TSTP Solution File: HWV003-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : HWV003-1 : TPTP v3.4.2. Released v1.1.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art05.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 159.0s
% Output : Assurance 159.0s
% 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/HWV/HWV003-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: heq
% detected subclass: medium
% detected subclass: short
%
% strategies selected:
% (binary-posweight-order 57 #f 4 1)
% (binary-unit 28 #f 4 1)
% (binary-double 28 #f 4 1)
% (binary 45 #t 4 1)
% (hyper 11 #t 4 1)
% (hyper 28 #f)
% (binary-unit-uniteq 16 #f)
% (binary-weightorder 22 #f)
% (binary-posweight-order 159 #f)
% (binary-posweight-lex-big-order 57 #f)
% (binary-posweight-lex-small-order 11 #f)
% (binary-order 28 #f)
% (binary-unit 45 #f)
% (binary 65 #t)
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(48,40,0,96,0,0,31475,3,2861,37485,4,4276,43658,5,5707,43658,1,5707,43658,50,5711,43658,40,5711,43706,0,5711,67529,3,7113,70969,4,7812,73566,5,8512,73566,1,8512,73566,50,8514,73566,40,8514,73614,0,8514,94388,3,9915,98706,4,10615,101096,5,11315,101096,1,11315,101096,50,11317,101096,40,11317,101144,0,11317,128572,3,13568,131743,4,14697,136728,5,15818,136728,1,15818,136728,50,15820,136728,40,15820,136776,0,15820,153491,4,16646)
%
%
% START OF PROOF
% 136730 [] equal(and(X,n0),n0).
% 136731 [] equal(and(X,n1),X).
% 136732 [] equal(or(X,n0),X).
% 136733 [] equal(or(X,n1),n1).
% 136734 [] equal(not(n0),n1).
% 136735 [] equal(not(n1),n0).
% 136736 [] equal(not(and(X,Y)),or(not(X),not(Y))).
% 136737 [] equal(not(or(X,Y)),and(not(X),not(Y))).
% 136738 [] equal(not(not(X)),X).
% 136739 [] equal(and(X,not(X)),n0).
% 136741 [] equal(and(X,X),X).
% 136743 [] equal(and(and(X,Y),not(Y)),n0).
% 136744 [] equal(and(and(X,Y),not(X)),n0).
% 136745 [] equal(or(or(X,Y),not(Y)),n1).
% 136746 [] equal(or(or(X,Y),not(X)),n1).
% 136747 [] equal(and(and(X,Y),Y),and(X,Y)).
% 136751 [] equal(or(and(X,Y),Y),Y).
% 136752 [] equal(or(and(X,Y),X),X).
% 136753 [] equal(or(or(and(X,Y),Z),Y),or(Z,Y)).
% 136754 [] equal(or(or(X,and(Y,Z)),Z),or(X,Z)).
% 136755 [] equal(or(and(X,not(Y)),Y),or(X,Y)).
% 136756 [] equal(or(not(or(X,Y)),Y),or(Y,not(X))).
% 136757 [] equal(or(and(and(X,Y),not(Z)),and(X,Z)),or(and(X,Y),and(X,Z))).
% 136758 [] equal(xor(X,Y),or(and(X,not(Y)),and(Y,not(X)))).
% 136759 [] equal(and(X,Y),and(Y,X)).
% 136760 [] equal(or(X,Y),or(Y,X)).
% 136761 [] equal(and(or(X,Y),Z),or(and(X,Z),and(Y,Z))).
% 136762 [] equal(and(and(X,Y),Z),and(and(X,Z),Y)).
% 136763 [] equal(or(or(X,Y),Z),or(or(X,Z),Y)).
% 136764 [] equal(carryout(X,Y,Z),or(and(X,or(Y,Z)),and(not(X),and(Y,Z)))).
% 136765 [] equal(sum(X,Y,Z),xor(xor(X,Y),Z)).
% 136766 [] equal(a11,not(and(a,b))).
% 136767 [] equal(a12,not(and(a11,a))).
% 136768 [] equal(a13,not(and(a11,b))).
% 136769 [] equal(a14,not(and(a12,a13))).
% 136770 [] equal(a15,not(and(a14,carryin))).
% 136771 [] equal(a16,not(and(a14,a15))).
% 136772 [] equal(a17,not(and(a15,carryin))).
% 136773 [] equal(s1,not(and(a16,a17))).
% 136774 [] equal(c1,not(and(a11,a15))).
% 136775 [] circuit(s1,c1).
% 136776 [] -circuit(sum(a,b,carryin),carryout(a,b,carryin)).
% 136777 [para:136766.1.2,136736.1.2.1] equal(not(and(and(a,b),X)),or(a11,not(X))).
% 136780 [para:136766.1.2,136737.1.2.2] equal(not(or(X,and(a,b))),and(not(X),a11)).
% 136781 [para:136766.1.2,136738.1.1.1] equal(not(a11),and(a,b)).
% 136788 [para:136766.1.2,136755.1.1.1.2,demod:136781] equal(or(and(X,a11),not(a11)),or(X,not(a11))).
% 136789 [para:136766.1.2,136757.1.1.1.2,demod:136781] equal(or(and(and(X,Y),a11),and(X,not(a11))),or(and(X,Y),and(X,not(a11)))).
% 136792 [para:136767.1.2,136736.1.2.1] equal(not(and(and(a11,a),X)),or(a12,not(X))).
% 136794 [para:136767.1.2,136737.1.2.1] equal(not(or(and(a11,a),X)),and(a12,not(X))).
% 136796 [para:136767.1.2,136738.1.1.1] equal(not(a12),and(a11,a)).
% 136797 [?] ?
% 136803 [para:136767.1.2,136755.1.1.1.2,demod:136796] equal(or(and(X,a12),not(a12)),or(X,not(a12))).
% 136804 [para:136767.1.2,136757.1.1.1.2,demod:136796] equal(or(and(and(X,Y),a12),and(X,not(a12))),or(and(X,Y),and(X,not(a12)))).
% 136805 [para:136767.1.2,136758.1.2.1.2,demod:136737,136796] equal(xor(X,not(a12)),or(and(X,a12),not(or(a12,X)))).
% 136806 [para:136767.1.2,136758.1.2.2.2,demod:136737,136796] equal(xor(not(a12),X),or(not(or(a12,X)),and(X,a12))).
% 136810 [para:136768.1.2,136737.1.2.2] equal(not(or(X,and(a11,b))),and(not(X),a13)).
% 136811 [para:136768.1.2,136738.1.1.1] equal(not(a13),and(a11,b)).
% 136818 [para:136768.1.2,136755.1.1.1.2,demod:136811] equal(or(and(X,a13),not(a13)),or(X,not(a13))).
% 136824 [para:136769.1.2,136737.1.2.1] equal(not(or(and(a12,a13),X)),and(a14,not(X))).
% 136825 [para:136769.1.2,136737.1.2.2] equal(not(or(X,and(a12,a13))),and(not(X),a14)).
% 136826 [para:136769.1.2,136738.1.1.1] equal(not(a14),and(a12,a13)).
% 136833 [para:136769.1.2,136755.1.1.1.2,demod:136826] equal(or(and(X,a14),not(a14)),or(X,not(a14))).
% 136834 [para:136769.1.2,136757.1.1.1.2,demod:136826] equal(or(and(and(X,Y),a14),and(X,not(a14))),or(and(X,Y),and(X,not(a14)))).
% 136836 [para:136769.1.2,136758.1.2.2.2,demod:136737,136826] equal(xor(not(a14),X),or(not(or(a14,X)),and(X,a14))).
% 136837 [para:136759.1.1,136730.1.1] equal(and(n0,X),n0).
% 136838 [para:136759.1.1,136731.1.1] equal(and(n1,X),X).
% 136840 [para:136759.1.1,136739.1.1] equal(and(not(X),X),n0).
% 136841 [para:136759.1.1,136743.1.1] equal(and(not(X),and(Y,X)),n0).
% 136842 [para:136759.1.1,136744.1.1] equal(and(not(X),and(X,Y)),n0).
% 136843 [para:136759.1.1,136747.1.1] equal(and(X,and(Y,X)),and(Y,X)).
% 136850 [para:136759.1.1,136754.1.1.1.2] equal(or(or(X,and(Y,Z)),Y),or(X,Y)).
% 136851 [para:136759.1.1,136755.1.1.1] equal(or(and(not(X),Y),X),or(Y,X)).
% 136852 [para:136759.1.1,136757.1.1.1] equal(or(and(not(X),and(Y,Z)),and(Y,X)),or(and(Y,Z),and(Y,X))).
% 136855 [para:136759.1.1,136758.1.2.1] equal(xor(X,Y),or(and(not(Y),X),and(Y,not(X)))).
% 136856 [para:136759.1.1,136758.1.2.2] equal(xor(X,Y),or(and(X,not(Y)),and(not(X),Y))).
% 136857 [para:136759.1.1,136766.1.2.1] equal(a11,not(and(b,a))).
% 136860 [para:136759.1.1,136769.1.2.1] equal(a14,not(and(a13,a12))).
% 136861 [para:136838.1.1,136753.1.1.1.1] equal(or(or(X,Y),X),or(Y,X)).
% 136863 [para:136838.1.1,136758.1.2.1,demod:136732,136730,136735] equal(xor(n1,X),not(X)).
% 136864 [para:136838.1.1,136758.1.2.2,demod:136730,136735] equal(xor(X,n1),or(n0,not(X))).
% 136865 [para:136837.1.1,136751.1.1.1] equal(or(n0,X),X).
% 136873 [para:136760.1.1,136751.1.1] equal(or(X,and(Y,X)),X).
% 136874 [para:136760.1.1,136752.1.1] equal(or(X,and(X,Y)),X).
% 136876 [para:136760.1.1,136754.1.1] equal(or(X,or(Y,and(Z,X))),or(Y,X)).
% 136879 [para:136760.1.1,136756.1.1.1.1] equal(or(not(or(X,Y)),X),or(X,not(Y))).
% 136882 [para:136840.1.1,136752.1.1.1,demod:136864] equal(xor(X,n1),not(X)).
% 136887 [para:136739.1.1,136761.1.2.2,demod:136732] equal(and(or(X,Y),not(Y)),and(X,not(Y))).
% 136888 [para:136741.1.1,136761.1.2.1,demod:136873] equal(and(or(X,Y),X),X).
% 136897 [para:136747.1.1,136761.1.2.2,demod:136761] equal(and(or(X,and(Y,Z)),Z),and(or(X,Y),Z)).
% 136898 [para:136759.1.1,136761.1.2.1] equal(and(or(X,Y),Z),or(and(Z,X),and(Y,Z))).
% 136899 [para:136759.1.1,136761.1.2.2] equal(and(or(X,Y),Z),or(and(X,Z),and(Z,Y))).
% 136907 [para:136770.1.2,136738.1.1.1] equal(not(a15),and(a14,carryin)).
% 136921 [para:136771.1.2,136738.1.1.1] equal(not(a16),and(a14,a15)).
% 136935 [para:136772.1.2,136738.1.1.1] equal(not(a17),and(a15,carryin)).
% 136949 [para:136773.1.2,136738.1.1.1] equal(not(s1),and(a16,a17)).
% 136963 [para:136774.1.2,136738.1.1.1] equal(not(c1),and(a11,a15)).
% 136978 [para:136762.1.1,136751.1.1.1] equal(or(and(and(X,Y),Z),Y),Y).
% 136979 [para:136762.1.1,136759.1.1] equal(and(and(X,Y),Z),and(Y,and(X,Z))).
% 136991 [para:136781.1.2,136757.1.1.1.1,demod:136781,136737] equal(or(not(or(a11,X)),and(a,X)),or(not(a11),and(a,X))).
% 136992 [para:136781.1.2,136759.1.1] equal(not(a11),and(b,a)).
% 136993 [para:136781.1.2,136761.1.2.1] equal(and(or(a,X),b),or(not(a11),and(X,b))).
% 136995 [para:136796.1.2,136743.1.1.1,demod:136737] equal(not(or(a12,a)),n0).
% 136996 [para:136796.1.2,136744.1.1.1,demod:136737] equal(not(or(a12,a11)),n0).
% 137002 [para:136796.1.2,136757.1.1.1.1,demod:136796,136737] equal(or(not(or(a12,X)),and(a11,X)),or(not(a12),and(a11,X))).
% 137003 [para:136796.1.2,136759.1.1] equal(not(a12),and(a,a11)).
% 137014 [para:136763.1.1,136760.1.1] equal(or(or(X,Y),Z),or(Y,or(X,Z))).
% 137015 [para:136760.1.1,136763.1.1.1,demod:137014] equal(or(X,or(Y,Z)),or(Z,or(X,Y))).
% 137019 [para:136811.1.2,136743.1.1.1,demod:136737] equal(not(or(a13,b)),n0).
% 137020 [para:136811.1.2,136744.1.1.1,demod:136737] equal(not(or(a13,a11)),n0).
% 137026 [para:136811.1.2,136759.1.1] equal(not(a13),and(b,a11)).
% 137029 [para:136826.1.2,136743.1.1.1,demod:136737] equal(not(or(a14,a13)),n0).
% 137035 [para:136826.1.2,136757.1.1.1.1,demod:136826,136737] equal(or(not(or(a14,X)),and(a12,X)),or(not(a14),and(a12,X))).
% 137036 [para:136826.1.2,136759.1.1] equal(not(a14),and(a13,a12)).
% 137037 [para:136826.1.2,136761.1.2.1] equal(and(or(a12,X),a13),or(not(a14),and(X,a13))).
% 137038 [para:136826.1.2,136761.1.2.2] equal(and(or(X,a12),a13),or(and(X,a13),not(a14))).
% 137040 [para:136731.1.1,136764.1.2.2.2,demod:136731,136733] equal(carryout(X,Y,n1),or(X,and(not(X),Y))).
% 137043 [para:136738.1.1,136764.1.2.2.1] equal(carryout(not(X),Y,Z),or(and(not(X),or(Y,Z)),and(X,and(Y,Z)))).
% 137048 [para:136745.1.1,136764.1.2.1.2,demod:137040,136887,136731] equal(carryout(X,or(Y,Z),not(Z)),carryout(X,and(Y,not(Z)),n1)).
% 137058 [para:136759.1.1,136764.1.2.1] equal(carryout(X,Y,Z),or(and(or(Y,Z),X),and(not(X),and(Y,Z)))).
% 137059 [para:136759.1.1,136764.1.2.2.2] equal(carryout(X,Y,Z),or(and(X,or(Y,Z)),and(not(X),and(Z,Y)))).
% 137062 [para:136764.1.2,136760.1.1] equal(carryout(X,Y,Z),or(and(not(X),and(Y,Z)),and(X,or(Y,Z)))).
% 137063 [para:136760.1.1,136764.1.2.1.2,demod:137059] equal(carryout(X,Y,Z),carryout(X,Z,Y)).
% 137065 [para:136840.1.1,136764.1.2.2,demod:136732,136979] equal(carryout(and(X,Y),X,Y),and(Y,and(X,or(X,Y)))).
% 137068 [para:136796.1.2,136764.1.2.2.2,demod:136737] equal(carryout(X,a11,a),or(and(X,or(a11,a)),not(or(X,a12)))).
% 137076 [para:136863.1.1,136765.1.2.1] equal(sum(n1,X,Y),xor(not(X),Y)).
% 137084 [para:136857.1.2,136757.1.1.1.2,demod:136992,136979] equal(or(and(X,and(Y,a11)),and(Y,not(a11))),or(and(Y,X),and(Y,not(a11)))).
% 137097 [para:136860.1.2,136737.1.2.1,demod:137036] equal(not(or(not(a14),X)),and(a14,not(X))).
% 137098 [para:136860.1.2,136737.1.2.2,demod:137036] equal(not(or(X,not(a14))),and(not(X),a14)).
% 137101 [para:136907.1.2,136744.1.1.1,demod:136737] equal(not(or(a15,a14)),n0).
% 137106 [para:136907.1.2,136757.1.1.1.1,demod:136907,136737] equal(or(not(or(a15,X)),and(a14,X)),or(not(a15),and(a14,X))).
% 137107 [para:136907.1.2,136759.1.1] equal(not(a15),and(carryin,a14)).
% 137113 [para:136743.1.1,136777.1.1.1,demod:136738,136734] equal(n1,or(a11,b)).
% 137114 [para:136744.1.1,136777.1.1.1,demod:136738,136734] equal(n1,or(a11,a)).
% 137115 [para:136747.1.1,136777.1.1.1,demod:136738,136781] equal(a11,or(a11,not(b))).
% 137117 [para:137113.1.2,136756.1.1.1.1,demod:136865,136735] equal(b,or(b,not(a11))).
% 137120 [para:137114.1.2,136756.1.1.1.1,demod:136865,136735] equal(a,or(a,not(a11))).
% 137121 [para:137114.1.2,136760.1.1] equal(n1,or(a,a11)).
% 137122 [para:137114.1.2,136764.1.2.1.2,demod:136737,136796,136731] equal(carryout(X,a11,a),or(X,not(or(X,a12)))).
% 137123 [para:137121.1.2,136756.1.1.1.1,demod:136865,136735] equal(a11,or(a11,not(a))).
% 137139 [para:136921.1.2,136759.1.1] equal(not(a16),and(a15,a14)).
% 137148 [para:136935.1.2,136743.1.1.1,demod:136737] equal(not(or(a17,carryin)),n0).
% 137149 [para:136935.1.2,136744.1.1.1,demod:136737] equal(not(or(a17,a15)),n0).
% 137172 [para:136949.1.2,136761.1.2.1] equal(and(or(a16,X),a17),or(not(s1),and(X,a17))).
% 137201 [para:136780.1.1,136738.1.1.1,demod:136781] equal(not(and(not(X),a11)),or(X,not(a11))).
% 137210 [para:136992.1.2,136757.1.1.1.1,demod:136992,136737] equal(or(not(or(a11,X)),and(b,X)),or(not(a11),and(b,X))).
% 137212 [para:136992.1.2,136761.1.2.2] equal(and(or(X,b),a),or(and(X,a),not(a11))).
% 137216 [para:136995.1.1,136737.1.2.1,demod:136837,137014] equal(not(or(a,or(a12,X))),n0).
% 137218 [para:136995.1.1,136738.1.1.1,demod:136734] equal(n1,or(a12,a)).
% 137219 [para:136995.1.1,136756.1.1.1,demod:136865] equal(a,or(a,not(a12))).
% 137227 [para:136996.1.1,136737.1.2.1,demod:136837,137014] equal(not(or(a11,or(a12,X))),n0).
% 137229 [para:136996.1.1,136738.1.1.1,demod:136734] equal(n1,or(a12,a11)).
% 137230 [para:136996.1.1,136756.1.1.1,demod:136865] equal(a11,or(a11,not(a12))).
% 137232 [para:137229.1.2,136760.1.1] equal(n1,or(a11,a12)).
% 137243 [para:137003.1.2,136757.1.1.1.1,demod:137003,136737] equal(or(not(or(a12,X)),and(a,X)),or(not(a12),and(a,X))).
% 137244 [para:137003.1.2,136761.1.2.1] equal(and(or(a,X),a11),or(not(a12),and(X,a11))).
% 137250 [para:137019.1.1,136738.1.1.1,demod:136734] equal(n1,or(a13,b)).
% 137253 [para:137250.1.2,136760.1.1] equal(n1,or(b,a13)).
% 137264 [para:137020.1.1,136738.1.1.1,demod:136734] equal(n1,or(a13,a11)).
% 137265 [para:137020.1.1,136756.1.1.1,demod:136865] equal(a11,or(a11,not(a13))).
% 137267 [para:137264.1.2,136760.1.1] equal(n1,or(a11,a13)).
% 137277 [para:137003.1.2,136788.1.1.1,demod:137120,136736] equal(not(and(a12,a11)),a).
% 137284 [para:137026.1.2,136788.1.1.1,demod:137117,136736] equal(not(and(a13,a11)),b).
% 137289 [para:137029.1.1,136738.1.1.1,demod:136734] equal(n1,or(a14,a13)).
% 137300 [para:136789.1.1,136754.1.1.1,demod:136979,136754] equal(or(and(X,Y),not(a11)),or(and(Y,and(X,a11)),not(a11))).
% 137302 [para:136759.1.1,136789.1.1.1.1,demod:136979] equal(or(and(X,and(Y,a11)),and(X,not(a11))),or(and(X,Y),and(X,not(a11)))).
% 137363 [para:137101.1.1,136738.1.1.1,demod:136734] equal(n1,or(a15,a14)).
% 137364 [para:137101.1.1,136756.1.1.1,demod:136865] equal(a14,or(a14,not(a15))).
% 137376 [para:137363.1.2,136760.1.1] equal(n1,or(a14,a15)).
% 137378 [para:137376.1.2,136756.1.1.1.1,demod:136865,136735] equal(a15,or(a15,not(a14))).
% 137388 [para:136792.1.1,136738.1.1.1,demod:136796] equal(not(or(a12,not(X))),and(not(a12),X)).
% 137440 [para:137148.1.1,136737.1.2.1,demod:136837,137014] equal(not(or(carryin,or(a17,X))),n0).
% 137442 [para:137148.1.1,136738.1.1.1,demod:136734] equal(n1,or(a17,carryin)).
% 137445 [para:137442.1.2,136760.1.1] equal(n1,or(carryin,a17)).
% 137454 [para:137445.1.2,136756.1.1.1.1,demod:136865,136735] equal(a17,or(a17,not(carryin))).
% 137460 [para:137149.1.1,136738.1.1.1,demod:136734] equal(n1,or(a17,a15)).
% 137463 [para:137460.1.2,136760.1.1] equal(n1,or(a15,a17)).
% 137553 [para:136796.1.2,136804.1.1.1.1,demod:136873,136796,136865,136797] equal(and(a11,not(a12)),not(a12)).
% 137576 [para:137230.1.2,136756.1.1.1.1,demod:137277,136736] equal(not(and(a11,a12)),a).
% 137588 [para:136805.1.2,136760.1.1,demod:137076,136806] equal(xor(X,not(a12)),sum(n1,a12,X)).
% 137611 [para:137265.1.2,136756.1.1.1.1,demod:137284,136736] equal(not(and(a11,a13)),b).
% 137619 [para:137277.1.1,136738.1.1.1] equal(not(a),and(a12,a11)).
% 137667 [para:137454.1.2,136760.1.1] equal(a17,or(not(carryin),a17)).
% 137714 [para:137576.1.1,136738.1.1.1] equal(not(a),and(a11,a12)).
% 137740 [para:137611.1.1,136738.1.1.1] equal(not(b),and(a11,a13)).
% 137796 [para:137714.1.2,136803.1.1.1,demod:137230,136736] equal(not(and(a,a12)),a11).
% 137803 [para:137740.1.2,136818.1.1.1,demod:137265,136736] equal(not(and(b,a13)),a11).
% 137808 [para:137796.1.1,136738.1.1.1] equal(not(a11),and(a,a12)).
% 137815 [para:136818.1.1,136824.1.1.1,demod:136738,137388] equal(and(not(a12),a13),and(a14,a13)).
% 137821 [para:137803.1.1,136738.1.1.1] equal(not(a11),and(b,a13)).
% 137826 [para:137808.1.2,136759.1.1] equal(not(a11),and(a12,a)).
% 137833 [para:137821.1.2,136759.1.1] equal(not(a11),and(a13,b)).
% 137849 [para:137826.1.2,136761.1.2.2,demod:137212] equal(and(or(X,a12),a),and(or(X,b),a)).
% 137864 [para:136874.1.1,136745.1.1.1] equal(or(X,not(and(X,Y))),n1).
% 137887 [para:136888.1.1,136759.1.1] equal(X,and(X,or(X,Y))).
% 137988 [para:137887.1.2,136764.1.2.1,demod:136732,136842] equal(carryout(X,X,Y),X).
% 138001 [para:137667.1.2,137887.1.2.2] equal(not(carryin),and(not(carryin),a17)).
% 138017 [para:137107.1.2,136833.1.1.1,demod:136738,137139,136736] equal(a16,or(carryin,not(a14))).
% 138020 [para:138017.1.2,136746.1.1.1] equal(or(a16,not(carryin)),n1).
% 138021 [para:138017.1.2,136760.1.1] equal(a16,or(not(a14),carryin)).
% 138022 [para:138017.1.2,136888.1.1.1] equal(and(a16,carryin),carryin).
% 138033 [para:138022.1.1,136874.1.1.2] equal(or(a16,carryin),a16).
% 138211 [para:136843.1.1,136789.1.1.1.1,demod:136899,136843,137302,136979] equal(or(and(X,Y),and(X,not(a11))),and(or(Y,not(a11)),X)).
% 138331 [para:137553.1.1,136757.1.1.2,demod:137553,137714,136979,136738] equal(or(and(X,not(a)),not(a12)),or(and(a11,X),not(a12))).
% 138403 [para:136761.1.2,136850.1.1.1] equal(or(and(or(X,Y),Z),Y),or(and(X,Z),Y)).
% 138426 [para:136738.1.1,136851.1.1.1.1] equal(or(and(X,Y),not(X)),or(Y,not(X))).
% 138427 [para:136851.1.1,136760.1.1,demod:137040] equal(or(X,Y),carryout(Y,X,n1)).
% 138452 [para:136759.1.1,136852.1.1.1.2] equal(or(and(not(X),and(Y,Z)),and(Z,X)),or(and(Z,Y),and(Z,X))).
% 138525 [para:136843.1.1,136852.1.1.1.2,demod:136899,136843,138452] equal(or(and(X,Y),and(X,Z)),and(or(Y,Z),X)).
% 138757 [para:136861.1.1,136756.1.1.1.1,demod:136756] equal(or(X,not(Y)),or(X,not(or(X,Y)))).
% 139148 [para:136752.1.1,136879.1.1.1.1,demod:138426] equal(or(not(X),and(X,Y)),or(Y,not(X))).
% 139655 [para:137216.1.1,136738.1.1.1,demod:136734] equal(n1,or(a,or(a12,X))).
% 139660 [para:136760.1.1,139655.1.2.2] equal(n1,or(a,or(X,a12))).
% 139663 [para:139660.1.2,136760.1.1,demod:137014] equal(n1,or(a12,or(X,a))).
% 139664 [para:139660.1.2,136764.1.2.1.2,demod:138427,137040,136731] equal(carryout(X,a,or(Y,a12)),or(and(a,or(Y,a12)),X)).
% 139670 [para:136760.1.1,139663.1.2.2] equal(n1,or(a12,or(a,X))).
% 139724 [para:137227.1.1,136879.1.1.1,demod:136865] equal(a11,or(a11,not(or(a12,X)))).
% 139795 [para:136898.1.2,136764.1.2,demod:136838,136733,137864,137014] equal(carryout(and(X,Y),X,Y),and(X,Y)).
% 139849 [para:136781.1.2,136899.1.2.1] equal(and(or(a,X),b),or(not(a11),and(b,X))).
% 139850 [para:136796.1.2,136899.1.2.1] equal(and(or(a11,X),a),or(not(a12),and(a,X))).
% 139855 [para:136935.1.2,136899.1.2.1] equal(and(or(a15,X),carryin),or(not(a17),and(carryin,X))).
% 139859 [para:136992.1.2,136899.1.2.1] equal(and(or(b,X),a),or(not(a11),and(a,X))).
% 139862 [para:137036.1.2,136899.1.2.1] equal(and(or(a13,X),a12),or(not(a14),and(a12,X))).
% 139863 [para:137107.1.2,136899.1.2.1] equal(and(or(carryin,X),a14),or(not(a15),and(a14,X))).
% 140189 [para:137440.1.1,136738.1.1.1,demod:136734] equal(n1,or(carryin,or(a17,X))).
% 140248 [para:136760.1.1,140189.1.2.2] equal(n1,or(carryin,or(X,a17))).
% 140251 [para:140248.1.2,136760.1.1,demod:137014] equal(n1,or(a17,or(X,carryin))).
% 140260 [para:138033.1.1,140251.1.2.2] equal(n1,or(a17,a16)).
% 140265 [para:140260.1.2,136756.1.1.1.1,demod:136865,136735] equal(a16,or(a16,not(a17))).
% 140266 [para:140260.1.2,136760.1.1] equal(n1,or(a16,a17)).
% 141161 [para:136810.1.1,139724.1.2.2,demod:137815] equal(a11,or(a11,and(a14,a13))).
% 141195 [para:136759.1.1,141161.1.2.2] equal(a11,or(a11,and(a13,a14))).
% 141226 [para:141195.1.2,136897.1.1.1,demod:136838,137267] equal(and(a11,a14),a14).
% 141227 [para:141226.1.1,136752.1.1.1] equal(or(a14,a11),a11).
% 141236 [para:141226.1.1,136836.1.2.2,demod:141227,137076] equal(sum(n1,a14,a11),or(not(a11),a14)).
% 141237 [para:141226.1.1,136842.1.1.2] equal(and(not(a11),a14),n0).
% 142344 [para:137267.1.2,136991.1.1.1.1,demod:136838,137253,139859,136865,136735] equal(and(a,a13),a).
% 142368 [para:142344.1.1,136751.1.1.1] equal(or(a,a13),a13).
% 142391 [para:142344.1.1,136978.1.1.1.1] equal(or(and(a,X),a13),a13).
% 142401 [para:142368.1.1,139670.1.2.2] equal(n1,or(a12,a13)).
% 142419 [para:142401.1.2,136764.1.2.1.2,demod:138757,136737,136826,136731] equal(carryout(X,a12,a13),or(X,not(a14))).
% 142530 [para:137740.1.2,137002.1.1.2,demod:136736,137740,136882,136864,136735,142401] equal(not(b),not(and(a12,b))).
% 142552 [para:137003.1.2,142391.1.1.1] equal(or(not(a12),a13),a13).
% 142557 [para:142552.1.1,137887.1.2.2,demod:137815] equal(not(a12),and(a14,a13)).
% 142563 [para:142557.1.2,136759.1.1] equal(not(a12),and(a13,a14)).
% 142566 [para:142557.1.2,136764.1.2.2.2,demod:137122,136737,136731,137289] equal(carryout(X,a14,a13),carryout(X,a11,a)).
% 142646 [para:142530.1.2,136738.1.1.1,demod:136738] equal(b,and(a12,b)).
% 142648 [para:142530.1.2,137864.1.1.2] equal(or(a12,not(b)),n1).
% 142654 [para:142646.1.2,136759.1.1] equal(b,and(b,a12)).
% 142691 [para:142654.1.2,136978.1.1.1.1] equal(or(and(b,X),a12),a12).
% 142840 [para:142691.1.1,136760.1.1] equal(a12,or(a12,and(b,X))).
% 142872 [para:142840.1.2,136805.1.2.2.1,demod:142654,136979,137588] equal(sum(n1,a12,and(b,X)),or(and(X,b),not(a12))).
% 142873 [para:142840.1.2,136806.1.2.1.1,demod:142654,136979,137076] equal(sum(n1,a12,and(b,X)),or(not(a12),and(X,b))).
% 143888 [para:137035.1.1,136754.1.1.1,demod:142419,136756,137036,138403,139862] equal(or(not(a14),X),carryout(X,a12,a13)).
% 143911 [para:142344.1.1,137037.1.2.2,demod:143888,136838,137218] equal(a13,carryout(a,a12,a13)).
% 143922 [para:137740.1.2,137038.1.2.1,demod:136736,136838,137232] equal(a13,not(and(b,a14))).
% 143930 [para:143922.1.2,136738.1.1.1] equal(not(a13),and(b,a14)).
% 143934 [para:143930.1.2,136759.1.1] equal(not(a13),and(a14,b)).
% 143938 [para:143930.1.2,136833.1.1.1,demod:142419,136738,142563,136736] equal(a12,carryout(b,a12,a13)).
% 143957 [para:143934.1.2,136993.1.2.2,demod:136738,137740,136736] equal(and(or(a,a14),b),b).
% 143982 [para:143957.1.1,136874.1.1.2,demod:137014] equal(or(a14,or(a,b)),or(a,a14)).
% 144066 [para:136811.1.2,137043.1.2.2.2,demod:136736,139148,136731,137113] equal(carryout(not(X),a11,b),not(and(a13,X))).
% 144071 [para:137121.1.2,137043.1.2.1.2,demod:136736,139148,137003,136731] equal(carryout(not(X),a,a11),not(and(a12,X))).
% 144072 [para:136921.1.2,137043.1.2.2.2,demod:136736,139148,136731,137376] equal(carryout(not(X),a14,a15),not(and(a16,X))).
% 144074 [para:136949.1.2,137043.1.2.2.2,demod:136736,139148,136731,140266] equal(carryout(not(X),a16,a17),not(and(s1,X))).
% 144079 [para:137218.1.2,137043.1.2.1.2,demod:136736,139148,137826,136731] equal(carryout(not(X),a12,a),not(and(a11,X))).
% 144461 [para:137115.1.2,137048.1.1.2,demod:138427,136811,136738] equal(carryout(X,a11,b),or(not(a13),X)).
% 144462 [para:137120.1.2,137048.1.1.2,demod:138427,137003,136738] equal(carryout(X,a,a11),or(not(a12),X)).
% 144463 [para:137123.1.2,137048.1.1.2,demod:144462,138427,136796,142566,136738] equal(carryout(X,a14,a13),carryout(X,a,a11)).
% 144465 [para:137219.1.2,137048.1.1.2,demod:138427,137808,136738] equal(carryout(X,a,a12),or(not(a11),X)).
% 144473 [para:137364.1.2,137048.1.1.2,demod:138427,136921,136738] equal(carryout(X,a14,a15),or(not(a16),X)).
% 144505 [para:140265.1.2,137048.1.1.2,demod:138427,136949,136738] equal(carryout(X,a16,a17),or(not(s1),X)).
% 145836 [para:137058.1.2,136760.1.1] equal(carryout(X,Y,Z),or(and(not(X),and(Y,Z)),and(or(Y,Z),X))).
% 146265 [para:137218.1.2,137062.1.2.2.2,demod:136879,136731,136737,137826] equal(carryout(X,a12,a),or(X,not(a11))).
% 146421 [para:139660.1.2,137065.1.2.2.2,demod:137849,136731,139795] equal(and(a,or(X,a12)),and(or(X,b),a)).
% 146536 [para:142691.1.1,137068.1.2.2.1,demod:142872,136731,136979,137114,142566] equal(carryout(and(b,X),a14,a13),sum(n1,a12,and(b,X))).
% 147115 [para:137084.1.1,136876.1.1.2,demod:137300,144465,146265,138211] equal(carryout(and(carryout(X,a12,a),Y),a,a12),carryout(and(Y,X),a12,a)).
% 147646 [para:138021.1.2,137097.1.1.1] equal(not(a16),and(a14,not(carryin))).
% 147738 [para:137098.1.1,136991.1.1.1,demod:137826,143938,142419,139859,136865,141237] equal(and(a,not(a14)),not(a11)).
% 147741 [para:147738.1.1,136755.1.1.1,demod:141236] equal(sum(n1,a14,a11),or(a,a14)).
% 147848 [para:137463.1.2,137106.1.1.1.1,demod:136838,137445,139863,136865,136735] equal(and(a14,a17),a14).
% 147880 [para:147848.1.1,136841.1.1.2] equal(and(not(a17),a14),n0).
% 150369 [para:138001.1.2,137172.1.2.2,demod:144074,144505,136838,138020] equal(a17,not(and(s1,carryin))).
% 150399 [para:150369.1.2,136738.1.1.1] equal(not(a17),and(s1,carryin)).
% 150409 [para:150399.1.2,136759.1.1] equal(not(a17),and(carryin,s1)).
% 150454 [para:150409.1.2,136834.1.1.1.1,demod:136935,137378,139855,150409,136865,147880] equal(and(carryin,not(a14)),not(a17)).
% 150540 [para:150454.1.1,136758.1.2.2,demod:136738,136949,144072,144473,147646] equal(xor(a14,carryin),s1).
% 151463 [para:136794.1.1,137201.1.1.1.1,demod:146265,144463,144462,136796,136738,136737,137619,136979] equal(or(X,a),carryout(carryout(X,a14,a13),a12,a)).
% 151870 [para:136825.1.1,137210.1.1.1,demod:137833,143911,142419,139849,136865,136826,141237] equal(and(b,not(a14)),not(a11)).
% 151899 [para:151870.1.1,136755.1.1.1,demod:147741,141236] equal(or(a,a14),or(b,a14)).
% 151968 [para:151899.1.2,136760.1.1] equal(or(a,a14),or(a14,b)).
% 151974 [para:151968.1.1,136760.1.1] equal(or(a14,b),or(a14,a)).
% 152010 [para:137212.1.2,136763.1.1.1,demod:137212,137014,139664,146421] equal(carryout(X,a,or(Y,a12)),or(X,and(a,or(Y,a12)))).
% 152022 [para:137212.1.2,137015.1.1.2,demod:144465,152010,146421] equal(carryout(X,a,or(Y,a12)),carryout(or(X,and(Y,a)),a,a12)).
% 152484 [para:142648.1.1,137243.1.1.1.1,demod:136796,137115,139850,136865,136735] equal(and(a,not(b)),not(a12)).
% 152533 [para:152484.1.1,136758.1.2.2,demod:136738,137036,144066,144461,136811,138331] equal(xor(b,a),a14).
% 152538 [para:152484.1.1,136855.1.2.2,demod:146536,142872,152533] equal(a14,carryout(and(b,not(a)),a14,a13)).
% 152539 [para:152484.1.1,136856.1.2.1,demod:152538,146536,142873] equal(xor(a,b),a14).
% 152561 [para:152539.1.1,136765.1.2.1] equal(sum(a,b,X),xor(a14,X)).
% 152567 [para:137026.1.2,137244.1.2.2,demod:136738,136826,144071,144462] equal(and(or(a,b),a11),a14).
% 152648 [para:152567.1.1,136752.1.1.1,demod:151974,151968,143982] equal(or(a14,a),or(a,b)).
% 152668 [para:152648.1.2,136760.1.1] equal(or(a14,a),or(b,a)).
% 153500 [para:137063.1.1,136776.1.2,demod:150540,152561] -circuit(s1,carryout(a,carryin,b)).
% 153505 [para:145836.1.1,153500.1.2,demod:152010,146421] -circuit(s1,carryout(and(not(a),and(carryin,b)),a,or(carryin,a12))).
% 154146 [para:152022.1.1,153505.1.2,demod:152668,138525,136852] -circuit(s1,carryout(and(or(a14,a),carryin),a,a12)).
% 154160 [para:151463.1.1,154146.1.2.1.1,demod:136738,136963,144079,137107,147115,137988,cut:136775] 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
% clause length limited to 1
% clause depth limited to 4
% seconds given: 11
%
%
% old unit clauses discarded
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 16954
% derived clauses: 2484838
% kept clauses: 153871
% kept size sum: 0
% kept mid-nuclei: 0
% kept new demods: 149081
% forw unit-subs: 2006350
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 263
% fast unit cutoff: 1
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 169.85
% process. runtime: 168.68
% 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/HWV/HWV003-1+eq_r.in")
%
%------------------------------------------------------------------------------