TSTP Solution File: SET959+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET959+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 12:35:37 EDT 2023
% Result : Theorem 0.15s 0.33s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 3 unt; 0 def)
% Number of atoms : 179 ( 45 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 196 ( 74 ~; 82 |; 25 &)
% ( 11 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 81 (; 61 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,conjecture,
! [A,B] :
( ( ! [C] :
~ ( in(C,A)
& ! [D,E] : C != ordered_pair(D,E) )
& ! [C] :
~ ( in(C,B)
& ! [D,E] : C != ordered_pair(D,E) )
& ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) )
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B] :
( ( ! [C] :
~ ( in(C,A)
& ! [D,E] : C != ordered_pair(D,E) )
& ! [C] :
~ ( in(C,B)
& ! [D,E] : C != ordered_pair(D,E) )
& ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) )
=> A = B ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
? [A,B] :
( ! [C] :
( ~ in(C,A)
| ? [D,E] : C = ordered_pair(D,E) )
& ! [C] :
( ~ in(C,B)
| ? [D,E] : C = ordered_pair(D,E) )
& ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) )
& A != B ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f20,plain,
? [A,B] :
( ! [C] :
( ~ in(C,A)
| ? [D,E] : C = ordered_pair(D,E) )
& ! [C] :
( ~ in(C,B)
| ? [D,E] : C = ordered_pair(D,E) )
& ! [C,D] :
( ( ~ in(ordered_pair(C,D),A)
| in(ordered_pair(C,D),B) )
& ( in(ordered_pair(C,D),A)
| ~ in(ordered_pair(C,D),B) ) )
& A != B ),
inference(NNF_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
? [A,B] :
( ! [C] :
( ~ in(C,A)
| ? [D,E] : C = ordered_pair(D,E) )
& ! [C] :
( ~ in(C,B)
| ? [D,E] : C = ordered_pair(D,E) )
& ! [C,D] :
( ~ in(ordered_pair(C,D),A)
| in(ordered_pair(C,D),B) )
& ! [C,D] :
( in(ordered_pair(C,D),A)
| ~ in(ordered_pair(C,D),B) )
& A != B ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f22,plain,
( ! [C] :
( ~ in(C,sk0_2)
| C = ordered_pair(sk0_4(C),sk0_5(C)) )
& ! [C] :
( ~ in(C,sk0_3)
| C = ordered_pair(sk0_6(C),sk0_7(C)) )
& ! [C,D] :
( ~ in(ordered_pair(C,D),sk0_2)
| in(ordered_pair(C,D),sk0_3) )
& ! [C,D] :
( in(ordered_pair(C,D),sk0_2)
| ~ in(ordered_pair(C,D),sk0_3) )
& sk0_2 != sk0_3 ),
inference(skolemization,[status(esa)],[f21]) ).
fof(f23,plain,
! [X0] :
( ~ in(X0,sk0_2)
| X0 = ordered_pair(sk0_4(X0),sk0_5(X0)) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [X0] :
( ~ in(X0,sk0_3)
| X0 = ordered_pair(sk0_6(X0),sk0_7(X0)) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sk0_2)
| in(ordered_pair(X0,X1),sk0_3) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( in(ordered_pair(X0,X1),sk0_2)
| ~ in(ordered_pair(X0,X1),sk0_3) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f27,plain,
sk0_2 != sk0_3,
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f28,plain,
! [A,B] :
( ? [C] :
( in(C,A)
<~> in(C,B) )
| A = B ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f29,plain,
! [A,B] :
( ? [C] :
( ( in(C,A)
| in(C,B) )
& ( ~ in(C,A)
| ~ in(C,B) ) )
| A = B ),
inference(NNF_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
! [A,B] :
( ( ( in(sk0_8(B,A),A)
| in(sk0_8(B,A),B) )
& ( ~ in(sk0_8(B,A),A)
| ~ in(sk0_8(B,A),B) ) )
| A = B ),
inference(skolemization,[status(esa)],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( in(sk0_8(X0,X1),X1)
| in(sk0_8(X0,X1),X0)
| X1 = X0 ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ~ in(sk0_8(X0,X1),X1)
| ~ in(sk0_8(X0,X1),X0)
| X1 = X0 ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f52,plain,
! [X0] :
( in(sk0_8(X0,sk0_3),X0)
| sk0_3 = X0
| sk0_8(X0,sk0_3) = ordered_pair(sk0_6(sk0_8(X0,sk0_3)),sk0_7(sk0_8(X0,sk0_3))) ),
inference(resolution,[status(thm)],[f31,f24]) ).
fof(f64,plain,
! [X0] :
( in(sk0_8(sk0_2,X0),X0)
| X0 = sk0_2
| sk0_8(sk0_2,X0) = ordered_pair(sk0_4(sk0_8(sk0_2,X0)),sk0_5(sk0_8(sk0_2,X0))) ),
inference(resolution,[status(thm)],[f31,f23]) ).
fof(f68,plain,
( spl0_4
<=> sk0_3 = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f69,plain,
( sk0_3 = sk0_2
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( spl0_5
<=> sk0_8(sk0_2,sk0_3) = ordered_pair(sk0_6(sk0_8(sk0_2,sk0_3)),sk0_7(sk0_8(sk0_2,sk0_3))) ),
introduced(split_symbol_definition) ).
fof(f72,plain,
( sk0_8(sk0_2,sk0_3) = ordered_pair(sk0_6(sk0_8(sk0_2,sk0_3)),sk0_7(sk0_8(sk0_2,sk0_3)))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( spl0_6
<=> sk0_8(sk0_2,sk0_3) = ordered_pair(sk0_4(sk0_8(sk0_2,sk0_3)),sk0_5(sk0_8(sk0_2,sk0_3))) ),
introduced(split_symbol_definition) ).
fof(f75,plain,
( sk0_8(sk0_2,sk0_3) = ordered_pair(sk0_4(sk0_8(sk0_2,sk0_3)),sk0_5(sk0_8(sk0_2,sk0_3)))
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( sk0_3 = sk0_2
| sk0_8(sk0_2,sk0_3) = ordered_pair(sk0_6(sk0_8(sk0_2,sk0_3)),sk0_7(sk0_8(sk0_2,sk0_3)))
| sk0_8(sk0_2,sk0_3) = ordered_pair(sk0_4(sk0_8(sk0_2,sk0_3)),sk0_5(sk0_8(sk0_2,sk0_3))) ),
inference(resolution,[status(thm)],[f52,f23]) ).
fof(f78,plain,
( spl0_4
| spl0_5
| spl0_6 ),
inference(split_clause,[status(thm)],[f77,f68,f71,f74]) ).
fof(f91,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f27]) ).
fof(f92,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f91]) ).
fof(f312,plain,
( spl0_11
<=> in(ordered_pair(sk0_6(sk0_8(sk0_2,sk0_3)),sk0_7(sk0_8(sk0_2,sk0_3))),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f313,plain,
( in(ordered_pair(sk0_6(sk0_8(sk0_2,sk0_3)),sk0_7(sk0_8(sk0_2,sk0_3))),sk0_2)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,plain,
( spl0_12
<=> in(sk0_8(sk0_2,sk0_3),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f316,plain,
( in(sk0_8(sk0_2,sk0_3),sk0_3)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f317,plain,
( ~ in(sk0_8(sk0_2,sk0_3),sk0_3)
| spl0_12 ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f318,plain,
( in(ordered_pair(sk0_6(sk0_8(sk0_2,sk0_3)),sk0_7(sk0_8(sk0_2,sk0_3))),sk0_2)
| ~ in(sk0_8(sk0_2,sk0_3),sk0_3)
| ~ spl0_5 ),
inference(paramodulation,[status(thm)],[f72,f26]) ).
fof(f319,plain,
( spl0_11
| ~ spl0_12
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f318,f312,f315,f71]) ).
fof(f320,plain,
( spl0_13
<=> in(sk0_8(sk0_2,sk0_3),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f322,plain,
( ~ in(sk0_8(sk0_2,sk0_3),sk0_2)
| spl0_13 ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f328,plain,
( sk0_3 = sk0_2
| sk0_8(sk0_2,sk0_3) = ordered_pair(sk0_4(sk0_8(sk0_2,sk0_3)),sk0_5(sk0_8(sk0_2,sk0_3)))
| spl0_12 ),
inference(resolution,[status(thm)],[f317,f64]) ).
fof(f329,plain,
( spl0_4
| spl0_6
| spl0_12 ),
inference(split_clause,[status(thm)],[f328,f68,f74,f315]) ).
fof(f330,plain,
( in(sk0_8(sk0_2,sk0_3),sk0_2)
| sk0_3 = sk0_2
| spl0_12 ),
inference(resolution,[status(thm)],[f317,f31]) ).
fof(f331,plain,
( spl0_13
| spl0_4
| spl0_12 ),
inference(split_clause,[status(thm)],[f330,f320,f68,f315]) ).
fof(f332,plain,
( in(sk0_8(sk0_2,sk0_3),sk0_2)
| ~ spl0_5
| ~ spl0_11 ),
inference(forward_demodulation,[status(thm)],[f72,f313]) ).
fof(f340,plain,
( $false
| ~ spl0_5
| ~ spl0_11
| spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f322,f332]) ).
fof(f341,plain,
( ~ spl0_5
| ~ spl0_11
| spl0_13 ),
inference(contradiction_clause,[status(thm)],[f340]) ).
fof(f366,plain,
( ~ in(sk0_8(sk0_2,sk0_3),sk0_2)
| sk0_3 = sk0_2
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f316,f32]) ).
fof(f367,plain,
( ~ spl0_13
| spl0_4
| ~ spl0_12 ),
inference(split_clause,[status(thm)],[f366,f320,f68,f315]) ).
fof(f368,plain,
( sk0_8(sk0_2,sk0_3) = ordered_pair(sk0_6(sk0_8(sk0_2,sk0_3)),sk0_7(sk0_8(sk0_2,sk0_3)))
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f316,f24]) ).
fof(f369,plain,
( spl0_5
| ~ spl0_12 ),
inference(split_clause,[status(thm)],[f368,f71,f315]) ).
fof(f469,plain,
( spl0_26
<=> in(ordered_pair(sk0_4(sk0_8(sk0_2,sk0_3)),sk0_5(sk0_8(sk0_2,sk0_3))),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f470,plain,
( in(ordered_pair(sk0_4(sk0_8(sk0_2,sk0_3)),sk0_5(sk0_8(sk0_2,sk0_3))),sk0_3)
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,plain,
( ~ in(sk0_8(sk0_2,sk0_3),sk0_2)
| in(ordered_pair(sk0_4(sk0_8(sk0_2,sk0_3)),sk0_5(sk0_8(sk0_2,sk0_3))),sk0_3)
| ~ spl0_6 ),
inference(paramodulation,[status(thm)],[f75,f25]) ).
fof(f473,plain,
( ~ spl0_13
| spl0_26
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f472,f320,f469,f74]) ).
fof(f474,plain,
( in(sk0_8(sk0_2,sk0_3),sk0_3)
| ~ spl0_6
| ~ spl0_26 ),
inference(forward_demodulation,[status(thm)],[f75,f470]) ).
fof(f475,plain,
( $false
| spl0_12
| ~ spl0_6
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f474,f317]) ).
fof(f476,plain,
( spl0_12
| ~ spl0_6
| ~ spl0_26 ),
inference(contradiction_clause,[status(thm)],[f475]) ).
fof(f477,plain,
$false,
inference(sat_refutation,[status(thm)],[f78,f92,f319,f329,f331,f341,f367,f369,f473,f476]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET959+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.05/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n004.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 10:12:22 EDT 2023
% 0.15/0.32 % CPUTime :
% 0.15/0.32 % Drodi V3.5.1
% 0.15/0.33 % Refutation found
% 0.15/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.57 % Elapsed time: 0.040218 seconds
% 0.17/0.57 % CPU time: 0.023186 seconds
% 0.17/0.57 % Memory used: 3.968 MB
%------------------------------------------------------------------------------