%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 0.85s 1.14s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 3 RR)
% Number of literals : 14 ( 13 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
implies(truth,x) != x,
file('theBenchmark.p',prove_wajsberg_axiom) ).
cnf(c2,axiom,
xor(X,X) = falsehood,
file('LCL002-0.ax',axiom_3) ).
cnf(c3,axiom,
and_star(X,truth) = X,
file('LCL002-0.ax',axiom_4) ).
cnf(c4,axiom,
xor(X,falsehood) = X,
file('LCL002-0.ax',axiom_2) ).
cnf(c7,axiom,
xor(X,Y) = xor(Y,X),
file('theBenchmark.p',xor_commutativity) ).
cnf(c8,axiom,
and_star(X,Y) = and_star(Y,X),
file('theBenchmark.p',and_star_commutativity) ).
cnf(c9,plain,
and_star(truth,X) = X,
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c10,plain,
xor(falsehood,X) = X,
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c16,axiom,
xor(X,xor(truth,Y)) = xor(xor(X,truth),Y),
file('LCL002-0.ax',axiom_7) ).
cnf(c17,plain,
xor(xor(X,truth),Y) = xor(X,xor(truth,Y)),
inference(equational,[status(thm)],[c16]) ).
cnf(c18,plain,
xor(truth,xor(truth,X)) = X,
inference(equational,[status(thm)],[c2,c10,c17]) ).
cnf(c25,axiom,
implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))),
file('theBenchmark.p',implies_definition) ).
cnf(g1,plain,
implies(truth,x) = x,
inference(equational,[status(thm)],[c9,c18,c25]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_Leo-III %s %d THM
% 0.06/0.33 % Computer : n006.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Sat Sep 5 08:54:16 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.85/1.14 % SZS status Unsatisfiable
% 0.85/1.14 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------