%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL109-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n031.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 01:14:04 PM UTC 2026
% Result : Unsatisfiable 61.37s 61.44s
% Output : CNFRefutation 61.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 5 RR)
% Number of literals : 43 ( 42 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 : 67 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('theBenchmark.p',prove_wajsberg_mv_4) ).
cnf(c1,axiom,
not(truth) = falsehood,
file('theBenchmark.p',false_definition) ).
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(c5,axiom,
and_star(X,falsehood) = falsehood,
file('LCL002-0.ax',axiom_5) ).
cnf(c6,axiom,
not(X) = xor(X,truth),
file('LCL002-0.ax',axiom_1) ).
cnf(c7,plain,
xor(X,truth) = not(X),
inference(equational,[status(thm)],[c6]) ).
cnf(c8,axiom,
xor(X,Y) = xor(Y,X),
file('theBenchmark.p',xor_commutativity) ).
cnf(c9,axiom,
and_star(X,Y) = and_star(Y,X),
file('theBenchmark.p',and_star_commutativity) ).
cnf(c10,plain,
and_star(truth,X) = X,
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c11,plain,
xor(falsehood,X) = X,
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c12,plain,
not(falsehood) = truth,
inference(equational,[status(thm)],[c7,c11]) ).
cnf(c13,plain,
and_star(falsehood,X) = falsehood,
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c14,plain,
xor(truth,X) = not(X),
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c15,axiom,
and_star(xor(truth,X),X) = falsehood,
file('LCL002-0.ax',axiom_6) ).
cnf(c16,plain,
and_star(X,not(X)) = falsehood,
inference(equational,[status(thm)],[c9,c14,c15]) ).
cnf(c17,axiom,
and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)),
file('theBenchmark.p',and_star_associativity) ).
cnf(c18,axiom,
xor(X,xor(truth,Y)) = xor(xor(X,truth),Y),
file('LCL002-0.ax',axiom_7) ).
cnf(c19,plain,
xor(not(X),Y) = xor(X,not(Y)),
inference(equational,[status(thm)],[c7,c14,c18]) ).
cnf(c20,plain,
not(not(X)) = X,
inference(equational,[status(thm)],[c1,c4,c7,c19]) ).
cnf(c23,plain,
and_star(X,and_star(not(X),Y)) = falsehood,
inference(equational,[status(thm)],[c13,c16,c17]) ).
cnf(c25,axiom,
implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))),
file('theBenchmark.p',implies_definition) ).
cnf(c26,plain,
not(and_star(X,not(Y))) = implies(X,Y),
inference(equational,[status(thm)],[c14,c25]) ).
cnf(c29,plain,
implies(truth,X) = X,
inference(equational,[status(thm)],[c10,c20,c26]) ).
cnf(c32,plain,
implies(X,not(Y)) = not(and_star(X,Y)),
inference(equational,[status(thm)],[c20,c26]) ).
cnf(c33,plain,
and_star(X,not(Y)) = not(implies(X,Y)),
inference(equational,[status(thm)],[c20,c26]) ).
cnf(c34,plain,
not(and_star(not(X),Y)) = implies(Y,X),
inference(equational,[status(thm)],[c9,c26]) ).
cnf(c36,plain,
implies(and_star(X,Y),X) = truth,
inference(equational,[status(thm)],[c12,c20,c23,c34]) ).
cnf(c37,plain,
and_star(not(X),Y) = not(implies(Y,X)),
inference(equational,[status(thm)],[c9,c33]) ).
cnf(c39,plain,
implies(X,implies(Y,X)) = truth,
inference(equational,[status(thm)],[c20,c32,c36,c37]) ).
cnf(c47,plain,
implies(and_star(X,Y),Z) = implies(X,implies(Y,Z)),
inference(equational,[status(thm)],[c17,c20,c26,c33]) ).
cnf(c48,plain,
implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)),
inference(equational,[status(thm)],[c9,c47]) ).
cnf(c68,axiom,
and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X),
file('LCL002-0.ax',axiom_8) ).
cnf(c69,plain,
and_star(X,implies(X,Y)) = and_star(Y,implies(Y,X)),
inference(equational,[status(thm)],[c1,c4,c9,c14,c19,c37,c68]) ).
cnf(c70,plain,
implies(X,and_star(X,Y)) = implies(implies(not(Y),X),Y),
inference(equational,[status(thm)],[c20,c32,c33,c34,c69]) ).
cnf(c71,plain,
implies(implies(X,Y),Y) = implies(implies(Y,X),X),
inference(equational,[status(thm)],[c20,c32,c37,c70]) ).
cnf(c76,plain,
and_star(X,implies(X,and_star(X,Y))) = and_star(X,Y),
inference(equational,[status(thm)],[c3,c17,c36,c69]) ).
cnf(c79,plain,
implies(X,implies(implies(X,Y),Z)) = implies(Y,implies(implies(Y,X),Z)),
inference(equational,[status(thm)],[c47,c69]) ).
cnf(c83,plain,
implies(implies(implies(X,Y),Y),Y) = implies(X,Y),
inference(equational,[status(thm)],[c20,c32,c34,c37,c76]) ).
cnf(c92,plain,
implies(implies(implies(X,Y),Y),X) = implies(Y,X),
inference(equational,[status(thm)],[c71,c83]) ).
cnf(c108,plain,
implies(X,implies(implies(Y,X),Y)) = implies(X,Y),
inference(equational,[status(thm)],[c29,c39,c48,c79,c92]) ).
cnf(g1,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = truth,
inference(equational,[status(thm)],[c39,c48,c71,c108]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL109-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_Leo-III %s %d THM
% 0.07/0.35 % Computer : n031.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 : Fri Sep 4 18:23:09 UTC 2026
% 0.07/0.35 % CPUTime :
% 61.37/61.44 % SZS status Unsatisfiable
% 61.37/61.44 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------