%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE044-10 : TPTP v9.2.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:35:35 PM UTC 2026
% Result : Unsatisfiable 179.47s 102.03s
% Output : CNFRefutation 180.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of clauses : 116 ( 116 unt; 0 nHn; 4 RR)
% Number of literals : 116 ( 115 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 216 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_associativity,axiom,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
cnf(additive_idempotence,axiom,
addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
cnf(additive_commutativity,axiom,
addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
cnf(right_distributivity,axiom,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
cnf(multiplicative_right_identity,axiom,
multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
cnf(order_1,axiom,
ifeq2(leq(X1,X2),true,addition(X1,X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order_1) ).
cnf(star_unfold_left,axiom,
leq(addition(one,multiplication(star(X1),X1)),star(X1)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_left) ).
cnf(ifeq_axiom_001,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(order,axiom,
ifeq3(addition(X1,X2),X2,leq(X1,X2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
cnf(ifeq_axiom,axiom,
ifeq3(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(left_distributivity,axiom,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
cnf(multiplicative_left_identity,axiom,
multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
cnf(star_unfold_right,axiom,
leq(addition(one,multiplication(X1,star(X1))),star(X1)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_right) ).
cnf(multiplicative_associativity,axiom,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
cnf(star_induction_right,axiom,
ifeq(leq(addition(multiplication(X1,X2),X3),X1),true,leq(multiplication(X3,star(X2)),X1),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_right) ).
cnf(ifeq_axiom_002,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(star_induction_left,axiom,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_left) ).
cnf(goals,negated_conjecture,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_18,axiom,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
additive_associativity ).
cnf(c_0_19,axiom,
addition(X1,X1) = X1,
additive_idempotence ).
cnf(c_0_20,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
addition(X1,X2) = addition(X2,X1),
additive_commutativity ).
cnf(c_0_22,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,axiom,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
right_distributivity ).
cnf(c_0_24,axiom,
multiplication(X1,one) = X1,
multiplicative_right_identity ).
cnf(c_0_25,plain,
addition(X1,addition(X2,addition(X1,X3))) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_22]),c_0_18]),c_0_18]) ).
cnf(c_0_26,axiom,
ifeq2(leq(X1,X2),true,addition(X1,X2),X2) = X2,
order_1 ).
cnf(c_0_27,axiom,
leq(addition(one,multiplication(star(X1),X1)),star(X1)) = true,
star_unfold_left ).
cnf(c_0_28,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_29,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21]) ).
cnf(c_0_30,axiom,
ifeq3(addition(X1,X2),X2,leq(X1,X2),true) = true,
order ).
cnf(c_0_31,axiom,
ifeq3(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_32,plain,
addition(multiplication(X1,X2),addition(X3,multiplication(X1,addition(X2,X4)))) = addition(X3,multiplication(X1,addition(X2,X4))),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_33,plain,
addition(one,multiplication(star(X1),addition(X1,one))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_18]),c_0_28]),c_0_21]),c_0_29]) ).
cnf(c_0_34,axiom,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
left_distributivity ).
cnf(c_0_35,axiom,
multiplication(one,X1) = X1,
multiplicative_left_identity ).
cnf(c_0_36,plain,
leq(X1,addition(X1,X2)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_20]),c_0_31]) ).
cnf(c_0_37,plain,
multiplication(star(X1),addition(X1,one)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_21]),c_0_29]) ).
cnf(c_0_38,axiom,
leq(addition(one,multiplication(X1,star(X1))),star(X1)) = true,
star_unfold_right ).
cnf(c_0_39,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_21]) ).
cnf(c_0_40,axiom,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
multiplicative_associativity ).
cnf(c_0_41,plain,
leq(multiplication(X1,X2),multiplication(X1,addition(X2,X3))) = true,
inference(spm,[status(thm)],[c_0_36,c_0_23]) ).
cnf(c_0_42,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(spm,[status(thm)],[c_0_37,c_0_21]) ).
cnf(c_0_43,axiom,
ifeq(leq(addition(multiplication(X1,X2),X3),X1),true,leq(multiplication(X3,star(X2)),X1),true) = true,
star_induction_right ).
cnf(c_0_44,plain,
addition(one,multiplication(addition(X1,one),star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_38]),c_0_18]),c_0_28]),c_0_21]),c_0_39]) ).
cnf(c_0_45,plain,
multiplication(star(X1),multiplication(addition(X1,one),X2)) = multiplication(star(X1),X2),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_46,plain,
multiplication(addition(X1,one),X1) = multiplication(X1,addition(X1,one)),
inference(spm,[status(thm)],[c_0_29,c_0_39]) ).
cnf(c_0_47,plain,
leq(X1,multiplication(X1,addition(one,X2))) = true,
inference(spm,[status(thm)],[c_0_41,c_0_24]) ).
cnf(c_0_48,plain,
multiplication(star(X1),addition(X2,addition(one,X1))) = multiplication(star(X1),addition(X2,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_42]),c_0_21]),c_0_29]) ).
cnf(c_0_49,plain,
addition(X1,addition(X2,addition(X3,X1))) = addition(X2,addition(X3,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_50,plain,
ifeq(leq(multiplication(X1,addition(X2,X3)),X1),true,leq(multiplication(X1,multiplication(X3,star(X2))),X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_23]),c_0_40]) ).
cnf(c_0_51,plain,
leq(X1,X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_31]) ).
cnf(c_0_52,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_002 ).
cnf(c_0_53,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_54,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_20,c_0_44]) ).
cnf(c_0_55,plain,
addition(multiplication(X1,X2),addition(X3,multiplication(addition(X1,X4),X2))) = addition(X3,multiplication(addition(X1,X4),X2)),
inference(spm,[status(thm)],[c_0_25,c_0_34]) ).
cnf(c_0_56,plain,
ifeq(leq(addition(one,multiplication(X1,X2)),X1),true,leq(star(X2),X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_35]),c_0_21]) ).
cnf(c_0_57,plain,
multiplication(star(X1),multiplication(X1,addition(X1,one))) = multiplication(star(X1),X1),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_58,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_59,plain,
leq(X1,multiplication(X1,addition(X2,one))) = true,
inference(spm,[status(thm)],[c_0_47,c_0_22]) ).
cnf(c_0_60,plain,
multiplication(star(addition(X1,X2)),addition(X2,one)) = star(addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_42]) ).
cnf(c_0_61,plain,
leq(multiplication(X1,X2),multiplication(addition(X1,X3),X2)) = true,
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_62,plain,
ifeq2(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_63,plain,
leq(multiplication(star(X1),star(X1)),star(X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_37]),c_0_51]),c_0_35]),c_0_52]) ).
cnf(c_0_64,plain,
addition(X1,multiplication(X1,star(X2))) = multiplication(X1,star(X2)),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_65,plain,
ifeq3(multiplication(X1,addition(X2,X3)),multiplication(X1,X3),leq(multiplication(X1,X2),multiplication(X1,X3)),true) = true,
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_66,plain,
addition(X1,star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_37]),c_0_18]),c_0_54]),c_0_21]),c_0_54]),c_0_37]) ).
cnf(c_0_67,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_44]),c_0_21]),c_0_39]) ).
cnf(c_0_68,plain,
leq(star(multiplication(X1,addition(X1,one))),star(X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_27]),c_0_52]) ).
cnf(c_0_69,plain,
addition(X1,addition(X2,multiplication(addition(X1,X2),X3))) = multiplication(addition(X1,X2),addition(X3,one)),
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_70,plain,
multiplication(addition(one,X1),X1) = multiplication(X1,addition(X1,one)),
inference(spm,[status(thm)],[c_0_29,c_0_58]) ).
cnf(c_0_71,plain,
addition(X1,multiplication(X1,addition(X2,one))) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_59]),c_0_28]) ).
cnf(c_0_72,plain,
leq(star(addition(X1,one)),star(addition(X2,X1))) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_60]),c_0_54]),c_0_51]),c_0_52]) ).
cnf(c_0_73,plain,
leq(X1,multiplication(addition(one,X2),X1)) = true,
inference(spm,[status(thm)],[c_0_61,c_0_35]) ).
cnf(c_0_74,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_28]) ).
cnf(c_0_75,plain,
leq(star(addition(X1,one)),star(X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_37]),c_0_54]),c_0_51]),c_0_52]) ).
cnf(c_0_76,plain,
leq(multiplication(X1,X2),multiplication(X1,star(X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_31]) ).
cnf(c_0_77,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_67,c_0_21]) ).
cnf(c_0_78,plain,
leq(star(addition(X1,multiplication(X1,X1))),star(X1)) = true,
inference(spm,[status(thm)],[c_0_68,c_0_29]) ).
cnf(c_0_79,plain,
multiplication(addition(X1,multiplication(X1,X2)),X3) = multiplication(X1,multiplication(addition(X2,one),X3)),
inference(spm,[status(thm)],[c_0_40,c_0_29]) ).
cnf(c_0_80,plain,
multiplication(addition(one,X1),addition(X1,one)) = addition(one,multiplication(X1,addition(X1,one))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_81,plain,
leq(star(addition(X1,one)),star(addition(X1,X2))) = true,
inference(spm,[status(thm)],[c_0_72,c_0_21]) ).
cnf(c_0_82,plain,
leq(X1,multiplication(addition(X2,one),X1)) = true,
inference(spm,[status(thm)],[c_0_73,c_0_22]) ).
cnf(c_0_83,plain,
multiplication(star(X1),addition(star(X1),X2)) = multiplication(star(X1),addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_74]),c_0_29]) ).
cnf(c_0_84,plain,
addition(star(X1),star(addition(X1,one))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_75]),c_0_28]),c_0_21]) ).
cnf(c_0_85,plain,
leq(multiplication(X1,addition(X1,one)),star(X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_70]) ).
cnf(c_0_86,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_21]),c_0_18]) ).
cnf(c_0_87,plain,
addition(star(X1),star(addition(X1,multiplication(X1,X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_78]),c_0_28]),c_0_21]) ).
cnf(c_0_88,plain,
multiplication(addition(X1,one),addition(X1,one)) = addition(one,multiplication(X1,addition(X1,one))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_35]),c_0_35]),c_0_35]),c_0_35]) ).
cnf(c_0_89,plain,
addition(star(addition(X1,one)),star(addition(X1,X2))) = star(addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_81]),c_0_28]) ).
cnf(c_0_90,plain,
addition(X1,addition(X2,multiplication(X1,addition(X3,one)))) = addition(X2,multiplication(X1,addition(X3,one))),
inference(spm,[status(thm)],[c_0_25,c_0_29]) ).
cnf(c_0_91,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_92,axiom,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
star_induction_left ).
cnf(c_0_93,plain,
multiplication(addition(one,X1),multiplication(star(X1),X2)) = multiplication(star(X1),X2),
inference(spm,[status(thm)],[c_0_40,c_0_77]) ).
cnf(c_0_94,plain,
addition(X1,multiplication(addition(X2,one),X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_82]),c_0_28]) ).
cnf(c_0_95,plain,
multiplication(star(X1),star(addition(X1,one))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_74]),c_0_21]),c_0_54]) ).
cnf(c_0_96,plain,
leq(addition(X1,multiplication(X1,X1)),star(X1)) = true,
inference(spm,[status(thm)],[c_0_85,c_0_29]) ).
cnf(c_0_97,plain,
addition(X1,addition(X2,star(X1))) = addition(X2,star(X1)),
inference(spm,[status(thm)],[c_0_86,c_0_66]) ).
cnf(c_0_98,plain,
star(addition(one,multiplication(X1,addition(X1,one)))) = star(addition(X1,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_18]),c_0_20]),c_0_89]),c_0_90]) ).
cnf(c_0_99,plain,
addition(X1,addition(multiplication(X1,X2),X3)) = addition(X3,multiplication(X1,addition(X2,one))),
inference(spm,[status(thm)],[c_0_91,c_0_29]) ).
cnf(c_0_100,plain,
ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true) = true,
inference(spm,[status(thm)],[c_0_92,c_0_34]) ).
cnf(c_0_101,plain,
multiplication(addition(X1,one),multiplication(star(addition(X1,one)),X2)) = multiplication(star(addition(X1,one)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_24]),c_0_24]),c_0_24]) ).
cnf(c_0_102,plain,
multiplication(star(X1),multiplication(star(addition(X1,one)),X2)) = multiplication(star(X1),X2),
inference(spm,[status(thm)],[c_0_40,c_0_95]) ).
cnf(c_0_103,plain,
addition(multiplication(X1,X1),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_96]),c_0_18]),c_0_97]),c_0_28]) ).
cnf(c_0_104,plain,
star(addition(X1,addition(one,multiplication(X1,X1)))) = star(addition(X1,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_21]) ).
cnf(c_0_105,plain,
leq(multiplication(star(X1),X2),multiplication(star(addition(X1,one)),X2)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_51]),c_0_35]),c_0_102]),c_0_52]) ).
cnf(c_0_106,plain,
addition(star(X1),multiplication(X1,X1)) = star(X1),
inference(spm,[status(thm)],[c_0_21,c_0_103]) ).
cnf(c_0_107,plain,
multiplication(star(addition(X1,one)),addition(one,multiplication(X1,X1))) = star(addition(X1,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_104]),c_0_18]),c_0_21]),c_0_20]) ).
cnf(c_0_108,plain,
multiplication(star(addition(X1,one)),X2) = multiplication(star(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_105]),c_0_34]),c_0_84]),c_0_28]) ).
cnf(c_0_109,plain,
multiplication(star(X1),addition(one,multiplication(X1,X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_106]),c_0_74]),c_0_21]) ).
cnf(c_0_110,negated_conjecture,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
goals ).
cnf(c_0_111,plain,
leq(star(addition(one,X1)),star(X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_42]),c_0_54]),c_0_51]),c_0_52]) ).
cnf(c_0_112,plain,
star(addition(X1,one)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).
cnf(c_0_113,negated_conjecture,
tuple(true,leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
inference(rw,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_114,plain,
star(addition(one,X1)) = star(X1),
inference(spm,[status(thm)],[c_0_112,c_0_21]) ).
cnf(c_0_115,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE044-10 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n005.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 20:27:15 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 179.47/102.03 % Version : CSE_E---1.7
% 179.47/102.03 % Problem : theBenchmark.p
% 179.47/102.03 % SZS status Unsatisfiable for theBenchmark.p
% 179.47/102.03 % SZS output start CNFRefutation
% See solution above
% 180.15/102.74 % Total time : 75.243s
%------------------------------------------------------------------------------