TSTP Solution File: RNG009-7 by Gandalf---c-2.6
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%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : RNG009-7 : 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 : art01.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 99.6s
% Output : Assurance 99.6s
% 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/RNG/RNG009-7+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 3 1)
% (binary-posweight-lex-big-order 30 #f 3 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(13,40,0,26,0,0,69,50,1,82,0,2,1840,3,2968,2160,4,4428,2297,5,5903,2297,1,5903,2297,50,5903,2297,40,5903,2310,0,5903,2330,50,5903,2343,0,5904,2428,50,5933,2441,0,5933,2664,50,7125,2677,0,7125,3611,3,8003,3611,4,8413,3611,5,8826,3611,1,8826,3611,50,8826,3611,40,8826,3624,0,8826)
%
%
% START OF PROOF
% 3613 [] equal(add(additive_identity,X),X).
% 3614 [] equal(add(X,additive_identity),X).
% 3615 [] equal(add(additive_inverse(X),X),additive_identity).
% 3616 [] equal(add(X,additive_inverse(X)),additive_identity).
% 3617 [] equal(add(X,add(Y,Z)),add(add(X,Y),Z)).
% 3618 [] equal(add(X,Y),add(Y,X)).
% 3619 [] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 3620 [] equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))).
% 3621 [] equal(multiply(add(X,Y),Z),add(multiply(X,Z),multiply(Y,Z))).
% 3622 [] equal(multiply(X,multiply(X,X)),X).
% 3623 [] equal(multiply(a,b),c).
% 3624 [] -equal(multiply(b,a),c).
% 3625 [para:3623.1.1,3619.1.2.1] equal(multiply(a,multiply(b,X)),multiply(c,X)).
% 3626 [para:3623.1.1,3620.1.2.1] equal(multiply(a,add(b,X)),add(c,multiply(a,X))).
% 3628 [para:3623.1.1,3621.1.2.1] equal(multiply(add(a,X),b),add(c,multiply(X,b))).
% 3630 [para:3622.1.1,3619.1.2,demod:3619] equal(multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,Y))))),multiply(X,Y)).
% 3631 [para:3622.1.1,3619.1.2.1,demod:3619] equal(multiply(X,multiply(X,multiply(X,Y))),multiply(X,Y)).
% 3632 [para:3622.1.1,3620.1.2.1] equal(multiply(X,add(multiply(X,X),Y)),add(X,multiply(X,Y))).
% 3635 [para:3622.1.1,3621.1.2.2] equal(multiply(add(X,Y),multiply(Y,Y)),add(multiply(X,multiply(Y,Y)),Y)).
% 3639 [para:3625.1.1,3621.1.2.2] equal(multiply(add(X,a),multiply(b,Y)),add(multiply(X,multiply(b,Y)),multiply(c,Y))).
% 3640 [para:3622.1.1,3625.1.1.2,demod:3623] equal(c,multiply(c,multiply(b,b))).
% 3641 [para:3640.1.2,3619.1.2.1,demod:3619] equal(multiply(c,multiply(b,multiply(b,X))),multiply(c,X)).
% 3646 [para:3614.1.1,3626.1.1.2,demod:3623] equal(c,add(c,multiply(a,additive_identity))).
% 3647 [para:3616.1.1,3626.1.1.2] equal(multiply(a,additive_identity),add(c,multiply(a,additive_inverse(b)))).
% 3648 [para:3626.1.1,3619.1.2.1] equal(multiply(a,multiply(add(b,X),Y)),multiply(add(c,multiply(a,X)),Y)).
% 3653 [para:3646.1.2,3618.1.1] equal(c,add(multiply(a,additive_identity),c)).
% 3654 [para:3653.1.2,3617.1.2.1] equal(add(multiply(a,additive_identity),add(c,X)),add(c,X)).
% 3656 [para:3647.1.2,3618.1.1] equal(multiply(a,additive_identity),add(multiply(a,additive_inverse(b)),c)).
% 3658 [para:3631.1.1,3619.1.2,demod:3619] equal(multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,multiply(Y,Z)))))),multiply(X,multiply(Y,Z))).
% 3659 [para:3631.1.1,3620.1.2.1,demod:3620] equal(multiply(X,add(multiply(X,multiply(X,Y)),Z)),multiply(X,add(Y,Z))).
% 3676 [para:3614.1.1,3628.1.1.1,demod:3623] equal(c,add(c,multiply(additive_identity,b))).
% 3677 [para:3616.1.1,3628.1.1.1] equal(multiply(additive_identity,b),add(c,multiply(additive_inverse(a),b))).
% 3684 [para:3676.1.2,3618.1.1] equal(c,add(multiply(additive_identity,b),c)).
% 3687 [para:3677.1.2,3618.1.1] equal(multiply(additive_identity,b),add(multiply(additive_inverse(a),b),c)).
% 3715 [para:3628.1.1,3630.1.1.2.2.2.2,demod:3628] equal(multiply(add(a,X),multiply(b,multiply(add(a,X),multiply(b,add(c,multiply(X,b)))))),add(c,multiply(X,b))).
% 3717 [para:3616.1.1,3654.1.1.2,demod:3616,3614] equal(multiply(a,additive_identity),additive_identity).
% 3720 [para:3717.1.1,3621.1.2.1,demod:3613] equal(multiply(add(a,X),additive_identity),multiply(X,additive_identity)).
% 3729 [para:3614.1.1,3632.1.1.2,demod:3622] equal(X,add(X,multiply(X,additive_identity))).
% 3737 [para:3621.1.2,3632.1.1.2] equal(multiply(X,multiply(add(X,Y),X)),add(X,multiply(X,multiply(Y,X)))).
% 3739 [para:3729.1.2,3613.1.1] equal(additive_identity,multiply(additive_identity,additive_identity)).
% 3741 [para:3729.1.2,3617.1.2.1] equal(add(X,add(multiply(X,additive_identity),Y)),add(X,Y)).
% 3742 [para:3729.1.2,3618.1.1] equal(X,add(multiply(X,additive_identity),X)).
% 3743 [para:3739.1.2,3619.1.2.1] equal(multiply(additive_identity,multiply(additive_identity,X)),multiply(additive_identity,X)).
% 3744 [para:3742.1.2,3617.1.2.1] equal(add(multiply(X,additive_identity),add(X,Y)),add(X,Y)).
% 3745 [para:3616.1.1,3720.1.1.1,demod:3739] equal(additive_identity,multiply(additive_inverse(a),additive_identity)).
% 3802 [para:3613.1.1,3635.1.1.1,demod:3622] equal(X,add(multiply(additive_identity,multiply(X,X)),X)).
% 3942 [para:3619.1.2,3639.1.2.1] equal(multiply(add(multiply(X,Y),a),multiply(b,Z)),add(multiply(X,multiply(Y,multiply(b,Z))),multiply(c,Z))).
% 3962 [para:3741.1.1,3618.1.1,demod:3617] equal(add(X,Y),add(multiply(X,additive_identity),add(Y,X))).
% 4009 [para:3616.1.1,3744.1.1.2,demod:3616,3614] equal(multiply(X,additive_identity),additive_identity).
% 4010 [para:4009.1.1,3619.1.2.1] equal(multiply(X,multiply(additive_identity,Y)),multiply(additive_identity,Y)).
% 4032 [para:3962.1.2,3617.1.2.1,demod:3613,3617,4009] equal(add(X,add(Y,Z)),add(Y,add(X,Z))).
% 4054 [para:3615.1.1,4032.1.1.2,demod:3614] equal(X,add(additive_inverse(Y),add(X,Y))).
% 4055 [para:3616.1.1,4032.1.1.2,demod:3614] equal(X,add(Y,add(X,additive_inverse(Y)))).
% 4084 [para:3616.1.1,4054.1.2.2,demod:3614] equal(X,additive_inverse(additive_inverse(X))).
% 4087 [para:3618.1.1,4054.1.2.2] equal(X,add(additive_inverse(Y),add(Y,X))).
% 4088 [para:3620.1.2,4054.1.2.2] equal(multiply(X,Y),add(additive_inverse(multiply(X,Z)),multiply(X,add(Y,Z)))).
% 4089 [para:3621.1.2,4054.1.2.2] equal(multiply(X,Y),add(additive_inverse(multiply(Z,Y)),multiply(add(X,Z),Y))).
% 4091 [para:3656.1.2,4054.1.2.2,demod:3614,3717] equal(multiply(a,additive_inverse(b)),additive_inverse(c)).
% 4093 [para:3684.1.2,4054.1.2.2,demod:3615] equal(multiply(additive_identity,b),additive_identity).
% 4095 [para:3687.1.2,4054.1.2.2,demod:3614,4093] equal(multiply(additive_inverse(a),b),additive_inverse(c)).
% 4099 [para:3802.1.2,4054.1.2.2,demod:3615] equal(multiply(additive_identity,multiply(X,X)),additive_identity).
% 4107 [para:4054.1.2,4054.1.2.2] equal(additive_inverse(X),add(additive_inverse(add(Y,X)),Y)).
% 4115 [para:4010.1.1,4099.1.1.2,demod:3743] equal(multiply(additive_identity,X),additive_identity).
% 4136 [para:4091.1.1,3619.1.2.1] equal(multiply(a,multiply(additive_inverse(b),X)),multiply(additive_inverse(c),X)).
% 4141 [para:4091.1.1,3631.1.1.2.2,demod:4091] equal(multiply(a,multiply(a,additive_inverse(c))),additive_inverse(c)).
% 4142 [para:4095.1.1,3619.1.2.1] equal(multiply(additive_inverse(a),multiply(b,X)),multiply(additive_inverse(c),X)).
% 4162 [para:3618.1.1,4055.1.2.2] equal(X,add(Y,add(additive_inverse(Y),X))).
% 4235 [para:4055.1.2,4107.1.2.1.1] equal(additive_inverse(add(X,additive_inverse(Y))),add(additive_inverse(X),Y)).
% 4334 [para:4141.1.1,3648.1.2.1.2,demod:4115,3616] equal(multiply(a,multiply(add(b,multiply(a,additive_inverse(c))),X)),additive_identity).
% 4391 [para:3640.1.2,3658.1.1.2.2.2.2,demod:3640] equal(multiply(c,multiply(b,multiply(c,multiply(b,c)))),c).
% 4469 [para:3616.1.1,3659.1.1.2,demod:4009] equal(additive_identity,multiply(X,add(Y,additive_inverse(multiply(X,multiply(X,Y)))))).
% 4800 [para:3631.1.1,4142.1.1.2,demod:4142] equal(multiply(additive_inverse(c),X),multiply(additive_inverse(c),multiply(b,multiply(b,X)))).
% 5424 [para:4469.1.2,3619.1.2.1,demod:4115] equal(multiply(X,multiply(add(Y,additive_inverse(multiply(X,multiply(X,Y)))),Z)),additive_identity).
% 5735 [para:4334.1.1,3658.1.1.2,demod:4009] equal(additive_identity,multiply(add(b,multiply(a,additive_inverse(c))),multiply(a,X))).
% 5923 [para:3623.1.1,5735.1.2.2] equal(additive_identity,multiply(add(b,multiply(a,additive_inverse(c))),c)).
% 5924 [para:3625.1.1,5735.1.2.2] equal(additive_identity,multiply(add(b,multiply(a,additive_inverse(c))),multiply(c,X))).
% 6096 [para:5924.1.2,3630.1.1.2,demod:4009] equal(additive_identity,multiply(c,add(b,multiply(a,additive_inverse(c))))).
% 9494 [para:3616.1.1,3737.1.1.2.1,demod:4009,4115] equal(additive_identity,add(X,multiply(X,multiply(additive_inverse(X),X)))).
% 9619 [para:9494.1.2,4087.1.2.2,demod:3614] equal(multiply(X,multiply(additive_inverse(X),X)),additive_inverse(X)).
% 9620 [para:9494.1.2,4162.1.2.2,demod:3614,4084] equal(multiply(additive_inverse(X),multiply(X,additive_inverse(X))),X).
% 9675 [para:9619.1.1,3619.1.2.1,demod:3619] equal(multiply(X,multiply(additive_inverse(X),multiply(X,Y))),multiply(additive_inverse(X),Y)).
% 9753 [para:9620.1.1,3630.1.1.2.2.2,demod:9675] equal(multiply(additive_inverse(X),X),multiply(X,additive_inverse(X))).
% 9792 [para:9753.1.1,3619.1.2.1,demod:3619] equal(multiply(additive_inverse(X),multiply(X,Y)),multiply(X,multiply(additive_inverse(X),Y))).
% 9808 [para:9753.1.1,4136.1.1.2,demod:3625] equal(multiply(c,additive_inverse(b)),multiply(additive_inverse(c),b)).
% 23947 [para:3615.1.1,4088.1.2.2.2,demod:3614,4009] equal(multiply(X,additive_inverse(Y)),additive_inverse(multiply(X,Y))).
% 23991 [para:6096.1.2,4088.1.2.2,demod:3614,4084,23947] equal(multiply(c,b),multiply(c,multiply(a,c))).
% 24109 [para:23947.1.1,3619.1.2.1] equal(multiply(X,multiply(additive_inverse(Y),Z)),multiply(additive_inverse(multiply(X,Y)),Z)).
% 24110 [para:23947.1.1,3620.1.2.1] equal(multiply(X,add(additive_inverse(Y),Z)),add(additive_inverse(multiply(X,Y)),multiply(X,Z))).
% 24118 [para:4235.1.1,23947.1.1.2] equal(multiply(X,add(additive_inverse(Y),Z)),additive_inverse(multiply(X,add(Y,additive_inverse(Z))))).
% 24192 [para:23991.1.2,3619.1.2.1,demod:3619] equal(multiply(c,multiply(a,multiply(c,X))),multiply(c,multiply(b,X))).
% 24673 [para:4391.1.1,24192.1.1.2.2,demod:3641,23991] equal(multiply(c,b),multiply(c,multiply(c,multiply(b,c)))).
% 24774 [para:24673.1.2,3631.1.1.2] equal(multiply(c,multiply(c,b)),multiply(c,multiply(b,c))).
% 25656 [para:3615.1.1,4089.1.2.2.1,demod:3614,4115] equal(multiply(additive_inverse(X),Y),additive_inverse(multiply(X,Y))).
% 25717 [para:5735.1.2,4089.1.2.2,demod:3614,4084,25656,24109,23947] equal(multiply(b,multiply(a,X)),multiply(a,multiply(c,multiply(a,X)))).
% 25718 [para:5923.1.2,4089.1.2.2,demod:3614,4084,25656,24109,23947] equal(multiply(b,c),multiply(a,multiply(c,c))).
% 25722 [para:5924.1.2,4089.1.2.2,demod:3614,4084,25656,9792,24109,23947] equal(multiply(b,multiply(c,X)),multiply(a,multiply(c,multiply(c,X)))).
% 26076 [para:24192.1.1,25717.1.2.2] equal(multiply(b,multiply(a,multiply(c,X))),multiply(a,multiply(c,multiply(b,X)))).
% 26204 [para:23991.1.2,25722.1.2.2.2,demod:25718,26076,24774,23991] equal(multiply(b,multiply(c,b)),multiply(b,multiply(b,c))).
% 28367 [para:5424.1.1,3715.1.1.2,demod:23947,4095,4009,3745,24109,3720] equal(additive_identity,add(c,additive_inverse(multiply(b,multiply(b,c))))).
% 28478 [para:28367.1.2,4054.1.2.2,demod:3614,4084] equal(c,multiply(b,multiply(b,c))).
% 28479 [para:28478.1.2,3619.1.2.1,demod:3619] equal(multiply(b,multiply(b,multiply(c,X))),multiply(c,X)).
% 28480 [para:28478.1.2,3620.1.2.1] equal(multiply(b,add(multiply(b,c),X)),add(c,multiply(b,X))).
% 28743 [para:23991.1.2,28479.1.1.2.2,demod:23991,28478,26204] equal(multiply(b,c),multiply(c,b)).
% 34049 [para:28480.1.1,24118.1.2.1,demod:4235,23947] equal(multiply(b,add(additive_inverse(multiply(b,c)),X)),add(additive_inverse(c),multiply(b,X))).
% 36244 [para:4800.1.2,3942.1.2.1,demod:4009,3615,24110,25656,28743,23947,9808] equal(multiply(add(additive_inverse(multiply(b,c)),a),multiply(b,X)),additive_identity).
% 36346 [para:36244.1.1,3630.1.1.2,demod:34049,4009] equal(additive_identity,add(additive_inverse(c),multiply(b,a))).
% 36391 [para:36346.1.2,4087.1.2.2,demod:3614,4084,cut:3624] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% 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: 30
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 3347
% derived clauses: 3771722
% kept clauses: 34240
% kept size sum: 920021
% kept mid-nuclei: 0
% kept new demods: 29491
% forw unit-subs: 955287
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 64
% fast unit cutoff: 1
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 103.99
% process. runtime: 103.43
% 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/RNG/RNG009-7+eq_r.in")
%
%------------------------------------------------------------------------------