%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : COL078-2 : TPTP v3.4.2. Released v1.2.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art02.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 30.0s
% Output : Assurance 30.0s
% 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/COL/COL078-2+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 4 3)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 4 3)
% (binary-posweight-lex-big-order 30 #f 4 3)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% **** EMPTY CLAUSE DERIVED ****
%
%
% timer checkpoints: c(6,40,0,12,0,0,16,50,0,22,0,0,200,50,38,206,0,39,3253,4,2234,3254,50,2241,3254,40,2241,3260,0,2241,26555,3,2864,27486,4,3142)
%
%
% START OF PROOF
% 3256 [] equal(apply(k(X),Y),X).
% 3257 [] equal(apply(apply(apply(abstraction,X),Y),Z),apply(apply(X,k(Z)),apply(Y,Z))).
% 3258 [] -equal(apply(X,n(X,Y)),apply(Y,n(X,Y))) | equal(X,Y).
% 3259 [] equal(apply(identity,X),X).
% 3260 [] -equal(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))).
% 3263 [para:3259.1.1,3258.1.2] -equal(apply(X,n(X,identity)),n(X,identity)) | equal(X,identity).
% 3265 [para:3256.1.1,3258.1.2] -equal(apply(X,n(X,k(Y))),Y) | equal(X,k(Y)).
% 3266 [binary:3260,3258.2,demod:3256] -equal(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity)))),k(identity)).
% 3269 [para:3256.1.1,3257.1.2.1] equal(apply(apply(apply(abstraction,k(X)),Y),Z),apply(X,apply(Y,Z))).
% 3483 [para:3265.2.2,3266.1.2] -equal(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity)))),X) | -equal(apply(X,n(X,k(identity))),identity).
% 3612 [para:3257.1.2,3269.1.1.1] equal(apply(apply(apply(apply(abstraction,abstraction),X),Y),Z),apply(Y,apply(apply(X,Y),Z))).
% 17560 [para:3612.1.1,3257.1.2,demod:3256,3257] equal(apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X)),Y),Z),Z).
% 17952 [binary:3483,3612] -equal(apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),identity).
% 28189 [binary:17560,3263,slowcut:17952] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit paramodulation strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 12
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 2139
% derived clauses: 764358
% kept clauses: 26476
% kept size sum: 703648
% kept mid-nuclei: 701
% kept new demods: 1609
% forw unit-subs: 276450
% forw double-subs: 20576
% forw overdouble-subs: 0
% backward subs: 690
% fast unit cutoff: 7
% full unit cutoff: 34
% dbl unit cutoff: 1
% real runtime : 32.26
% process. runtime: 32.25
% 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/COL/COL078-2+eq_r.in")
%
%------------------------------------------------------------------------------