TSTP Solution File: KLE041+1 by Enigma---0.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : KLE041+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n014.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 01:49:48 EDT 2022
% Result : Theorem 9.74s 2.66s
% Output : CNFRefutation 9.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 79 ( 57 unt; 0 def)
% Number of atoms : 103 ( 51 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 44 ( 20 ~; 17 |; 2 &)
% ( 1 <=>; 4 =>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
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(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(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(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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_left_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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(goals,conjecture,
! [X4,X5] :
( leq(X4,X5)
=> leq(star(X4),star(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(c_0_14,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_15,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_16,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_19,plain,
! [X26,X27] :
( ( ~ leq(X26,X27)
| addition(X26,X27) = X27 )
& ( addition(X26,X27) != X27
| leq(X26,X27) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_20,plain,
! [X28] : leq(addition(one,multiplication(X28,star(X28))),star(X28)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
fof(c_0_21,plain,
! [X33,X34,X35] :
( ~ leq(addition(multiplication(X33,X34),X35),X33)
| leq(multiplication(X35,star(X34)),X33) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_right])]) ).
fof(c_0_22,plain,
! [X30,X31,X32] :
( ~ leq(addition(multiplication(X30,X31),X32),X31)
| leq(multiplication(star(X30),X32),X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_left])]) ).
cnf(c_0_23,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_28,plain,
! [X29] : leq(addition(one,multiplication(star(X29),X29)),star(X29)),
inference(variable_rename,[status(thm)],[star_unfold_left]) ).
fof(c_0_29,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_30,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,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_25,c_0_26]),c_0_16]),c_0_24]) ).
cnf(c_0_33,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(X1,multiplication(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_34,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_36,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_37,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_38,plain,
( leq(multiplication(star(X1),X2),X3)
| ~ leq(addition(X2,multiplication(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_39,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_31,c_0_32]),c_0_16]),c_0_24]),c_0_23]) ).
cnf(c_0_40,plain,
leq(star(X1),star(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_41,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,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_25,c_0_34]),c_0_16]),c_0_24]) ).
cnf(c_0_44,plain,
leq(multiplication(star(X1),star(X1)),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_45,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_24]) ).
cnf(c_0_46,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_47,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_31,c_0_43]),c_0_16]),c_0_24]),c_0_23]) ).
cnf(c_0_48,plain,
multiplication(star(X1),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_25,c_0_44]),c_0_24]),c_0_45]),c_0_24]),c_0_46]) ).
fof(c_0_49,negated_conjecture,
~ ! [X4,X5] :
( leq(X4,X5)
=> leq(star(X4),star(X5)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_50,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_51,plain,
multiplication(star(X1),addition(X1,one)) = star(X1),
inference(rw,[status(thm)],[c_0_47,c_0_45]) ).
cnf(c_0_52,plain,
( leq(multiplication(star(star(X1)),X2),star(X1))
| ~ leq(addition(star(X1),X2),star(X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_48]) ).
fof(c_0_53,negated_conjecture,
( leq(esk1_0,esk2_0)
& ~ leq(star(esk1_0),star(esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])]) ).
cnf(c_0_54,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(spm,[status(thm)],[c_0_51,c_0_24]) ).
cnf(c_0_56,plain,
leq(star(star(X1)),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_42]),c_0_24]),c_0_46]),c_0_40])]) ).
cnf(c_0_57,negated_conjecture,
leq(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_58,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_59,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_35]),c_0_24]) ).
cnf(c_0_60,plain,
multiplication(star(star(X1)),star(X1)) = star(star(X1)),
inference(spm,[status(thm)],[c_0_55,c_0_46]) ).
cnf(c_0_61,plain,
addition(star(X1),star(star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_56]),c_0_24]) ).
cnf(c_0_62,negated_conjecture,
addition(esk1_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_25,c_0_57]) ).
cnf(c_0_63,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_64,plain,
( leq(multiplication(star(star(X1)),X2),star(X1))
| ~ leq(addition(X2,star(X1)),star(X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_48]) ).
cnf(c_0_65,plain,
star(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_59,c_0_60]),c_0_61]),c_0_24]),c_0_46]),c_0_60]) ).
cnf(c_0_66,negated_conjecture,
addition(esk1_0,addition(esk2_0,X1)) = addition(esk2_0,X1),
inference(spm,[status(thm)],[c_0_16,c_0_62]) ).
cnf(c_0_67,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_59,c_0_51]),c_0_16]),c_0_46]),c_0_24]),c_0_46]),c_0_51]) ).
cnf(c_0_68,plain,
( leq(multiplication(X1,multiplication(X2,star(X2))),X3)
| ~ leq(multiplication(addition(X1,X3),X2),X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_54]),c_0_63]) ).
cnf(c_0_69,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_70,plain,
( leq(multiplication(star(X1),X2),star(X1))
| ~ leq(addition(X2,star(X1)),star(X1)) ),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,negated_conjecture,
addition(esk1_0,star(esk2_0)) = star(esk2_0),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,plain,
( leq(multiplication(X1,star(X1)),star(X2))
| ~ leq(multiplication(star(X2),X1),star(X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_46]),c_0_35]) ).
cnf(c_0_73,plain,
( leq(multiplication(X1,star(X2)),X3)
| addition(X1,multiplication(X3,addition(X2,one))) != X3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_69]),c_0_16]),c_0_24]),c_0_45]) ).
cnf(c_0_74,negated_conjecture,
leq(multiplication(star(esk2_0),esk1_0),star(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_40])]) ).
cnf(c_0_75,negated_conjecture,
~ leq(star(esk1_0),star(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_76,plain,
( leq(star(X1),star(X2))
| multiplication(star(X2),addition(X1,one)) != star(X2) ),
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_72,c_0_73]),c_0_65]),c_0_48]),c_0_45]),c_0_16]),c_0_17]) ).
cnf(c_0_77,negated_conjecture,
multiplication(star(esk2_0),addition(one,esk1_0)) = star(esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_74]),c_0_24]),c_0_45]),c_0_24]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_24]),c_0_77])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE041+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.12/0.33 % Computer : n014.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 : 600
% 0.12/0.33 % DateTime : Thu Jun 16 14:14:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.44 # ENIGMATIC: Selected SinE mode:
% 0.19/0.44 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.19/0.44 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.19/0.44 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 9.74/2.66 # ENIGMATIC: Solved by autoschedule:
% 9.74/2.66 # No SInE strategy applied
% 9.74/2.66 # Trying AutoSched0 for 150 seconds
% 9.74/2.66 # AutoSched0-Mode selected heuristic G_____0010_evo
% 9.74/2.66 # and selection function SelectMaxLComplexAvoidPosPred.
% 9.74/2.66 #
% 9.74/2.66 # Preprocessing time : 0.024 s
% 9.74/2.66
% 9.74/2.66 # Proof found!
% 9.74/2.66 # SZS status Theorem
% 9.74/2.66 # SZS output start CNFRefutation
% See solution above
% 9.74/2.66 # Training examples: 0 positive, 0 negative
% 9.74/2.66
% 9.74/2.66 # -------------------------------------------------
% 9.74/2.66 # User time : 0.292 s
% 9.74/2.66 # System time : 0.015 s
% 9.74/2.66 # Total time : 0.306 s
% 9.74/2.66 # Maximum resident set size: 7124 pages
% 9.74/2.66
%------------------------------------------------------------------------------