%------------------------------------------------------------------------------
% File : MaedMax---1.4
% Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_maedmax %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:38:42 PM UTC 2026
% Result : Unsatisfiable 34.24s 34.56s
% Output : CNFRefutation 34.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of clauses : 84 ( 84 unt; 0 nHn; 17 RR)
% Number of literals : 84 ( 83 equ; 9 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 : 112 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
not(X) = xor(X,truth),
file('/tmp/MaedMax_4131692') ).
cnf(eq_1,axiom,
X = xor(X,falsehood),
file('/tmp/MaedMax_4131692') ).
cnf(eq_2,axiom,
xor(X,X) = falsehood,
file('/tmp/MaedMax_4131692') ).
cnf(eq_3,axiom,
X = and_star(X,truth),
file('/tmp/MaedMax_4131692') ).
cnf(eq_4,axiom,
falsehood = and_star(X,falsehood),
file('/tmp/MaedMax_4131692') ).
cnf(eq_5,axiom,
falsehood = and_star(xor(truth,X),X),
file('/tmp/MaedMax_4131692') ).
cnf(eq_6,axiom,
xor(X,xor(truth,Y)) = xor(xor(X,truth),Y),
file('/tmp/MaedMax_4131692') ).
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_4131692') ).
cnf(eq_8,axiom,
xor(X,Y) = xor(Y,X),
file('/tmp/MaedMax_4131692') ).
cnf(eq_9,axiom,
and_star(X,and_star(Y,Z)) = and_star(and_star(X,Y),Z),
file('/tmp/MaedMax_4131692') ).
cnf(eq_10,axiom,
and_star(X,Y) = and_star(Y,X),
file('/tmp/MaedMax_4131692') ).
cnf(eq_11,axiom,
not(truth) = falsehood,
file('/tmp/MaedMax_4131692') ).
cnf(eq_12,axiom,
xor(truth,and_star(X,xor(truth,Y))) = implies(X,Y),
file('/tmp/MaedMax_4131692') ).
cnf(eq_13,negated_conjecture,
truth != implies(implies(x,y),implies(implies(y,z),implies(x,z))),
file('/tmp/MaedMax_4131692') ).
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) = and_star(X,xor(truth,X)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_5,eq_11]),eq_10]) ).
cnf(eq_17,plain,
not(truth) = and_star(X,not(truth)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_4,eq_11]),eq_11]) ).
cnf(eq_18,plain,
and_star(truth,X) = X,
inference(cp,[status(thm)],[eq_10,eq_3]) ).
cnf(eq_19,plain,
and_star(and_star(Y,X),x102) = and_star(X,and_star(Y,x102)),
inference(cp,[status(thm)],[eq_10,eq_9]) ).
cnf(eq_20,plain,
xor(x100,xor(X,truth)) = xor(not(x100),X),
inference(cp,[status(thm)],[eq_8,eq_14]) ).
cnf(eq_21,plain,
not(X) = xor(truth,X),
inference(cp,[status(thm)],[eq_0,eq_8]) ).
cnf(eq_22,plain,
X = xor(not(truth),X),
inference(cp,[status(thm)],[eq_15,eq_8]) ).
cnf(eq_23,plain,
not(truth) = and_star(not(truth),X),
inference(cp,[status(thm)],[eq_17,eq_10]) ).
cnf(eq_24,plain,
and_star(X,and_star(Y,Z)) = and_star(Z,and_star(X,Y)),
inference(cp,[status(thm)],[eq_9,eq_10]) ).
cnf(eq_25,plain,
and_star(X,xor(X,truth)) = not(truth),
inference(cp,[status(thm)],[eq_8,eq_16]) ).
cnf(eq_26,plain,
and_star(X,and_star(Y,Z)) = and_star(Y,and_star(Z,X)),
eq_24 ).
cnf(eq_27,plain,
xor(X,not(Y)) = xor(not(X),Y),
inference(rw,[status(thm)],[eq_20,eq_0]) ).
cnf(eq_28,plain,
and_star(X,and_star(Y,Z)) = and_star(Y,and_star(X,Z)),
inference(rw,[status(thm)],[eq_19,eq_9]) ).
cnf(eq_29,plain,
not(truth) = and_star(X,not(X)),
inference(rw,[status(thm)],[eq_25,eq_0]) ).
cnf(eq_30,plain,
not(not(truth)) = truth,
inference(cp,[status(thm)],[eq_0,eq_22]) ).
cnf(eq_31,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_21]),eq_0]),eq_10]),eq_21]),eq_0]),eq_10]) ).
cnf(eq_32,plain,
not(and_star(X,not(Y))) = implies(X,Y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_12,eq_21]),eq_21]) ).
cnf(eq_33,plain,
and_star(not(truth),x102) = and_star(X,and_star(not(X),x102)),
inference(cp,[status(thm)],[eq_29,eq_9]) ).
cnf(eq_34,plain,
not(not(x101)) = implies(truth,x101),
inference(cp,[status(thm)],[eq_18,eq_32]) ).
cnf(eq_35,plain,
not(and_star(Y,not(and_star(not(X),Y)))) = implies(X,and_star(not(Y),X)),
inference(cp,[status(thm)],[eq_31,eq_32]) ).
cnf(eq_36,plain,
not(and_star(not(x101),X)) = implies(X,x101),
inference(cp,[status(thm)],[eq_10,eq_32]) ).
cnf(eq_37,plain,
not(and_star(x100,truth)) = implies(x100,not(truth)),
inference(cp,[status(thm)],[eq_30,eq_32]) ).
cnf(eq_38,plain,
X = xor(not(X),truth),
inference(cp,[status(thm)],[eq_15,eq_27]) ).
cnf(eq_39,plain,
not(truth) = and_star(X,and_star(not(X),Y)),
inference(rw,[status(thm)],[eq_33,eq_23]) ).
cnf(eq_40,plain,
X = not(not(X)),
inference(rw,[status(thm)],[eq_38,eq_0]) ).
cnf(eq_41,plain,
not(and_star(not(X),Y)) = implies(Y,X),
eq_36 ).
cnf(eq_42,plain,
not(not(X)) = implies(truth,X),
eq_34 ).
cnf(eq_43,plain,
not(X) = implies(X,not(truth)),
inference(rw,[status(thm)],[eq_37,eq_3]) ).
cnf(eq_44,plain,
not(and_star(X,not(and_star(not(Y),X)))) = implies(Y,and_star(not(X),Y)),
eq_35 ).
cnf(eq_45,negated_conjecture,
implies(implies(x,y),not(and_star(implies(y,z),not(implies(x,z))))) != truth,
inference(cp,[status(thm)],[eq_32,eq_13]) ).
cnf(eq_46,plain,
not(implies(truth,not(truth))) = truth,
inference(cp,[status(thm)],[eq_43,eq_30]) ).
cnf(eq_47,plain,
implies(truth,X) = X,
inference(cp,[status(thm)],[eq_42,eq_40]) ).
cnf(eq_48,plain,
not(implies(X,Y)) = and_star(X,not(Y)),
inference(cp,[status(thm)],[eq_32,eq_40]) ).
cnf(eq_49,plain,
not(and_star(x100,X)) = implies(x100,not(X)),
inference(cp,[status(thm)],[eq_40,eq_32]) ).
cnf(eq_50,plain,
not(and_star(X,Y)) = implies(X,not(Y)),
eq_49 ).
cnf(eq_51,plain,
not(not(truth)) = implies(and_star(not(not(x100)),Y),x100),
inference(cp,[status(thm)],[eq_39,eq_41]) ).
cnf(eq_52,plain,
truth = implies(and_star(X,Y),X),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_51,eq_40]),eq_40]) ).
cnf(eq_53,negated_conjecture,
implies(implies(x,y),not(and_star(implies(y,z),not(not(and_star(not(z),x)))))) != truth,
inference(cp,[status(thm)],[eq_41,eq_45]) ).
cnf(eq_54,negated_conjecture,
truth != implies(implies(x,y),not(and_star(x,and_star(not(z),implies(y,z))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_53,eq_10]),eq_40]),eq_28]),eq_10]) ).
cnf(eq_55,plain,
not(falsehood) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_46,eq_11]),eq_47]) ).
cnf(eq_56,plain,
not(X) = implies(X,falsehood),
inference(rw,[status(thm)],[eq_43,eq_11]) ).
cnf(eq_57,plain,
implies(X,Y) = implies(not(Y),not(X)),
inference(rw,[status(thm)],[eq_41,eq_50]) ).
cnf(eq_58,plain,
not(implies(X,not(Y))) = and_star(X,Y),
inference(cp,[status(thm)],[eq_50,eq_40]) ).
cnf(eq_59,plain,
implies(and_star(Y,X),X) = truth,
inference(cp,[status(thm)],[eq_10,eq_52]) ).
cnf(eq_60,plain,
truth = implies(and_star(X,Y),Y),
eq_59 ).
cnf(eq_61,plain,
xor(truth,X) = implies(X,falsehood),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_43,eq_21]),eq_21]),eq_2]) ).
cnf(eq_62,plain,
xor(truth,implies(X,Y)) = and_star(X,xor(truth,Y)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_48,eq_21]),eq_21]) ).
cnf(eq_63,plain,
and_star(x100,truth) = xor(truth,implies(x100,falsehood)),
inference(cp,[status(thm)],[eq_1,eq_62]) ).
cnf(eq_64,plain,
X = xor(truth,implies(X,falsehood)),
inference(rw,[status(thm)],[eq_63,eq_3]) ).
cnf(eq_65,plain,
X = implies(implies(X,falsehood),falsehood),
inference(rw,[status(thm)],[eq_64,eq_61]) ).
cnf(eq_66,plain,
implies(X,Y) = implies(and_star(X,implies(Y,falsehood)),falsehood),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_12,eq_61]),eq_61]) ).
cnf(eq_67,plain,
implies(and_star(x100,X),falsehood) = implies(x100,implies(X,falsehood)),
inference(cp,[status(thm)],[eq_65,eq_66]) ).
cnf(eq_68,plain,
implies(X,implies(Y,falsehood)) = implies(and_star(X,Y),falsehood),
eq_67 ).
cnf(eq_69,plain,
implies(and_star(X,and_star(Y,Z)),and_star(Z,X)) = truth,
inference(cp,[status(thm)],[eq_26,eq_60]) ).
cnf(eq_70,plain,
truth = implies(and_star(X,and_star(Y,Z)),and_star(Z,X)),
eq_69 ).
cnf(eq_71,negated_conjecture,
truth != implies(implies(x,y),implies(and_star(x,and_star(implies(y,z),implies(z,falsehood))),falsehood)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_54,eq_56]),eq_10]),eq_56]) ).
cnf(eq_72,negated_conjecture,
truth != implies(implies(x,y),implies(x,implies(implies(y,z),z))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_71,eq_68]),eq_68]),eq_65]) ).
cnf(eq_73,negated_conjecture,
not(falsehood) != implies(implies(x,y),implies(x,implies(implies(y,z),z))),
inference(rw,[status(thm)],[eq_72,eq_55]) ).
cnf(eq_74,plain,
not(falsehood) = implies(implies(X,not(Y)),implies(Y,implies(Z,not(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)],[eq_70,eq_55]),eq_58]),eq_58]),eq_58]),eq_40]),eq_57]) ).
cnf(eq_75,plain,
implies(X,not(implies(X,Y))) = implies(Y,not(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)],[eq_44,eq_58]),eq_57]),eq_40]),eq_58]),eq_40]),eq_58]),eq_57]) ).
cnf(eq_76,plain,
implies(implies(not(X),not(x101)),implies(x101,implies(x102,X))) = not(falsehood),
inference(cp,[status(thm)],[eq_40,eq_74]) ).
cnf(eq_77,plain,
not(falsehood) = implies(implies(X,Y),implies(X,implies(Z,Y))),
inference(rw,[status(thm)],[eq_76,eq_57]) ).
cnf(eq_78,plain,
truth = implies(implies(X,Y),implies(X,implies(Z,Y))),
inference(rw,[status(thm)],[eq_77,eq_55]) ).
cnf(eq_79,plain,
implies(not(Y),not(implies(X,Y))) = implies(not(X),not(implies(not(X),not(Y)))),
inference(cp,[status(thm)],[eq_57,eq_75]) ).
cnf(eq_80,plain,
implies(implies(X,Y),Y) = implies(implies(Y,X),X),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_79,eq_57]),eq_57]),eq_57]) ).
cnf(eq_81,negated_conjecture,
implies(implies(x,y),implies(x,implies(implies(z,y),y))) != not(falsehood),
inference(cp,[status(thm)],[eq_80,eq_73]) ).
cnf(eq_82,negated_conjecture,
truth != truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_81,eq_78]),eq_55]) ).
cnf(bot,negated_conjecture,
$false,
inference(cn,[status(thm)],[eq_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_maedmax %d %s
% 0.10/0.35 % Computer : n010.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 4 19:21:08 UTC 2026
% 0.10/0.35 % CPUTime :
% 34.24/34.56 % SZS status Unsatisfiable
% 34.24/34.56 % SZS output start CNFRefutation for /tmp/MaedMax_4131692
% See solution above
% 34.24/34.56
%------------------------------------------------------------------------------