%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : BOO007-1 : TPTP v3.4.2. Bugfixed v1.2.1.
% 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 49.4s
% Output : Assurance 49.4s
% 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/BOO/BOO007-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: heq
% detected subclass: medium
% detected subclass: long
%
% strategies selected:
% (hyper 58 #f 2 9)
% (binary-posweight-order 29 #f 2 9)
% (binary-unit 29 #f 2 9)
% (binary-double 29 #f 2 9)
% (binary 29 #t 2 9)
% (hyper 29 #t)
% (hyper 105 #f)
% (binary-unit-uniteq 17 #f)
% (binary-weightorder 23 #f)
% (binary-posweight-order 70 #f)
% (binary-posweight-lex-big-order 29 #f)
% (binary-posweight-lex-small-order 11 #f)
% (binary-order 29 #f)
% (binary-unit 46 #f)
% (binary 67 #t)
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(28,40,0,56,0,0,882184,4,4507,1029659,5,5801,1029664,1,5801,1029664,50,5801,1029664,40,5801,1029692,0,5801)
%
%
% START OF PROOF
% 531213 [?] ?
% 882468 [?] ?
% 1029666 [] sum(X,Y,add(X,Y)).
% 1029667 [] product(X,Y,multiply(X,Y)).
% 1029668 [] -sum(X,Y,Z) | sum(Y,X,Z).
% 1029669 [] -product(X,Y,Z) | product(Y,X,Z).
% 1029670 [] sum(additive_identity,X,X).
% 1029672 [] product(multiplicative_identity,X,X).
% 1029673 [] product(X,multiplicative_identity,X).
% 1029674 [] -product(X,U,V) | -product(X,W,X1) | -product(X,Y,Z) | -sum(W,Y,U) | sum(X1,Z,V).
% 1029675 [] -product(X,Y,Z) | -product(X,U,V) | -sum(Z,V,X1) | -sum(Y,U,W) | product(X,W,X1).
% 1029676 [] -product(U,Y,V) | -product(W,Y,X1) | -product(X,Y,Z) | -sum(W,X,U) | sum(X1,Z,V).
% 1029682 [] sum(inverse(X),X,multiplicative_identity).
% 1029685 [] product(X,inverse(X),additive_identity).
% 1029686 [] -sum(X,Y,U) | -sum(X,Y,Z) | equal(Z,U).
% 1029687 [] -product(X,Y,U) | -product(X,Y,Z) | equal(Z,U).
% 1029688 [] product(y,z,y_times_z).
% 1029689 [] product(x,y_times_z,x_times__y_times_z).
% 1029690 [] product(x,y,x_times_y).
% 1029691 [] product(x_times_y,z,x_times_y__times_z).
% 1029694 [input:1029674,factor:factor] -product(X,Y,Z) | -product(X,U,V) | -sum(U,Y,Y) | sum(V,Z,Z).
% 1029699 [input:1029676,factor:factor] -product(X,Y,Z) | -product(U,Y,V) | -sum(U,X,X) | sum(V,Z,Z).
% 1029704 [binary:1029666,1029668] sum(X,Y,add(Y,X)).
% 1029706 [binary:1029688,1029669] product(z,y,y_times_z).
% 1029707 [binary:1029689,1029669] product(y_times_z,x,x_times__y_times_z).
% 1029708 [binary:1029690,1029669] product(y,x,x_times_y).
% 1029709 [binary:1029691,1029669] product(z,x_times_y,x_times_y__times_z).
% 1029710 [binary:1029667,1029669] product(X,Y,multiply(Y,X)).
% 1029712 [binary:1029688,1029674] -product(y,X,Y) | -product(y,Z,U) | -sum(X,Z,z) | sum(Y,U,y_times_z).
% 1029733 [binary:1029704,1029686] equal(X,add(Y,Z)) | -sum(Z,Y,X).
% 1029738 [binary:1029672,1029675] -product(multiplicative_identity,X,Y) | product(multiplicative_identity,Z,U) | -sum(V,X,Z) | -sum(V,Y,U).
% 1029744 [binary:1029685,1029675] -sum(inverse(X),Y,Z) | -sum(additive_identity,U,V) | -product(X,Y,U) | product(X,Z,V).
% 1029745 [binary:1029667,1029675] -sum(multiply(X,Y),Z,U) | -product(X,V,Z) | -sum(Y,V,W) | product(X,W,U).
% 1029756 [binary:1029688,1029712] -sum(z,X,z) | sum(y_times_z,Y,y_times_z) | -product(y,X,Y).
% 1029889 [binary:1029673,1029687] -product(X,multiplicative_identity,Y) | equal(Y,X).
% 1029900 [binary:1029710,1029687] equal(X,multiply(Y,Z)) | -product(Z,Y,X).
% 1029909 [binary:1029673,1029694,cut:531213] -product(X,Y,Z) | sum(Z,X,X).
% 1029910 [binary:1029689,1029694] -sum(X,y_times_z,y_times_z) | sum(Y,x_times__y_times_z,x_times__y_times_z) | -product(x,X,Y).
% 1029911 [binary:1029690,1029694] -sum(X,y,y) | sum(Y,x_times_y,x_times_y) | -product(x,X,Y).
% 1029912 [binary:1029691,1029694] -sum(X,z,z) | sum(Y,x_times_y__times_z,x_times_y__times_z) | -product(x_times_y,X,Y).
% 1029961 [binary:1029672,1029699,cut:531213] -product(X,Y,Z) | sum(Z,Y,Y).
% 1029997 [binary:1029688,1029909] sum(y_times_z,y,y).
% 1030000 [binary:1029690,1029909] sum(x_times_y,x,x).
% 1030001 [binary:1029691,1029909] sum(x_times_y__times_z,x_times_y,x_times_y).
% 1030002 [binary:1029667,1029909] sum(multiply(X,Y),X,X).
% 1030003 [binary:1029706,1029909] sum(y_times_z,z,z).
% 1030004 [binary:1029707,1029909] sum(x_times__y_times_z,y_times_z,y_times_z).
% 1030005 [binary:1029708,1029909] sum(x_times_y,y,y).
% 1030006 [binary:1029709,1029909] sum(x_times_y__times_z,z,z).
% 1030036 [binary:1029668,1030000] sum(x,x_times_y,x).
% 1030040 [binary:1029668,1030001] sum(x_times_y,x_times_y__times_z,x_times_y).
% 1030044 [binary:1029668,1030003] sum(z,y_times_z,z).
% 1030055 [binary:1029668,1030004] sum(y_times_z,x_times__y_times_z,y_times_z).
% 1030059 [binary:1029668,1030005] sum(y,x_times_y,y).
% 1030063 [binary:1029668,1030006] sum(z,x_times_y__times_z,z).
% 1030084 [binary:1029756,1030063] -product(y,x_times_y__times_z,X) | sum(y_times_z,X,y_times_z).
% 1030219 [binary:1029667,1030084] sum(y_times_z,multiply(y,x_times_y__times_z),y_times_z).
% 1030228 [binary:1029668,1030219] sum(multiply(y,x_times_y__times_z),y_times_z,y_times_z).
% 1030267 [binary:1029672,1029738] product(multiplicative_identity,X,Y) | -sum(Z,U,X) | -sum(Z,U,Y).
% 1030319 [binary:1029666,1030267.2] product(multiplicative_identity,add(X,Y),Z) | -sum(X,Y,Z).
% 1030354 [binary:1029682,1029744] -sum(additive_identity,X,Y) | product(Z,multiplicative_identity,Y) | -product(Z,Z,X).
% 1030369 [binary:1030002,1029745] -product(X,Y,X) | -sum(Z,Y,U) | product(X,U,X).
% 1030702 [binary:1029670,1030354] product(X,multiplicative_identity,Y) | -product(X,X,Y).
% 1030705 [binary:1029667,1030702.2] product(X,multiplicative_identity,multiply(X,X)).
% 1030724 [binary:1029889,1030705] equal(multiply(X,X),X).
% 1030725 [para:1030724.1.1,1029667.1.3] product(X,X,X).
% 1030764 [binary:1030369,1030725] -sum(X,Y,Z) | product(Y,Z,Y).
% 1030790 [binary:1030040,1030764] product(x_times_y__times_z,x_times_y,x_times_y__times_z).
% 1030792 [binary:1030055,1030764] product(x_times__y_times_z,y_times_z,x_times__y_times_z).
% 1030895 [binary:1030369,1030790] product(x_times_y__times_z,X,x_times_y__times_z) | -sum(Y,x_times_y,X).
% 1030943 [binary:1030369,1030792] product(x_times__y_times_z,X,x_times__y_times_z) | -sum(Y,y_times_z,X).
% 1032009 [binary:1030036,1030895.2] product(x_times_y__times_z,x,x_times_y__times_z).
% 1032010 [binary:1030059,1030895.2] product(x_times_y__times_z,y,x_times_y__times_z).
% 1032030 [binary:1029900.2,1032009] equal(x_times_y__times_z,multiply(x,x_times_y__times_z)).
% 1032057 [binary:1029900.2,1032010] equal(x_times_y__times_z,multiply(y,x_times_y__times_z)).
% 1032493 [binary:1030044,1030943.2] product(x_times__y_times_z,z,x_times__y_times_z).
% 1032536 [binary:1029961,1032493] sum(x_times__y_times_z,z,z).
% 1034033 [binary:1030228,1029910,demod:1032057] -product(x,x_times_y__times_z,X) | sum(X,x_times__y_times_z,x_times__y_times_z).
% 1034042 [binary:1029997,1029911] -product(x,y_times_z,X) | sum(X,x_times_y,x_times_y).
% 1034058 [binary:1032536,1029912] -product(x_times_y,x_times__y_times_z,X) | sum(X,x_times_y__times_z,x_times_y__times_z).
% 1034161 [binary:1029667,1034033,demod:1032030] sum(x_times_y__times_z,x_times__y_times_z,x_times__y_times_z).
% 1034165 [binary:1029733.2,1034161] equal(x_times__y_times_z,add(x_times__y_times_z,x_times_y__times_z)).
% 1034443 [binary:1029689,1034042] sum(x_times__y_times_z,x_times_y,x_times_y).
% 1034444 [binary:1029668,1034443] sum(x_times_y,x_times__y_times_z,x_times_y).
% 1034455 [binary:1030764,1034444] product(x_times__y_times_z,x_times_y,x_times__y_times_z).
% 1034479 [binary:1029900.2,1034455] equal(x_times__y_times_z,multiply(x_times_y,x_times__y_times_z)).
% 1034681 [binary:1029667,1034058,demod:1034479] sum(x_times__y_times_z,x_times_y__times_z,x_times_y__times_z).
% 1034686 [binary:1030319.2,1034681,demod:1034165,cut:882468] 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 9
% clause depth limited to 2
% seconds given: 29
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 1056
% derived clauses: 5856048
% kept clauses: 8688
% kept size sum: 117870
% kept mid-nuclei: 1020908
% kept new demods: 123
% forw unit-subs: 4391288
% forw double-subs: 9493
% forw overdouble-subs: 7716
% backward subs: 21
% fast unit cutoff: 12884
% full unit cutoff: 4311
% dbl unit cutoff: 0
% real runtime : 59.46
% process. runtime: 58.79
% specific non-discr-tree subsumption statistics:
% tried: 3239831
% length fails: 72180
% strength fails: 1033311
% predlist fails: 104656
% aux str. fails: 511872
% by-lit fails: 13481
% full subs tried: 1492737
% full subs fail: 1484248
%
% ; 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/BOO/BOO007-1+eq_r.in")
%
%------------------------------------------------------------------------------