%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : NUN134-1 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 07:37:09 AM UTC 2025
% Result : Unsatisfiable 0.92s 1.13s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 5 RR)
% Number of literals : 19 ( 18 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 : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
file('theBenchmark.p',goal) ).
cnf(c5,axiom,
times(X,Y) = times(Y,X),
file('theBenchmark.p',times_comm) ).
cnf(c6,axiom,
'+'(X,Y) = '+'(Y,X),
file('theBenchmark.p',plus_comm) ).
cnf(c10,axiom,
'+'(s(X),Y) = s('+'(X,Y)),
file('theBenchmark.p',plus_s) ).
cnf(c11,plain,
s('+'(X,Y)) = '+'(s(X),Y),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,plain,
'+'(s(X),Y) = '+'(s(Y),X),
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c13,axiom,
sum(s(X)) = '+'(s(X),sum(X)),
file('theBenchmark.p',sum_s) ).
cnf(c15,axiom,
times(s(X),Y) = '+'(Y,times(X,Y)),
file('theBenchmark.p',times_s) ).
cnf(c20,axiom,
'+'(X,'+'(Y,Z)) = '+'('+'(X,Y),Z),
file('theBenchmark.p',plus_assoc) ).
cnf(c21,plain,
'+'('+'(X,Y),Z) = '+'(X,'+'(Y,Z)),
inference(equational,[status(thm)],[c20]) ).
cnf(c26,axiom,
'+'(sum(a),sum(a)) = times(a,s(a)),
file('theBenchmark.p',induction_hypothesis) ).
cnf(c27,plain,
times(a,s(a)) = '+'(sum(a),sum(a)),
inference(equational,[status(thm)],[c26]) ).
cnf(c28,plain,
'+'(X,times(Y,X)) = times(X,s(Y)),
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c29,plain,
'+'(X,'+'(Y,Z)) = '+'(Y,'+'(X,Z)),
inference(equational,[status(thm)],[c6,c21]) ).
cnf(c32,plain,
times(X,s(Y)) = '+'(X,times(X,Y)),
inference(equational,[status(thm)],[c5,c28]) ).
cnf(c54,plain,
'+'(X,'+'(s(Y),Z)) = '+'(s(X),'+'(Z,Y)),
inference(equational,[status(thm)],[c11,c12,c21,c29]) ).
cnf(c70,plain,
'+'(X,'+'(s(Y),Z)) = '+'(s(X),'+'(Y,Z)),
inference(equational,[status(thm)],[c12,c54]) ).
cnf(g1,plain,
'+'(sum(s(a)),sum(s(a))) = times(s(a),s(s(a))),
inference(equational,[status(thm)],[c13,c15,c21,c27,c29,c32,c70]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUN134-1 : TPTP v9.0.0. Released v8.1.0.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n016.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 15:42:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.92/1.13 % SZS status Unsatisfiable
% 0.92/1.13 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------