%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL154-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 0.72s 1.30s
% Output : CNFRefutation 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 6 RR)
% Number of literals : 41 ( 40 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
xor(x,falsehood) != x,
file('theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c1,axiom,
not(truth) = falsehood,
file('LCL002-1.ax',false_definition) ).
cnf(c2,plain,
falsehood = not(truth),
inference(equational,[status(thm)],[c1]) ).
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(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(c11,axiom,
or(or(X,Y),Z) = or(X,or(Y,Z)),
file('LCL001-2.ax',or_associativity) ).
cnf(c14,plain,
implies(implies(X,truth),truth) = implies(X,X),
inference(equational,[status(thm)],[c3,c10]) ).
cnf(c18,axiom,
and(X,Y) = not(or(not(X),not(Y))),
file('LCL001-2.ax',and_definition) ).
cnf(c21,plain,
or(X,not(X)) = implies(or(X,truth),truth),
inference(equational,[status(thm)],[c9,c14]) ).
cnf(c22,plain,
implies(implies(X,not(Y)),not(Y)) = implies(or(Y,X),X),
inference(equational,[status(thm)],[c9,c10]) ).
cnf(c23,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('LCL001-0.ax',wajsberg_4) ).
cnf(c24,plain,
implies(or(X,not(Y)),implies(Y,X)) = truth,
inference(equational,[status(thm)],[c9,c23]) ).
cnf(c25,plain,
implies(or(X,not(truth)),X) = truth,
inference(equational,[status(thm)],[c3,c24]) ).
cnf(c26,plain,
implies(or(not(truth),X),X) = truth,
inference(equational,[status(thm)],[c4,c25]) ).
cnf(c27,plain,
not(not(truth)) = truth,
inference(equational,[status(thm)],[c3,c21,c26]) ).
cnf(c28,plain,
implies(X,X) = truth,
inference(equational,[status(thm)],[c14,c22,c26,c27]) ).
cnf(c29,plain,
or(not(truth),X) = X,
inference(equational,[status(thm)],[c3,c9,c27]) ).
cnf(c30,plain,
or(X,not(truth)) = X,
inference(equational,[status(thm)],[c4,c29]) ).
cnf(c31,plain,
implies(or(X,truth),truth) = truth,
inference(equational,[status(thm)],[c9,c21,c28]) ).
cnf(c32,plain,
implies(or(not(X),Y),implies(X,Y)) = truth,
inference(equational,[status(thm)],[c4,c24]) ).
cnf(c33,plain,
implies(X,not(not(X))) = truth,
inference(equational,[status(thm)],[c3,c21,c31,c32]) ).
cnf(c36,plain,
not(not(X)) = X,
inference(equational,[status(thm)],[c3,c4,c21,c22,c31,c33]) ).
cnf(c37,plain,
implies(X,Y) = or(not(X),Y),
inference(equational,[status(thm)],[c9,c36]) ).
cnf(c38,plain,
implies(X,not(truth)) = not(X),
inference(equational,[status(thm)],[c30,c37]) ).
cnf(c42,plain,
implies(or(truth,X),X) = X,
inference(equational,[status(thm)],[c9,c10,c30,c38]) ).
cnf(c43,axiom,
xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)),
file('LCL002-1.ax',xor_definition) ).
cnf(c44,plain,
xor(X,Y) = or(implies(or(not(X),Y),not(truth)),implies(or(X,not(Y)),not(truth))),
inference(equational,[status(thm)],[c18,c36,c38,c43]) ).
cnf(c45,plain,
implies(or(X,Y),or(Y,X)) = truth,
inference(equational,[status(thm)],[c9,c24,c36]) ).
cnf(c49,plain,
or(X,or(not(X),Y)) = or(truth,Y),
inference(equational,[status(thm)],[c11,c21,c31]) ).
cnf(c50,plain,
or(X,or(Y,not(X))) = or(truth,Y),
inference(equational,[status(thm)],[c4,c49]) ).
cnf(c51,plain,
or(X,implies(X,Y)) = or(truth,Y),
inference(equational,[status(thm)],[c37,c49]) ).
cnf(c52,plain,
or(not(X),or(Y,X)) = or(truth,Y),
inference(equational,[status(thm)],[c36,c50]) ).
cnf(c53,plain,
implies(X,or(Y,X)) = or(truth,Y),
inference(equational,[status(thm)],[c37,c52]) ).
cnf(c57,plain,
or(X,or(truth,truth)) = or(truth,truth),
inference(equational,[status(thm)],[c11,c31,c51]) ).
cnf(c58,plain,
or(truth,X) = truth,
inference(equational,[status(thm)],[c45,c53,c57]) ).
cnf(g1,plain,
xor(x,falsehood) = x,
inference(equational,[status(thm)],[c2,c3,c4,c5,c22,c27,c29,c30,c38,c42,c44,c58]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL154-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_Leo-III %s %d THM
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 5 00:27:50 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.72/1.30 % SZS status Unsatisfiable
% 0.72/1.30 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------