TSTP Solution File: LCL109-6 by MaedMax---1.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : MaedMax---1.4
% Problem : LCL109-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_maedmax %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 26 07:06:14 EDT 2022
% Result : Unsatisfiable 191.48s 191.77s
% Output : CNFRefutation 191.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of clauses : 112 ( 112 unt; 0 nHn; 18 RR)
% Number of literals : 112 ( 111 equ; 13 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 163 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
not(X) = xor(X,truth),
file('/tmp/MaedMax_24589') ).
cnf(eq_1,axiom,
X = xor(X,falsehood),
file('/tmp/MaedMax_24589') ).
cnf(eq_2,axiom,
xor(X,X) = falsehood,
file('/tmp/MaedMax_24589') ).
cnf(eq_3,axiom,
X = and_star(X,truth),
file('/tmp/MaedMax_24589') ).
cnf(eq_4,axiom,
falsehood = and_star(X,falsehood),
file('/tmp/MaedMax_24589') ).
cnf(eq_5,axiom,
falsehood = and_star(xor(truth,X),X),
file('/tmp/MaedMax_24589') ).
cnf(eq_6,axiom,
xor(X,xor(truth,Y)) = xor(xor(X,truth),Y),
file('/tmp/MaedMax_24589') ).
cnf(eq_7,axiom,
and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X),
file('/tmp/MaedMax_24589') ).
cnf(eq_8,axiom,
xor(X,Y) = xor(Y,X),
file('/tmp/MaedMax_24589') ).
cnf(eq_9,axiom,
and_star(X,and_star(Y,Z)) = and_star(and_star(X,Y),Z),
file('/tmp/MaedMax_24589') ).
cnf(eq_10,axiom,
and_star(X,Y) = and_star(Y,X),
file('/tmp/MaedMax_24589') ).
cnf(eq_11,axiom,
not(truth) = falsehood,
file('/tmp/MaedMax_24589') ).
cnf(eq_12,axiom,
xor(truth,and_star(X,xor(truth,Y))) = implies(X,Y),
file('/tmp/MaedMax_24589') ).
cnf(eq_13,negated_conjecture,
truth != implies(implies(implies(a,b),implies(b,a)),implies(b,a)),
file('/tmp/MaedMax_24589') ).
cnf(eq_14,plain,
xor(X,xor(truth,Y)) = xor(not(X),Y),
inference(rw,[status(thm)],[eq_6,eq_0]) ).
cnf(eq_15,plain,
X = xor(X,not(truth)),
inference(rw,[status(thm)],[eq_1,eq_11]) ).
cnf(eq_16,plain,
not(truth) = xor(X,X),
inference(rw,[status(thm)],[eq_2,eq_11]) ).
cnf(eq_17,plain,
not(truth) = and_star(X,xor(truth,X)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_5,eq_11]),eq_10]) ).
cnf(eq_18,plain,
not(truth) = and_star(X,not(truth)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_4,eq_11]),eq_11]) ).
cnf(eq_19,plain,
xor(x100,xor(X,truth)) = xor(not(x100),X),
inference(cp,[status(thm)],[eq_8,eq_14]) ).
cnf(eq_20,plain,
not(X) = xor(truth,X),
inference(cp,[status(thm)],[eq_0,eq_8]) ).
cnf(eq_21,plain,
X = xor(not(truth),X),
inference(cp,[status(thm)],[eq_15,eq_8]) ).
cnf(eq_22,plain,
X = and_star(truth,X),
inference(cp,[status(thm)],[eq_3,eq_10]) ).
cnf(eq_23,plain,
not(truth) = and_star(not(truth),X),
inference(cp,[status(thm)],[eq_18,eq_10]) ).
cnf(eq_24,plain,
and_star(X,xor(X,truth)) = not(truth),
inference(cp,[status(thm)],[eq_8,eq_17]) ).
cnf(eq_25,plain,
xor(X,not(Y)) = xor(not(X),Y),
inference(rw,[status(thm)],[eq_19,eq_0]) ).
cnf(eq_26,plain,
not(truth) = and_star(X,not(X)),
inference(rw,[status(thm)],[eq_24,eq_0]) ).
cnf(eq_27,plain,
not(not(truth)) = truth,
inference(cp,[status(thm)],[eq_0,eq_21]) ).
cnf(eq_28,plain,
and_star(X,not(and_star(not(Y),X))) = and_star(Y,not(and_star(not(X),Y))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_7,eq_20]),eq_0]),eq_10]),eq_20]),eq_0]),eq_10]) ).
cnf(eq_29,plain,
not(and_star(X,not(Y))) = implies(X,Y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_12,eq_20]),eq_20]) ).
cnf(eq_30,plain,
and_star(not(truth),x102) = and_star(X,and_star(not(X),x102)),
inference(cp,[status(thm)],[eq_26,eq_9]) ).
cnf(eq_31,plain,
not(and_star(not(x101),X)) = implies(X,x101),
inference(cp,[status(thm)],[eq_10,eq_29]) ).
cnf(eq_32,plain,
not(and_star(X,and_star(Y,not(x101)))) = implies(and_star(X,Y),x101),
inference(cp,[status(thm)],[eq_9,eq_29]) ).
cnf(eq_33,plain,
not(and_star(x100,truth)) = implies(x100,not(truth)),
inference(cp,[status(thm)],[eq_27,eq_29]) ).
cnf(eq_34,plain,
X = xor(not(X),truth),
inference(cp,[status(thm)],[eq_15,eq_25]) ).
cnf(eq_35,plain,
and_star(not(Y),implies(not(x101),Y)) = and_star(x101,not(and_star(not(not(Y)),x101))),
inference(cp,[status(thm)],[eq_29,eq_28]) ).
cnf(eq_36,plain,
not(truth) = and_star(X,and_star(not(X),Y)),
inference(rw,[status(thm)],[eq_30,eq_23]) ).
cnf(eq_37,plain,
X = not(not(X)),
inference(rw,[status(thm)],[eq_34,eq_0]) ).
cnf(eq_38,plain,
not(and_star(not(X),Y)) = implies(Y,X),
eq_31 ).
cnf(eq_39,plain,
not(X) = implies(X,not(truth)),
inference(rw,[status(thm)],[eq_33,eq_3]) ).
cnf(eq_40,plain,
not(and_star(X,and_star(Y,not(Z)))) = implies(and_star(X,Y),Z),
eq_32 ).
cnf(eq_41,negated_conjecture,
implies(not(and_star(implies(a,b),not(implies(b,a)))),implies(b,a)) != truth,
inference(cp,[status(thm)],[eq_29,eq_13]) ).
cnf(eq_42,plain,
not(implies(X,Y)) = and_star(X,not(Y)),
inference(cp,[status(thm)],[eq_29,eq_37]) ).
cnf(eq_43,plain,
not(and_star(x100,X)) = implies(x100,not(X)),
inference(cp,[status(thm)],[eq_37,eq_29]) ).
cnf(eq_44,plain,
not(and_star(X,Y)) = implies(X,not(Y)),
eq_43 ).
cnf(eq_45,negated_conjecture,
implies(not(and_star(implies(a,b),not(not(and_star(b,not(a)))))),implies(b,a)) != truth,
inference(cp,[status(thm)],[eq_29,eq_41]) ).
cnf(eq_46,negated_conjecture,
truth != implies(not(and_star(not(not(and_star(b,not(a)))),implies(a,b))),implies(b,a)),
inference(rw,[status(thm)],[eq_45,eq_10]) ).
cnf(eq_47,plain,
and_star(X,not(and_star(Y,X))) = and_star(not(Y),implies(not(X),Y)),
inference(rw,[status(thm)],[eq_35,eq_37]) ).
cnf(eq_48,plain,
not(implies(Y,X)) = and_star(not(X),Y),
inference(cp,[status(thm)],[eq_38,eq_37]) ).
cnf(eq_49,plain,
implies(not(x101),X) = implies(not(X),x101),
inference(cp,[status(thm)],[eq_38,eq_29]) ).
cnf(eq_50,plain,
not(not(truth)) = implies(X,truth),
inference(cp,[status(thm)],[eq_23,eq_38]) ).
cnf(eq_51,plain,
not(not(truth)) = implies(and_star(not(not(x100)),Y),x100),
inference(cp,[status(thm)],[eq_36,eq_38]) ).
cnf(eq_52,plain,
not(and_star(X,x101)) = implies(x101,not(X)),
inference(cp,[status(thm)],[eq_37,eq_38]) ).
cnf(eq_53,plain,
implies(not(X),Y) = implies(not(Y),X),
eq_49 ).
cnf(eq_54,plain,
not(and_star(X,Y)) = implies(Y,not(X)),
eq_52 ).
cnf(eq_55,plain,
truth = implies(X,truth),
inference(rw,[status(thm)],[eq_50,eq_37]) ).
cnf(eq_56,plain,
truth = implies(and_star(X,Y),X),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_51,eq_37]),eq_37]) ).
cnf(eq_57,plain,
not(implies(X,Y)) = and_star(not(Y),X),
eq_48 ).
cnf(eq_58,negated_conjecture,
truth != implies(not(and_star(b,and_star(not(a),implies(a,b)))),implies(b,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_46,eq_37]),eq_9]) ).
cnf(eq_59,plain,
implies(X,Y) = implies(not(Y),not(X)),
inference(rw,[status(thm)],[eq_38,eq_44]) ).
cnf(eq_60,negated_conjecture,
truth != implies(implies(b,implies(not(a),not(implies(a,b)))),implies(b,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_58,eq_44]),eq_44]) ).
cnf(eq_61,plain,
implies(and_star(Y,X),X) = truth,
inference(cp,[status(thm)],[eq_10,eq_56]) ).
cnf(eq_62,plain,
implies(X,not(x101)) = implies(x101,not(X)),
inference(cp,[status(thm)],[eq_37,eq_59]) ).
cnf(eq_63,plain,
implies(X,not(Y)) = implies(Y,not(X)),
eq_62 ).
cnf(eq_64,plain,
truth = implies(and_star(X,Y),Y),
eq_61 ).
cnf(eq_65,negated_conjecture,
implies(implies(b,implies(implies(a,b),a)),implies(b,a)) != truth,
inference(cp,[status(thm)],[eq_59,eq_60]) ).
cnf(eq_66,plain,
and_star(X,implies(X,Y)) = and_star(Y,implies(Y,X)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_7,eq_20]),eq_0]),eq_38]),eq_10]),eq_20]),eq_0]),eq_38]),eq_10]) ).
cnf(eq_67,plain,
not(and_star(and_star(X,not(Y)),x101)) = implies(x101,implies(X,Y)),
inference(cp,[status(thm)],[eq_42,eq_38]) ).
cnf(eq_68,plain,
implies(and_star(X,and_star(Y,Z)),Z) = truth,
inference(cp,[status(thm)],[eq_9,eq_64]) ).
cnf(eq_69,plain,
not(and_star(X,and_star(not(Y),Z))) = implies(Z,implies(X,Y)),
inference(rw,[status(thm)],[eq_67,eq_9]) ).
cnf(eq_70,plain,
and_star(X,x101) = not(implies(x101,not(X))),
inference(cp,[status(thm)],[eq_37,eq_57]) ).
cnf(eq_71,plain,
not(implies(X,not(Y))) = and_star(Y,X),
eq_70 ).
cnf(eq_72,plain,
implies(X,not(and_star(x100,and_star(x101,not(X))))) = truth,
inference(cp,[status(thm)],[eq_63,eq_68]) ).
cnf(eq_73,plain,
truth = implies(X,implies(Y,implies(Z,X))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_72,eq_42]),eq_42]),eq_37]) ).
cnf(eq_74,plain,
and_star(Y,X) = xor(truth,implies(X,xor(truth,Y))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_71,eq_20]),eq_20]) ).
cnf(eq_75,plain,
X = xor(truth,implies(X,falsehood)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_22,eq_74]),eq_2]) ).
cnf(eq_76,plain,
xor(truth,X) = implies(X,falsehood),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_39,eq_20]),eq_20]),eq_2]) ).
cnf(eq_77,plain,
X = implies(implies(X,falsehood),falsehood),
inference(cp,[status(thm)],[eq_75,eq_76]) ).
cnf(eq_78,plain,
not(X) = implies(X,falsehood),
inference(rw,[status(thm)],[eq_20,eq_76]) ).
cnf(eq_79,plain,
implies(implies(X,falsehood),Y) = implies(implies(Y,falsehood),X),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_53,eq_78]),eq_78]) ).
cnf(eq_80,plain,
implies(X,Y) = implies(implies(Y,falsehood),implies(X,falsehood)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_59,eq_78]),eq_78]) ).
cnf(eq_81,plain,
not(xor(X,X)) = truth,
inference(cp,[status(thm)],[eq_16,eq_37]) ).
cnf(eq_82,plain,
not(falsehood) = truth,
inference(rw,[status(thm)],[eq_81,eq_2]) ).
cnf(eq_83,plain,
implies(X,implies(Y,falsehood)) = implies(and_star(Y,X),falsehood),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_54,eq_78]),eq_78]) ).
cnf(eq_84,plain,
implies(and_star(Y,X),falsehood) = implies(Y,implies(X,falsehood)),
inference(cp,[status(thm)],[eq_10,eq_83]) ).
cnf(eq_85,plain,
implies(implies(X,implies(Y,falsehood)),falsehood) = and_star(Y,X),
inference(cp,[status(thm)],[eq_83,eq_77]) ).
cnf(eq_86,plain,
and_star(X,Y) = implies(implies(Y,implies(X,falsehood)),falsehood),
eq_85 ).
cnf(eq_87,plain,
implies(X,implies(Y,falsehood)) = implies(and_star(X,Y),falsehood),
eq_84 ).
cnf(eq_88,plain,
implies(implies(X,implies(Y,falsehood)),falsehood) = and_star(X,Y),
inference(cp,[status(thm)],[eq_87,eq_77]) ).
cnf(eq_89,plain,
and_star(X,Y) = implies(implies(X,implies(Y,falsehood)),falsehood),
eq_88 ).
cnf(eq_90,plain,
implies(and_star(Y,implies(Y,X)),falsehood) = implies(implies(X,Y),implies(X,falsehood)),
inference(cp,[status(thm)],[eq_66,eq_83]) ).
cnf(eq_91,plain,
implies(implies(X,Y),implies(X,falsehood)) = implies(implies(Y,X),implies(Y,falsehood)),
inference(rw,[status(thm)],[eq_90,eq_83]) ).
cnf(eq_92,plain,
not(falsehood) = implies(X,implies(Y,implies(Z,X))),
inference(rw,[status(thm)],[eq_73,eq_82]) ).
cnf(eq_93,plain,
implies(X,implies(Y,Z)) = implies(implies(implies(X,implies(Y,falsehood)),falsehood),Z),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_40,eq_78]),eq_89]),eq_77]),eq_89]),eq_77]),eq_78]),eq_77]),eq_89]) ).
cnf(eq_94,plain,
implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_69,eq_78]),eq_86]),eq_77]),eq_86]),eq_80]),eq_78]),eq_77]) ).
cnf(eq_95,plain,
implies(x100,implies(X,Y)) = implies(implies(Y,falsehood),implies(x100,implies(X,falsehood))),
inference(cp,[status(thm)],[eq_80,eq_94]) ).
cnf(eq_96,plain,
implies(x100,implies(Y,implies(X,Z))) = implies(X,implies(x100,implies(Y,Z))),
inference(cp,[status(thm)],[eq_94,eq_94]) ).
cnf(eq_97,plain,
implies(X,implies(Y,Z)) = implies(implies(Z,falsehood),implies(X,implies(Y,falsehood))),
eq_95 ).
cnf(eq_98,plain,
implies(X,implies(Y,implies(Z,x3))) = implies(Y,implies(Z,implies(X,x3))),
eq_96 ).
cnf(eq_99,negated_conjecture,
implies(implies(implies(implies(b,implies(implies(a,b),a)),implies(b,falsehood)),falsehood),a) != truth,
inference(cp,[status(thm)],[eq_93,eq_65]) ).
cnf(eq_100,negated_conjecture,
implies(implies(a,falsehood),implies(implies(b,implies(implies(a,b),a)),implies(b,falsehood))) != truth,
inference(cp,[status(thm)],[eq_79,eq_99]) ).
cnf(eq_101,plain,
not(and_star(not(Y),implies(not(not(x100)),Y))) = implies(not(and_star(Y,not(x100))),x100),
inference(cp,[status(thm)],[eq_47,eq_38]) ).
cnf(eq_102,plain,
implies(implies(X,Y),Y) = implies(implies(Y,X),X),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_101,eq_37]),eq_38]),eq_29]) ).
cnf(eq_103,plain,
implies(x100,implies(implies(implies(x102,x100),X),X)) = not(falsehood),
inference(cp,[status(thm)],[eq_102,eq_92]) ).
cnf(eq_104,plain,
truth = implies(X,implies(implies(implies(Y,X),Z),Z)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_103,eq_11]),eq_37]) ).
cnf(eq_105,plain,
implies(x100,truth) = implies(implies(implies(Y,X),Z),implies(x100,implies(X,Z))),
inference(cp,[status(thm)],[eq_104,eq_98]) ).
cnf(eq_106,plain,
truth = implies(implies(implies(X,Y),Z),implies(x3,implies(Y,Z))),
inference(rw,[status(thm)],[eq_105,eq_55]) ).
cnf(eq_107,negated_conjecture,
implies(implies(a,falsehood),implies(implies(implies(implies(a,b),a),b),implies(implies(implies(a,b),a),falsehood))) != truth,
inference(cp,[status(thm)],[eq_91,eq_100]) ).
cnf(eq_108,negated_conjecture,
truth != implies(implies(implies(implies(a,b),a),b),implies(implies(implies(a,b),a),a)),
inference(rw,[status(thm)],[eq_107,eq_97]) ).
cnf(eq_109,negated_conjecture,
implies(implies(implies(implies(a,b),a),b),implies(implies(a,implies(a,b)),implies(a,b))) != truth,
inference(cp,[status(thm)],[eq_102,eq_108]) ).
cnf(eq_110,negated_conjecture,
truth != truth,
inference(rw,[status(thm)],[eq_109,eq_106]) ).
cnf(bot,negated_conjecture,
$false,
inference(cn,[status(thm)],[eq_110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL109-6 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : run_maedmax %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Jul 26 05:29:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 191.48/191.77 % SZS status Unsatisfiable
% 191.48/191.77 % SZS output start CNFRefutation for /tmp/MaedMax_24589
% See solution above
% 191.48/191.78
%------------------------------------------------------------------------------