%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL026-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 26.48s 26.73s
% Output : CNFRefutation 26.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 3 RR)
% Number of literals : 42 ( 41 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 100 ( 26 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
is_a_theorem(implies(implies(implies(a,b),a),a)) != true,
file('theBenchmark.p',prove_c0_3) ).
cnf(c1,axiom,
ifeq(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c2,axiom,
is_a_theorem(implies(X,implies(Y,X))) = true,
file('theBenchmark.p',c0_2) ).
cnf(c3,axiom,
is_a_theorem(implies(implies(implies(X,falsehood),falsehood),X)) = true,
file('theBenchmark.p',c0_5) ).
cnf(c4,axiom,
is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) = true,
file('theBenchmark.p',c0_6) ).
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(Y,X)),true) = true,
inference(equational,[status(thm)],[c1,c2,c5]) ).
cnf(c8,plain,
is_a_theorem(implies(X,implies(Y,implies(Z,Y)))) = true,
inference(equational,[status(thm)],[c1,c2,c6]) ).
cnf(c9,plain,
is_a_theorem(implies(X,implies(implies(implies(Y,falsehood),falsehood),Y))) = true,
inference(equational,[status(thm)],[c1,c3,c6]) ).
cnf(c18,plain,
ifeq(is_a_theorem(implies(implies(X,implies(Y,X)),Z)),true,is_a_theorem(Z),true) = true,
inference(equational,[status(thm)],[c1,c2,c5]) ).
cnf(c19,plain,
is_a_theorem(implies(implies(X,Y),implies(X,X))) = true,
inference(equational,[status(thm)],[c1,c4,c18]) ).
cnf(c20,plain,
is_a_theorem(implies(X,X)) = true,
inference(equational,[status(thm)],[c1,c18,c19]) ).
cnf(c24,plain,
ifeq(is_a_theorem(implies(implies(X,X),Y)),true,is_a_theorem(Y),true) = true,
inference(equational,[status(thm)],[c1,c5,c20]) ).
cnf(c28,plain,
is_a_theorem(implies(implies(implies(X,Y),X),implies(implies(X,Y),Y))) = true,
inference(equational,[status(thm)],[c1,c4,c24]) ).
cnf(c41,plain,
ifeq(is_a_theorem(implies(implies(X,implies(Y,implies(Z,Y))),W)),true,is_a_theorem(W),true) = true,
inference(equational,[status(thm)],[c1,c5,c8]) ).
cnf(c62,plain,
is_a_theorem(implies(X,implies(implies(Y,implies(Z,W)),implies(implies(Y,Z),implies(Y,W))))) = true,
inference(equational,[status(thm)],[c1,c4,c6]) ).
cnf(c68,plain,
ifeq(is_a_theorem(implies(X,implies(Y,Z))),true,is_a_theorem(implies(implies(X,Y),implies(X,Z))),true) = true,
inference(equational,[status(thm)],[c1,c4,c5]) ).
cnf(c69,plain,
is_a_theorem(implies(implies(X,implies(implies(Y,falsehood),falsehood)),implies(X,Y))) = true,
inference(equational,[status(thm)],[c1,c9,c68]) ).
cnf(c70,plain,
is_a_theorem(implies(falsehood,X)) = true,
inference(equational,[status(thm)],[c1,c18,c69]) ).
cnf(c71,plain,
is_a_theorem(implies(X,implies(falsehood,Y))) = true,
inference(equational,[status(thm)],[c1,c6,c70]) ).
cnf(c74,plain,
is_a_theorem(implies(implies(X,falsehood),implies(X,Y))) = true,
inference(equational,[status(thm)],[c1,c68,c71]) ).
cnf(c118,plain,
ifeq(is_a_theorem(implies(X,implies(implies(Y,falsehood),falsehood))),true,is_a_theorem(implies(X,Y)),true) = true,
inference(equational,[status(thm)],[c1,c5,c69]) ).
cnf(c119,plain,
is_a_theorem(implies(implies(implies(X,falsehood),X),X)) = true,
inference(equational,[status(thm)],[c1,c28,c118]) ).
cnf(c123,plain,
ifeq(is_a_theorem(implies(implies(X,falsehood),X)),true,is_a_theorem(X),true) = true,
inference(equational,[status(thm)],[c1,c5,c119]) ).
cnf(c339,plain,
ifeq(is_a_theorem(implies(implies(implies(X,falsehood),implies(X,Y)),Z)),true,is_a_theorem(Z),true) = true,
inference(equational,[status(thm)],[c1,c5,c74]) ).
cnf(c359,plain,
is_a_theorem(implies(implies(X,implies(Y,implies(Z,W))),implies(X,implies(implies(Y,Z),implies(Y,W))))) = true,
inference(equational,[status(thm)],[c1,c62,c68]) ).
cnf(c360,plain,
is_a_theorem(implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y)))) = true,
inference(equational,[status(thm)],[c1,c18,c359]) ).
cnf(c363,plain,
ifeq(is_a_theorem(implies(X,Y)),true,is_a_theorem(implies(implies(Z,X),implies(Z,Y))),true) = true,
inference(equational,[status(thm)],[c1,c5,c360]) ).
cnf(c364,plain,
is_a_theorem(implies(implies(implies(X,Y),implies(Z,X)),implies(implies(X,Y),implies(Z,Y)))) = true,
inference(equational,[status(thm)],[c1,c68,c360]) ).
cnf(c365,plain,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))) = true,
inference(equational,[status(thm)],[c1,c41,c364]) ).
cnf(c372,plain,
ifeq(is_a_theorem(implies(implies(X,Y),Z)),true,is_a_theorem(implies(Y,Z)),true) = true,
inference(equational,[status(thm)],[c1,c5,c365]) ).
cnf(c373,plain,
is_a_theorem(implies(X,implies(implies(X,Y),Y))) = true,
inference(equational,[status(thm)],[c1,c28,c372]) ).
cnf(c386,plain,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) = true,
inference(equational,[status(thm)],[c1,c364,c372]) ).
cnf(c416,plain,
is_a_theorem(implies(implies(X,implies(implies(Y,Z),W)),implies(X,implies(Z,W)))) = true,
inference(equational,[status(thm)],[c1,c363,c365]) ).
cnf(c417,plain,
is_a_theorem(implies(implies(implies(X,Y),falsehood),implies(Y,Z))) = true,
inference(equational,[status(thm)],[c1,c339,c416]) ).
cnf(c735,plain,
ifeq(is_a_theorem(implies(implies(X,implies(implies(X,Y),Y)),Z)),true,is_a_theorem(Z),true) = true,
inference(equational,[status(thm)],[c1,c5,c373]) ).
cnf(c779,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,c5,c386]) ).
cnf(c809,plain,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(implies(W,X),falsehood),Z))) = true,
inference(equational,[status(thm)],[c1,c417,c779]) ).
cnf(c903,plain,
is_a_theorem(implies(implies(implies(X,Y),falsehood),implies(implies(implies(Y,Z),W),W))) = true,
inference(equational,[status(thm)],[c1,c735,c809]) ).
cnf(c904,plain,
is_a_theorem(implies(implies(implies(X,Y),X),X)) = true,
inference(equational,[status(thm)],[c1,c123,c903]) ).
cnf(g1,plain,
is_a_theorem(implies(implies(implies(a,b),a),a)) = true,
inference(equational,[status(thm)],[c904]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL026-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.02 % Command : run_Leo-III %s %d THM
% 0.07/0.33 % Computer : n016.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 5 10:22:44 UTC 2026
% 0.07/0.33 % CPUTime :
% 26.48/26.73 % SZS status Unsatisfiable
% 26.48/26.73 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------