%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO004-10 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 06:14:42 AM UTC 2025
% Result : Unsatisfiable 60.51s 60.73s
% Output : CNFRefutation 60.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 3 RR)
% Number of literals : 21 ( 20 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 44 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
sum(x,x,x) != true,
file('theBenchmark.p',prove_both_equalities) ).
cnf(c1,axiom,
sum(additive_identity,X,X) = true,
file('theBenchmark.p',additive_identity1) ).
cnf(c4,axiom,
product(X,multiplicative_identity,X) = true,
file('theBenchmark.p',multiplicative_identity2) ).
cnf(c5,axiom,
ifeq(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom_001) ).
cnf(c6,axiom,
ifeq2(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c7,axiom,
sum(inverse(X),X,multiplicative_identity) = true,
file('theBenchmark.p',additive_inverse1) ).
cnf(c10,axiom,
product(X,inverse(X),additive_identity) = true,
file('theBenchmark.p',multiplicative_inverse2) ).
cnf(c11,axiom,
sum(X,Y,add(X,Y)) = true,
file('theBenchmark.p',closure_of_addition) ).
cnf(c13,axiom,
ifeq(sum(X,Y,Z),true,sum(Y,X,Z),true) = true,
file('theBenchmark.p',commutativity_of_addition) ).
cnf(c14,plain,
sum(X,Y,add(Y,X)) = true,
inference(equational,[status(thm)],[c5,c11,c13]) ).
cnf(c17,axiom,
ifeq2(sum(X,Y,Z),true,ifeq2(sum(X,Y,W),true,W,Z),Z) = Z,
file('theBenchmark.p',addition_is_well_defined) ).
cnf(c24,plain,
ifeq2(sum(additive_identity,X,Y),true,X,Y) = Y,
inference(equational,[status(thm)],[c1,c6,c17]) ).
cnf(c55,axiom,
ifeq(product(X,Y,Z),true,ifeq(product(W,V,U),true,ifeq(sum(V,U2,Y),true,ifeq(sum(W,U2,X),true,sum(U,U2,Z),true),true),true),true) = true,
file('theBenchmark.p',distributivity8) ).
cnf(c179,plain,
ifeq(product(X,Y,Z),true,ifeq(sum(Y,W,multiplicative_identity),true,ifeq(sum(X,W,V),true,sum(Z,W,V),true),true),true) = true,
inference(equational,[status(thm)],[c4,c5,c55]) ).
cnf(c252,plain,
ifeq(product(X,inverse(Y),Z),true,ifeq(sum(X,Y,W),true,sum(Z,Y,W),true),true) = true,
inference(equational,[status(thm)],[c5,c7,c179]) ).
cnf(c253,plain,
ifeq(sum(X,X,Y),true,sum(additive_identity,X,Y),true) = true,
inference(equational,[status(thm)],[c5,c10,c252]) ).
cnf(c254,plain,
sum(additive_identity,X,add(X,X)) = true,
inference(equational,[status(thm)],[c5,c14,c253]) ).
cnf(c255,plain,
add(X,X) = X,
inference(equational,[status(thm)],[c6,c24,c254]) ).
cnf(c256,plain,
sum(X,X,X) = true,
inference(equational,[status(thm)],[c11,c255]) ).
cnf(g1,plain,
sum(x,x,x) = true,
inference(equational,[status(thm)],[c256]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : BOO004-10 : TPTP v9.0.0. Released v7.5.0.
% 0.11/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 04:21:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 60.51/60.73 % SZS status Unsatisfiable
% 60.51/60.73 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------