)
& ~ in(sk0_1(C,B,A),B) ) )
& ( in(sk0_1(C,B,A),C)
| in(sk0_1(C,B,A),A)
| in(sk0_1(C,B,A),B) ) ) ) ),
inference(skolemization,[status(esa)],[f60]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( X0 != set_union2(X1,X2)
| in(X3,X0)
| ~ in(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f115,plain,
? [A] : ~ in(A,succ(A)),
inference(pre_NNF_transformation,[status(esa)],[f33]) ).
fof(f116,plain,
~ in(sk0_12,succ(sk0_12)),
inference(skolemization,[status(esa)],[f115]) ).
fof(f117,plain,
~ in(sk0_12,succ(sk0_12)),
inference(cnf_transformation,[status(esa)],[f116]) ).
fof(f132,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(esa)],[f56]) ).
fof(f134,plain,
! [X0,X1,X2] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f63]) ).
fof(f229,plain,
! [X0,X1] : in(X0,set_union2(singleton(X0),X1)),
inference(resolution,[status(thm)],[f134,f132]) ).
fof(f352,plain,
! [X0,X1] : in(X0,set_union2(X1,singleton(X0))),
inference(paramodulation,[status(thm)],[f50,f229]) ).
fof(f369,plain,
! [X0] : in(X0,succ(X0)),
inference(paramodulation,[status(thm)],[f51,f352]) ).
fof(f374,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f117,f369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU230+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n029.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 09:23:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.20/0.39 % Refutation found
% 0.20/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.61 % Elapsed time: 0.045137 seconds
% 0.25/0.61 % CPU time: 0.027179 seconds
% 0.25/0.61 % Memory used: 5.622 MB
%------------------------------------------------------------------------------