%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LDA001-1 : TPTP v9.0.0. 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 : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 07:18:09 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 8 RR)
% Number of literals : 12 ( 11 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 : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
f(f(n3,n2),u) != f(f(u,u),u),
file('theBenchmark.p',prove_equation) ).
cnf(c1,axiom,
n2 = f(n1,n1),
file('theBenchmark.p',clause_2) ).
cnf(c2,axiom,
n3 = f(n2,n1),
file('theBenchmark.p',clause_3) ).
cnf(c3,plain,
n3 = f(f(n1,n1),n1),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,axiom,
u = f(n2,n2),
file('theBenchmark.p',clause_4) ).
cnf(c5,plain,
u = f(f(n1,n1),f(n1,n1)),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,axiom,
f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)),
file('theBenchmark.p',a1) ).
cnf(c7,plain,
f(f(X,Y),f(X,Z)) = f(X,f(Y,Z)),
inference(equational,[status(thm)],[c6]) ).
cnf(c9,plain,
f(f(f(X,Y),Z),f(X,f(Y,W))) = f(f(X,Y),f(Z,f(X,W))),
inference(equational,[status(thm)],[c7]) ).
cnf(c11,plain,
f(f(f(f(X,Y),X),Z),f(X,f(Y,W))) = f(f(f(X,Y),X),f(Z,f(f(X,Y),W))),
inference(equational,[status(thm)],[c7,c9]) ).
cnf(g1,plain,
f(f(n3,n2),u) = f(f(u,u),u),
inference(equational,[status(thm)],[c1,c3,c5,c7,c11]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LDA001-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.34 % DateTime : Mon Jul 14 13:51:19 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.19/0.51 % SZS status Unsatisfiable
% 0.19/0.51 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------