TSTP Solution File: KLE167+1 by Enigma---0.5.1
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%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : KLE167+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n016.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 01:50:42 EDT 2022
% Result : Theorem 7.48s 2.25s
% Output : CNFRefutation 7.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 56 ( 37 unt; 0 def)
% Number of atoms : 81 ( 50 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 23 ~; 17 |; 4 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 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 : 85 ( 3 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( ( multiplication(X4,X5) = zero
=> leq(multiplication(X4,star(X5)),X4) )
& leq(X4,multiplication(X4,star(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(distributivity1,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
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_unfold1,axiom,
! [X1] : addition(one,multiplication(X1,star(X1))) = star(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
fof(c_0_13,negated_conjecture,
~ ! [X4,X5] :
( ( multiplication(X4,X5) = zero
=> leq(multiplication(X4,star(X5)),X4) )
& leq(X4,multiplication(X4,star(X5))) ),
inference(assume_negation,[status(cth)],[goals]) ).
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)],[idempotence]) ).
fof(c_0_16,plain,
! [X30,X31,X32] :
( ~ leq(addition(multiplication(X32,X30),X31),X32)
| leq(multiplication(X31,star(X30)),X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction2])]) ).
fof(c_0_17,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_18,plain,
! [X24] : multiplication(zero,X24) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_19,negated_conjecture,
( ( multiplication(esk1_0,esk2_0) = zero
| ~ leq(esk1_0,multiplication(esk1_0,star(esk2_0))) )
& ( ~ leq(multiplication(esk1_0,star(esk2_0)),esk1_0)
| ~ leq(esk1_0,multiplication(esk1_0,star(esk2_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_20,plain,
! [X38,X39] :
( ( ~ leq(X38,X39)
| addition(X38,X39) = X39 )
& ( addition(X38,X39) != X39
| leq(X38,X39) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_21,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_22,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
fof(c_0_23,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_24,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_25,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_27,plain,
! [X26] : addition(one,multiplication(star(X26),X26)) = star(X26),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
cnf(c_0_28,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_29,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,negated_conjecture,
( ~ leq(multiplication(esk1_0,star(esk2_0)),esk1_0)
| ~ leq(esk1_0,multiplication(esk1_0,star(esk2_0))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_32,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_34,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_36,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_37,plain,
! [X25] : addition(one,multiplication(X25,star(X25))) = star(X25),
inference(variable_rename,[status(thm)],[star_unfold1]) ).
cnf(c_0_38,negated_conjecture,
( multiplication(esk1_0,esk2_0) = zero
| ~ leq(esk1_0,multiplication(esk1_0,star(esk2_0))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_39,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_40,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_41,plain,
( leq(zero,X1)
| ~ leq(multiplication(X1,X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_42,negated_conjecture,
( addition(esk1_0,multiplication(esk1_0,star(esk2_0))) != multiplication(esk1_0,star(esk2_0))
| ~ leq(multiplication(esk1_0,star(esk2_0)),esk1_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_43,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_44,plain,
( leq(multiplication(X1,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(X1,X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_33]) ).
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_34,c_0_35]),c_0_36]) ).
cnf(c_0_46,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_47,negated_conjecture,
( multiplication(esk1_0,esk2_0) = zero
| addition(esk1_0,multiplication(esk1_0,star(esk2_0))) != multiplication(esk1_0,star(esk2_0)) ),
inference(spm,[status(thm)],[c_0_38,c_0_32]) ).
cnf(c_0_48,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,plain,
( leq(zero,X1)
| ~ leq(X1,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_35]) ).
cnf(c_0_50,negated_conjecture,
( addition(esk1_0,multiplication(esk1_0,star(esk2_0))) != multiplication(esk1_0,star(esk2_0))
| addition(esk1_0,multiplication(esk1_0,star(esk2_0))) != esk1_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_32]),c_0_36]) ).
cnf(c_0_51,plain,
( multiplication(X1,star(X2)) = X1
| ~ leq(multiplication(X1,X2),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_36]),c_0_45]),c_0_36]),c_0_46]) ).
cnf(c_0_52,negated_conjecture,
multiplication(esk1_0,esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_45]),c_0_36]),c_0_48])]) ).
cnf(c_0_53,plain,
leq(zero,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_32]),c_0_26])]) ).
cnf(c_0_54,negated_conjecture,
multiplication(esk1_0,star(esk2_0)) != 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)],[c_0_50,c_0_45]),c_0_36]),c_0_48]),c_0_45]),c_0_36]),c_0_48])]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]),c_0_54]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE167+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jun 16 15:03:21 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.19/0.44 # ENIGMATIC: Selected SinE mode:
% 0.19/0.44 # Parsing /export/starexec/sandbox2/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
% 7.48/2.25 # ENIGMATIC: Solved by autoschedule:
% 7.48/2.25 # No SInE strategy applied
% 7.48/2.25 # Trying AutoSched0 for 150 seconds
% 7.48/2.25 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_S059I
% 7.48/2.25 # and selection function SelectComplexExceptUniqMaxPosHorn.
% 7.48/2.25 #
% 7.48/2.25 # Preprocessing time : 0.026 s
% 7.48/2.25 # Presaturation interreduction done
% 7.48/2.25
% 7.48/2.25 # Proof found!
% 7.48/2.25 # SZS status Theorem
% 7.48/2.25 # SZS output start CNFRefutation
% See solution above
% 7.48/2.25 # Training examples: 0 positive, 0 negative
% 7.48/2.25
% 7.48/2.25 # -------------------------------------------------
% 7.48/2.25 # User time : 0.056 s
% 7.48/2.25 # System time : 0.013 s
% 7.48/2.25 # Total time : 0.070 s
% 7.48/2.25 # Maximum resident set size: 7116 pages
% 7.48/2.25
%------------------------------------------------------------------------------