%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE145-10 : TPTP v9.2.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n007.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 04:35:48 PM UTC 2026
% Result : Unsatisfiable 20.06s 12.76s
% Output : CNFRefutation 20.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of clauses : 74 ( 74 unt; 0 nHn; 3 RR)
% Number of literals : 74 ( 73 equ; 2 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 : 136 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_associativity,axiom,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
cnf(idempotence,axiom,
addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).
cnf(additive_commutativity,axiom,
addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
cnf(star_induction1,axiom,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction1) ).
cnf(infty_unfold1,axiom,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_unfold1) ).
cnf(order,axiom,
ifeq3(addition(X1,X2),X2,leq(X1,X2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
cnf(ifeq_axiom,axiom,
ifeq3(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(order_1,axiom,
ifeq2(leq(X1,X2),true,addition(X1,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order_1) ).
cnf(ifeq_axiom_002,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(distributivity2,axiom,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
cnf(multiplicative_left_identity,axiom,
multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
cnf(star_unfold2,axiom,
addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold2) ).
cnf(distributivity1,axiom,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
cnf(multiplicative_right_identity,axiom,
multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
cnf(multiplicative_associativity,axiom,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
cnf(isolation,axiom,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isolation) ).
cnf(additive_identity,axiom,
addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
cnf(ifeq_axiom_001,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(left_annihilation,axiom,
multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
cnf(star_induction2,axiom,
ifeq(leq(addition(multiplication(X1,X2),X3),X1),true,leq(multiplication(X3,star(X2)),X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction2) ).
cnf(goals,negated_conjecture,
star(strong_iteration(sK1_goals_X0)) != strong_iteration(sK1_goals_X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_21,axiom,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
additive_associativity ).
cnf(c_0_22,axiom,
addition(X1,X1) = X1,
idempotence ).
cnf(c_0_23,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,axiom,
addition(X1,X2) = addition(X2,X1),
additive_commutativity ).
cnf(c_0_25,axiom,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
star_induction1 ).
cnf(c_0_26,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,axiom,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
infty_unfold1 ).
cnf(c_0_28,axiom,
ifeq3(addition(X1,X2),X2,leq(X1,X2),true) = true,
order ).
cnf(c_0_29,axiom,
ifeq3(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_30,axiom,
ifeq2(leq(X1,X2),true,addition(X1,X2),X2) = X2,
order_1 ).
cnf(c_0_31,plain,
ifeq(leq(addition(X1,multiplication(X2,X3)),X3),true,leq(multiplication(star(X2),addition(X1,multiplication(X2,X3))),X3),true) = true,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_33,plain,
leq(X1,X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_22]),c_0_29]) ).
cnf(c_0_34,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_002 ).
cnf(c_0_35,axiom,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
distributivity2 ).
cnf(c_0_36,axiom,
multiplication(one,X1) = X1,
multiplicative_left_identity ).
cnf(c_0_37,axiom,
addition(one,multiplication(star(X1),X1)) = star(X1),
star_unfold2 ).
cnf(c_0_38,axiom,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
distributivity1 ).
cnf(c_0_39,axiom,
multiplication(X1,one) = X1,
multiplicative_right_identity ).
cnf(c_0_40,axiom,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
multiplicative_associativity ).
cnf(c_0_41,axiom,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
isolation ).
cnf(c_0_42,axiom,
addition(X1,zero) = X1,
additive_identity ).
cnf(c_0_43,plain,
ifeq2(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_44,plain,
leq(multiplication(star(X1),strong_iteration(X1)),strong_iteration(X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]) ).
cnf(c_0_45,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_24]) ).
cnf(c_0_46,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_47,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_48,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_24]),c_0_21]) ).
cnf(c_0_49,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_24]) ).
cnf(c_0_50,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(X4,X3)) = multiplication(addition(multiplication(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_35,c_0_40]) ).
cnf(c_0_51,axiom,
multiplication(zero,X1) = zero,
left_annihilation ).
cnf(c_0_52,plain,
addition(star(X1),addition(multiplication(strong_iteration(X1),zero),X2)) = addition(strong_iteration(X1),X2),
inference(spm,[status(thm)],[c_0_21,c_0_41]) ).
cnf(c_0_53,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_24]) ).
cnf(c_0_54,plain,
multiplication(star(X1),strong_iteration(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_24]),c_0_46]),c_0_47]) ).
cnf(c_0_55,plain,
addition(X1,addition(X2,multiplication(X1,X3))) = addition(X2,multiplication(X1,addition(X3,one))),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,plain,
addition(multiplication(X1,zero),multiplication(X2,X3)) = multiplication(addition(multiplication(X1,zero),X2),X3),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
addition(star(X1),multiplication(strong_iteration(X1),X2)) = multiplication(strong_iteration(X1),addition(X2,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_38]),c_0_53]),c_0_49]) ).
cnf(c_0_58,plain,
addition(strong_iteration(X1),multiplication(star(X1),X2)) = multiplication(star(X1),addition(strong_iteration(X1),X2)),
inference(spm,[status(thm)],[c_0_38,c_0_54]) ).
cnf(c_0_59,plain,
addition(star(X1),multiplication(star(X1),X1)) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_37]),c_0_24]) ).
cnf(c_0_60,axiom,
ifeq(leq(addition(multiplication(X1,X2),X3),X1),true,leq(multiplication(X3,star(X2)),X1),true) = true,
star_induction2 ).
cnf(c_0_61,plain,
multiplication(star(X1),addition(strong_iteration(X1),X2)) = multiplication(strong_iteration(X1),addition(X2,one)),
inference(rw,[status(thm)],[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_52,c_0_55]),c_0_56]),c_0_24]),c_0_57]),c_0_53]),c_0_39]),c_0_58]) ).
cnf(c_0_62,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_63,plain,
multiplication(star(X1),addition(X1,one)) = star(X1),
inference(rw,[status(thm)],[c_0_59,c_0_49]) ).
cnf(c_0_64,plain,
addition(one,addition(star(X1),X2)) = addition(star(X1),X2),
inference(spm,[status(thm)],[c_0_21,c_0_46]) ).
cnf(c_0_65,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_60,c_0_36]),c_0_24]) ).
cnf(c_0_66,plain,
multiplication(strong_iteration(X1),strong_iteration(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_22]),c_0_54]),c_0_24]),c_0_62]) ).
cnf(c_0_67,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(spm,[status(thm)],[c_0_63,c_0_24]) ).
cnf(c_0_68,plain,
addition(one,addition(X1,star(X2))) = addition(X1,star(X2)),
inference(spm,[status(thm)],[c_0_64,c_0_26]) ).
cnf(c_0_69,plain,
leq(star(strong_iteration(X1)),strong_iteration(X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_62]),c_0_33]),c_0_34]) ).
cnf(c_0_70,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_45,c_0_67]),c_0_21]),c_0_68]),c_0_24]),c_0_46]),c_0_67]) ).
cnf(c_0_71,negated_conjecture,
star(strong_iteration(sK1_goals_X0)) != strong_iteration(sK1_goals_X0),
goals ).
cnf(c_0_72,plain,
star(strong_iteration(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_69]),c_0_24]),c_0_70]),c_0_47]) ).
cnf(c_0_73,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE145-10 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n007.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 20:31:09 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 20.06/12.76 % Version : CSE_E---1.7
% 20.06/12.76 % Problem : theBenchmark.p
% 20.06/12.76 % SZS status Unsatisfiable for theBenchmark.p
% 20.06/12.76 % SZS output start CNFRefutation
% See solution above
% 20.16/12.85 % Total time : 9.384s
%------------------------------------------------------------------------------