%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL134-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 01:14:07 PM UTC 2026
% Result : Unsatisfiable 0.31s 0.72s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 3 RR)
% Number of literals : 10 ( 9 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
implies(x,truth) != truth,
file('theBenchmark.p',prove_wajsberg_lemma) ).
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(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(g1,plain,
implies(x,truth) = truth,
inference(equational,[status(thm)],[c10]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL134-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_Leo-III %s %d THM
% 0.16/0.40 % Computer : n004.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Fri Sep 4 18:16:44 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.31/0.72 % SZS status Unsatisfiable
% 0.31/0.72 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------