TSTP Solution File: KLE044+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE044+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n003.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 : Thu Aug 31 05:25:51 EDT 2023
% Result : Theorem 99.26s 99.30s
% Output : CNFRefutation 99.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 23
% Syntax : Number of formulae : 131 ( 88 unt; 7 typ; 0 def)
% Number of atoms : 162 ( 81 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 36 ~; 32 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 209 ( 6 sgn; 60 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
addition: ( $i * $i ) > $i ).
tff(decl_23,type,
zero: $i ).
tff(decl_24,type,
multiplication: ( $i * $i ) > $i ).
tff(decl_25,type,
one: $i ).
tff(decl_26,type,
leq: ( $i * $i ) > $o ).
tff(decl_27,type,
star: $i > $i ).
tff(decl_28,type,
esk1_0: $i ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).
fof(star_unfold_right,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
fof(star_induction_right,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X1)
=> leq(multiplication(X3,star(X2)),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_induction_right) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_identity) ).
fof(star_induction_left,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X2)
=> leq(multiplication(star(X1),X3),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_induction_left) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).
fof(star_unfold_left,axiom,
! [X1] : leq(addition(one,multiplication(star(X1),X1)),star(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',left_distributivity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_associativity) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',right_annihilation) ).
fof(goals,conjecture,
! [X4] :
( leq(star(addition(one,X4)),star(X4))
& leq(star(X4),star(addition(one,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_16,plain,
! [X7,X8,X9] : addition(X9,addition(X8,X7)) = addition(addition(X9,X8),X7),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_17,plain,
! [X11] : addition(X11,X11) = X11,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_18,plain,
! [X25,X26] :
( ( ~ leq(X25,X26)
| addition(X25,X26) = X26 )
& ( addition(X25,X26) != X26
| leq(X25,X26) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_19,plain,
! [X27] : leq(addition(one,multiplication(X27,star(X27))),star(X27)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
fof(c_0_20,plain,
! [X5,X6] : addition(X5,X6) = addition(X6,X5),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_21,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X32,X33,X34] :
( ~ leq(addition(multiplication(X32,X33),X34),X32)
| leq(multiplication(X34,star(X33)),X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_right])]) ).
fof(c_0_27,plain,
! [X16] : multiplication(one,X16) = X16,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_28,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,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_23,c_0_24]),c_0_21]),c_0_25]) ).
fof(c_0_30,plain,
! [X10] : addition(X10,zero) = X10,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_31,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( leq(multiplication(X1,star(X2)),one)
| ~ leq(addition(X2,X1),one) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
addition(star(X1),one) = star(X1),
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_37,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_38,plain,
( leq(star(star(X1)),one)
| ~ leq(star(X1),one) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_32]) ).
cnf(c_0_39,plain,
( leq(multiplication(X1,star(zero)),one)
| ~ leq(X1,one) ),
inference(spm,[status(thm)],[c_0_35,c_0_37]) ).
cnf(c_0_40,plain,
( star(star(X1)) = one
| ~ leq(star(X1),one) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_38]),c_0_36]) ).
cnf(c_0_41,plain,
( leq(star(zero),one)
| ~ leq(one,one) ),
inference(spm,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_42,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_43,plain,
( star(star(star(X1))) = one
| ~ leq(star(X1),one) ),
inference(spm,[status(thm)],[c_0_40,c_0_38]) ).
cnf(c_0_44,plain,
leq(star(zero),one),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_22])]) ).
fof(c_0_45,plain,
! [X29,X30,X31] :
( ~ leq(addition(multiplication(X29,X30),X31),X30)
| leq(multiplication(star(X29),X31),X30) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_left])]) ).
fof(c_0_46,plain,
! [X15] : multiplication(X15,one) = X15,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_47,plain,
( star(star(star(star(X1)))) = one
| ~ leq(star(X1),one) ),
inference(spm,[status(thm)],[c_0_43,c_0_38]) ).
cnf(c_0_48,plain,
one = star(zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_44]),c_0_36]) ).
cnf(c_0_49,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,plain,
leq(addition(multiplication(X1,star(X1)),one),star(X1)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_51,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,plain,
( star(star(X1)) = one
| star(X1) != one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_42]),c_0_36]) ).
cnf(c_0_53,plain,
( star(star(star(star(X1)))) = star(zero)
| ~ leq(star(X1),star(zero)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_48]) ).
cnf(c_0_54,plain,
leq(star(X1),star(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_55,plain,
( star(star(X1)) = star(zero)
| star(X1) != star(zero) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_48]),c_0_48]) ).
cnf(c_0_56,plain,
star(star(star(star(zero)))) = star(zero),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(X1,multiplication(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_58,plain,
multiplication(X1,star(zero)) = X1,
inference(rw,[status(thm)],[c_0_51,c_0_48]) ).
cnf(c_0_59,plain,
star(star(zero)) = star(zero),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,plain,
( leq(X1,X2)
| ~ leq(addition(X1,X2),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_58]) ).
cnf(c_0_61,plain,
( leq(X1,addition(X1,X2))
| ~ leq(addition(X1,X2),addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_60,c_0_28]) ).
fof(c_0_62,plain,
! [X17,X18,X19] : multiplication(X17,addition(X18,X19)) = addition(multiplication(X17,X18),multiplication(X17,X19)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_63,plain,
! [X28] : leq(addition(one,multiplication(star(X28),X28)),star(X28)),
inference(variable_rename,[status(thm)],[star_unfold_left]) ).
cnf(c_0_64,plain,
leq(X1,addition(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_42]),c_0_22])]) ).
cnf(c_0_65,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_66,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_67,plain,
addition(one,addition(star(X1),X2)) = addition(star(X1),X2),
inference(spm,[status(thm)],[c_0_21,c_0_33]) ).
fof(c_0_68,plain,
! [X20,X21,X22] : multiplication(addition(X20,X21),X22) = addition(multiplication(X20,X22),multiplication(X21,X22)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_69,plain,
! [X12,X13,X14] : multiplication(X12,multiplication(X13,X14)) = multiplication(multiplication(X12,X13),X14),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_70,plain,
leq(multiplication(X1,X2),multiplication(X1,addition(X2,X3))),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,plain,
addition(star(zero),star(X1)) = star(X1),
inference(rw,[status(thm)],[c_0_33,c_0_48]) ).
cnf(c_0_72,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_23,c_0_66]),c_0_21]),c_0_25]),c_0_67]) ).
cnf(c_0_73,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_74,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_75,plain,
multiplication(star(zero),X1) = X1,
inference(rw,[status(thm)],[c_0_32,c_0_48]) ).
cnf(c_0_76,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_25]),c_0_21]) ).
cnf(c_0_77,plain,
addition(star(X1),multiplication(X1,star(X1))) = star(X1),
inference(rw,[status(thm)],[c_0_29,c_0_67]) ).
cnf(c_0_78,plain,
leq(X1,multiplication(X1,star(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_58]) ).
cnf(c_0_79,plain,
leq(multiplication(star(X1),star(X1)),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_72]),c_0_54])]) ).
cnf(c_0_80,plain,
( leq(multiplication(addition(multiplication(X1,X2),X3),star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_28]) ).
cnf(c_0_81,plain,
addition(multiplication(addition(X1,X2),X3),X4) = addition(multiplication(X1,X3),addition(multiplication(X2,X3),X4)),
inference(spm,[status(thm)],[c_0_21,c_0_73]) ).
cnf(c_0_82,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X3,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_25]) ).
cnf(c_0_83,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(X4,X3)) = multiplication(addition(multiplication(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
fof(c_0_84,plain,
! [X23] : multiplication(X23,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_85,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(star(zero),X2),X1),
inference(spm,[status(thm)],[c_0_73,c_0_75]) ).
cnf(c_0_86,plain,
leq(multiplication(X1,X2),multiplication(addition(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_64,c_0_73]) ).
cnf(c_0_87,plain,
addition(star(X1),addition(X2,multiplication(X1,star(X1)))) = addition(X2,star(X1)),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_88,plain,
addition(X1,multiplication(X1,star(X2))) = multiplication(X1,star(X2)),
inference(spm,[status(thm)],[c_0_23,c_0_78]) ).
cnf(c_0_89,plain,
( leq(multiplication(star(X1),X2),X3)
| ~ leq(addition(X2,multiplication(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_49,c_0_25]) ).
cnf(c_0_90,plain,
addition(star(X1),multiplication(star(X1),star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_79]),c_0_25]) ).
fof(c_0_91,negated_conjecture,
~ ! [X4] :
( leq(star(addition(one,X4)),star(X4))
& leq(star(X4),star(addition(one,X4))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_92,plain,
( leq(X1,X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_25]) ).
cnf(c_0_93,plain,
( addition(X1,multiplication(addition(multiplication(X1,X2),X3),star(X2))) = X1
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_80]),c_0_81]),c_0_74]),c_0_82]),c_0_83]) ).
cnf(c_0_94,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_95,plain,
( leq(multiplication(star(X1),multiplication(X1,X2)),X2)
| ~ leq(multiplication(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_22]) ).
cnf(c_0_96,plain,
multiplication(addition(star(zero),X1),star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_77,c_0_85]) ).
cnf(c_0_97,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_64,c_0_34]) ).
cnf(c_0_98,plain,
leq(X1,multiplication(star(X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_71]),c_0_75]) ).
cnf(c_0_99,plain,
addition(X1,star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_77]) ).
cnf(c_0_100,plain,
leq(multiplication(star(star(X1)),star(X1)),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_54])]) ).
cnf(c_0_101,plain,
multiplication(star(star(X1)),star(X1)) = star(star(X1)),
inference(spm,[status(thm)],[c_0_72,c_0_88]) ).
fof(c_0_102,negated_conjecture,
( ~ leq(star(addition(one,esk1_0)),star(esk1_0))
| ~ leq(star(esk1_0),star(addition(one,esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_91])])]) ).
cnf(c_0_103,plain,
( leq(multiplication(X1,star(X2)),X3)
| addition(X3,addition(multiplication(X3,X2),X1)) != X3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_42]),c_0_21]),c_0_82]) ).
cnf(c_0_104,plain,
addition(star(X1),addition(X2,one)) = addition(star(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_67]),c_0_21]) ).
cnf(c_0_105,plain,
( leq(multiplication(X1,multiplication(X2,star(X3))),X1)
| ~ leq(multiplication(X1,addition(X3,X2)),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_65]),c_0_74]) ).
cnf(c_0_106,plain,
leq(multiplication(star(X1),X1),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_72]),c_0_54])]) ).
cnf(c_0_107,plain,
( addition(X1,X2) = X1
| ~ leq(X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_37]),c_0_58]),c_0_37]) ).
cnf(c_0_108,plain,
leq(multiplication(star(addition(star(zero),X1)),star(X1)),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97])]) ).
cnf(c_0_109,plain,
addition(X1,multiplication(star(X2),X1)) = multiplication(star(X2),X1),
inference(spm,[status(thm)],[c_0_23,c_0_98]) ).
cnf(c_0_110,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_111,plain,
addition(X1,addition(X2,star(addition(X1,X2)))) = star(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_99]) ).
cnf(c_0_112,plain,
leq(star(star(X1)),star(X1)),
inference(rw,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_113,negated_conjecture,
( ~ leq(star(addition(one,esk1_0)),star(esk1_0))
| ~ leq(star(esk1_0),star(addition(one,esk1_0))) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_114,plain,
( leq(star(X1),X2)
| addition(X2,addition(multiplication(X2,X1),star(zero))) != X2 ),
inference(spm,[status(thm)],[c_0_103,c_0_75]) ).
cnf(c_0_115,plain,
addition(multiplication(X1,addition(X2,X3)),X4) = addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)),
inference(spm,[status(thm)],[c_0_21,c_0_65]) ).
cnf(c_0_116,plain,
addition(star(X1),addition(X2,star(zero))) = addition(star(X1),X2),
inference(spm,[status(thm)],[c_0_104,c_0_48]) ).
cnf(c_0_117,plain,
leq(multiplication(star(addition(X1,X2)),multiplication(X2,star(X1))),star(addition(X1,X2))),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_118,plain,
multiplication(star(addition(star(zero),X1)),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).
cnf(c_0_119,plain,
addition(X1,star(addition(X2,X1))) = star(addition(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_21]),c_0_22]) ).
cnf(c_0_120,plain,
star(star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_112]),c_0_25]),c_0_99]) ).
cnf(c_0_121,negated_conjecture,
~ leq(star(esk1_0),star(addition(star(zero),esk1_0))),
inference(cn,[status(thm)],[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_48]),c_0_48]),c_0_115]),c_0_58]),c_0_116]),c_0_72]),c_0_22])]) ).
cnf(c_0_122,plain,
leq(star(X1),star(addition(star(zero),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_117,c_0_118]),c_0_119]),c_0_120]),c_0_118]),c_0_119]),c_0_120]) ).
cnf(c_0_123,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_122])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE044+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 12:36:55 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.56 start to proof: theBenchmark
% 99.26/99.30 % Version : CSE_E---1.5
% 99.26/99.30 % Problem : theBenchmark.p
% 99.26/99.30 % Proof found
% 99.26/99.30 % SZS status Theorem for theBenchmark.p
% 99.26/99.30 % SZS output start Proof
% See solution above
% 99.26/99.31 % Total time : 98.746000 s
% 99.26/99.31 % SZS output end Proof
% 99.26/99.31 % Total time : 98.753000 s
%------------------------------------------------------------------------------