%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LDA002-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n008.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 10.07s 10.22s
% Output : CNFRefutation 10.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 22 RR)
% Number of literals : 27 ( 26 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 : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
f(a,v) != f(b,v),
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,
u1 = f(u,n1),
file('theBenchmark.p',clause_5) ).
cnf(c7,plain,
u1 = f(f(f(n1,n1),f(n1,n1)),n1),
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c8,axiom,
u2 = f(u,n2),
file('theBenchmark.p',clause_6) ).
cnf(c9,plain,
u2 = f(f(f(n1,n1),f(n1,n1)),f(n1,n1)),
inference(equational,[status(thm)],[c1,c5,c8]) ).
cnf(c10,axiom,
u3 = f(u,n3),
file('theBenchmark.p',clause_7) ).
cnf(c11,plain,
u3 = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1)),
inference(equational,[status(thm)],[c3,c5,c10]) ).
cnf(c12,axiom,
uu = f(u,u),
file('theBenchmark.p',clause_8) ).
cnf(c13,plain,
uu = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),
inference(equational,[status(thm)],[c5,c12]) ).
cnf(c14,axiom,
b = f(u1,u3),
file('theBenchmark.p',clause_10) ).
cnf(c15,plain,
b = f(f(f(f(n1,n1),f(n1,n1)),n1),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1))),
inference(equational,[status(thm)],[c7,c11,c14]) ).
cnf(c16,axiom,
v = f(uu,uu),
file('theBenchmark.p',clause_11) ).
cnf(c17,plain,
v = f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(equational,[status(thm)],[c13,c16]) ).
cnf(c18,axiom,
a = f(f(n3,n2),u2),
file('theBenchmark.p',clause_9) ).
cnf(c19,plain,
a = f(f(f(f(n1,n1),n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(n1,n1))),
inference(equational,[status(thm)],[c1,c3,c9,c18]) ).
cnf(c20,axiom,
f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)),
file('theBenchmark.p',a1) ).
cnf(c21,plain,
f(f(X,Y),f(X,Z)) = f(X,f(Y,Z)),
inference(equational,[status(thm)],[c20]) ).
cnf(c23,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)],[c21]) ).
cnf(c25,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)],[c21,c23]) ).
cnf(c52,plain,
f(f(f(f(f(X,Y),X),f(X,Y)),Z),f(X,f(Y,W))) = f(f(f(f(X,Y),X),f(X,Y)),f(Z,f(f(f(X,Y),X),W))),
inference(equational,[status(thm)],[c21,c25]) ).
cnf(g1,plain,
f(a,v) = f(b,v),
inference(equational,[status(thm)],[c15,c17,c19,c21,c23,c25,c52]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LDA002-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 13:51:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 10.07/10.22 % SZS status Unsatisfiable
% 10.07/10.22 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------