%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL400-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n018.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 01:14:33 PM UTC 2026
% Result : Unsatisfiable 45.55s 45.81s
% Output : CNFRefutation 45.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of clauses : 66 ( 66 unt; 0 nHn; 3 RR)
% Number of literals : 66 ( 65 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 : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 185 ( 52 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
is_a_theorem(implies(not(implies(x,y)),x)) != true,
file('theBenchmark.p',prove_cn_66) ).
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(c15,plain,
is_a_theorem(implies(X,X)) = true,
inference(equational,[status(thm)],[c1,c12,c14]) ).
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(c22,plain,
ifeq(is_a_theorem(implies(implies(X,X),Y)),true,is_a_theorem(Y),true) = true,
inference(equational,[status(thm)],[c1,c5,c15]) ).
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(c43,plain,
is_a_theorem(implies(X,implies(implies(not(not(X)),not(X)),Y))) = true,
inference(equational,[status(thm)],[c1,c18,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(c55,plain,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(implies(not(X),W),Y),Z))) = true,
inference(equational,[status(thm)],[c1,c12,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(c83,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X)),not(X)),Y),Z),implies(X,Z))) = true,
inference(equational,[status(thm)],[c1,c32,c43]) ).
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(c144,plain,
ifeq(is_a_theorem(implies(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),W)),true,is_a_theorem(W),true) = true,
inference(equational,[status(thm)],[c1,c4,c5]) ).
cnf(c145,plain,
is_a_theorem(implies(implies(implies(not(X),Y),Z),implies(implies(Z,W),implies(X,W)))) = true,
inference(equational,[status(thm)],[c1,c55,c144]) ).
cnf(c147,plain,
is_a_theorem(implies(implies(X,Y),implies(implies(implies(X,Z),W),implies(implies(Y,Z),W)))) = true,
inference(equational,[status(thm)],[c1,c61,c144]) ).
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(c175,plain,
is_a_theorem(implies(implies(X,not(Y)),implies(Y,implies(X,Z)))) = true,
inference(equational,[status(thm)],[c1,c61,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(c183,plain,
ifeq(is_a_theorem(implies(X,not(Y))),true,is_a_theorem(implies(Y,implies(X,Z))),true) = true,
inference(equational,[status(thm)],[c1,c5,c175]) ).
cnf(c300,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X),X),Y),Z)),true,is_a_theorem(implies(implies(X,Y),Z)),true) = true,
inference(equational,[status(thm)],[c1,c5,c53]) ).
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(c357,plain,
is_a_theorem(implies(implies(X,implies(not(not(Y)),not(Y))),implies(Y,implies(X,Z)))) = true,
inference(equational,[status(thm)],[c1,c83,c342]) ).
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(c513,plain,
is_a_theorem(implies(X,implies(Y,implies(Z,X)))) = true,
inference(equational,[status(thm)],[c1,c348,c512]) ).
cnf(c514,plain,
is_a_theorem(implies(not(X),implies(X,implies(Y,Z)))) = true,
inference(equational,[status(thm)],[c1,c357,c512]) ).
cnf(c530,plain,
is_a_theorem(implies(implies(implies(X,implies(Y,Z)),W),implies(not(X),W))) = true,
inference(equational,[status(thm)],[c1,c32,c514]) ).
cnf(c566,plain,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(not(implies(X,Y))),Z))) = true,
inference(equational,[status(thm)],[c1,c300,c530]) ).
cnf(c567,plain,
is_a_theorem(implies(not(not(implies(not(X),X))),X)) = true,
inference(equational,[status(thm)],[c1,c14,c566]) ).
cnf(c637,plain,
ifeq(is_a_theorem(implies(implies(not(X),Y),Z)),true,is_a_theorem(implies(implies(Z,W),implies(X,W))),true) = true,
inference(equational,[status(thm)],[c1,c5,c145]) ).
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(c711,plain,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(X,implies(not(Y),Y)),Z))) = true,
inference(equational,[status(thm)],[c1,c348,c707]) ).
cnf(c712,plain,
is_a_theorem(implies(implies(implies(not(X),Y),implies(not(Z),Z)),implies(X,Z))) = true,
inference(equational,[status(thm)],[c1,c173,c711]) ).
cnf(c713,plain,
is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) = true,
inference(equational,[status(thm)],[c1,c342,c712]) ).
cnf(c729,plain,
ifeq(is_a_theorem(implies(not(X),not(Y))),true,is_a_theorem(implies(Y,X)),true) = true,
inference(equational,[status(thm)],[c1,c5,c713]) ).
cnf(c730,plain,
is_a_theorem(implies(X,not(implies(not(not(X)),not(X))))) = true,
inference(equational,[status(thm)],[c1,c567,c729]) ).
cnf(c731,plain,
is_a_theorem(implies(implies(not(not(X)),not(X)),implies(X,Y))) = true,
inference(equational,[status(thm)],[c1,c183,c730]) ).
cnf(c749,plain,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))) = true,
inference(equational,[status(thm)],[c1,c637,c731]) ).
cnf(c913,plain,
ifeq(is_a_theorem(implies(X,Y)),true,is_a_theorem(implies(implies(implies(X,Z),W),implies(implies(Y,Z),W))),true) = true,
inference(equational,[status(thm)],[c1,c5,c147]) ).
cnf(c989,plain,
is_a_theorem(implies(implies(X,Y),implies(implies(implies(X,Z),X),Y))) = true,
inference(equational,[status(thm)],[c1,c707,c749]) ).
cnf(c990,plain,
is_a_theorem(implies(implies(implies(X,Y),X),X)) = true,
inference(equational,[status(thm)],[c1,c22,c989]) ).
cnf(c1448,plain,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(implies(W,implies(V,X)),Y),Z))) = true,
inference(equational,[status(thm)],[c1,c513,c913]) ).
cnf(c1452,plain,
is_a_theorem(implies(implies(implies(X,implies(Y,Z)),W),implies(not(implies(Z,W)),V))) = true,
inference(equational,[status(thm)],[c1,c11,c1448]) ).
cnf(c1454,plain,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(implies(Y,Z)),W))) = true,
inference(equational,[status(thm)],[c1,c300,c1452]) ).
cnf(c1599,plain,
ifeq(is_a_theorem(implies(implies(X,Y),X)),true,is_a_theorem(X),true) = true,
inference(equational,[status(thm)],[c1,c5,c990]) ).
cnf(c1600,plain,
is_a_theorem(implies(not(implies(X,Y)),X)) = true,
inference(equational,[status(thm)],[c1,c1454,c1599]) ).
cnf(g1,plain,
is_a_theorem(implies(not(implies(x,y)),x)) = true,
inference(equational,[status(thm)],[c1600]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL400-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_Leo-III %s %d THM
% 0.16/0.42 % Computer : n018.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 5 06:19:33 UTC 2026
% 0.16/0.42 % CPUTime :
% 45.55/45.81 % SZS status Unsatisfiable
% 45.55/45.81 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------