TSTP Solution File: SEU171+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU171+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 12:36:07 EDT 2023
% Result : Theorem 2.10s 0.64s
% Output : CNFRefutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 155 ( 24 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 178 ( 66 ~; 59 |; 32 &)
% ( 9 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 67 (; 62 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [A,B] :
( ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) )
& ( empty(A)
=> ( element(B,A)
<=> empty(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f101,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f144,plain,
! [A,B] :
( ( empty(A)
| ( element(B,A)
<=> in(B,A) ) )
& ( ~ empty(A)
| ( element(B,A)
<=> empty(B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f145,plain,
! [A,B] :
( ( empty(A)
| ( ( ~ element(B,A)
| in(B,A) )
& ( element(B,A)
| ~ in(B,A) ) ) )
& ( ~ empty(A)
| ( ( ~ element(B,A)
| empty(B) )
& ( element(B,A)
| ~ empty(B) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f144]) ).
fof(f146,plain,
( ! [A] :
( empty(A)
| ( ! [B] :
( ~ element(B,A)
| in(B,A) )
& ! [B] :
( element(B,A)
| ~ in(B,A) ) ) )
& ! [A] :
( ~ empty(A)
| ( ! [B] :
( ~ element(B,A)
| empty(B) )
& ! [B] :
( element(B,A)
| ~ empty(B) ) ) ) ),
inference(miniscoping,[status(esa)],[f145]) ).
fof(f147,plain,
! [X0,X1] :
( empty(X0)
| ~ element(X1,X0)
| in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f203,plain,
! [A,B,C] :
( ( C != set_difference(A,B)
| ! [D] :
( ( ~ in(D,C)
| ( in(D,A)
& ~ in(D,B) ) )
& ( in(D,C)
| ~ in(D,A)
| in(D,B) ) ) )
& ( C = set_difference(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)],[f17]) ).
fof(f204,plain,
( ! [A,B,C] :
( C != set_difference(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_difference(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)],[f203]) ).
fof(f205,plain,
( ! [A,B,C] :
( C != set_difference(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_difference(A,B)
| ( ( ~ in(sk0_15(C,B,A),C)
| ~ in(sk0_15(C,B,A),A)
| in(sk0_15(C,B,A),B) )
& ( in(sk0_15(C,B,A),C)
| ( in(sk0_15(C,B,A),A)
& ~ in(sk0_15(C,B,A),B) ) ) ) ) ),
inference(skolemization,[status(esa)],[f204]) ).
fof(f208,plain,
! [X0,X1,X2,X3] :
( X0 != set_difference(X1,X2)
| in(X3,X0)
| ~ in(X3,X1)
| in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f205]) ).
fof(f212,plain,
! [A,B] :
( ~ element(B,powerset(A))
| subset_complement(A,B) = set_difference(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f213,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset_complement(X1,X0) = set_difference(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f212]) ).
fof(f386,plain,
? [A] :
( A != empty_set
& ? [B] :
( element(B,powerset(A))
& ? [C] :
( element(C,A)
& ~ in(C,B)
& ~ in(C,subset_complement(A,B)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f96]) ).
fof(f387,plain,
( sk0_25 != empty_set
& element(sk0_26,powerset(sk0_25))
& element(sk0_27,sk0_25)
& ~ in(sk0_27,sk0_26)
& ~ in(sk0_27,subset_complement(sk0_25,sk0_26)) ),
inference(skolemization,[status(esa)],[f386]) ).
fof(f388,plain,
sk0_25 != empty_set,
inference(cnf_transformation,[status(esa)],[f387]) ).
fof(f389,plain,
element(sk0_26,powerset(sk0_25)),
inference(cnf_transformation,[status(esa)],[f387]) ).
fof(f390,plain,
element(sk0_27,sk0_25),
inference(cnf_transformation,[status(esa)],[f387]) ).
fof(f391,plain,
~ in(sk0_27,sk0_26),
inference(cnf_transformation,[status(esa)],[f387]) ).
fof(f392,plain,
~ in(sk0_27,subset_complement(sk0_25,sk0_26)),
inference(cnf_transformation,[status(esa)],[f387]) ).
fof(f403,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f101]) ).
fof(f404,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f403]) ).
fof(f466,plain,
! [X0,X1,X2] :
( in(X0,set_difference(X1,X2))
| ~ in(X0,X1)
| in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f208]) ).
fof(f486,plain,
subset_complement(sk0_25,sk0_26) = set_difference(sk0_25,sk0_26),
inference(resolution,[status(thm)],[f213,f389]) ).
fof(f488,plain,
~ in(sk0_27,set_difference(sk0_25,sk0_26)),
inference(backward_demodulation,[status(thm)],[f486,f392]) ).
fof(f500,plain,
! [X0,X1] :
( X0 = empty_set
| ~ element(X1,X0)
| in(X1,X0) ),
inference(resolution,[status(thm)],[f404,f147]) ).
fof(f758,plain,
( spl0_18
<=> sk0_25 = empty_set ),
introduced(split_symbol_definition) ).
fof(f759,plain,
( sk0_25 = empty_set
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f758]) ).
fof(f761,plain,
( spl0_19
<=> in(sk0_27,sk0_25) ),
introduced(split_symbol_definition) ).
fof(f764,plain,
( sk0_25 = empty_set
| in(sk0_27,sk0_25) ),
inference(resolution,[status(thm)],[f500,f390]) ).
fof(f765,plain,
( spl0_18
| spl0_19 ),
inference(split_clause,[status(thm)],[f764,f758,f761]) ).
fof(f766,plain,
( $false
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f759,f388]) ).
fof(f767,plain,
~ spl0_18,
inference(contradiction_clause,[status(thm)],[f766]) ).
fof(f1716,plain,
( spl0_82
<=> in(sk0_27,sk0_26) ),
introduced(split_symbol_definition) ).
fof(f1717,plain,
( in(sk0_27,sk0_26)
| ~ spl0_82 ),
inference(component_clause,[status(thm)],[f1716]) ).
fof(f1719,plain,
( ~ in(sk0_27,sk0_25)
| in(sk0_27,sk0_26) ),
inference(resolution,[status(thm)],[f466,f488]) ).
fof(f1720,plain,
( ~ spl0_19
| spl0_82 ),
inference(split_clause,[status(thm)],[f1719,f761,f1716]) ).
fof(f1727,plain,
( $false
| ~ spl0_82 ),
inference(forward_subsumption_resolution,[status(thm)],[f1717,f391]) ).
fof(f1728,plain,
~ spl0_82,
inference(contradiction_clause,[status(thm)],[f1727]) ).
fof(f1729,plain,
$false,
inference(sat_refutation,[status(thm)],[f765,f767,f1720,f1728]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU171+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 08:57:02 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 2.10/0.64 % Refutation found
% 2.10/0.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.10/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.10/0.66 % Elapsed time: 0.316572 seconds
% 2.10/0.66 % CPU time: 2.340013 seconds
% 2.10/0.66 % Memory used: 88.058 MB
%------------------------------------------------------------------------------