%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% 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 01:14:04 PM UTC 2026
% Result : Unsatisfiable 10.62s 11.04s
% Output : CNFRefutation 10.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 3 RR)
% Number of literals : 24 ( 23 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 2 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(c3,axiom,
not(not(X)) = X,
file('theBenchmark.p',lemma_9) ).
cnf(c5,axiom,
implies(X,not(truth)) = not(X),
file('theBenchmark.p',lemma_8) ).
cnf(c7,axiom,
implies(X,implies(Y,X)) = truth,
file('theBenchmark.p',lemma_4) ).
cnf(c8,axiom,
implies(not(X),not(Y)) = implies(Y,X),
file('theBenchmark.p',lemma_10) ).
cnf(c9,plain,
implies(X,not(Y)) = implies(Y,not(X)),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c10,plain,
implies(not(X),Y) = implies(not(Y),X),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c12,axiom,
implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)),
file('theBenchmark.p',lemma_7) ).
cnf(c13,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('theBenchmark.p',wajsberg_3) ).
cnf(c14,plain,
implies(not(X),not(implies(Y,X))) = implies(not(Y),not(implies(X,Y))),
inference(equational,[status(thm)],[c8,c13]) ).
cnf(c15,plain,
implies(X,implies(not(X),Y)) = truth,
inference(equational,[status(thm)],[c7,c8,c12]) ).
cnf(c20,plain,
implies(X,implies(Y,Z)) = implies(not(Z),implies(X,not(Y))),
inference(equational,[status(thm)],[c8,c12]) ).
cnf(c22,plain,
implies(X,implies(Y,Z)) = implies(not(implies(X,Z)),not(Y)),
inference(equational,[status(thm)],[c8,c12]) ).
cnf(c23,plain,
implies(not(implies(X,Y)),Z) = implies(X,implies(not(Y),Z)),
inference(equational,[status(thm)],[c3,c10,c22]) ).
cnf(c40,plain,
implies(not(X),implies(Y,not(Z))) = implies(Z,implies(Y,X)),
inference(equational,[status(thm)],[c12,c20]) ).
cnf(c46,plain,
implies(X,not(implies(not(Y),not(X)))) = implies(Y,not(implies(Y,X))),
inference(equational,[status(thm)],[c3,c8,c14]) ).
cnf(c47,plain,
implies(X,not(implies(X,Y))) = implies(Y,not(implies(Y,X))),
inference(equational,[status(thm)],[c8,c46]) ).
cnf(c52,plain,
implies(X,not(implies(Y,not(X)))) = implies(not(Y),not(implies(not(X),Y))),
inference(equational,[status(thm)],[c3,c14]) ).
cnf(c55,plain,
implies(X,not(implies(X,not(implies(X,Y))))) = implies(X,Y),
inference(equational,[status(thm)],[c3,c5,c9,c15,c23,c52]) ).
cnf(c114,plain,
implies(X,not(implies(Y,not(implies(Y,X))))) = implies(X,Y),
inference(equational,[status(thm)],[c47,c55]) ).
cnf(c146,plain,
implies(X,implies(not(Y),not(implies(Z,Y)))) = implies(not(Z),implies(X,not(implies(Y,Z)))),
inference(equational,[status(thm)],[c12,c14]) ).
cnf(c147,plain,
implies(not(X),implies(Y,not(implies(X,Y)))) = implies(Y,X),
inference(equational,[status(thm)],[c3,c5,c7,c23,c40,c114,c146]) ).
cnf(g1,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = truth,
inference(equational,[status(thm)],[c3,c8,c9,c12,c15,c23,c46,c147]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_Leo-III %s %d THM
% 0.09/0.34 % Computer : n027.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 5 22:12:59 UTC 2026
% 0.09/0.35 % CPUTime :
% 10.62/11.04 % SZS status Unsatisfiable
% 10.62/11.04 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------