TSTP Solution File: ALG012-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : ALG012-1 : TPTP v3.4.2. Released v2.7.0.
% 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 20.0s
% Output : Assurance 20.0s
% 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/ALG/ALG012-1+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 3 7)
% (binary-unit 9 #f 3 7)
% (binary-double 9 #f 3 7)
% (binary-double 15 #f)
% (binary-double 15 #t)
% (binary 50 #t 3 7)
% (binary-order 25 #f 3 7)
% (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(12,40,2,24,0,2,28303,4,1903,57578,5,2515,57579,1,2515,57579,50,2517,57579,40,2517,57591,0,2517,57658,50,2517,57670,0,2517,57767,50,2517,57779,0,2523,57892,50,2523,57904,0,2523,58039,50,2524,58051,0,2524,58202,50,2525,58214,0,2529,58387,50,2530,58399,0,2530,58588,50,2532,58600,0,2537,58811,50,2539,58823,0,2539,59050,50,2542,59062,0,2542,59311,50,2546,59323,0,2550,59588,50,2554,59600,0,2554,59887,50,2559,59899,0,2564,60202,50,2570,60214,0,2570,60539,50,2578,60551,0,2579,60892,50,2588,60904,0,2592,61267,50,2604,61279,0,2604,61658,50,2617,61670,0,2622,62071,50,2638,62083,0,2638,62500,50,2657,62500,40,2657,62512,0,2657)
%
%
% START OF PROOF
% 62502 [] equal(f(X,f(Y,Z)),f(f(X,Y),Z)).
% 62503 [] d2(X) | d1(X) | c(X).
% 62504 [] -d1(X) | -c(X).
% 62505 [] -d2(X) | -c(X).
% 62506 [] -d2(X) | -d1(X).
% 62507 [] c(a1).
% 62508 [] d1(a2).
% 62509 [] d2(a3).
% 62510 [] d2(f(X,Y)) | d1(f(X,Y)) | -c(X) | -c(Y).
% 62511 [] c(f(X,Y)) | -d1(X) | -d1(Y).
% 62512 [] c(f(X,Y)) | -d2(X) | -d2(Y).
% 62513 [input:62510,factor] d2(f(X,X)) | d1(f(X,X)) | -c(X).
% 62514 [input:62511,factor] c(f(X,X)) | -d1(X).
% 62515 [input:62512,factor] c(f(X,X)) | -d2(X).
% 62526 [binary:62507,62510.3] d2(f(a1,X)) | d1(f(a1,X)) | -c(X).
% 62527 [binary:62507,62510.4] d2(f(X,a1)) | d1(f(X,a1)) | -c(X).
% 62529 [binary:62504,62510.2,binarycut:62505] -c(f(X,Y)) | -c(Y) | -c(X).
% 62532 [binary:62508,62514.2] c(f(a2,a2)).
% 62543 [binary:62508,62511.2] c(f(a2,X)) | -d1(X).
% 62544 [binary:62508,62511.3] c(f(X,a2)) | -d1(X).
% 62548 [binary:62509,62515.2] c(f(a3,a3)).
% 62559 [binary:62509,62512.2] c(f(a3,X)) | -d2(X).
% 62560 [binary:62509,62512.3] c(f(X,a3)) | -d2(X).
% 62571 [para:62502.1.2,62510.1.1,demod:62502] d2(f(X,f(Y,Z))) | d1(f(X,f(Y,Z))) | -c(f(X,Y)) | -c(Z).
% 62573 [para:62502.1.2,62512.1.1] c(f(X,f(Y,Z))) | -d2(f(X,Y)) | -d2(Z).
% 62575 [binary:62504.2,62543] -d1(f(a2,X)) | -d1(X).
% 62576 [binary:62505.2,62543] -d2(f(a2,X)) | -d1(X).
% 62589 [para:62502.1.2,62544.1.1] c(f(X,f(Y,a2))) | -d1(f(X,Y)).
% 62592 [binary:62505.2,62559] -d2(f(a3,X)) | -d2(X).
% 62600 [binary:62505.2,62560] -d2(f(X,a3)) | -d2(X).
% 62605 [para:62502.1.2,62560.1.1] c(f(X,f(Y,a3))) | -d2(f(X,Y)).
% 62608 [binary:62503.2,62575.2] -d1(f(a2,X)) | d2(X) | c(X).
% 62612 [binary:62504,62513.2,binarycut:62505] -c(f(X,X)) | -c(X).
% 62627 [binary:62504,62526.2,binarycut:62505] -c(f(a1,X)) | -c(X).
% 62653 [binary:62532,62527.3,demod:62502,binarydemod:62575,62576] -d1(f(a2,a1)).
% 62657 [para:62502.1.2,62527.1.1,demod:62502] d2(f(X,f(Y,a1))) | d1(f(X,f(Y,a1))) | -c(f(X,Y)).
% 62660 [binary:62543,62527.3,demod:62502,binarydemod:62575,62576] -d1(f(X,a1)) | -d1(X).
% 62688 [binary:62503,62592.2] -d2(f(a3,X)) | d1(X) | c(X).
% 62697 [binary:62532,62529.3,demod:62502,binarydemod:62543] -d1(f(a2,X)) | -c(X).
% 62700 [binary:62548,62529.2] -c(f(X,f(a3,a3))) | -c(X).
% 62702 [binary:62548,62529.3,demod:62502,binarydemod:62559] -d2(f(a3,X)) | -c(X).
% 62721 [binary:62503,62600.2] -d2(f(X,a3)) | d1(X) | c(X).
% 62732 [binary:62548,62627.2] -c(f(a1,f(a3,a3))).
% 62753 [binary:62503.2,62660] d2(f(X,a1)) | c(f(X,a1)) | -d1(X).
% 63044 [binary:62697.2,62608.3] -d1(f(a2,X)) | d2(X).
% 63050 [binary:62512.3,63044.2] -d1(f(a2,X)) | c(f(Y,X)) | -d2(Y).
% 63134 [binary:62575,62571.2,binarycut:62576] -c(f(a2,X)) | -d1(f(X,Y)) | -c(Y).
% 63152 [binary:62702.2,62688.3] -d2(f(a3,X)) | d1(X).
% 63163 [binary:62653,63152.2] -d2(f(a3,f(a2,a1))).
% 63267 [binary:62732,62573,cut:62509] -d2(f(a1,a3)).
% 63270 [binary:62503,63267] d1(f(a1,a3)) | c(f(a1,a3)).
% 63273 [binary:63044.2,63267] -d1(f(a2,f(a1,a3))).
% 63778 [binary:62627,62589] -d1(f(a1,X)) | -c(f(X,a2)).
% 64130 [binary:62721.3,62700.2,binarycut:62605] -d2(f(X,a3)) | d1(X).
% 64131 [binary:62573,62700,cut:62509] -d2(f(X,a3)) | -c(X).
% 64156 [binary:62653,64130.2,demod:62502] -d2(f(a2,f(a1,a3))).
% 64161 [binary:62697,64130.2,demod:62502] -d2(f(a2,f(X,a3))) | -c(X).
% 64231 [binary:63044.2,64131] -d1(f(a2,f(X,a3))) | -c(X).
% 64239 [binary:62503,64156,cut:63273] c(f(a2,f(a1,a3))).
% 64350 [binary:62612,62605,demod:62502] -d2(f(X,f(a3,X))) | -c(f(X,a3)).
% 65553 [binary:62503,64161,binarycut:64231] c(f(a2,f(X,a3))) | -c(X).
% 65937 [binary:63778,63270] -c(f(a3,a2)) | c(f(a1,a3)).
% 67016 [binary:62575,62657.2,binarycut:62576] -d1(f(X,a1)) | -c(f(a2,X)).
% 67086 [binary:64239,67016.2,demod:62502] -d1(f(a1,f(a3,a1))).
% 67100 [binary:62571.2,67086,cut:62507,binarycut:64350] -c(f(a1,a3)).
% 67101 [binary:62503.3,67100,cut:63267] d1(f(a1,a3)).
% 67105 [binary:65937.2,67100] -c(f(a3,a2)).
% 67106 [binary:62511.2,67101,demod:62502] c(f(a1,f(a3,X))) | -d1(X).
% 67107 [binary:62511.3,67101] c(f(X,f(a1,a3))) | -d1(X).
% 67116 [binary:62503.3,67105] d2(f(a3,a2)) | d1(f(a3,a2)).
% 67260 [binary:62529,67106,cut:62507] -c(f(a3,X)) | -d1(X).
% 69165 [binary:67116,63050.3,demod:62502,binarycut:67260] d1(f(a3,a2)) | -d1(f(a2,X)).
% 69174 [binary:62506.2,69165] -d2(f(a3,a2)) | -d1(f(a2,X)).
% 69388 [binary:65553,63134,demod:62502,factor] -d1(f(X,f(a3,X))) | -c(X).
% 69476 [binary:62571.2,69388,binarycut:64350] -c(f(X,a3)) | -c(X).
% 69500 [binary:62503.3,69476,binarycut:64131] d1(f(X,a3)) | -c(X).
% 69598 [binary:62532,69500.2,demod:62502] d1(f(a2,f(a2,a3))).
% 69732 [binary:69476.2,62753.2,demod:62502,binarycut:67107] d2(f(X,a1)) | -d1(X).
% 69786 [binary:67116.2,69732.2,demod:62502,cut:63163,binarydemod:69174,slowcut:69598] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using double 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 7
% clause depth limited to 3
% seconds given: 9
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 3268
% derived clauses: 387248
% kept clauses: 53543
% kept size sum: 165738
% kept mid-nuclei: 2798
% kept new demods: 21
% forw unit-subs: 34527
% forw double-subs: 21899
% forw overdouble-subs: 69767
% backward subs: 124
% fast unit cutoff: 818
% full unit cutoff: 0
% dbl unit cutoff: 65
% real runtime : 27.59
% process. runtime: 27.60
% specific non-discr-tree subsumption statistics:
% tried: 18637995
% length fails: 1605045
% strength fails: 5359061
% predlist fails: 4690018
% aux str. fails: 384641
% by-lit fails: 329368
% full subs tried: 5714496
% full subs fail: 5644765
%
% ; 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/ALG/ALG012-1+eq_r.in")
%
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