TSTP Solution File: NUM555+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM555+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 12:29:41 EDT 2023
% Result : Theorem 0.10s 0.27s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 10 unt; 1 def)
% Number of atoms : 145 ( 18 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 173 ( 67 ~; 62 |; 31 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 58 (; 56 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,definition,
! [W0,W1] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& W3 != W1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,hypothesis,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,hypothesis,
( aElement0(xy)
& aElementOf0(xy,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,hypothesis,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,conjecture,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,negated_conjecture,
~ ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f79,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[status(esa)],[f79]) ).
fof(f126,plain,
! [W0,W1] :
( ~ aSet0(W0)
| ~ aElement0(W1)
| ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& W3 != W1 ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f127,plain,
! [W0,W1,W3] :
( pd0_0(W3,W1,W0)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& W3 != W1 ) ),
introduced(predicate_definition,[f126]) ).
fof(f128,plain,
! [W0,W1] :
( ~ aSet0(W0)
| ~ aElement0(W1)
| ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> pd0_0(W3,W1,W0) ) ) ) ),
inference(formula_renaming,[status(thm)],[f126,f127]) ).
fof(f129,plain,
! [W0,W1] :
( ~ aSet0(W0)
| ~ aElement0(W1)
| ! [W2] :
( ( W2 != sdtmndt0(W0,W1)
| ( aSet0(W2)
& ! [W3] :
( ( ~ aElementOf0(W3,W2)
| pd0_0(W3,W1,W0) )
& ( aElementOf0(W3,W2)
| ~ pd0_0(W3,W1,W0) ) ) ) )
& ( W2 = sdtmndt0(W0,W1)
| ~ aSet0(W2)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
| ~ pd0_0(W3,W1,W0) )
& ( aElementOf0(W3,W2)
| pd0_0(W3,W1,W0) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f128]) ).
fof(f130,plain,
! [W0,W1] :
( ~ aSet0(W0)
| ~ aElement0(W1)
| ( ! [W2] :
( W2 != sdtmndt0(W0,W1)
| ( aSet0(W2)
& ! [W3] :
( ~ aElementOf0(W3,W2)
| pd0_0(W3,W1,W0) )
& ! [W3] :
( aElementOf0(W3,W2)
| ~ pd0_0(W3,W1,W0) ) ) )
& ! [W2] :
( W2 = sdtmndt0(W0,W1)
| ~ aSet0(W2)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
| ~ pd0_0(W3,W1,W0) )
& ( aElementOf0(W3,W2)
| pd0_0(W3,W1,W0) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f129]) ).
fof(f131,plain,
! [W0,W1] :
( ~ aSet0(W0)
| ~ aElement0(W1)
| ( ! [W2] :
( W2 != sdtmndt0(W0,W1)
| ( aSet0(W2)
& ! [W3] :
( ~ aElementOf0(W3,W2)
| pd0_0(W3,W1,W0) )
& ! [W3] :
( aElementOf0(W3,W2)
| ~ pd0_0(W3,W1,W0) ) ) )
& ! [W2] :
( W2 = sdtmndt0(W0,W1)
| ~ aSet0(W2)
| ( ( ~ aElementOf0(sk0_3(W2,W1,W0),W2)
| ~ pd0_0(sk0_3(W2,W1,W0),W1,W0) )
& ( aElementOf0(sk0_3(W2,W1,W0),W2)
| pd0_0(sk0_3(W2,W1,W0),W1,W0) ) ) ) ) ),
inference(skolemization,[status(esa)],[f130]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( ~ aSet0(X0)
| ~ aElement0(X1)
| X2 != sdtmndt0(X0,X1)
| ~ aElementOf0(X3,X2)
| pd0_0(X3,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f131]) ).
fof(f279,plain,
aSet0(xQ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f283,plain,
aElementOf0(xy,xQ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f284,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f287,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cnf_transformation,[status(esa)],[f72]) ).
fof(f288,plain,
! [W0,W1,W3] :
( ( ~ pd0_0(W3,W1,W0)
| ( aElement0(W3)
& aElementOf0(W3,W0)
& W3 != W1 ) )
& ( pd0_0(W3,W1,W0)
| ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| W3 = W1 ) ),
inference(NNF_transformation,[status(esa)],[f127]) ).
fof(f289,plain,
( ! [W0,W1,W3] :
( ~ pd0_0(W3,W1,W0)
| ( aElement0(W3)
& aElementOf0(W3,W0)
& W3 != W1 ) )
& ! [W0,W1,W3] :
( pd0_0(W3,W1,W0)
| ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| W3 = W1 ) ),
inference(miniscoping,[status(esa)],[f288]) ).
fof(f291,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| aElementOf0(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f289]) ).
fof(f304,plain,
! [X0,X1,X2] :
( ~ aSet0(X0)
| ~ aElement0(X1)
| ~ aElementOf0(X2,sdtmndt0(X0,X1))
| pd0_0(X2,X1,X0) ),
inference(destructive_equality_resolution,[status(esa)],[f133]) ).
fof(f322,plain,
( spl0_0
<=> aSet0(xQ) ),
introduced(split_symbol_definition) ).
fof(f324,plain,
( ~ aSet0(xQ)
| spl0_0 ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,plain,
( spl0_1
<=> aElement0(xy) ),
introduced(split_symbol_definition) ).
fof(f328,plain,
( ~ aSet0(xQ)
| aElement0(xy) ),
inference(resolution,[status(thm)],[f80,f283]) ).
fof(f329,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f328,f322,f325]) ).
fof(f343,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f324,f279]) ).
fof(f344,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f343]) ).
fof(f1052,plain,
( spl0_106
<=> pd0_0(xx,xy,xQ) ),
introduced(split_symbol_definition) ).
fof(f1053,plain,
( pd0_0(xx,xy,xQ)
| ~ spl0_106 ),
inference(component_clause,[status(thm)],[f1052]) ).
fof(f1055,plain,
( ~ aSet0(xQ)
| ~ aElement0(xy)
| pd0_0(xx,xy,xQ) ),
inference(resolution,[status(thm)],[f304,f287]) ).
fof(f1056,plain,
( ~ spl0_0
| ~ spl0_1
| spl0_106 ),
inference(split_clause,[status(thm)],[f1055,f322,f325,f1052]) ).
fof(f1071,plain,
( aElementOf0(xx,xQ)
| ~ spl0_106 ),
inference(resolution,[status(thm)],[f1053,f291]) ).
fof(f1072,plain,
( $false
| ~ spl0_106 ),
inference(forward_subsumption_resolution,[status(thm)],[f1071,f284]) ).
fof(f1073,plain,
~ spl0_106,
inference(contradiction_clause,[status(thm)],[f1072]) ).
fof(f1074,plain,
$false,
inference(sat_refutation,[status(thm)],[f329,f344,f1056,f1073]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : NUM555+1 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.26 % Computer : n002.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Tue May 30 10:08:27 EDT 2023
% 0.10/0.26 % CPUTime :
% 0.10/0.26 % Drodi V3.5.1
% 0.10/0.27 % Refutation found
% 0.10/0.27 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.28 % Elapsed time: 0.023525 seconds
% 0.10/0.28 % CPU time: 0.070277 seconds
% 0.10/0.28 % Memory used: 19.793 MB
%------------------------------------------------------------------------------