TSTP Solution File: KLE045+1 by Enigma---0.5.1
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%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : KLE045+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n032.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 01:49:51 EDT 2022
% Result : Theorem 16.16s 3.30s
% Output : CNFRefutation 16.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 80 ( 61 unt; 0 def)
% Number of atoms : 101 ( 56 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 17 ~; 14 |; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 144 ( 0 sgn 60 !; 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(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(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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_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_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(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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_associativity) ).
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(goals,conjecture,
! [X4,X5,X6] :
( leq(multiplication(X4,X6),multiplication(X6,X5))
=> leq(multiplication(star(X4),X6),multiplication(X6,star(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_14,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_15,plain,
! [X13] : addition(X13,X13) = X13,
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,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_19,plain,
! [X27,X28] :
( ( ~ leq(X27,X28)
| addition(X27,X28) = X28 )
& ( addition(X27,X28) != X28
| leq(X27,X28) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_20,plain,
! [X30] : leq(addition(one,multiplication(star(X30),X30)),star(X30)),
inference(variable_rename,[status(thm)],[star_unfold_left]) ).
cnf(c_0_21,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_25,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_26,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_27,plain,
! [X29] : leq(addition(one,multiplication(X29,star(X29))),star(X29)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
cnf(c_0_28,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,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_23,c_0_24]),c_0_16]),c_0_22]) ).
cnf(c_0_30,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,plain,
! [X34,X35,X36] :
( ~ leq(addition(multiplication(X34,X35),X36),X34)
| leq(multiplication(X36,star(X35)),X34) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_right])]) ).
cnf(c_0_33,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_34,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_35,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_36,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_37,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_28,c_0_29]),c_0_16]),c_0_22]),c_0_21]) ).
cnf(c_0_38,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_22]) ).
cnf(c_0_39,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,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_33]),c_0_16]),c_0_22]) ).
cnf(c_0_41,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_43,plain,
! [X31,X32,X33] :
( ~ leq(addition(multiplication(X31,X32),X33),X32)
| leq(multiplication(star(X31),X33),X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_left])]) ).
cnf(c_0_44,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
multiplication(star(X1),addition(X1,one)) = star(X1),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(X1,multiplication(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_22]) ).
cnf(c_0_47,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_28,c_0_40]),c_0_16]),c_0_22]),c_0_21]) ).
cnf(c_0_48,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_22]) ).
fof(c_0_49,negated_conjecture,
~ ! [X4,X5,X6] :
( leq(multiplication(X4,X6),multiplication(X6,X5))
=> leq(multiplication(star(X4),X6),multiplication(X6,star(X5))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_50,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,plain,
( leq(multiplication(X1,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(X1,X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_17]),c_0_44]) ).
cnf(c_0_52,plain,
multiplication(star(X1),multiplication(addition(X1,one),X2)) = multiplication(star(X1),X2),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,plain,
leq(star(X1),star(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_24]),c_0_42]) ).
cnf(c_0_54,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_55,negated_conjecture,
( leq(multiplication(esk1_0,esk3_0),multiplication(esk3_0,esk2_0))
& ~ leq(multiplication(star(esk1_0),esk3_0),multiplication(esk3_0,star(esk2_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])]) ).
cnf(c_0_56,plain,
( leq(multiplication(star(X1),multiplication(X2,X3)),X3)
| ~ leq(multiplication(addition(X1,X2),X3),X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_41]) ).
cnf(c_0_57,plain,
leq(multiplication(star(X1),star(addition(X1,one))),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_45]),c_0_53])]) ).
cnf(c_0_58,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_21,c_0_40]) ).
cnf(c_0_59,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_54,c_0_22]) ).
cnf(c_0_60,negated_conjecture,
leq(multiplication(esk1_0,esk3_0),multiplication(esk3_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,plain,
( leq(multiplication(star(X1),X2),X2)
| ~ leq(multiplication(addition(X1,one),X2),X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_42]) ).
cnf(c_0_62,plain,
multiplication(star(X1),star(addition(X1,one))) = star(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_57]),c_0_22]),c_0_38]),c_0_22]),c_0_58]) ).
cnf(c_0_63,plain,
multiplication(addition(X1,one),star(addition(X1,one))) = star(addition(X1,one)),
inference(spm,[status(thm)],[c_0_59,c_0_28]) ).
cnf(c_0_64,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(X4,X2))) = multiplication(addition(X1,multiplication(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_41,c_0_44]) ).
cnf(c_0_65,plain,
addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_16,c_0_30]) ).
cnf(c_0_66,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(esk1_0,esk3_0)) = multiplication(esk3_0,esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_60]),c_0_22]) ).
cnf(c_0_67,plain,
leq(star(X1),star(addition(X1,one))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_53])]) ).
cnf(c_0_68,plain,
addition(star(X1),star(addition(X1,one))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_62]),c_0_22]),c_0_58]),c_0_62]),c_0_22]) ).
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,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_71,plain,
multiplication(addition(X1,multiplication(X2,addition(one,X3))),star(X3)) = multiplication(addition(X1,X2),star(X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_59]),c_0_41]) ).
cnf(c_0_72,negated_conjecture,
addition(multiplication(esk1_0,esk3_0),multiplication(esk3_0,addition(X1,esk2_0))) = multiplication(esk3_0,addition(X1,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_30]),c_0_22]) ).
cnf(c_0_73,plain,
star(addition(X1,one)) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_67]),c_0_68]) ).
cnf(c_0_74,plain,
( leq(multiplication(star(X1),X2),X3)
| addition(X3,addition(multiplication(X1,X3),X2)) != X3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_69]),c_0_16]),c_0_70]) ).
cnf(c_0_75,negated_conjecture,
multiplication(addition(one,esk1_0),multiplication(esk3_0,star(esk2_0))) = multiplication(esk3_0,star(esk2_0)),
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_71,c_0_72]),c_0_44]),c_0_59]),c_0_22]),c_0_48]),c_0_22]),c_0_44]) ).
cnf(c_0_76,plain,
star(addition(one,X1)) = star(X1),
inference(spm,[status(thm)],[c_0_73,c_0_22]) ).
cnf(c_0_77,negated_conjecture,
~ leq(multiplication(star(esk1_0),esk3_0),multiplication(esk3_0,star(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_78,negated_conjecture,
( leq(multiplication(star(esk1_0),X1),multiplication(esk3_0,star(esk2_0)))
| addition(multiplication(esk3_0,star(esk2_0)),X1) != multiplication(esk3_0,star(esk2_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_65]),c_0_17]) ).
cnf(c_0_79,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_22]),c_0_38]),c_0_22]),c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : KLE045+1 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.10 % Command : enigmatic-eprover.py %s %d 1
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Thu Jun 16 07:31:31 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.14/0.36 # ENIGMATIC: Selected SinE mode:
% 0.14/0.36 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.14/0.36 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.14/0.36 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 16.16/3.30 # ENIGMATIC: Solved by autoschedule:
% 16.16/3.30 # No SInE strategy applied
% 16.16/3.30 # Trying AutoSched0 for 150 seconds
% 16.16/3.30 # AutoSched0-Mode selected heuristic G_____0010_evo
% 16.16/3.30 # and selection function SelectMaxLComplexAvoidPosPred.
% 16.16/3.30 #
% 16.16/3.30 # Preprocessing time : 0.013 s
% 16.16/3.30
% 16.16/3.30 # Proof found!
% 16.16/3.30 # SZS status Theorem
% 16.16/3.30 # SZS output start CNFRefutation
% See solution above
% 16.16/3.30 # Training examples: 0 positive, 0 negative
% 16.16/3.30
% 16.16/3.30 # -------------------------------------------------
% 16.16/3.30 # User time : 1.103 s
% 16.16/3.30 # System time : 0.072 s
% 16.16/3.30 # Total time : 1.175 s
% 16.16/3.30 # Maximum resident set size: 7120 pages
% 16.16/3.30
%------------------------------------------------------------------------------