TSTP Solution File: PUZ062-2 by Gandalf---c-2.6
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%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : PUZ062-2 : 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 : art02.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 14.8s
% Output : Assurance 14.8s
% 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/SystemOnTPTP21563/PUZ/PUZ062-2+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 6 5)
% (binary-unit 9 #f 6 5)
% (binary-double 9 #f 6 5)
% (binary-double 15 #f)
% (binary-double 15 #t)
% (binary 50 #t 6 5)
% (binary-order 25 #f 6 5)
% (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(14,40,0,28,0,0,98657,4,1879)
%
%
% START OF PROOF
% 15 [] equal(X,X).
% 16 [] equal(c_^finite__^set_^ocard(c_insert(X,Y,Z),Z),c_^suc(c_^finite__^set_^ocard(Y,Z))) | -c_in(Y,c_^finite__^set_^o^finites,tc_set(Z)) | c_in(X,Y,Z).
% 17 [] c_in(c_inter(X,Y,Z),c_^finite__^set_^o^finites,tc_set(Z)) | -c_in(Y,c_^finite__^set_^o^finites,tc_set(Z)).
% 18 [] -c_in(X,c_^mutil_^otiling(c_^mutil_^odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) | c_in(X,c_^finite__^set_^o^finites,tc_set(tc_prod(tc_nat,tc_nat))).
% 19 [] -c_in(X,c_inter(Y,Z,U),U) | c_in(X,Z,U).
% 20 [] c_in(X,c_inter(Y,Z,U),U) | -c_in(X,Y,U) | -c_in(X,Z,U).
% 21 [] c_in(X,c_insert(X,Y,Z),Z).
% 22 [] -c_in(X,c_emptyset,Y).
% 23 [] c_in(v_t,c_^mutil_^otiling(c_^mutil_^odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))).
% 24 [] equal(c_^finite__^set_^ocard(c_inter(c_^mutil_^ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),c_^finite__^set_^ocard(c_inter(c_^mutil_^ocoloured(c_^suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))).
% 25 [] equal(c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)),c_emptyset).
% 26 [] equal(c_inter(c_^mutil_^ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),c_insert(c_^pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat))).
% 27 [] equal(c_inter(c_^mutil_^ocoloured(c_^suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)),c_insert(c_^pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat))).
% 28 [] -equal(c_^finite__^set_^ocard(c_insert(c_^pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_^mutil_^ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),c_^finite__^set_^ocard(c_insert(c_^pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_^mutil_^ocoloured(c_^suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))).
% 33 [hyper:18,23] c_in(v_t,c_^finite__^set_^o^finites,tc_set(tc_prod(tc_nat,tc_nat))).
% 40 [hyper:17,33] c_in(c_inter(X,v_t,tc_prod(tc_nat,tc_nat)),c_^finite__^set_^o^finites,tc_set(tc_prod(tc_nat,tc_nat))).
% 48 [hyper:16,40] equal(c_^finite__^set_^ocard(c_insert(X,c_inter(Y,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),c_^suc(c_^finite__^set_^ocard(c_inter(Y,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))) | c_in(X,c_inter(Y,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)).
% 134 [para:26.1.2,21.1.2] c_in(c_^pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_^mutil_^ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)).
% 137 [hyper:19,134] c_in(c_^pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)).
% 179 [para:27.1.2,21.1.2] c_in(c_^pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_^mutil_^ocoloured(c_^suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)).
% 215 [hyper:19,179] c_in(c_^pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)).
% 725 [hyper:19,48] equal(c_^finite__^set_^ocard(c_insert(X,c_inter(Y,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),c_^suc(c_^finite__^set_^ocard(c_inter(Y,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))) | c_in(X,v_t,tc_prod(tc_nat,tc_nat)).
% 2543 [hyper:20,725,137,demod:25,cut:22] equal(c_^finite__^set_^ocard(c_insert(c_^pair(v_i,v_j,tc_nat,tc_nat),c_inter(X,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),c_^suc(c_^finite__^set_^ocard(c_inter(X,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))).
% 2545 [hyper:20,725,215,demod:25,cut:22] equal(c_^finite__^set_^ocard(c_insert(c_^pair(v_m,v_n,tc_nat,tc_nat),c_inter(X,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),c_^suc(c_^finite__^set_^ocard(c_inter(X,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))).
% 99301 [para:2545.1.1,28.1.2,demod:24,2543,cut:15] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 5
% clause depth limited to 6
% seconds given: 25
%
%
% old unit clauses discarded
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 2257
% derived clauses: 564588
% kept clauses: 29198
% kept size sum: 0
% kept mid-nuclei: 1944
% kept new demods: 15
% forw unit-subs: 96625
% forw double-subs: 3572
% forw overdouble-subs: 883
% backward subs: 47
% fast unit cutoff: 651
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 19.24
% process. runtime: 19.5
% specific non-discr-tree subsumption statistics:
% tried: 22820
% length fails: 2
% strength fails: 36
% predlist fails: 182
% aux str. fails: 0
% by-lit fails: 77
% full subs tried: 22143
% full subs fail: 21086
%
% ; program args: ("/home/graph/tptp/Systems/Gandalf---c-2.6/gandalf" "-time" "600" "/tmp/SystemOnTPTP21563/PUZ/PUZ062-2+eq_r.in")
% WARNING: TreeLimitedRun lost 14.82s, total lost is 14.82s
%
%------------------------------------------------------------------------------