%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n027.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 16.25s 16.79s
% Output : CNFRefutation 16.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 5 RR)
% Number of literals : 41 ( 40 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
file('theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c3,axiom,
implies(truth,X) = X,
file('LCL001-0.ax',wajsberg_1) ).
cnf(c4,axiom,
or(X,Y) = or(Y,X),
file('LCL001-2.ax',or_commutativity) ).
cnf(c5,axiom,
xor(X,Y) = xor(Y,X),
file('LCL002-1.ax',xor_commutativity) ).
cnf(c7,axiom,
and_star(X,Y) = and_star(Y,X),
file('LCL002-1.ax',and_star_commutativity) ).
cnf(c8,axiom,
or(X,Y) = implies(not(X),Y),
file('LCL001-2.ax',or_definition) ).
cnf(c9,plain,
implies(not(X),Y) = or(X,Y),
inference(equational,[status(thm)],[c8]) ).
cnf(c10,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('LCL001-0.ax',wajsberg_3) ).
cnf(c12,axiom,
and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)),
file('LCL002-1.ax',and_star_associativity) ).
cnf(c14,plain,
implies(implies(X,truth),truth) = implies(X,X),
inference(equational,[status(thm)],[c3,c10]) ).
cnf(c16,plain,
and_star(X,and_star(Y,Z)) = and_star(Y,and_star(X,Z)),
inference(equational,[status(thm)],[c7,c12]) ).
cnf(c18,axiom,
and(X,Y) = not(or(not(X),not(Y))),
file('LCL001-2.ax',and_definition) ).
cnf(c19,axiom,
and_star(X,Y) = not(or(not(X),not(Y))),
file('LCL002-1.ax',and_star_definition) ).
cnf(c20,plain,
not(or(not(X),not(not(or(not(Y),not(Z)))))) = not(or(not(Z),not(not(or(not(X),not(Y)))))),
inference(equational,[status(thm)],[c7,c16,c19]) ).
cnf(c21,plain,
implies(or(X,truth),truth) = or(X,not(X)),
inference(equational,[status(thm)],[c9,c14]) ).
cnf(c23,plain,
implies(implies(X,not(Y)),not(Y)) = implies(or(Y,X),X),
inference(equational,[status(thm)],[c9,c10]) ).
cnf(c24,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('LCL001-0.ax',wajsberg_4) ).
cnf(c25,plain,
implies(or(X,not(Y)),implies(Y,X)) = truth,
inference(equational,[status(thm)],[c9,c24]) ).
cnf(c26,plain,
implies(or(X,not(truth)),X) = truth,
inference(equational,[status(thm)],[c3,c25]) ).
cnf(c27,plain,
implies(or(not(truth),X),X) = truth,
inference(equational,[status(thm)],[c4,c26]) ).
cnf(c28,plain,
or(not(truth),not(not(truth))) = truth,
inference(equational,[status(thm)],[c21,c27]) ).
cnf(c29,plain,
not(not(truth)) = truth,
inference(equational,[status(thm)],[c3,c27,c28]) ).
cnf(c30,plain,
implies(X,X) = truth,
inference(equational,[status(thm)],[c14,c23,c27,c29]) ).
cnf(c32,plain,
or(not(truth),X) = X,
inference(equational,[status(thm)],[c3,c9,c29]) ).
cnf(c33,plain,
or(X,not(X)) = truth,
inference(equational,[status(thm)],[c9,c30]) ).
cnf(c34,plain,
or(X,not(truth)) = X,
inference(equational,[status(thm)],[c4,c32]) ).
cnf(c37,axiom,
xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)),
file('LCL002-1.ax',xor_definition) ).
cnf(c38,plain,
xor(X,Y) = or(not(or(not(X),not(not(Y)))),not(or(not(not(X)),not(Y)))),
inference(equational,[status(thm)],[c18,c37]) ).
cnf(c41,plain,
implies(or(X,not(not(Y))),or(Y,X)) = truth,
inference(equational,[status(thm)],[c9,c25]) ).
cnf(c42,plain,
implies(or(X,not(Y)),not(Y)) = implies(or(Y,not(X)),not(X)),
inference(equational,[status(thm)],[c9,c23]) ).
cnf(c45,plain,
implies(or(not(not(X)),Y),or(X,Y)) = truth,
inference(equational,[status(thm)],[c4,c41]) ).
cnf(c47,plain,
implies(or(not(X),Y),not(X)) = implies(or(X,not(Y)),not(Y)),
inference(equational,[status(thm)],[c4,c42]) ).
cnf(c48,plain,
or(X,not(not(not(X)))) = truth,
inference(equational,[status(thm)],[c3,c33,c45]) ).
cnf(c49,plain,
not(not(not(X))) = not(X),
inference(equational,[status(thm)],[c3,c33,c47,c48]) ).
cnf(c55,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('LCL001-0.ax',wajsberg_2) ).
cnf(c56,plain,
implies(X,implies(implies(X,Y),Y)) = truth,
inference(equational,[status(thm)],[c3,c55]) ).
cnf(c57,plain,
implies(X,truth) = truth,
inference(equational,[status(thm)],[c14,c30,c56]) ).
cnf(c58,plain,
or(X,truth) = truth,
inference(equational,[status(thm)],[c9,c57]) ).
cnf(c59,plain,
or(truth,X) = truth,
inference(equational,[status(thm)],[c4,c58]) ).
cnf(g1,plain,
xor(x,xor(truth,y)) = xor(xor(x,truth),y),
inference(equational,[status(thm)],[c4,c5,c20,c29,c32,c34,c38,c49,c59]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_Leo-III %s %d THM
% 0.07/0.33 % Computer : n027.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 5 16:51:28 UTC 2026
% 0.07/0.34 % CPUTime :
% 16.25/16.79 % SZS status Unsatisfiable
% 16.25/16.79 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------