TSTP Solution File: SET872+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET872+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : Tue Apr 30 20:40:36 EDT 2024
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 143 ( 60 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 168 ( 62 ~; 67 |; 30 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 90 ( 82 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B] : subset(singleton(A),unordered_pair(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B] : subset(singleton(A),unordered_pair(A,B)),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f14,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)],[f3]) ).
fof(f15,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)],[f14]) ).
fof(f16,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)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f21,plain,
! [A,B,C] :
( ( C != unordered_pair(A,B)
| ! [D] :
( ( ~ in(D,C)
| D = A
| D = B )
& ( in(D,C)
| ( D != A
& D != B ) ) ) )
& ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( D != A
& D != B ) )
& ( in(D,C)
| D = A
| D = B ) ) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f22,plain,
( ! [A,B,C] :
( C != unordered_pair(A,B)
| ( ! [D] :
( ~ in(D,C)
| D = A
| D = B )
& ! [D] :
( in(D,C)
| ( D != A
& D != B ) ) ) )
& ! [A,B,C] :
( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( D != A
& D != B ) )
& ( in(D,C)
| D = A
| D = B ) ) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f23,plain,
( ! [A,B,C] :
( C != unordered_pair(A,B)
| ( ! [D] :
( ~ in(D,C)
| D = A
| D = B )
& ! [D] :
( in(D,C)
| ( D != A
& D != B ) ) ) )
& ! [A,B,C] :
( C = unordered_pair(A,B)
| ( ( ~ in(sk0_1(C,B,A),C)
| ( sk0_1(C,B,A) != A
& sk0_1(C,B,A) != B ) )
& ( in(sk0_1(C,B,A),C)
| sk0_1(C,B,A) = A
| sk0_1(C,B,A) = B ) ) ) ),
inference(skolemization,[status(esa)],[f22]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| in(X3,X0)
| X3 != X1 ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f30,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f31,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f31]) ).
fof(f33,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_2(B,A),A)
& ~ in(sk0_2(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f32]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_2(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f36,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_2(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f43,plain,
? [A,B] : ~ subset(singleton(A),unordered_pair(A,B)),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f44,plain,
~ subset(singleton(sk0_5),unordered_pair(sk0_5,sk0_6)),
inference(skolemization,[status(esa)],[f43]) ).
fof(f45,plain,
~ subset(singleton(sk0_5),unordered_pair(sk0_5,sk0_6)),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f17]) ).
fof(f49,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(esa)],[f25]) ).
fof(f65,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| sk0_2(X1,singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[f35,f46]) ).
fof(f69,plain,
sk0_2(unordered_pair(sk0_5,sk0_6),singleton(sk0_5)) = sk0_5,
inference(resolution,[status(thm)],[f65,f45]) ).
fof(f71,plain,
( spl0_0
<=> subset(singleton(sk0_5),unordered_pair(sk0_5,sk0_6)) ),
introduced(split_symbol_definition) ).
fof(f72,plain,
( subset(singleton(sk0_5),unordered_pair(sk0_5,sk0_6))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f79,plain,
( spl0_2
<=> in(sk0_5,unordered_pair(sk0_5,sk0_6)) ),
introduced(split_symbol_definition) ).
fof(f81,plain,
( ~ in(sk0_5,unordered_pair(sk0_5,sk0_6))
| spl0_2 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( subset(singleton(sk0_5),unordered_pair(sk0_5,sk0_6))
| ~ in(sk0_5,unordered_pair(sk0_5,sk0_6)) ),
inference(paramodulation,[status(thm)],[f69,f36]) ).
fof(f83,plain,
( spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f82,f71,f79]) ).
fof(f89,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f45]) ).
fof(f90,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f89]) ).
fof(f91,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f49]) ).
fof(f92,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f91]) ).
fof(f93,plain,
$false,
inference(sat_refutation,[status(thm)],[f83,f90,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET872+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : Mon Apr 29 21:58:49 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 0.13/0.35 % Refutation found
% 0.13/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.37 % Elapsed time: 0.020287 seconds
% 0.13/0.37 % CPU time: 0.030156 seconds
% 0.13/0.37 % Total memory used: 12.772 MB
% 0.13/0.37 % Net memory used: 12.656 MB
%------------------------------------------------------------------------------