%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE151-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 : Tue Sep 29 11:39:55 AM UTC 2026
% Result : Unsatisfiable 24.68s 3.62s
% Output : CNFRefutation 24.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of clauses : 69 ( 69 unt; 0 nHn; 3 RR)
% Number of literals : 69 ( 68 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 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 : 134 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
leq(multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(c3,plain,
ifeq(true,true,leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(strong_iteration(multiplication(X2,X)),X2)),true) = leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(strong_iteration(multiplication(X2,X)),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(strong_iteration(multiplication(X2,X)),X2)) = ifeq(true,true,leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(strong_iteration(multiplication(X2,X)),X2)),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
ifeq3(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c6,plain,
ifeq3(X,X,leq(X,X),true) = leq(X,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
leq(X,X) = ifeq3(X,X,leq(X,X),true),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
addition(A2,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).
cnf(c9,plain,
addition(X,X) = X,
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
X = addition(X,X),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
ifeq3(X,X,leq(X,X),true) = ifeq3(addition(X,X),X,leq(X,X),true),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
ifeq3(addition(A2,B2),B2,leq(A2,B2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
cnf(c13,plain,
ifeq3(addition(X,X),X,leq(X,X),true) = true,
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
ifeq3(X,X,leq(X,X),true) = true,
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
leq(X,X) = true,
inference(transitivity,[status(thm)],[c7,c14]) ).
cnf(c16,plain,
leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(X2,strong_iteration(multiplication(X,X2)))) = true,
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
true = leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(X2,strong_iteration(multiplication(X,X2)))),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
ifeq(true,true,leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(strong_iteration(multiplication(X2,X)),X2)),true) = ifeq(leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(X2,strong_iteration(multiplication(X,X2)))),true,leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(strong_iteration(multiplication(X2,X)),X2)),true),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
multiplication(A2,multiplication(B2,C2)) = multiplication(multiplication(A2,B2),C2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
cnf(c20,plain,
multiplication(X2,multiplication(X,X3)) = multiplication(multiplication(X2,X),X3),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
multiplication(multiplication(X3,X2),X) = multiplication(X3,multiplication(X2,X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
addition(X3,multiplication(multiplication(X3,X2),X)) = addition(X3,multiplication(X3,multiplication(X2,X))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,axiom,
multiplication(A2,one) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
cnf(c24,plain,
multiplication(X,one) = X,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
X = multiplication(X,one),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
addition(X2,multiplication(X2,X)) = addition(multiplication(X2,one),multiplication(X2,X)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,axiom,
multiplication(A2,addition(B2,C2)) = addition(multiplication(A2,B2),multiplication(A2,C2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
cnf(c28,plain,
multiplication(X2,addition(one,X)) = addition(multiplication(X2,one),multiplication(X2,X)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
addition(multiplication(X2,one),multiplication(X2,X)) = multiplication(X2,addition(one,X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,axiom,
addition(A2,B2) = addition(B2,A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
cnf(c31,plain,
addition(one,X) = addition(X,one),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
multiplication(X2,addition(one,X)) = multiplication(X2,addition(X,one)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
addition(multiplication(X2,one),multiplication(X2,X)) = multiplication(X2,addition(X,one)),
inference(transitivity,[status(thm)],[c29,c32]) ).
cnf(c34,plain,
addition(X2,multiplication(X2,X)) = multiplication(X2,addition(X,one)),
inference(transitivity,[status(thm)],[c26,c33]) ).
cnf(c35,plain,
addition(X3,multiplication(X3,multiplication(X2,X))) = multiplication(X3,addition(multiplication(X2,X),one)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
addition(multiplication(X2,X),one) = addition(one,multiplication(X2,X)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c37,plain,
multiplication(X3,addition(multiplication(X2,X),one)) = multiplication(X3,addition(one,multiplication(X2,X))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
addition(X3,multiplication(X3,multiplication(X2,X))) = multiplication(X3,addition(one,multiplication(X2,X))),
inference(transitivity,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
addition(X3,multiplication(multiplication(X3,X2),X)) = multiplication(X3,addition(one,multiplication(X2,X))),
inference(transitivity,[status(thm)],[c22,c38]) ).
cnf(c40,plain,
addition(X3,multiplication(multiplication(X3,X2),multiplication(X,strong_iteration(multiplication(X2,X))))) = multiplication(X3,addition(one,multiplication(X2,multiplication(X,strong_iteration(multiplication(X2,X)))))),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
multiplication(X2,multiplication(X,strong_iteration(multiplication(X2,X)))) = multiplication(multiplication(X2,X),strong_iteration(multiplication(X2,X))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c42,plain,
addition(one,multiplication(X2,multiplication(X,strong_iteration(multiplication(X2,X))))) = addition(one,multiplication(multiplication(X2,X),strong_iteration(multiplication(X2,X)))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
addition(multiplication(X,strong_iteration(X)),one) = addition(one,multiplication(X,strong_iteration(X))),
inference(substitution,[status(thm)],[c30]) ).
cnf(c44,plain,
addition(one,multiplication(X,strong_iteration(X))) = addition(multiplication(X,strong_iteration(X)),one),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,axiom,
strong_iteration(A2) = addition(multiplication(A2,strong_iteration(A2)),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_unfold1) ).
cnf(c46,plain,
strong_iteration(X) = addition(multiplication(X,strong_iteration(X)),one),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
addition(multiplication(X,strong_iteration(X)),one) = strong_iteration(X),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
addition(one,multiplication(X,strong_iteration(X))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c44,c47]) ).
cnf(c49,plain,
addition(one,multiplication(multiplication(X2,X),strong_iteration(multiplication(X2,X)))) = strong_iteration(multiplication(X2,X)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
addition(one,multiplication(X2,multiplication(X,strong_iteration(multiplication(X2,X))))) = strong_iteration(multiplication(X2,X)),
inference(transitivity,[status(thm)],[c42,c49]) ).
cnf(c51,plain,
multiplication(X3,addition(one,multiplication(X2,multiplication(X,strong_iteration(multiplication(X2,X)))))) = multiplication(X3,strong_iteration(multiplication(X2,X))),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
addition(X3,multiplication(multiplication(X3,X2),multiplication(X,strong_iteration(multiplication(X2,X))))) = multiplication(X3,strong_iteration(multiplication(X2,X))),
inference(transitivity,[status(thm)],[c40,c51]) ).
cnf(c53,plain,
addition(X2,multiplication(multiplication(X2,X),multiplication(X2,strong_iteration(multiplication(X,X2))))) = multiplication(X2,strong_iteration(multiplication(X,X2))),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
multiplication(X2,strong_iteration(multiplication(X,X2))) = addition(X2,multiplication(multiplication(X2,X),multiplication(X2,strong_iteration(multiplication(X,X2))))),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(X2,strong_iteration(multiplication(X,X2)))) = leq(multiplication(X2,strong_iteration(multiplication(X,X2))),addition(X2,multiplication(multiplication(X2,X),multiplication(X2,strong_iteration(multiplication(X,X2)))))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
ifeq(leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(X2,strong_iteration(multiplication(X,X2)))),true,leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(strong_iteration(multiplication(X2,X)),X2)),true) = ifeq(leq(multiplication(X2,strong_iteration(multiplication(X,X2))),addition(X2,multiplication(multiplication(X2,X),multiplication(X2,strong_iteration(multiplication(X,X2)))))),true,leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(strong_iteration(multiplication(X2,X)),X2)),true),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
addition(multiplication(X,X3),X2) = addition(X2,multiplication(X,X3)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c58,plain,
addition(X2,multiplication(X,X3)) = addition(multiplication(X,X3),X2),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
leq(X3,addition(X2,multiplication(X,X3))) = leq(X3,addition(multiplication(X,X3),X2)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
ifeq(leq(X3,addition(X2,multiplication(X,X3))),true,leq(X3,multiplication(strong_iteration(X),X2)),true) = ifeq(leq(X3,addition(multiplication(X,X3),X2)),true,leq(X3,multiplication(strong_iteration(X),X2)),true),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,axiom,
ifeq(leq(C2,addition(multiplication(A2,C2),B2)),true,leq(C2,multiplication(strong_iteration(A2),B2)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_coinduction) ).
cnf(c62,plain,
ifeq(leq(X3,addition(multiplication(X,X3),X2)),true,leq(X3,multiplication(strong_iteration(X),X2)),true) = true,
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
ifeq(leq(X3,addition(X2,multiplication(X,X3))),true,leq(X3,multiplication(strong_iteration(X),X2)),true) = true,
inference(transitivity,[status(thm)],[c60,c62]) ).
cnf(c64,plain,
ifeq(leq(multiplication(X2,strong_iteration(multiplication(X,X2))),addition(X2,multiplication(multiplication(X2,X),multiplication(X2,strong_iteration(multiplication(X,X2)))))),true,leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(strong_iteration(multiplication(X2,X)),X2)),true) = true,
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
ifeq(leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(X2,strong_iteration(multiplication(X,X2)))),true,leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(strong_iteration(multiplication(X2,X)),X2)),true) = true,
inference(transitivity,[status(thm)],[c56,c64]) ).
cnf(c66,plain,
ifeq(true,true,leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(strong_iteration(multiplication(X2,X)),X2)),true) = true,
inference(transitivity,[status(thm)],[c18,c65]) ).
cnf(c67,plain,
leq(multiplication(X2,strong_iteration(multiplication(X,X2))),multiplication(strong_iteration(multiplication(X2,X)),X2)) = true,
inference(transitivity,[status(thm)],[c4,c66]) ).
cnf(c68,plain,
leq(multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)) = true,
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
$false,
inference(resolution,[status(thm)],[c1,c68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE151-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.40 % Computer : n004.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 13:12:51 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.68/3.62 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 24.68/3.62
% 24.68/3.62 % SZS status Unsatisfiable
% 24.68/3.62
% 24.68/3.63 % SZS output start CNFRefutation
% See solution above
% 24.68/3.69
% 24.68/3.69 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------