%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL138-1 : 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 01:14:07 PM UTC 2026
% Result : Unsatisfiable 7.71s 8.07s
% Output : CNFRefutation 7.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 3 RR)
% Number of literals : 11 ( 10 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
implies(x,implies(y,z)) != implies(y,implies(x,z)),
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(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(c30,plain,
implies(implies(implies(implies(X,Y),Y),Z),implies(X,Z)) = truth,
inference(equational,[status(thm)],[c1,c7,c8]) ).
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(g1,plain,
implies(x,implies(y,z)) = implies(y,implies(x,z)),
inference(equational,[status(thm)],[c204]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL138-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_Leo-III %s %d THM
% 0.07/0.34 % Computer : n031.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 5 00:13:24 UTC 2026
% 0.07/0.34 % CPUTime :
% 7.71/8.07 % SZS status Unsatisfiable
% 7.71/8.07 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------