TSTP Solution File: SWV282-2 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : SWV282-2 : 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 : art08.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 29.8s
% Output : Assurance 29.8s
% 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/SystemOnTPTP21181/SWV/SWV282-2+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 11)
% (binary-unit 9 #f 4 11)
% (binary-double 9 #f 4 11)
% (binary-double 15 #f)
% (binary-double 15 #t)
% (binary 50 #t 4 11)
% (binary-order 25 #f 4 11)
% (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(15,40,0,30,0,0,16520,4,1890,26047,5,2504,26048,1,2504,26048,50,2505,26048,40,2505,26063,0,2505,42795,3,2956)
%
%
% START OF PROOF
% 26049 [] equal(X,X).
% 26050 [] equal(c_^binomial_^obinomial(X,c_^suc(c_0)),X).
% 26051 [] equal(c_^binomial_^obinomial(c_^suc(X),c_^suc(Y)),c_plus(c_^binomial_^obinomial(X,Y),c_^binomial_^obinomial(X,c_^suc(Y)),tc_nat)).
% 26052 [] equal(c_^binomial_^obinomial(X,c_0),c_1).
% 26053 [] equal(c_1,c_^suc(c_0)).
% 26054 [] -equal(c_minus(X,Y,tc_nat),c_0) | c_lessequals(X,Y,tc_nat).
% 26055 [] equal(c_minus(X,X,tc_nat),c_0).
% 26056 [] c_lessequals(X,c_plus(X,Y,tc_nat),tc_nat).
% 26057 [] c_less(X,c_^suc(X),tc_nat).
% 26058 [] c_less(X,c_^suc(Y),tc_nat) | -c_lessequals(X,Y,tc_nat).
% 26059 [] -c_lessequals(c_plus(X,Y,tc_nat),c_plus(X,Z,tc_nat),tc_nat) | c_lessequals(Y,Z,tc_nat).
% 26060 [] -c_less(c_plus(X,Y,tc_nat),Y,tc_nat).
% 26061 [] -c_in(c_^message_^omsg_^o^nonce(X),c_^event_^oused(Y),tc_^message_^omsg) | -c_lessequals(v_sko__ur^x(Y),X,tc_nat).
% 26063 [] c_in(c_^message_^omsg_^o^nonce(Z),c_^event_^oused(v_evs_^h),tc_^message_^omsg) | c_in(c_^message_^omsg_^o^nonce(X),c_^event_^oused(v_evs),tc_^message_^omsg) | c_in(c_^message_^omsg_^o^nonce(Y),c_^event_^oused(v_evs_^h_^h),tc_^message_^omsg) | equal(Z,Y) | equal(X,Z) | equal(X,Y).
% 26066 [para:26053.1.2,26050.1.1.2] equal(c_^binomial_^obinomial(X,c_1),X).
% 26067 [para:26053.1.2,26051.1.2.2.2,demod:26052,26066,26053] equal(c_^suc(X),c_plus(c_1,X,tc_nat)).
% 26068 [para:26050.1.1,26051.1.2.1,demod:26053] equal(c_^binomial_^obinomial(c_^suc(X),c_^suc(c_1)),c_plus(X,c_^binomial_^obinomial(X,c_^suc(c_1)),tc_nat)).
% 26072 [para:26067.1.2,26060.1.1] -c_less(c_^suc(X),X,tc_nat).
% 26076 [para:26055.1.1,26054.1.1,cut:26049] c_lessequals(X,X,tc_nat).
% 26079 [binary:26056,26058.2] c_less(X,c_^suc(c_plus(X,Y,tc_nat)),tc_nat).
% 26080 [binary:26060,26058] -c_lessequals(c_plus(X,c_^suc(Y),tc_nat),Y,tc_nat).
% 26081 [binary:26072,26058] -c_lessequals(c_^suc(c_^suc(X)),X,tc_nat).
% 26089 [para:26067.1.2,26059.1.1,demod:26067] -c_lessequals(c_^suc(X),c_^suc(Y),tc_nat) | c_lessequals(X,Y,tc_nat).
% 26090 [binary:26081,26059.2] -c_lessequals(c_plus(X,c_^suc(c_^suc(Y)),tc_nat),c_plus(X,Y,tc_nat),tc_nat).
% 26096 [para:26053.1.2,26080.1.1.2] -c_lessequals(c_plus(X,c_1,tc_nat),c_0,tc_nat).
% 26102 [binary:26056,26061.2] -c_in(c_^message_^omsg_^o^nonce(c_plus(v_sko__ur^x(X),Y,tc_nat)),c_^event_^oused(X),tc_^message_^omsg).
% 26103 [binary:26076,26061.2] -c_in(c_^message_^omsg_^o^nonce(v_sko__ur^x(X)),c_^event_^oused(X),tc_^message_^omsg).
% 26104 [binary:26063,26103] c_in(c_^message_^omsg_^o^nonce(X),c_^event_^oused(v_evs),tc_^message_^omsg) | c_in(c_^message_^omsg_^o^nonce(Y),c_^event_^oused(v_evs_^h_^h),tc_^message_^omsg) | equal(X,v_sko__ur^x(v_evs_^h)) | equal(v_sko__ur^x(v_evs_^h),Y) | equal(X,Y).
% 26105 [binary:26063.2,26103] c_in(c_^message_^omsg_^o^nonce(X),c_^event_^oused(v_evs_^h),tc_^message_^omsg) | c_in(c_^message_^omsg_^o^nonce(Y),c_^event_^oused(v_evs_^h_^h),tc_^message_^omsg) | equal(v_sko__ur^x(v_evs),X) | equal(v_sko__ur^x(v_evs),Y) | equal(X,Y).
% 26109 [binary:26103,26104] equal(v_sko__ur^x(v_evs),v_sko__ur^x(v_evs_^h)) | c_in(c_^message_^omsg_^o^nonce(X),c_^event_^oused(v_evs_^h_^h),tc_^message_^omsg) | equal(v_sko__ur^x(v_evs_^h),X) | equal(v_sko__ur^x(v_evs),X).
% 26110 [binary:26103,26104.2] equal(v_sko__ur^x(v_evs_^h),v_sko__ur^x(v_evs_^h_^h)) | c_in(c_^message_^omsg_^o^nonce(X),c_^event_^oused(v_evs),tc_^message_^omsg) | equal(X,v_sko__ur^x(v_evs_^h_^h)) | equal(X,v_sko__ur^x(v_evs_^h)).
% 26122 [para:26068.1.2,26079.1.2.1] c_less(X,c_^suc(c_^binomial_^obinomial(c_^suc(X),c_^suc(c_1))),tc_nat).
% 26137 [binary:26096,26089.2,demod:26053] -c_lessequals(c_^suc(c_plus(X,c_1,tc_nat)),c_1,tc_nat).
% 26143 [binary:26059.2,26137] -c_lessequals(c_plus(X,c_^suc(c_plus(Y,c_1,tc_nat)),tc_nat),c_plus(X,c_1,tc_nat),tc_nat).
% 26149 [binary:26104,26102] equal(c_plus(v_sko__ur^x(v_evs),X,tc_nat),v_sko__ur^x(v_evs_^h)) | equal(c_plus(v_sko__ur^x(v_evs),X,tc_nat),Y) | c_in(c_^message_^omsg_^o^nonce(Y),c_^event_^oused(v_evs_^h_^h),tc_^message_^omsg) | equal(v_sko__ur^x(v_evs_^h),Y).
% 26154 [binary:26109.2,26102] equal(v_sko__ur^x(v_evs),v_sko__ur^x(v_evs_^h)) | equal(v_sko__ur^x(v_evs_^h),c_plus(v_sko__ur^x(v_evs_^h_^h),X,tc_nat)) | equal(v_sko__ur^x(v_evs),c_plus(v_sko__ur^x(v_evs_^h_^h),X,tc_nat)).
% 26283 [binary:26103,26105.2] equal(v_sko__ur^x(v_evs),v_sko__ur^x(v_evs_^h_^h)) | c_in(c_^message_^omsg_^o^nonce(X),c_^event_^oused(v_evs_^h),tc_^message_^omsg) | equal(X,v_sko__ur^x(v_evs_^h_^h)) | equal(v_sko__ur^x(v_evs),X).
% 26287 [binary:26102,26105] equal(v_sko__ur^x(v_evs),c_plus(v_sko__ur^x(v_evs_^h),X,tc_nat)) | equal(c_plus(v_sko__ur^x(v_evs_^h),X,tc_nat),Y) | c_in(c_^message_^omsg_^o^nonce(Y),c_^event_^oused(v_evs_^h_^h),tc_^message_^omsg) | equal(v_sko__ur^x(v_evs),Y).
% 26333 [binary:26102,26110.2] equal(v_sko__ur^x(v_evs_^h),v_sko__ur^x(v_evs_^h_^h)) | equal(c_plus(v_sko__ur^x(v_evs),X,tc_nat),v_sko__ur^x(v_evs_^h_^h)) | equal(c_plus(v_sko__ur^x(v_evs),X,tc_nat),v_sko__ur^x(v_evs_^h)).
% 26344 [binary:26102,26283.2] equal(v_sko__ur^x(v_evs),v_sko__ur^x(v_evs_^h_^h)) | equal(c_plus(v_sko__ur^x(v_evs_^h),X,tc_nat),v_sko__ur^x(v_evs_^h_^h)) | equal(v_sko__ur^x(v_evs),c_plus(v_sko__ur^x(v_evs_^h),X,tc_nat)).
% 26590 [para:26154.2.2,26060.1.1] equal(v_sko__ur^x(v_evs),v_sko__ur^x(v_evs_^h)) | equal(v_sko__ur^x(v_evs),c_plus(v_sko__ur^x(v_evs_^h_^h),X,tc_nat)) | -c_less(v_sko__ur^x(v_evs_^h),X,tc_nat).
% 26720 [para:26590.2.2,26143.1.1,slowcut:26079] -c_lessequals(v_sko__ur^x(v_evs),c_plus(v_sko__ur^x(v_evs_^h_^h),c_1,tc_nat),tc_nat) | equal(v_sko__ur^x(v_evs),v_sko__ur^x(v_evs_^h)).
% 27069 [para:26149.1.1,26060.1.1] equal(c_plus(v_sko__ur^x(v_evs),X,tc_nat),Y) | c_in(c_^message_^omsg_^o^nonce(Y),c_^event_^oused(v_evs_^h_^h),tc_^message_^omsg) | -c_less(v_sko__ur^x(v_evs_^h),X,tc_nat) | equal(v_sko__ur^x(v_evs_^h),Y).
% 28306 [para:26333.2.1,26060.1.1] equal(v_sko__ur^x(v_evs_^h),v_sko__ur^x(v_evs_^h_^h)) | equal(c_plus(v_sko__ur^x(v_evs),X,tc_nat),v_sko__ur^x(v_evs_^h)) | -c_less(v_sko__ur^x(v_evs_^h_^h),X,tc_nat).
% 28397 [binary:26057,28306.3] equal(c_plus(v_sko__ur^x(v_evs),c_^suc(v_sko__ur^x(v_evs_^h_^h)),tc_nat),v_sko__ur^x(v_evs_^h)) | equal(v_sko__ur^x(v_evs_^h),v_sko__ur^x(v_evs_^h_^h)).
% 28504 [para:28397.1.1,26080.1.1] -c_lessequals(v_sko__ur^x(v_evs_^h),v_sko__ur^x(v_evs_^h_^h),tc_nat) | equal(v_sko__ur^x(v_evs_^h),v_sko__ur^x(v_evs_^h_^h)).
% 28512 [para:28504.2.2,26102.1.1.1.1] -c_lessequals(v_sko__ur^x(v_evs_^h),v_sko__ur^x(v_evs_^h_^h),tc_nat) | -c_in(c_^message_^omsg_^o^nonce(c_plus(v_sko__ur^x(v_evs_^h),X,tc_nat)),c_^event_^oused(v_evs_^h_^h),tc_^message_^omsg).
% 29527 [para:26344.2.1,26060.1.1] equal(v_sko__ur^x(v_evs),v_sko__ur^x(v_evs_^h_^h)) | equal(v_sko__ur^x(v_evs),c_plus(v_sko__ur^x(v_evs_^h),X,tc_nat)) | -c_less(v_sko__ur^x(v_evs_^h_^h),X,tc_nat).
% 29632 [para:29527.2.2,26080.1.1] equal(v_sko__ur^x(v_evs),v_sko__ur^x(v_evs_^h_^h)) | -c_less(v_sko__ur^x(v_evs_^h_^h),c_^suc(X),tc_nat) | -c_lessequals(v_sko__ur^x(v_evs),X,tc_nat).
% 29761 [binary:26079,29632.2] equal(v_sko__ur^x(v_evs),v_sko__ur^x(v_evs_^h_^h)) | -c_lessequals(v_sko__ur^x(v_evs),c_plus(v_sko__ur^x(v_evs_^h_^h),X,tc_nat),tc_nat).
% 32113 [para:27069.1.1,26056.1.2,slowcut:26122] c_in(c_^message_^omsg_^o^nonce(X),c_^event_^oused(v_evs_^h_^h),tc_^message_^omsg) | c_lessequals(v_sko__ur^x(v_evs),X,tc_nat) | equal(v_sko__ur^x(v_evs_^h),X).
% 32145 [para:27069.1.1,26143.1.1,slowcut:26079] -c_lessequals(X,c_plus(v_sko__ur^x(v_evs),c_1,tc_nat),tc_nat) | c_in(c_^message_^omsg_^o^nonce(X),c_^event_^oused(v_evs_^h_^h),tc_^message_^omsg) | equal(v_sko__ur^x(v_evs_^h),X).
% 32166 [binary:26102,32113] c_lessequals(v_sko__ur^x(v_evs),c_plus(v_sko__ur^x(v_evs_^h_^h),X,tc_nat),tc_nat) | equal(v_sko__ur^x(v_evs_^h),c_plus(v_sko__ur^x(v_evs_^h_^h),X,tc_nat)).
% 32200 [para:32166.2.2,26060.1.1] c_lessequals(v_sko__ur^x(v_evs),c_plus(v_sko__ur^x(v_evs_^h_^h),X,tc_nat),tc_nat) | -c_less(v_sko__ur^x(v_evs_^h),X,tc_nat).
% 32249 [binary:26057,32200.2] c_lessequals(v_sko__ur^x(v_evs),c_plus(v_sko__ur^x(v_evs_^h_^h),c_^suc(v_sko__ur^x(v_evs_^h)),tc_nat),tc_nat).
% 32519 [binary:29761.2,32249] equal(v_sko__ur^x(v_evs),v_sko__ur^x(v_evs_^h_^h)).
% 32624 [para:32519.1.2,26720.1.2.1,cut:26056] equal(v_sko__ur^x(v_evs),v_sko__ur^x(v_evs_^h)).
% 32632 [para:32519.1.2,28512.1.2,demod:32624,cut:26076] -c_in(c_^message_^omsg_^o^nonce(c_plus(v_sko__ur^x(v_evs_^h),X,tc_nat)),c_^event_^oused(v_evs_^h_^h),tc_^message_^omsg).
% 33037 [binary:26076,32145,demod:32624,cut:32632] equal(v_sko__ur^x(v_evs_^h),c_plus(v_sko__ur^x(v_evs_^h),c_1,tc_nat)).
% 33040 [binary:26102,32145.2,demod:33037,32624,32519] -c_lessequals(c_plus(v_sko__ur^x(v_evs_^h),X,tc_nat),v_sko__ur^x(v_evs_^h),tc_nat) | equal(v_sko__ur^x(v_evs_^h),c_plus(v_sko__ur^x(v_evs_^h),X,tc_nat)).
% 34051 [para:33040.2.2,26090.1.1,cut:26056] -c_lessequals(c_plus(v_sko__ur^x(v_evs_^h),c_^suc(c_^suc(X)),tc_nat),v_sko__ur^x(v_evs_^h),tc_nat).
% 34115 [para:26287.1.2,34051.1.1,demod:32624,cut:26076] equal(c_plus(v_sko__ur^x(v_evs_^h),c_^suc(c_^suc(X)),tc_nat),Y) | c_in(c_^message_^omsg_^o^nonce(Y),c_^event_^oused(v_evs_^h_^h),tc_^message_^omsg) | equal(v_sko__ur^x(v_evs_^h),Y).
% 39247 [para:34115.1.1,26090.1.1] -c_lessequals(X,c_plus(v_sko__ur^x(v_evs_^h),Y,tc_nat),tc_nat) | c_in(c_^message_^omsg_^o^nonce(X),c_^event_^oused(v_evs_^h_^h),tc_^message_^omsg) | equal(v_sko__ur^x(v_evs_^h),X).
% 42971 [binary:26076,39247,cut:32632] equal(v_sko__ur^x(v_evs_^h),c_plus(v_sko__ur^x(v_evs_^h),X,tc_nat)).
% 42973 [para:42971.1.2,26060.1.1,slowcut:26122] 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
% clause length limited to 11
% clause depth limited to 4
% seconds given: 9
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 2295
% derived clauses: 164859
% kept clauses: 33292
% kept size sum: 398772
% kept mid-nuclei: 1806
% kept new demods: 25
% forw unit-subs: 21531
% forw double-subs: 3476
% forw overdouble-subs: 25611
% backward subs: 1270
% fast unit cutoff: 480
% full unit cutoff: 32
% dbl unit cutoff: 144
% real runtime : 30.76
% process. runtime: 30.55
% specific non-discr-tree subsumption statistics:
% tried: 15047733
% length fails: 655003
% strength fails: 1987188
% predlist fails: 5122302
% aux str. fails: 25126
% by-lit fails: 2308683
% full subs tried: 4388323
% full subs fail: 4363759
%
% ; program args: ("/home/graph/tptp/Systems/Gandalf---c-2.6/gandalf" "-time" "600" "/tmp/SystemOnTPTP21181/SWV/SWV282-2+eq_r.in")
% WARNING: TreeLimitedRun lost 29.83s, total lost is 29.83s
%
%------------------------------------------------------------------------------