%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE039+1 : TPTP v9.2.1. Released v4.0.0.
% 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 : n010.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 04:35:34 PM UTC 2026
% Result : Theorem 1.41s 1.77s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 75 ( 53 unt; 0 def)
% Number of atoms : 99 ( 54 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 23 ~; 20 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(star_induction_right,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X1)
=> leq(multiplication(X3,star(X2)),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_induction_right) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(star_unfold_right,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(star_induction_left,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X2)
=> leq(multiplication(star(X1),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_induction_left) ).
fof(star_unfold_left,axiom,
! [X1] : leq(addition(one,multiplication(star(X1),X1)),star(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',left_distributivity) ).
fof(goals,conjecture,
! [X4] : star(star(X4)) = star(X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_13,plain,
! [X38,X39,X40] : addition(X40,addition(X39,X38)) = addition(addition(X40,X39),X38),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_14,plain,
! [X42] : addition(X42,X42) = X42,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_15,plain,
! [X63,X64,X65] :
( ~ leq(addition(multiplication(X63,X64),X65),X63)
| leq(multiplication(X65,star(X64)),X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_right])]) ).
fof(c_0_16,plain,
! [X46] : multiplication(X46,one) = X46,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_17,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X36,X37] : addition(X36,X37) = addition(X37,X36),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_20,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X56,X57] :
( ( ~ leq(X56,X57)
| addition(X56,X57) = X57 )
& ( addition(X56,X57) != X57
| leq(X56,X57) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_23,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_28,plain,
! [X47] : multiplication(one,X47) = X47,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_29,plain,
! [X58] : leq(addition(one,multiplication(X58,star(X58))),star(X58)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
cnf(c_0_30,plain,
( leq(multiplication(X1,star(one)),X2)
| addition(X1,X2) != X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_17]),c_0_27]) ).
cnf(c_0_31,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_32,plain,
! [X60,X61,X62] :
( ~ leq(addition(multiplication(X60,X61),X62),X61)
| leq(multiplication(star(X60),X62),X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_left])]) ).
cnf(c_0_33,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,plain,
( leq(star(one),X1)
| addition(one,X1) != X1 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
leq(addition(one,star(one)),star(one)),
inference(spm,[status(thm)],[c_0_33,c_0_31]) ).
cnf(c_0_38,plain,
( addition(star(one),X1) = X1
| addition(one,X1) != X1 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( leq(multiplication(star(one),X1),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_40,plain,
addition(one,star(one)) = star(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_37]),c_0_17]),c_0_18]) ).
cnf(c_0_41,plain,
( addition(X1,star(one)) = X1
| addition(one,X1) != X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_38]) ).
cnf(c_0_42,plain,
( leq(multiplication(star(one),X1),X2)
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_24]) ).
cnf(c_0_43,plain,
star(one) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_18])]) ).
cnf(c_0_44,plain,
( leq(X1,X2)
| ~ leq(addition(X1,X2),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_31]) ).
cnf(c_0_45,plain,
( leq(addition(X1,X2),X3)
| ~ leq(addition(X1,addition(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_44,c_0_17]) ).
cnf(c_0_46,plain,
( leq(addition(X1,X2),X1)
| ~ leq(addition(X2,X1),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_18]),c_0_17]),c_0_27]) ).
cnf(c_0_47,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_33]),c_0_17]),c_0_24]) ).
cnf(c_0_48,plain,
( leq(addition(X1,X2),X1)
| addition(X2,X1) != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_26]),c_0_17]),c_0_18]) ).
cnf(c_0_49,plain,
( leq(multiplication(star(X1),X2),X3)
| ~ leq(addition(X2,multiplication(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_24]) ).
cnf(c_0_50,plain,
addition(star(X1),multiplication(X1,star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_47]),c_0_17]),c_0_24]),c_0_23]) ).
cnf(c_0_51,plain,
leq(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_48]),c_0_18])]) ).
fof(c_0_52,plain,
! [X59] : leq(addition(one,multiplication(star(X59),X59)),star(X59)),
inference(variable_rename,[status(thm)],[star_unfold_left]) ).
cnf(c_0_53,plain,
leq(multiplication(star(X1),star(X1)),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_54,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_55,plain,
! [X48,X49,X50] : multiplication(X48,addition(X49,X50)) = addition(multiplication(X48,X49),multiplication(X48,X50)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_56,plain,
addition(star(X1),multiplication(star(X1),star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_53]),c_0_24]) ).
fof(c_0_57,plain,
! [X51,X52,X53] : multiplication(addition(X51,X52),X53) = addition(multiplication(X51,X53),multiplication(X52,X53)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_58,plain,
addition(one,addition(star(X1),multiplication(star(X1),X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_54]),c_0_17]),c_0_24]) ).
cnf(c_0_59,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_60,plain,
leq(multiplication(star(star(X1)),star(X1)),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_56]),c_0_51])]) ).
cnf(c_0_61,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_62,plain,
addition(star(X1),multiplication(star(X1),X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_58]),c_0_17]),c_0_24]),c_0_23]) ).
cnf(c_0_63,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_21]),c_0_24]) ).
fof(c_0_64,negated_conjecture,
~ ! [X4] : star(star(X4)) = star(X4),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_65,plain,
addition(star(X1),multiplication(star(star(X1)),star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_60]),c_0_24]) ).
cnf(c_0_66,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_31]),c_0_24]) ).
cnf(c_0_67,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_23,c_0_47]) ).
cnf(c_0_68,plain,
multiplication(star(X1),addition(X1,one)) = star(X1),
inference(rw,[status(thm)],[c_0_62,c_0_63]) ).
fof(c_0_69,negated_conjecture,
star(star(esk1_0)) != star(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])]) ).
cnf(c_0_70,plain,
multiplication(star(star(X1)),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_24]),c_0_67]) ).
cnf(c_0_71,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_66,c_0_68]),c_0_17]),c_0_67]),c_0_24]),c_0_67]),c_0_68]) ).
cnf(c_0_72,negated_conjecture,
star(star(esk1_0)) != star(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_73,plain,
star(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_63,c_0_70]),c_0_24]),c_0_71]),c_0_24]),c_0_67]),c_0_70]) ).
cnf(c_0_74,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE039+1 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.15/0.33 % Computer : n010.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 20:25:51 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.41/1.77 % Version : CSE_E---1.7
% 1.41/1.77 % Problem : theBenchmark.p
% 1.41/1.77 % SZS status Theorem for theBenchmark.p
% 1.41/1.77 % SZS output start CNFRefutation
% See solution above
% 1.41/1.77 % Total time : 1.370s
%------------------------------------------------------------------------------