%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL050-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:14:00 PM UTC 2026
% Result : Unsatisfiable 14.41s 14.71s
% Output : CNFRefutation 14.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 3 RR)
% Number of literals : 41 ( 40 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 110 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))) != true,
file('theBenchmark.p',prove_cn_21) ).
cnf(c1,axiom,
ifeq(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c2,axiom,
is_a_theorem(implies(implies(not(X),X),X)) = true,
file('theBenchmark.p',cn_2) ).
cnf(c3,axiom,
is_a_theorem(implies(X,implies(not(X),Y))) = true,
file('theBenchmark.p',cn_3) ).
cnf(c4,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) = true,
file('theBenchmark.p',cn_1) ).
cnf(c5,axiom,
ifeq(is_a_theorem(implies(X,Y)),true,ifeq(is_a_theorem(X),true,is_a_theorem(Y),true),true) = true,
file('theBenchmark.p',condensed_detachment) ).
cnf(c6,plain,
ifeq(is_a_theorem(X),true,is_a_theorem(implies(not(X),Y)),true) = true,
inference(equational,[status(thm)],[c1,c3,c5]) ).
cnf(c9,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),Y)) = true,
inference(equational,[status(thm)],[c1,c2,c6]) ).
cnf(c11,plain,
ifeq(is_a_theorem(implies(implies(X,implies(not(X),Y)),Z)),true,is_a_theorem(Z),true) = true,
inference(equational,[status(thm)],[c1,c3,c5]) ).
cnf(c12,plain,
is_a_theorem(implies(implies(implies(not(X),Y),Z),implies(X,Z))) = true,
inference(equational,[status(thm)],[c1,c4,c11]) ).
cnf(c14,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X),X),X),Y)),true,is_a_theorem(Y),true) = true,
inference(equational,[status(thm)],[c1,c2,c5]) ).
cnf(c18,plain,
is_a_theorem(implies(implies(X,Y),implies(implies(not(X),X),Y))) = true,
inference(equational,[status(thm)],[c1,c4,c14]) ).
cnf(c32,plain,
ifeq(is_a_theorem(implies(X,Y)),true,is_a_theorem(implies(implies(Y,Z),implies(X,Z))),true) = true,
inference(equational,[status(thm)],[c1,c4,c5]) ).
cnf(c35,plain,
is_a_theorem(implies(implies(X,Y),implies(not(implies(implies(not(Z),Z),Z)),Y))) = true,
inference(equational,[status(thm)],[c1,c9,c32]) ).
cnf(c40,plain,
ifeq(is_a_theorem(implies(implies(not(X),Y),Z)),true,is_a_theorem(implies(X,Z)),true) = true,
inference(equational,[status(thm)],[c1,c5,c12]) ).
cnf(c42,plain,
is_a_theorem(implies(X,implies(implies(Y,Z),implies(not(X),Z)))) = true,
inference(equational,[status(thm)],[c1,c4,c40]) ).
cnf(c44,plain,
is_a_theorem(implies(X,implies(not(implies(implies(not(Y),Y),Y)),Z))) = true,
inference(equational,[status(thm)],[c1,c35,c40]) ).
cnf(c53,plain,
is_a_theorem(implies(implies(implies(implies(not(X),X),Y),Z),implies(implies(X,Y),Z))) = true,
inference(equational,[status(thm)],[c1,c18,c32]) ).
cnf(c61,plain,
is_a_theorem(implies(implies(implies(implies(X,Y),implies(Z,Y)),W),implies(implies(Z,X),W))) = true,
inference(equational,[status(thm)],[c1,c4,c32]) ).
cnf(c82,plain,
is_a_theorem(implies(implies(implies(implies(X,Y),implies(not(Z),Y)),W),implies(Z,W))) = true,
inference(equational,[status(thm)],[c1,c32,c42]) ).
cnf(c105,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X),X),X)),Y),Z),implies(W,Z))) = true,
inference(equational,[status(thm)],[c1,c32,c44]) ).
cnf(c106,plain,
is_a_theorem(implies(X,implies(implies(not(Y),Y),Y))) = true,
inference(equational,[status(thm)],[c1,c14,c105]) ).
cnf(c108,plain,
is_a_theorem(implies(implies(implies(implies(not(X),X),X),Y),implies(Z,Y))) = true,
inference(equational,[status(thm)],[c1,c32,c106]) ).
cnf(c167,plain,
ifeq(is_a_theorem(implies(implies(implies(X,Y),implies(implies(not(X),X),Y)),Z)),true,is_a_theorem(Z),true) = true,
inference(equational,[status(thm)],[c1,c5,c18]) ).
cnf(c173,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X),Y),Z),implies(X,Z)),W)),true,is_a_theorem(W),true) = true,
inference(equational,[status(thm)],[c1,c5,c12]) ).
cnf(c174,plain,
is_a_theorem(implies(X,implies(Y,implies(not(X),Z)))) = true,
inference(equational,[status(thm)],[c1,c82,c173]) ).
cnf(c181,plain,
is_a_theorem(implies(implies(implies(X,implies(not(Y),Z)),W),implies(Y,W))) = true,
inference(equational,[status(thm)],[c1,c32,c174]) ).
cnf(c342,plain,
ifeq(is_a_theorem(implies(implies(implies(X,Y),implies(Z,Y)),W)),true,is_a_theorem(implies(implies(Z,X),W)),true) = true,
inference(equational,[status(thm)],[c1,c5,c61]) ).
cnf(c345,plain,
is_a_theorem(implies(implies(X,implies(not(Y),Y)),implies(implies(Y,Z),implies(X,Z)))) = true,
inference(equational,[status(thm)],[c1,c53,c342]) ).
cnf(c348,plain,
is_a_theorem(implies(implies(X,implies(not(Y),Y)),implies(Z,implies(X,Y)))) = true,
inference(equational,[status(thm)],[c1,c108,c342]) ).
cnf(c352,plain,
is_a_theorem(implies(implies(not(X),Y),implies(Z,implies(implies(Y,X),X)))) = true,
inference(equational,[status(thm)],[c1,c342,c348]) ).
cnf(c512,plain,
ifeq(is_a_theorem(implies(implies(X,implies(not(Y),Z)),W)),true,is_a_theorem(implies(Y,W)),true) = true,
inference(equational,[status(thm)],[c1,c5,c181]) ).
cnf(c707,plain,
ifeq(is_a_theorem(implies(X,implies(not(Y),Y))),true,is_a_theorem(implies(implies(Y,Z),implies(X,Z))),true) = true,
inference(equational,[status(thm)],[c1,c5,c345]) ).
cnf(c791,plain,
is_a_theorem(implies(implies(implies(implies(X,Y),Y),Z),implies(implies(not(Y),X),Z))) = true,
inference(equational,[status(thm)],[c1,c352,c707]) ).
cnf(c1102,plain,
is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(not(Z),Y),implies(X,Z)))) = true,
inference(equational,[status(thm)],[c1,c342,c791]) ).
cnf(c1106,plain,
is_a_theorem(implies(implies(not(X),implies(not(Y),Y)),implies(implies(Y,X),X))) = true,
inference(equational,[status(thm)],[c1,c167,c1102]) ).
cnf(c1107,plain,
is_a_theorem(implies(X,implies(implies(X,Y),Y))) = true,
inference(equational,[status(thm)],[c1,c512,c1106]) ).
cnf(c1113,plain,
is_a_theorem(implies(implies(implies(implies(X,Y),Y),Z),implies(X,Z))) = true,
inference(equational,[status(thm)],[c1,c32,c1107]) ).
cnf(c1118,plain,
is_a_theorem(implies(implies(X,implies(Y,Z)),implies(Y,implies(X,Z)))) = true,
inference(equational,[status(thm)],[c1,c342,c1113]) ).
cnf(g1,plain,
is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))) = true,
inference(equational,[status(thm)],[c1118]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL050-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.01 % Command : run_Leo-III %s %d THM
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 5 17:28:42 UTC 2026
% 0.03/0.29 % CPUTime :
% 14.41/14.71 % SZS status Unsatisfiable
% 14.41/14.71 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------