%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : COL062-1 : 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 : art06.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/COL/COL062-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: ueq
%
% strategies selected:
% (binary-posweight-kb-big-order 60 #f 5 1)
% (binary-posweight-lex-big-order 30 #f 5 1)
% (binary 30 #t)
% (binary-posweight-kb-big-order 180 #f)
% (binary-posweight-lex-big-order 120 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-posweight-kb-small-order 60 #f)
% (binary-posweight-lex-small-order 60 #f)
%
%
% **** EMPTY CLAUSE DERIVED ****
%
%
% timer checkpoints: c(4,40,1,8,0,1,10,50,1,14,0,1,19,50,1,23,0,1,30,50,1,34,0,1,55,50,1,59,0,1,133,50,2,137,0,2,535,50,9,539,0,9)
%
%
% START OF PROOF
% 537 [] equal(apply(apply(apply(b,X),Y),Z),apply(X,apply(Y,Z))).
% 538 [] equal(apply(apply(t,X),Y),apply(Y,X)).
% 539 [] -equal(apply(apply(apply(X,f(X)),g(X)),h(X)),apply(apply(f(X),h(X)),g(X))).
% 544 [para:537.1.1,539.1.1.1.1] -equal(apply(apply(apply(X,apply(Y,f(apply(apply(b,X),Y)))),g(apply(apply(b,X),Y))),h(apply(apply(b,X),Y))),apply(apply(f(apply(apply(b,X),Y)),h(apply(apply(b,X),Y))),g(apply(apply(b,X),Y)))).
% 552 [para:538.1.1,544.1.1.1.1] -equal(apply(apply(apply(apply(X,f(apply(apply(b,apply(t,Y)),X))),Y),g(apply(apply(b,apply(t,Y)),X))),h(apply(apply(b,apply(t,Y)),X))),apply(apply(f(apply(apply(b,apply(t,Y)),X)),h(apply(apply(b,apply(t,Y)),X))),g(apply(apply(b,apply(t,Y)),X)))).
% 577 [para:537.1.1,552.1.1.1.1.1] -equal(apply(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y))))),Z),g(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y)))),apply(apply(f(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y))),h(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y)))),g(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y))))).
% 635 [para:537.1.1,577.1.1.1] -equal(apply(apply(apply(X,f(apply(apply(b,apply(t,Y)),apply(apply(b,b),X)))),apply(Y,g(apply(apply(b,apply(t,Y)),apply(apply(b,b),X))))),h(apply(apply(b,apply(t,Y)),apply(apply(b,b),X)))),apply(apply(f(apply(apply(b,apply(t,Y)),apply(apply(b,b),X))),h(apply(apply(b,apply(t,Y)),apply(apply(b,b),X)))),g(apply(apply(b,apply(t,Y)),apply(apply(b,b),X))))).
% 749 [para:538.1.1,635.1.1.1] -equal(apply(apply(apply(X,g(apply(apply(b,apply(t,X)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X)),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,X)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X)),apply(apply(b,b),t))))).
% 953 [para:537.1.1,749.1.1.1.1] -equal(apply(apply(apply(X,apply(Y,g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))).
% 1281 [para:537.1.1,953.1.1,slowcut:538] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% using first neg lit preferred strategy
% not using sos strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% clause length limited to 1
% clause depth limited to 11
% seconds given: 60
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 949
% derived clauses: 2844
% kept clauses: 1247
% kept size sum: 121398
% kept mid-nuclei: 0
% kept new demods: 14
% forw unit-subs: 486
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 0
% fast unit cutoff: 0
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 0.23
% process. runtime: 0.21
% 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/COL062-1+eq_r.in")
%
%------------------------------------------------------------------------------