TSTP Solution File: KLE142+2 by Enigma---0.5.1
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%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : KLE142+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n006.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 : 600s
% DateTime : Sun Jul 17 01:50:31 EDT 2022
% Result : Theorem 7.67s 2.32s
% Output : CNFRefutation 7.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 82 ( 54 unt; 0 def)
% Number of atoms : 112 ( 53 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 29 ~; 23 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 116 ( 15 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(star_induction2,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X3,X1),X2),X3)
=> leq(multiplication(X2,star(X1)),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_induction2) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(star_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(star_induction1,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X3),X2),X3)
=> leq(multiplication(star(X1),X2),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_induction1) ).
fof(infty_coinduction,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(goals,conjecture,
! [X4] :
( leq(strong_iteration(strong_iteration(X4)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(strong_iteration(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(isolation,axiom,
! [X1] : strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',isolation) ).
fof(c_0_15,plain,
! [X29,X30,X31] :
( ~ leq(addition(multiplication(X31,X29),X30),X31)
| leq(multiplication(X30,star(X29)),X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction2])]) ).
fof(c_0_16,plain,
! [X15] : multiplication(X15,one) = X15,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_17,plain,
! [X7,X8,X9] : addition(X9,addition(X8,X7)) = addition(addition(X9,X8),X7),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_18,plain,
! [X11] : addition(X11,X11) = X11,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_19,plain,
! [X32] : strong_iteration(X32) = addition(multiplication(X32,strong_iteration(X32)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
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,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_30,plain,
! [X16] : multiplication(one,X16) = X16,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_31,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_32,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_34,plain,
! [X37,X38] :
( ( ~ leq(X37,X38)
| addition(X37,X38) = X38 )
& ( addition(X37,X38) != X38
| leq(X37,X38) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_35,plain,
! [X23] : multiplication(zero,X23) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_36,plain,
! [X10] : addition(X10,zero) = X10,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_37,plain,
( leq(star(one),strong_iteration(X1))
| ~ leq(strong_iteration(X1),strong_iteration(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_38,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_41,plain,
! [X25] : addition(one,multiplication(star(X25),X25)) = star(X25),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
fof(c_0_42,plain,
! [X26,X27,X28] :
( ~ leq(addition(multiplication(X26,X28),X27),X28)
| leq(multiplication(star(X26),X27),X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction1])]) ).
cnf(c_0_43,plain,
leq(star(one),strong_iteration(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_24])]) ).
cnf(c_0_44,plain,
strong_iteration(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_39]),c_0_40]) ).
cnf(c_0_45,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_46,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_48,plain,
leq(star(one),one),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_28,c_0_45]) ).
fof(c_0_50,plain,
! [X33,X34,X35] :
( ~ leq(X35,addition(multiplication(X33,X35),X34))
| leq(X35,multiplication(strong_iteration(X33),X34)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).
cnf(c_0_51,plain,
( leq(multiplication(star(one),X1),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_33]) ).
cnf(c_0_52,plain,
star(one) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_26]),c_0_49]) ).
cnf(c_0_53,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_54,plain,
( leq(X1,X2)
| ~ leq(addition(X2,X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_33]) ).
cnf(c_0_55,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_53,c_0_33]) ).
cnf(c_0_56,plain,
( leq(X1,X2)
| addition(X2,addition(X1,X2)) != X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_38]),c_0_23]) ).
cnf(c_0_57,plain,
addition(X1,addition(X2,addition(X1,X2))) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_58,plain,
leq(X1,multiplication(strong_iteration(one),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_28]),c_0_23]),c_0_57])]) ).
fof(c_0_59,negated_conjecture,
~ ! [X4] :
( leq(strong_iteration(strong_iteration(X4)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(strong_iteration(X4))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_60,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X2,X1)) ),
inference(spm,[status(thm)],[c_0_55,c_0_26]) ).
cnf(c_0_61,plain,
leq(X1,strong_iteration(one)),
inference(spm,[status(thm)],[c_0_58,c_0_22]) ).
fof(c_0_62,negated_conjecture,
( ~ leq(strong_iteration(strong_iteration(esk1_0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(strong_iteration(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])]) ).
cnf(c_0_63,plain,
( leq(strong_iteration(X1),strong_iteration(one))
| ~ leq(strong_iteration(X1),strong_iteration(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_32]),c_0_22]) ).
cnf(c_0_64,plain,
addition(X1,strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_47,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
( ~ leq(strong_iteration(strong_iteration(esk1_0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(strong_iteration(esk1_0))) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_66,plain,
leq(strong_iteration(X1),strong_iteration(one)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_38]),c_0_24])]) ).
fof(c_0_67,plain,
! [X36] : strong_iteration(X36) = addition(star(X36),multiplication(strong_iteration(X36),zero)),
inference(variable_rename,[status(thm)],[isolation]) ).
cnf(c_0_68,plain,
( leq(X1,multiplication(strong_iteration(X2),zero))
| ~ leq(X1,multiplication(X2,X1)) ),
inference(spm,[status(thm)],[c_0_53,c_0_40]) ).
cnf(c_0_69,plain,
leq(X1,multiplication(strong_iteration(X2),strong_iteration(one))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_64]),c_0_61])]) ).
cnf(c_0_70,negated_conjecture,
( addition(strong_iteration(one),strong_iteration(strong_iteration(esk1_0))) != strong_iteration(strong_iteration(esk1_0))
| ~ leq(strong_iteration(strong_iteration(esk1_0)),strong_iteration(one)) ),
inference(spm,[status(thm)],[c_0_65,c_0_38]) ).
cnf(c_0_71,plain,
addition(strong_iteration(X1),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_47,c_0_66]) ).
cnf(c_0_72,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_73,plain,
leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X1)),zero)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_26,c_0_64]) ).
cnf(c_0_75,negated_conjecture,
addition(strong_iteration(one),strong_iteration(strong_iteration(esk1_0))) != strong_iteration(strong_iteration(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_66])]) ).
cnf(c_0_76,plain,
addition(strong_iteration(one),strong_iteration(X1)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_26,c_0_71]) ).
cnf(c_0_77,plain,
addition(multiplication(strong_iteration(X1),zero),star(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_72,c_0_26]) ).
cnf(c_0_78,plain,
multiplication(strong_iteration(strong_iteration(X1)),zero) = strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_73]),c_0_74]) ).
cnf(c_0_79,negated_conjecture,
strong_iteration(strong_iteration(esk1_0)) != strong_iteration(one),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,plain,
strong_iteration(strong_iteration(X1)) = strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_74]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE142+2 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 09:21:13 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.44 # ENIGMATIC: Selected SinE mode:
% 0.20/0.45 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.20/0.45 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.20/0.45 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 7.67/2.32 # ENIGMATIC: Solved by autoschedule:
% 7.67/2.32 # No SInE strategy applied
% 7.67/2.32 # Trying AutoSched0 for 150 seconds
% 7.67/2.32 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_S059I
% 7.67/2.32 # and selection function SelectComplexExceptUniqMaxPosHorn.
% 7.67/2.32 #
% 7.67/2.32 # Preprocessing time : 0.022 s
% 7.67/2.32 # Presaturation interreduction done
% 7.67/2.32
% 7.67/2.32 # Proof found!
% 7.67/2.32 # SZS status Theorem
% 7.67/2.32 # SZS output start CNFRefutation
% See solution above
% 7.67/2.32 # Training examples: 0 positive, 0 negative
% 7.67/2.32
% 7.67/2.32 # -------------------------------------------------
% 7.67/2.32 # User time : 0.030 s
% 7.67/2.32 # System time : 0.006 s
% 7.67/2.32 # Total time : 0.036 s
% 7.67/2.32 # Maximum resident set size: 7120 pages
% 7.67/2.32
%------------------------------------------------------------------------------