TSTP Solution File: SET861-2 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : SET861-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art10.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% Result : Unsatisfiable 353.9s
% Output : Assurance 353.9s
% 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: /tmp/SystemOnTPTP6538/SET/SET861-2+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: neq
% detected subclass: medium
%
% strategies selected:
% (hyper 25 #f 4 9)
% (binary-unit 9 #f 4 9)
% (binary-double 9 #f 4 9)
% (binary-double 15 #f)
% (binary-double 15 #t)
% (binary 50 #t 4 9)
% (binary-order 25 #f 4 9)
% (binary-posweight-order 101 #f)
% (binary-posweight-lex-big-order 25 #f)
% (binary-posweight-lex-small-order 9 #f)
% (binary-order-sos 50 #t)
% (binary-unit-uniteq 25 #f)
% (binary-weightorder 50 #f)
% (binary-order 50 #f)
% (hyper-order 30 #f)
% (binary 112 #t)
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(16,40,0,32,0,0,24373,4,2057,34970,5,2501,34970,1,2501,34970,50,2501,34970,40,2501,34986,0,2501,35063,50,2501,35079,0,2501,35331,50,2503,35347,0,2507,35814,50,2510,35830,0,2510,36636,50,2515,36652,0,2515,37981,50,2526,37997,0,2530,40077,50,2556,40093,0,2556,43196,50,2632,43212,0,2637,47654,50,2823,47670,0,2823,52926,3,3074,53781,4,3199,53811,50,3219,53811,40,3219,53827,0,3219,68332,3,3670,69816,4,3895,71070,5,4120,71070,1,4120,71070,50,4120,71070,40,4120,71086,0,4120,110589,3,4871,123801,4,5246,134584,5,5621,134585,5,5622,134585,1,5622,134585,50,5625,134585,40,5625,134601,0,5625,173088,3,6376,188244,4,6751,204898,5,7126,204899,5,7126,204900,1,7126,204900,50,7128,204900,40,7128,204916,0,7128,265479,3,9633,266709,4,10879,267863,1,12129,267863,50,12131,267863,40,12131,267879,0,12131,303012,3,13395,303983,4,14007,306422,5,14632,306423,5,14632,306423,1,14632,306423,50,14633,306423,40,14633,306439,0,14633,559230,3,19689,570359,4,22209,581519,1,24734,581519,50,24734,581519,40,24734,581535,0,24734,633578,3,25987,635989,4,26610,637735,1,27235,637735,50,27236,637735,40,27236,637751,0,27236,666759,3,27724,667387,4,27912,668303,5,28137,668304,5,28137,668304,1,28137,668304,50,28137,668304,40,28137,668320,0,28138,712161,3,30764,721495,4,31889,794501,5,33139,794502,5,33139,794502,1,33139,794502,50,33140,794502,40,33140,794518,0,33140,809241,3,34391,812419,4,35016,816086,5,35641,816086,5,35641,816087,1,35641,816087,50,35642,816087,40,35642,816103,0,35642)
%
%
% START OF PROOF
% 794539 [?] ?
% 816089 [] -c_lessequals(Y,X,tc_set(Z)) | -c_lessequals(X,Y,tc_set(Z)) | equal(Y,X).
% 816090 [] -c_lessequals(X,Y,tc_set(Z)) | -c_in(U,X,Z) | c_in(U,Y,Z).
% 816091 [] c_in(c_^main_^osubset^i__1(X,Y,Z),X,Z) | c_lessequals(X,Y,tc_set(Z)).
% 816092 [] -c_in(c_^main_^osubset^i__1(X,Y,Z),Y,Z) | c_lessequals(X,Y,tc_set(Z)).
% 816093 [] c_in(c_union(c_insert(X,c_emptyset,tc_set(Y)),Z,tc_set(Y)),c_^zorn_^ochain(U,Y),tc_set(tc_set(Y))) | -c_in(Z,c_^zorn_^ochain(U,Y),tc_set(tc_set(Y))) | c_in(c_^zorn_^ochain__extend__1(Z,X,Y),Z,tc_set(Y)) | -c_in(X,U,tc_set(Y)).
% 816094 [] c_in(c_union(c_insert(X,c_emptyset,tc_set(Y)),Z,tc_set(Y)),c_^zorn_^ochain(U,Y),tc_set(tc_set(Y))) | -c_in(Z,c_^zorn_^ochain(U,Y),tc_set(tc_set(Y))) | -c_lessequals(c_^zorn_^ochain__extend__1(Z,X,Y),X,tc_set(Y)) | -c_in(X,U,tc_set(Y)).
% 816095 [] c_in(c_^zorn_^o^hausdorff__1(X,Y),c_^zorn_^omaxchain(X,Y),tc_set(tc_set(Y))).
% 816096 [] c_lessequals(c_^zorn_^omaxchain(X,Y),c_^zorn_^ochain(X,Y),tc_set(tc_set(tc_set(Y)))).
% 816097 [] -c_in(c_union(c_insert(X,c_emptyset,tc_set(Y)),Z,tc_set(Y)),c_^zorn_^ochain(U,Y),tc_set(tc_set(Y))) | -c_in(Z,c_^zorn_^omaxchain(U,Y),tc_set(tc_set(Y))) | c_in(c_^zorn_^omaxchain__super__lemma__1(Z,V,Y),Z,tc_set(Y)) | -c_in(W,X,Y) | c_in(W,V,Y).
% 816098 [] -c_in(c_union(c_insert(X,c_emptyset,tc_set(Y)),Z,tc_set(Y)),c_^zorn_^ochain(U,Y),tc_set(tc_set(Y))) | -c_in(Z,c_^zorn_^omaxchain(U,Y),tc_set(tc_set(Y))) | -c_lessequals(c_^zorn_^omaxchain__super__lemma__1(Z,V,Y),V,tc_set(Y)) | -c_in(W,X,Y) | c_in(W,V,Y).
% 816099 [] -c_in(X,c_^zorn_^ochain(v_^s,t_a),tc_set(tc_set(t_a))) | c_in(v_x(X),v_^s,tc_set(t_a)).
% 816101 [] c_lessequals(X,v_xa(X),tc_set(t_a)) | -c_in(X,v_^s,tc_set(t_a)).
% 816102 [] -c_in(X,v_^s,tc_set(t_a)) | -equal(X,v_xa(X)).
% 816103 [] -c_in(X,c_^zorn_^ochain(v_^s,t_a),tc_set(tc_set(t_a))) | c_lessequals(Y,v_x(X),tc_set(t_a)) | -c_in(Y,X,tc_set(t_a)).
% 816120 [binary:816101,816089] -c_lessequals(v_xa(X),X,tc_set(t_a)) | -c_in(X,v_^s,tc_set(t_a)) | equal(X,v_xa(X)).
% 816122 [binary:816096,816090] -c_in(X,c_^zorn_^omaxchain(Y,Z),tc_set(tc_set(Z))) | c_in(X,c_^zorn_^ochain(Y,Z),tc_set(tc_set(Z))).
% 816123 [binary:816101,816090] -c_in(X,v_^s,tc_set(t_a)) | c_in(Y,v_xa(X),t_a) | -c_in(Y,X,t_a).
% 816132 [binary:816095,816122] c_in(c_^zorn_^o^hausdorff__1(X,Y),c_^zorn_^ochain(X,Y),tc_set(tc_set(Y))).
% 816134 [binary:816099,816132] c_in(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),v_^s,tc_set(t_a)).
% 816135 [binary:816103,816132] c_lessequals(X,v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),tc_set(t_a)) | -c_in(X,c_^zorn_^o^hausdorff__1(v_^s,t_a),tc_set(t_a)).
% 816136 [binary:816102,816134] -equal(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)))).
% 816137 [binary:816123,816134] c_in(X,v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),t_a) | -c_in(X,v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),t_a).
% 816140 [binary:816090,816135] c_in(X,v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),t_a) | -c_in(Y,c_^zorn_^o^hausdorff__1(v_^s,t_a),tc_set(t_a)) | -c_in(X,Y,t_a).
% 816146 [binary:816092,816137] -c_in(c_^main_^osubset^i__1(X,v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),t_a),v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),t_a) | c_lessequals(X,v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),tc_set(t_a)).
% 816153 [binary:816093,816097] -c_in(X,c_^zorn_^ochain(Y,Z),tc_set(tc_set(Z))) | -c_in(X,c_^zorn_^omaxchain(Y,Z),tc_set(tc_set(Z))) | c_in(c_^zorn_^ochain__extend__1(X,V,Z),X,tc_set(Z)) | c_in(c_^zorn_^omaxchain__super__lemma__1(X,U,Z),X,tc_set(Z)) | -c_in(V,Y,tc_set(Z)) | -c_in(W,V,Z) | c_in(W,U,Z).
% 816154 [binary:816094,816097] -c_in(X,c_^zorn_^ochain(Y,Z),tc_set(tc_set(Z))) | -c_in(X,c_^zorn_^omaxchain(Y,Z),tc_set(tc_set(Z))) | -c_lessequals(c_^zorn_^ochain__extend__1(X,U,Z),U,tc_set(Z)) | c_in(c_^zorn_^omaxchain__super__lemma__1(X,V,Z),X,tc_set(Z)) | -c_in(U,Y,tc_set(Z)) | -c_in(W,U,Z) | c_in(W,V,Z).
% 816169 [binary:816093,816098] -c_in(X,c_^zorn_^ochain(Y,Z),tc_set(tc_set(Z))) | -c_in(X,c_^zorn_^omaxchain(Y,Z),tc_set(tc_set(Z))) | -c_lessequals(c_^zorn_^omaxchain__super__lemma__1(X,U,Z),U,tc_set(Z)) | c_in(c_^zorn_^ochain__extend__1(X,V,Z),X,tc_set(Z)) | -c_in(V,Y,tc_set(Z)) | -c_in(W,V,Z) | c_in(W,U,Z).
% 816170 [binary:816094,816098] -c_in(X,c_^zorn_^ochain(Y,Z),tc_set(tc_set(Z))) | -c_in(X,c_^zorn_^omaxchain(Y,Z),tc_set(tc_set(Z))) | -c_lessequals(c_^zorn_^ochain__extend__1(X,V,Z),V,tc_set(Z)) | -c_lessequals(c_^zorn_^omaxchain__super__lemma__1(X,U,Z),U,tc_set(Z)) | -c_in(V,Y,tc_set(Z)) | -c_in(W,V,Z) | c_in(W,U,Z).
% 816176 [binary:816091,816146] c_lessequals(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),tc_set(t_a)).
% 816177 [binary:816140,816146] -c_in(c_^main_^osubset^i__1(X,v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),t_a),Y,t_a) | c_lessequals(X,v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),tc_set(t_a)) | -c_in(Y,c_^zorn_^o^hausdorff__1(v_^s,t_a),tc_set(t_a)).
% 816178 [binary:816089,816176,cut:816136] -c_lessequals(v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),tc_set(t_a)).
% 816264 [binary:816132,816153,cut:816095] c_in(c_^zorn_^ochain__extend__1(c_^zorn_^o^hausdorff__1(X,Y),Z,Y),c_^zorn_^o^hausdorff__1(X,Y),tc_set(Y)) | c_in(c_^zorn_^omaxchain__super__lemma__1(c_^zorn_^o^hausdorff__1(X,Y),U,Y),c_^zorn_^o^hausdorff__1(X,Y),tc_set(Y)) | -c_in(Z,X,tc_set(Y)) | -c_in(V,Z,Y) | c_in(V,U,Y).
% 816274 [binary:816091,816177] c_lessequals(X,v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),tc_set(t_a)) | -c_in(X,c_^zorn_^o^hausdorff__1(v_^s,t_a),tc_set(t_a)).
% 816289 [binary:816132,816154,cut:816095] c_in(c_^zorn_^omaxchain__super__lemma__1(c_^zorn_^o^hausdorff__1(X,Y),Z,Y),c_^zorn_^o^hausdorff__1(X,Y),tc_set(Y)) | -c_lessequals(c_^zorn_^ochain__extend__1(c_^zorn_^o^hausdorff__1(X,Y),U,Y),U,tc_set(Y)) | -c_in(U,X,tc_set(Y)) | -c_in(V,U,Y) | c_in(V,Z,Y).
% 816343 [binary:816132,816169,cut:816095] c_in(c_^zorn_^ochain__extend__1(c_^zorn_^o^hausdorff__1(X,Y),Z,Y),c_^zorn_^o^hausdorff__1(X,Y),tc_set(Y)) | -c_lessequals(c_^zorn_^omaxchain__super__lemma__1(c_^zorn_^o^hausdorff__1(X,Y),U,Y),U,tc_set(Y)) | -c_in(Z,X,tc_set(Y)) | -c_in(V,Z,Y) | c_in(V,U,Y).
% 816360 [binary:816132,816170,cut:816095] -c_lessequals(c_^zorn_^ochain__extend__1(c_^zorn_^o^hausdorff__1(X,Y),Z,Y),Z,tc_set(Y)) | -c_lessequals(c_^zorn_^omaxchain__super__lemma__1(c_^zorn_^o^hausdorff__1(X,Y),U,Y),U,tc_set(Y)) | -c_in(Z,X,tc_set(Y)) | -c_in(V,Z,Y) | c_in(V,U,Y).
% 816594 [binary:816274,816360] -c_in(c_^zorn_^ochain__extend__1(c_^zorn_^o^hausdorff__1(X,t_a),v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),t_a),c_^zorn_^o^hausdorff__1(v_^s,t_a),tc_set(t_a)) | -c_in(v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),X,tc_set(t_a)) | -c_in(Y,v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),t_a) | -c_lessequals(c_^zorn_^omaxchain__super__lemma__1(c_^zorn_^o^hausdorff__1(X,t_a),Z,t_a),Z,tc_set(t_a)) | c_in(Y,Z,t_a).
% 819444 [binary:816343,816594,cut:794539,factor:factor:factor] -c_in(X,v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),t_a) | -c_lessequals(c_^zorn_^omaxchain__super__lemma__1(c_^zorn_^o^hausdorff__1(v_^s,t_a),Y,t_a),Y,tc_set(t_a)) | c_in(X,Y,t_a).
% 819446 [binary:816091,819444] c_in(c_^main_^osubset^i__1(v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),X,t_a),Y,t_a) | c_lessequals(v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),X,tc_set(t_a)) | -c_lessequals(c_^zorn_^omaxchain__super__lemma__1(c_^zorn_^o^hausdorff__1(v_^s,t_a),Y,t_a),Y,tc_set(t_a)).
% 819455 [binary:816092,819446] c_lessequals(v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),X,tc_set(t_a)) | -c_lessequals(c_^zorn_^omaxchain__super__lemma__1(c_^zorn_^o^hausdorff__1(v_^s,t_a),X,t_a),X,tc_set(t_a)).
% 819535 [binary:816120,819455,cut:816134,cut:816136] -c_lessequals(c_^zorn_^omaxchain__super__lemma__1(c_^zorn_^o^hausdorff__1(v_^s,t_a),v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),t_a),v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),tc_set(t_a)).
% 819536 [binary:816135,819535] -c_in(c_^zorn_^omaxchain__super__lemma__1(c_^zorn_^o^hausdorff__1(v_^s,t_a),v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),t_a),c_^zorn_^o^hausdorff__1(v_^s,t_a),tc_set(t_a)).
% 819537 [binary:816289,819536] -c_lessequals(c_^zorn_^ochain__extend__1(c_^zorn_^o^hausdorff__1(v_^s,t_a),X,t_a),X,tc_set(t_a)) | c_in(Y,v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),t_a) | -c_in(X,v_^s,tc_set(t_a)) | -c_in(Y,X,t_a).
% 819549 [binary:816274,819537,cut:794539] -c_in(c_^zorn_^ochain__extend__1(c_^zorn_^o^hausdorff__1(v_^s,t_a),v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),t_a),c_^zorn_^o^hausdorff__1(v_^s,t_a),tc_set(t_a)) | -c_in(X,v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),t_a) | c_in(X,v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),t_a).
% 819591 [binary:816264,819549,cut:794539,factor:factor:cut:819536] -c_in(X,v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),t_a) | c_in(X,v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),t_a).
% 819593 [binary:816091,819591] c_in(c_^main_^osubset^i__1(v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),X,t_a),v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a)),t_a) | c_lessequals(v_xa(v_x(c_^zorn_^o^hausdorff__1(v_^s,t_a))),X,tc_set(t_a)).
% 819596 [binary:816092,819593,cut:816178] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% using weight-order 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
% seconds given: 50
%
%
% old unit clauses discarded
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 39978
% derived clauses: 1807505
% kept clauses: 328066
% kept size sum: 0
% kept mid-nuclei: 106838
% kept new demods: 0
% forw unit-subs: 269775
% forw double-subs: 195790
% forw overdouble-subs: 305212
% backward subs: 1253
% fast unit cutoff: 110099
% full unit cutoff: 0
% dbl unit cutoff: 4717
% real runtime : 358.48
% process. runtime: 357.4
% specific non-discr-tree subsumption statistics:
% tried: 97407393
% length fails: 2321891
% strength fails: 12168348
% predlist fails: 52117060
% aux str. fails: 1953217
% by-lit fails: 5070611
% full subs tried: 22473058
% full subs fail: 22165221
%
% ; program args: ("/home/graph/tptp/Systems/Gandalf---c-2.6/gandalf" "-time" "600" "/tmp/SystemOnTPTP6538/SET/SET861-2+eq_r.in")
% WARNING: TreeLimitedRun lost 353.87s, total lost is 353.87s
%
%------------------------------------------------------------------------------