%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL160-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 01:14:09 PM UTC 2026
% Result : Unsatisfiable 60.20s 60.61s
% Output : CNFRefutation 60.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of clauses : 70 ( 70 unt; 0 nHn; 7 RR)
% Number of literals : 70 ( 69 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 100 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
and_star(xor(and_star(xor(truth,x),y),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
file('theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c1,axiom,
not(truth) = falsehood,
file('LCL002-1.ax',false_definition) ).
cnf(c2,axiom,
implies(truth,X) = X,
file('LCL001-0.ax',wajsberg_1) ).
cnf(c3,axiom,
or(X,Y) = or(Y,X),
file('LCL001-2.ax',or_commutativity) ).
cnf(c4,axiom,
xor(X,Y) = xor(Y,X),
file('LCL002-1.ax',xor_commutativity) ).
cnf(c5,axiom,
and(X,Y) = and(Y,X),
file('LCL001-2.ax',and_commutativity) ).
cnf(c6,axiom,
and_star(X,Y) = and_star(Y,X),
file('LCL002-1.ax',and_star_commutativity) ).
cnf(c7,axiom,
or(X,Y) = implies(not(X),Y),
file('LCL001-2.ax',or_definition) ).
cnf(c8,plain,
implies(not(X),Y) = or(X,Y),
inference(equational,[status(thm)],[c7]) ).
cnf(c9,plain,
implies(falsehood,X) = or(truth,X),
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c10,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('LCL001-0.ax',wajsberg_3) ).
cnf(c11,axiom,
or(or(X,Y),Z) = or(X,or(Y,Z)),
file('LCL001-2.ax',or_associativity) ).
cnf(c14,plain,
implies(X,X) = implies(implies(X,truth),truth),
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c15,plain,
or(X,or(Y,Z)) = or(Y,or(X,Z)),
inference(equational,[status(thm)],[c3,c11]) ).
cnf(c18,axiom,
and(X,Y) = not(or(not(X),not(Y))),
file('LCL001-2.ax',and_definition) ).
cnf(c19,plain,
not(or(not(X),not(Y))) = and(X,Y),
inference(equational,[status(thm)],[c18]) ).
cnf(c20,plain,
not(or(falsehood,not(X))) = and(truth,X),
inference(equational,[status(thm)],[c1,c19]) ).
cnf(c22,axiom,
and_star(X,Y) = not(or(not(X),not(Y))),
file('LCL002-1.ax',and_star_definition) ).
cnf(c23,plain,
and_star(X,Y) = and(X,Y),
inference(equational,[status(thm)],[c19,c22]) ).
cnf(c25,plain,
implies(or(X,truth),truth) = or(X,not(X)),
inference(equational,[status(thm)],[c8,c14]) ).
cnf(c30,plain,
or(falsehood,or(not(X),Y)) = implies(and(truth,X),Y),
inference(equational,[status(thm)],[c8,c11,c20]) ).
cnf(c31,plain,
implies(or(X,Y),Y) = implies(implies(Y,not(X)),not(X)),
inference(equational,[status(thm)],[c8,c10]) ).
cnf(c34,plain,
or(falsehood,or(X,not(Y))) = implies(and(truth,Y),X),
inference(equational,[status(thm)],[c3,c30]) ).
cnf(c35,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('LCL001-0.ax',wajsberg_4) ).
cnf(c36,plain,
implies(or(X,not(Y)),implies(Y,X)) = truth,
inference(equational,[status(thm)],[c8,c35]) ).
cnf(c37,plain,
implies(or(X,falsehood),X) = truth,
inference(equational,[status(thm)],[c1,c2,c36]) ).
cnf(c38,plain,
implies(or(falsehood,X),X) = truth,
inference(equational,[status(thm)],[c3,c37]) ).
cnf(c39,plain,
or(falsehood,not(falsehood)) = truth,
inference(equational,[status(thm)],[c25,c38]) ).
cnf(c40,plain,
not(falsehood) = truth,
inference(equational,[status(thm)],[c2,c38,c39]) ).
cnf(c42,plain,
or(falsehood,truth) = truth,
inference(equational,[status(thm)],[c2,c3,c9,c36,c39]) ).
cnf(c43,plain,
or(falsehood,X) = X,
inference(equational,[status(thm)],[c2,c8,c40]) ).
cnf(c44,plain,
implies(X,X) = truth,
inference(equational,[status(thm)],[c3,c37,c43]) ).
cnf(c46,plain,
or(X,not(X)) = truth,
inference(equational,[status(thm)],[c8,c44]) ).
cnf(c48,plain,
or(X,falsehood) = X,
inference(equational,[status(thm)],[c3,c43]) ).
cnf(c49,plain,
implies(implies(X,truth),truth) = truth,
inference(equational,[status(thm)],[c14,c44]) ).
cnf(c50,plain,
not(not(X)) = and(truth,X),
inference(equational,[status(thm)],[c20,c43]) ).
cnf(c51,plain,
implies(and(truth,X),X) = truth,
inference(equational,[status(thm)],[c34,c42,c46]) ).
cnf(c52,plain,
implies(or(X,truth),truth) = truth,
inference(equational,[status(thm)],[c8,c49]) ).
cnf(c57,plain,
implies(or(not(X),Y),implies(X,Y)) = truth,
inference(equational,[status(thm)],[c3,c36]) ).
cnf(c58,plain,
implies(X,and(truth,X)) = truth,
inference(equational,[status(thm)],[c2,c25,c50,c52,c57]) ).
cnf(c59,plain,
and(truth,X) = X,
inference(equational,[status(thm)],[c2,c10,c51,c58]) ).
cnf(c60,plain,
and(X,truth) = X,
inference(equational,[status(thm)],[c5,c59]) ).
cnf(c62,plain,
not(or(truth,not(X))) = and(falsehood,X),
inference(equational,[status(thm)],[c19,c40]) ).
cnf(c66,plain,
or(X,or(Y,not(X))) = or(Y,truth),
inference(equational,[status(thm)],[c15,c46]) ).
cnf(c67,plain,
or(truth,not(X)) = implies(X,truth),
inference(equational,[status(thm)],[c3,c30,c40,c59,c66]) ).
cnf(c71,plain,
or(truth,and(falsehood,X)) = truth,
inference(equational,[status(thm)],[c49,c62,c67]) ).
cnf(c75,plain,
implies(X,falsehood) = not(X),
inference(equational,[status(thm)],[c34,c43,c59]) ).
cnf(c77,plain,
not(or(and(X,Y),not(Z))) = and(or(not(X),not(Y)),Z),
inference(equational,[status(thm)],[c19]) ).
cnf(c78,plain,
or(not(X),not(Y)) = not(and(X,Y)),
inference(equational,[status(thm)],[c1,c48,c60,c77]) ).
cnf(c79,plain,
implies(X,not(Y)) = not(and(X,Y)),
inference(equational,[status(thm)],[c30,c43,c59,c78]) ).
cnf(c80,plain,
not(and(not(X),Y)) = or(X,not(Y)),
inference(equational,[status(thm)],[c20,c43,c59,c78]) ).
cnf(c81,plain,
not(implies(X,Y)) = and(not(Y),X),
inference(equational,[status(thm)],[c20,c34,c59,c80]) ).
cnf(c82,plain,
or(X,not(Y)) = implies(Y,X),
inference(equational,[status(thm)],[c20,c43,c59,c80,c81]) ).
cnf(c83,plain,
not(and(X,not(Y))) = or(not(X),Y),
inference(equational,[status(thm)],[c20,c43,c59,c78]) ).
cnf(c84,plain,
or(not(X),Y) = implies(X,Y),
inference(equational,[status(thm)],[c5,c80,c82,c83]) ).
cnf(c89,plain,
implies(X,and(Y,X)) = implies(or(X,Y),Y),
inference(equational,[status(thm)],[c8,c31,c50,c59,c78,c82]) ).
cnf(c95,plain,
and(not(X),not(Y)) = not(or(Y,X)),
inference(equational,[status(thm)],[c8,c81]) ).
cnf(c96,plain,
not(or(X,truth)) = and(falsehood,not(X)),
inference(equational,[status(thm)],[c1,c95]) ).
cnf(c97,plain,
or(X,truth) = truth,
inference(equational,[status(thm)],[c11,c46,c71,c96]) ).
cnf(c98,plain,
implies(X,truth) = truth,
inference(equational,[status(thm)],[c84,c97]) ).
cnf(c101,plain,
and(falsehood,X) = falsehood,
inference(equational,[status(thm)],[c1,c81,c98]) ).
cnf(c108,plain,
and(X,falsehood) = falsehood,
inference(equational,[status(thm)],[c5,c101]) ).
cnf(c114,axiom,
xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)),
file('LCL002-1.ax',xor_definition) ).
cnf(c115,plain,
or(and(X,not(Y)),and(not(X),Y)) = xor(X,Y),
inference(equational,[status(thm)],[c114]) ).
cnf(c116,plain,
xor(X,truth) = not(X),
inference(equational,[status(thm)],[c1,c43,c60,c108,c115]) ).
cnf(c117,plain,
xor(truth,X) = not(X),
inference(equational,[status(thm)],[c1,c59,c75,c84,c101,c115]) ).
cnf(c131,plain,
implies(X,and(not(Y),X)) = not(and(Y,implies(Y,X))),
inference(equational,[status(thm)],[c5,c79,c82,c89]) ).
cnf(c132,plain,
and(X,implies(X,Y)) = and(Y,implies(Y,X)),
inference(equational,[status(thm)],[c5,c20,c43,c59,c80,c81,c82,c131]) ).
cnf(g1,plain,
and_star(xor(and_star(xor(truth,x),y),truth),y) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(equational,[status(thm)],[c4,c6,c23,c83,c84,c116,c117,c132]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL160-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_Leo-III %s %d THM
% 0.07/0.34 % Computer : n003.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 4 15:18:49 UTC 2026
% 0.07/0.34 % CPUTime :
% 60.20/60.61 % SZS status Unsatisfiable
% 60.20/60.61 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------