TSTP Solution File: COL006-3 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : COL006-3 : TPTP v8.1.2. Released v1.0.0.
% 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 20:13:31 EDT 2024
% Result : Unsatisfiable 6.96s 1.26s
% Output : CNFRefutation 7.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 27 unt; 0 def)
% Number of atoms : 31 ( 26 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 18 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : apply(apply(k,X),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Strong_fixed_point] :
( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt))
| fixed_point(Strong_fixed_point) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,plain,
! [X0,X1,X2] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f6,plain,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f7,plain,
! [X0] :
( apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt))
| fixed_point(X0) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f8,plain,
~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))))),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f9,plain,
apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt) != apply(fixed_pt,apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt)),
inference(resolution,[status(thm)],[f7,f8]) ).
fof(f13,plain,
! [X0,X1] : apply(apply(apply(s,k),X0),X1) = X1,
inference(paramodulation,[status(thm)],[f6,f5]) ).
fof(f15,plain,
! [X0,X1,X2] : apply(apply(apply(s,apply(k,X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(paramodulation,[status(thm)],[f6,f5]) ).
fof(f18,plain,
! [X0,X1,X2] : apply(apply(apply(s,X0),apply(k,X1)),X2) = apply(apply(X0,X2),X1),
inference(paramodulation,[status(thm)],[f6,f5]) ).
fof(f35,plain,
! [X0,X1,X2] : apply(apply(apply(s,X0),apply(apply(s,k),X1)),X2) = apply(apply(X0,X2),X2),
inference(paramodulation,[status(thm)],[f13,f5]) ).
fof(f36,plain,
! [X0,X1,X2] : apply(apply(apply(s,apply(apply(s,k),X0)),X1),X2) = apply(X2,apply(X1,X2)),
inference(paramodulation,[status(thm)],[f13,f5]) ).
fof(f71,plain,
apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt))),
inference(backward_demodulation,[status(thm)],[f15,f9]) ).
fof(f72,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt))),
inference(forward_demodulation,[status(thm)],[f15,f71]) ).
fof(f73,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(apply(s,apply(k,s)),k),fixed_pt),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt))),
inference(forward_demodulation,[status(thm)],[f18,f72]) ).
fof(f74,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt))),
inference(forward_demodulation,[status(thm)],[f15,f73]) ).
fof(f75,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(apply(s,apply(k,s)),k),fixed_pt),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(forward_demodulation,[status(thm)],[f18,f74]) ).
fof(f76,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(forward_demodulation,[status(thm)],[f15,f75]) ).
fof(f462,plain,
! [X0,X1,X2,X3] : apply(apply(apply(s,X0),apply(apply(s,k),X1)),X2) = apply(apply(apply(s,X0),apply(apply(s,k),X3)),X2),
inference(paramodulation,[status(thm)],[f35,f35]) ).
fof(f1892,plain,
! [X0] : apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),X0)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(paramodulation,[status(thm)],[f462,f76]) ).
fof(f2688,plain,
! [X0] : apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),X0)),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(paramodulation,[status(thm)],[f36,f1892]) ).
fof(f4973,plain,
! [X0,X1] : apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),X0)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),X1)),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(paramodulation,[status(thm)],[f462,f2688]) ).
fof(f4995,plain,
! [X0] : apply(apply(apply(apply(s,k),k),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),X0)),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(paramodulation,[status(thm)],[f35,f4973]) ).
fof(f4996,plain,
! [X0] : apply(apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),X0)),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(forward_demodulation,[status(thm)],[f13,f4995]) ).
fof(f4997,plain,
! [X0] : apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),X0)),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(forward_demodulation,[status(thm)],[f15,f4996]) ).
fof(f5115,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(paramodulation,[status(thm)],[f36,f4997]) ).
fof(f5116,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f5115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL006-3 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13 % 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 22:47:34 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 6.96/1.26 % Refutation found
% 6.96/1.26 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.96/1.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.21/1.30 % Elapsed time: 0.950880 seconds
% 7.21/1.30 % CPU time: 7.382957 seconds
% 7.21/1.30 % Total memory used: 221.938 MB
% 7.21/1.30 % Net memory used: 220.895 MB
%------------------------------------------------------------------------------