%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL024-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.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 01:13:58 PM UTC 2026
% Result : Unsatisfiable 208.92s 208.71s
% Output : CNFRefutation 208.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 3 RR)
% Number of literals : 32 ( 31 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 92 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),c),equivalent(b,a))) != true,
file('theBenchmark.p',prove_pyo) ).
cnf(c1,axiom,
ifeq(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c2,axiom,
is_a_theorem(equivalent(X,equivalent(equivalent(Y,equivalent(Z,X)),equivalent(Z,Y)))) = true,
file('theBenchmark.p',xgk) ).
cnf(c3,axiom,
ifeq(is_a_theorem(equivalent(X,Y)),true,ifeq(is_a_theorem(X),true,is_a_theorem(Y),true),true) = true,
file('theBenchmark.p',condensed_detachment) ).
cnf(c4,plain,
ifeq(is_a_theorem(X),true,is_a_theorem(equivalent(equivalent(Y,equivalent(Z,X)),equivalent(Z,Y))),true) = true,
inference(equational,[status(thm)],[c1,c2,c3]) ).
cnf(c5,plain,
ifeq(is_a_theorem(equivalent(equivalent(X,equivalent(equivalent(Y,equivalent(Z,X)),equivalent(Z,Y))),W)),true,is_a_theorem(W),true) = true,
inference(equational,[status(thm)],[c1,c2,c3]) ).
cnf(c6,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(Y,equivalent(Z,equivalent(equivalent(W,equivalent(V,Z)),equivalent(V,W))))),equivalent(Y,X))) = true,
inference(equational,[status(thm)],[c1,c2,c5]) ).
cnf(c7,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Y,X)),equivalent(Z,W)),W)) = true,
inference(equational,[status(thm)],[c1,c5,c6]) ).
cnf(c9,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Y,X)),equivalent(Z,W))),true,is_a_theorem(W),true) = true,
inference(equational,[status(thm)],[c1,c3,c7]) ).
cnf(c10,plain,
is_a_theorem(equivalent(X,X)) = true,
inference(equational,[status(thm)],[c1,c7,c9]) ).
cnf(c13,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(Y,equivalent(Z,Z))),equivalent(Y,X))) = true,
inference(equational,[status(thm)],[c1,c4,c10]) ).
cnf(c16,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(X,Y)),Y)) = true,
inference(equational,[status(thm)],[c1,c5,c13]) ).
cnf(c17,plain,
ifeq(is_a_theorem(equivalent(X,equivalent(X,Y))),true,is_a_theorem(Y),true) = true,
inference(equational,[status(thm)],[c1,c3,c16]) ).
cnf(c39,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X,equivalent(X,Y)),Y),Z)),true,is_a_theorem(Z),true) = true,
inference(equational,[status(thm)],[c1,c3,c16]) ).
cnf(c471,plain,
ifeq(is_a_theorem(equivalent(X,equivalent(Y,equivalent(Z,equivalent(equivalent(W,equivalent(V,Z)),equivalent(V,W)))))),true,is_a_theorem(equivalent(Y,X)),true) = true,
inference(equational,[status(thm)],[c1,c3,c6]) ).
cnf(c501,plain,
is_a_theorem(equivalent(X,equivalent(Y,equivalent(Y,equivalent(X,equivalent(Z,equivalent(equivalent(W,equivalent(V,Z)),equivalent(V,W)))))))) = true,
inference(equational,[status(thm)],[c1,c16,c471]) ).
cnf(c502,plain,
is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(Y,equivalent(Z,W)),equivalent(Z,Y)),equivalent(W,X)))) = true,
inference(equational,[status(thm)],[c1,c471,c501]) ).
cnf(c1000,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Y,X)),equivalent(equivalent(W,equivalent(V,Z)),equivalent(V,W)))) = true,
inference(equational,[status(thm)],[c1,c471,c502]) ).
cnf(c1001,plain,
is_a_theorem(equivalent(X,equivalent(Y,equivalent(X,Y)))) = true,
inference(equational,[status(thm)],[c1,c17,c1000]) ).
cnf(c1008,plain,
ifeq(is_a_theorem(equivalent(equivalent(X,equivalent(Y,equivalent(X,Y))),Z)),true,is_a_theorem(Z),true) = true,
inference(equational,[status(thm)],[c1,c3,c1001]) ).
cnf(c1012,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(Y,equivalent(Z,equivalent(W,equivalent(Z,W))))),equivalent(Y,X))) = true,
inference(equational,[status(thm)],[c1,c4,c1001]) ).
cnf(c1013,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(Y,X)),Y)) = true,
inference(equational,[status(thm)],[c1,c1008,c1012]) ).
cnf(c1014,plain,
ifeq(is_a_theorem(equivalent(X,equivalent(Y,X))),true,is_a_theorem(Y),true) = true,
inference(equational,[status(thm)],[c1,c3,c1013]) ).
cnf(c1024,plain,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Y,equivalent(X,Z)),Z))) = true,
inference(equational,[status(thm)],[c1,c1000,c1014]) ).
cnf(c1101,plain,
is_a_theorem(equivalent(X,equivalent(Y,equivalent(Y,equivalent(X,equivalent(Z,equivalent(W,equivalent(Z,W)))))))) = true,
inference(equational,[status(thm)],[c1,c39,c1012]) ).
cnf(c1102,plain,
is_a_theorem(equivalent(X,equivalent(equivalent(Y,equivalent(Z,Y)),equivalent(Z,X)))) = true,
inference(equational,[status(thm)],[c1,c471,c1101]) ).
cnf(c1299,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(Y,X)),equivalent(equivalent(Z,equivalent(W,Y)),equivalent(W,Z)))) = true,
inference(equational,[status(thm)],[c1,c471,c1102]) ).
cnf(c1300,plain,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(Y,X))) = true,
inference(equational,[status(thm)],[c1,c1014,c1299]) ).
cnf(c1301,plain,
ifeq(is_a_theorem(equivalent(X,Y)),true,is_a_theorem(equivalent(Y,X)),true) = true,
inference(equational,[status(thm)],[c1,c3,c1300]) ).
cnf(c1318,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,equivalent(Y,Z)),Z),equivalent(Y,X))) = true,
inference(equational,[status(thm)],[c1,c1024,c1301]) ).
cnf(g1,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),c),equivalent(b,a))) = true,
inference(equational,[status(thm)],[c1318]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL024-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_Leo-III %s %d THM
% 0.15/0.41 % Computer : n014.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 5 03:24:57 UTC 2026
% 0.15/0.42 % CPUTime :
% 208.92/208.71 % SZS status Unsatisfiable
% 208.92/208.71 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------