%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n028.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 01:14:10 PM UTC 2026
% Result : Unsatisfiable 0.73s 1.20s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 3 RR)
% Number of literals : 18 ( 17 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; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
implies(implies(not(x),not(y)),implies(y,x)) != truth,
file('theBenchmark.p',prove_wajsberg_axiom) ).
cnf(c2,axiom,
xor(X,X) = falsehood,
file('LCL002-0.ax',axiom_3) ).
cnf(c4,axiom,
xor(X,falsehood) = X,
file('LCL002-0.ax',axiom_2) ).
cnf(c6,axiom,
not(X) = xor(X,truth),
file('LCL002-0.ax',axiom_1) ).
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(c10,plain,
xor(falsehood,X) = X,
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c12,axiom,
and_star(xor(truth,X),X) = falsehood,
file('LCL002-0.ax',axiom_6) ).
cnf(c13,plain,
and_star(X,xor(truth,X)) = falsehood,
inference(equational,[status(thm)],[c8,c12]) ).
cnf(c15,axiom,
and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)),
file('theBenchmark.p',and_star_associativity) ).
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(c20,plain,
and_star(X,and_star(Y,Z)) = and_star(Y,and_star(X,Z)),
inference(equational,[status(thm)],[c8,c15]) ).
cnf(c25,axiom,
implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))),
file('theBenchmark.p',implies_definition) ).
cnf(c32,plain,
and_star(X,and_star(Y,xor(truth,and_star(X,Y)))) = falsehood,
inference(equational,[status(thm)],[c13,c15]) ).
cnf(g1,plain,
implies(implies(not(x),not(y)),implies(y,x)) = truth,
inference(equational,[status(thm)],[c4,c6,c7,c8,c18,c20,c25,c32]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_Leo-III %s %d THM
% 0.08/0.36 % Computer : n028.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 5 06:44:44 UTC 2026
% 0.01/0.36 % CPUTime :
% 0.73/1.20 % SZS status Unsatisfiable
% 0.73/1.20 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------