%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : LCL039-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art08.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 0.0s
% Output : Assurance 0.0s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/LCL/LCL039-1+noeq.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: hne
% detected subclass: small
% detected subclass: short
%
% strategies selected:
% (hyper 29 #f 5 5)
% (binary-unit 11 #f 5 5)
% (binary-double 17 #f 5 5)
% (hyper 29 #f)
% (binary-unit 34 #f)
% (binary-weightorder 40 #f)
% (binary 17 #t)
% (binary-order 29 #f)
% (binary-posweight-order 111 #f 5 5)
% (binary-posweight-order 283 #f)
%
%
% **** EMPTY CLAUSE DERIVED ****
%
%
% timer checkpoints: c(8,40,0,16,0,0)
%
%
% START OF PROOF
% 9 [] -is_a_theorem(implies(X,Y)) | -is_a_theorem(X) | is_a_theorem(Y).
% 10 [] is_a_theorem(implies(X,implies(Y,X))).
% 11 [] is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))).
% 12 [] is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))).
% 14 [] is_a_theorem(implies(necessary(X),X)).
% 16 [] -is_a_theorem(implies(necessary(a),not(necessary(not(a))))).
% 22 [hyper:9,10,14] is_a_theorem(implies(X,implies(necessary(Y),Y))).
% 23 [hyper:9,10,10] is_a_theorem(implies(X,implies(Y,implies(Z,Y)))).
% 46 [hyper:9,11,10] is_a_theorem(implies(implies(X,Y),implies(X,X))).
% 47 [hyper:9,11,22] is_a_theorem(implies(implies(X,necessary(Y)),implies(X,Y))).
% 49 [hyper:9,11,11] is_a_theorem(implies(implies(implies(X,implies(Y,Z)),implies(X,Y)),implies(implies(X,implies(Y,Z)),implies(X,Z)))).
% 51 [hyper:9,11,10] is_a_theorem(implies(X,implies(implies(Y,implies(Z,U)),implies(implies(Y,Z),implies(Y,U))))).
% 56 [hyper:9,46,slowcut:51] is_a_theorem(implies(X,X)).
% 62 [hyper:9,56,10] is_a_theorem(implies(X,implies(Y,Y))).
% 72 [hyper:9,12,10] is_a_theorem(implies(X,implies(implies(not(Y),not(Z)),implies(Z,Y)))).
% 177 [hyper:9,49,22] is_a_theorem(implies(implies(necessary(X),implies(X,Y)),implies(necessary(X),Y))).
% 178 [hyper:9,49,23] is_a_theorem(implies(implies(X,implies(implies(Y,X),Z)),implies(X,Z))).
% 179 [hyper:9,49,62] is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))).
% 400 [hyper:9,178,51] is_a_theorem(implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y)))).
% 401 [hyper:9,178,72] is_a_theorem(implies(not(X),implies(X,Y))).
% 405 [hyper:9,401,10] is_a_theorem(implies(X,implies(not(Y),implies(Y,Z)))).
% 441 [hyper:9,405,49] is_a_theorem(implies(implies(not(X),implies(implies(X,Y),Z)),implies(not(X),Z))).
% 617 [hyper:9,400,12] is_a_theorem(implies(implies(X,implies(not(Y),not(Z))),implies(X,implies(Z,Y)))).
% 620 [hyper:9,400,47] is_a_theorem(implies(implies(X,implies(Y,necessary(Z))),implies(X,implies(Y,Z)))).
% 636 [hyper:9,400,177] is_a_theorem(implies(implies(X,implies(necessary(Y),implies(Y,Z))),implies(X,implies(necessary(Y),Z)))).
% 872 [hyper:9,620,179] is_a_theorem(implies(implies(X,implies(X,necessary(Y))),implies(X,Y))).
% 1058 [hyper:9,441,72] is_a_theorem(implies(not(not(X)),implies(Y,X))).
% 1065 [hyper:9,1058,179] is_a_theorem(implies(not(not(X)),X)).
% 1071 [hyper:9,1058,872] is_a_theorem(implies(not(not(necessary(X))),X)).
% 1077 [hyper:9,1065,12] is_a_theorem(implies(X,not(not(X)))).
% 1099 [hyper:9,1077,400] is_a_theorem(implies(implies(X,Y),implies(X,not(not(Y))))).
% 1436 [hyper:9,617,1099] is_a_theorem(implies(implies(not(X),Y),implies(not(Y),X))).
% 1570 [hyper:9,1436,1071] is_a_theorem(implies(not(X),not(necessary(X)))).
% 1584 [hyper:9,1436,617] is_a_theorem(implies(implies(not(not(X)),Y),implies(X,Y))).
% 1924 [hyper:9,1584,1570] is_a_theorem(implies(X,not(necessary(not(X))))).
% 1934 [hyper:9,636,10] is_a_theorem(implies(implies(X,Y),implies(necessary(X),Y))).
% 2020 [hyper:9,1934,1924,slowcut:16] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 5
% clause depth limited to 5
% seconds given: 29
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 448
% derived clauses: 36365
% kept clauses: 1213
% kept size sum: 15887
% kept mid-nuclei: 760
% kept new demods: 0
% forw unit-subs: 16126
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 5
% fast unit cutoff: 0
% full unit cutoff: 27
% dbl unit cutoff: 0
% real runtime : 0.25
% process. runtime: 0.23
% specific non-discr-tree subsumption statistics:
% tried: 0
% length fails: 0
% strength fails: 0
% predlist fails: 0
% aux str. fails: 0
% by-lit fails: 0
% full subs tried: 0
% full subs fail: 0
%
% ; program args: ("/home/graph/tptp/Systems/Gandalf---c-2.6/gandalf" "-time" "600" "/home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/LCL/LCL039-1+noeq.in")
%
%------------------------------------------------------------------------------