%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : RNG128-1 : TPTP v9.0.0. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n015.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 07:42:59 AM UTC 2025
% Result : Unsatisfiable 0.41s 0.63s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 5 RR)
% Number of literals : 35 ( 34 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
add(x0,x1) != mult(x0,x1),
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
add(zero,X) = X,
file('theBenchmark.p',sos_004) ).
cnf(c2,axiom,
mult(X,unit) = X,
file('theBenchmark.p',sos_005) ).
cnf(c3,axiom,
mult(X,Y) = mult(Y,X),
file('theBenchmark.p',sos_002) ).
cnf(c4,axiom,
add(X,Y) = add(Y,X),
file('theBenchmark.p',sos_001) ).
cnf(c5,plain,
add(X,zero) = X,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,plain,
mult(unit,X) = X,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c7,axiom,
add(X,add(Y,Z)) = add(add(X,Y),Z),
file('theBenchmark.p',sos) ).
cnf(c8,plain,
add(add(X,Y),Z) = add(X,add(Y,Z)),
inference(equational,[status(thm)],[c7]) ).
cnf(c10,axiom,
add(unit,add(X,mult(X,X))) = X,
file('theBenchmark.p',sos_006) ).
cnf(c12,plain,
add(unit,add(unit,unit)) = unit,
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c14,axiom,
mult(X,add(Y,Z)) = add(mult(X,Y),mult(X,Z)),
file('theBenchmark.p',sos_003) ).
cnf(c15,plain,
add(X,add(X,X)) = X,
inference(equational,[status(thm)],[c2,c12,c14]) ).
cnf(c16,plain,
add(mult(X,zero),mult(X,Y)) = mult(X,Y),
inference(equational,[status(thm)],[c1,c14]) ).
cnf(c17,plain,
add(X,mult(X,zero)) = X,
inference(equational,[status(thm)],[c2,c4,c16]) ).
cnf(c18,plain,
zero = unit,
inference(equational,[status(thm)],[c5,c10,c17]) ).
cnf(c19,plain,
add(X,X) = X,
inference(equational,[status(thm)],[c2,c17,c18]) ).
cnf(c21,plain,
add(unit,X) = X,
inference(equational,[status(thm)],[c1,c18]) ).
cnf(c22,plain,
add(X,mult(X,Y)) = mult(X,Y),
inference(equational,[status(thm)],[c2,c16,c18]) ).
cnf(c23,plain,
mult(X,X) = X,
inference(equational,[status(thm)],[c10,c21,c22]) ).
cnf(c24,plain,
add(X,mult(Y,X)) = mult(X,Y),
inference(equational,[status(thm)],[c3,c22]) ).
cnf(c27,plain,
add(mult(X,Y),mult(X,Z)) = mult(add(Y,Z),X),
inference(equational,[status(thm)],[c3,c14]) ).
cnf(c28,plain,
add(X,mult(Y,X)) = mult(Y,X),
inference(equational,[status(thm)],[c3,c24]) ).
cnf(c29,plain,
mult(add(X,Y),Z) = add(mult(Z,Y),mult(Z,X)),
inference(equational,[status(thm)],[c4,c27]) ).
cnf(c31,plain,
add(mult(X,Y),mult(Z,X)) = mult(add(Y,Z),X),
inference(equational,[status(thm)],[c3,c27]) ).
cnf(c32,plain,
add(mult(X,Y),mult(Y,X)) = mult(X,Y),
inference(equational,[status(thm)],[c15,c19,c27]) ).
cnf(c33,plain,
mult(add(X,Y),Z) = add(mult(X,Z),mult(Y,Z)),
inference(equational,[status(thm)],[c3,c31]) ).
cnf(c36,plain,
mult(mult(X,Y),Z) = add(mult(Z,X),mult(Z,mult(X,Y))),
inference(equational,[status(thm)],[c2,c16,c18,c27]) ).
cnf(c42,plain,
add(mult(X,Y),mult(mult(Y,Z),X)) = mult(mult(Y,Z),X),
inference(equational,[status(thm)],[c2,c16,c18,c31]) ).
cnf(c43,plain,
mult(mult(X,Y),Z) = add(mult(Z,Y),mult(Z,mult(Y,X))),
inference(equational,[status(thm)],[c3,c36]) ).
cnf(c44,plain,
mult(mult(X,Y),mult(Y,X)) = mult(Y,X),
inference(equational,[status(thm)],[c23,c42,c43]) ).
cnf(c45,plain,
mult(mult(X,Y),mult(X,Z)) = add(mult(Y,X),mult(Z,X)),
inference(equational,[status(thm)],[c8,c14,c22,c23,c28,c29,c32,c33,c44]) ).
cnf(c46,plain,
mult(X,Y) = add(X,Y),
inference(equational,[status(thm)],[c2,c6,c45]) ).
cnf(g1,plain,
add(x0,x1) = mult(x0,x1),
inference(equational,[status(thm)],[c46]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : RNG128-1 : TPTP v9.0.0. Released v5.4.0.
% 0.02/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n015.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 16:38:49 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.41/0.63 % SZS status Unsatisfiable
% 0.41/0.63 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------