%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL109-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 31.29s 31.62s
% Output : CNFRefutation 31.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of clauses : 50 ( 50 unt; 0 nHn; 3 RR)
% Number of literals : 50 ( 49 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 : 106 ( 7 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,
implies(truth,X) = X,
file('LCL001-0.ax',wajsberg_1) ).
cnf(c2,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('LCL001-0.ax',wajsberg_3) ).
cnf(c3,plain,
implies(implies(X,truth),truth) = implies(X,X),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('LCL001-0.ax',wajsberg_4) ).
cnf(c5,plain,
implies(implies(not(X),not(truth)),X) = truth,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c7,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('LCL001-0.ax',wajsberg_2) ).
cnf(c8,plain,
implies(X,implies(implies(X,Y),Y)) = truth,
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c9,plain,
implies(X,X) = truth,
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c10,plain,
implies(X,truth) = truth,
inference(equational,[status(thm)],[c3,c8,c9]) ).
cnf(c11,plain,
implies(X,implies(Y,X)) = truth,
inference(equational,[status(thm)],[c1,c7,c10]) ).
cnf(c12,plain,
implies(implies(implies(X,Y),Y),X) = implies(Y,X),
inference(equational,[status(thm)],[c1,c2,c11]) ).
cnf(c17,plain,
implies(implies(implies(X,Y),Z),implies(Y,Z)) = truth,
inference(equational,[status(thm)],[c1,c7,c11]) ).
cnf(c18,plain,
implies(not(truth),X) = truth,
inference(equational,[status(thm)],[c1,c5,c17]) ).
cnf(c20,plain,
implies(not(X),implies(X,Y)) = truth,
inference(equational,[status(thm)],[c1,c4,c17]) ).
cnf(c24,plain,
implies(implies(X,not(truth)),implies(X,Y)) = truth,
inference(equational,[status(thm)],[c1,c7,c18]) ).
cnf(c30,plain,
implies(implies(implies(implies(X,Y),Y),Z),implies(X,Z)) = truth,
inference(equational,[status(thm)],[c1,c7,c8]) ).
cnf(c33,plain,
implies(implies(X,Y),implies(implies(not(X),not(truth)),Y)) = truth,
inference(equational,[status(thm)],[c1,c5,c7]) ).
cnf(c34,plain,
implies(implies(X,not(truth)),not(X)) = truth,
inference(equational,[status(thm)],[c1,c2,c18,c33]) ).
cnf(c35,plain,
implies(X,not(truth)) = not(X),
inference(equational,[status(thm)],[c1,c2,c20,c34]) ).
cnf(c36,plain,
not(not(X)) = X,
inference(equational,[status(thm)],[c1,c2,c18,c35]) ).
cnf(c37,plain,
implies(X,implies(not(X),Y)) = truth,
inference(equational,[status(thm)],[c20,c36]) ).
cnf(c42,plain,
implies(implies(X,Y),implies(not(Y),not(X))) = truth,
inference(equational,[status(thm)],[c7,c35]) ).
cnf(c43,plain,
implies(not(X),not(Y)) = implies(Y,X),
inference(equational,[status(thm)],[c1,c2,c4,c42]) ).
cnf(c44,plain,
implies(X,not(Y)) = implies(Y,not(X)),
inference(equational,[status(thm)],[c36,c43]) ).
cnf(c45,plain,
implies(not(X),Y) = implies(not(Y),X),
inference(equational,[status(thm)],[c36,c43]) ).
cnf(c50,plain,
implies(not(X),not(implies(Y,X))) = implies(not(Y),not(implies(X,Y))),
inference(equational,[status(thm)],[c2,c43]) ).
cnf(c51,plain,
implies(not(X),not(implies(not(X),not(Y)))) = implies(not(Y),not(implies(X,Y))),
inference(equational,[status(thm)],[c2,c43]) ).
cnf(c72,plain,
implies(X,not(implies(not(Y),not(X)))) = implies(Y,not(implies(Y,X))),
inference(equational,[status(thm)],[c2,c43,c44]) ).
cnf(c80,plain,
implies(implies(implies(X,Y),Z),implies(implies(not(Y),not(X)),Z)) = truth,
inference(equational,[status(thm)],[c1,c4,c7]) ).
cnf(c100,plain,
implies(not(implies(X,Y)),not(implies(not(Y),not(X)))) = truth,
inference(equational,[status(thm)],[c35,c80]) ).
cnf(c158,plain,
implies(not(implies(not(X),not(Y))),not(implies(Y,X))) = truth,
inference(equational,[status(thm)],[c1,c42]) ).
cnf(c202,plain,
implies(implies(implies(implies(X,Y),implies(Z,Y)),W),implies(implies(Z,X),W)) = truth,
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c203,plain,
implies(implies(X,implies(Y,Z)),implies(Y,implies(X,Z))) = truth,
inference(equational,[status(thm)],[c1,c30,c202]) ).
cnf(c204,plain,
implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)),
inference(equational,[status(thm)],[c1,c2,c203]) ).
cnf(c205,plain,
implies(X,implies(Y,implies(Z,W))) = implies(Z,implies(X,implies(Y,W))),
inference(equational,[status(thm)],[c204]) ).
cnf(c206,plain,
implies(X,implies(Y,not(Z))) = implies(Y,implies(Z,not(X))),
inference(equational,[status(thm)],[c35,c205]) ).
cnf(c207,plain,
implies(X,implies(not(Y),not(implies(Z,Y)))) = implies(implies(Y,Z),implies(X,Z)),
inference(equational,[status(thm)],[c2,c43,c204]) ).
cnf(c211,plain,
implies(X,implies(Y,Z)) = implies(X,implies(not(Z),not(Y))),
inference(equational,[status(thm)],[c1,c4,c35,c36,c42,c207]) ).
cnf(c217,plain,
implies(X,implies(Y,Z)) = implies(not(Z),implies(X,not(Y))),
inference(equational,[status(thm)],[c204,c211]) ).
cnf(c219,plain,
implies(X,implies(Y,Z)) = implies(Y,implies(not(Z),not(X))),
inference(equational,[status(thm)],[c36,c206]) ).
cnf(c220,plain,
implies(not(implies(X,Y)),Z) = implies(X,implies(not(Y),Z)),
inference(equational,[status(thm)],[c36,c45,c219]) ).
cnf(c221,plain,
implies(X,implies(Y,Z)) = implies(not(Z),implies(Y,not(X))),
inference(equational,[status(thm)],[c43,c206]) ).
cnf(c229,plain,
implies(X,implies(Y,Z)) = implies(not(Z),implies(implies(not(Y),not(implies(Z,Y))),not(X))),
inference(equational,[status(thm)],[c12,c43,c204,c217]) ).
cnf(c230,plain,
implies(X,not(implies(not(Y),not(Z)))) = implies(X,not(implies(Z,Y))),
inference(equational,[status(thm)],[c1,c35,c36,c100,c158,c207]) ).
cnf(c241,plain,
implies(X,not(implies(not(Y),not(Z)))) = implies(implies(Z,Y),not(X)),
inference(equational,[status(thm)],[c36,c43,c230]) ).
cnf(c253,plain,
implies(X,implies(implies(X,Y),not(Z))) = implies(Z,implies(Y,not(implies(Y,X)))),
inference(equational,[status(thm)],[c24,c35,c36,c72,c220,c229,c241]) ).
cnf(c302,plain,
implies(X,implies(Y,not(implies(not(X),Y)))) = implies(X,not(Y)),
inference(equational,[status(thm)],[c11,c12,c35,c36,c221,c253]) ).
cnf(g1,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = truth,
inference(equational,[status(thm)],[c36,c37,c43,c50,c51,c220,c302]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL109-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_Leo-III %s %d THM
% 0.07/0.35 % Computer : n001.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 18:46:29 UTC 2026
% 0.07/0.35 % CPUTime :
% 31.29/31.62 % SZS status Unsatisfiable
% 31.29/31.62 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------