TSTP Solution File: KLE143+1 by Enigma---0.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : KLE143+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n027.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 01:50:32 EDT 2022
% Result : Theorem 13.94s 3.25s
% Output : CNFRefutation 13.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 69 ( 59 unt; 0 def)
% Number of atoms : 81 ( 61 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 12 ~; 9 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 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 : 118 ( 2 sgn 52 !; 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/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(distributivity2,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+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/KLE004+0.ax',multiplicative_associativity) ).
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(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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
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(goals,conjecture,
! [X4] : multiplication(strong_iteration(X4),strong_iteration(X4)) = strong_iteration(X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_14,plain,
! [X7,X8,X9] : addition(X9,addition(X8,X7)) = addition(addition(X9,X8),X7),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_15,plain,
! [X11] : addition(X11,X11) = X11,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_16,plain,
! [X32] : strong_iteration(X32) = addition(multiplication(X32,strong_iteration(X32)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_17,plain,
! [X5,X6] : addition(X5,X6) = addition(X6,X5),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_18,plain,
! [X20,X21,X22] : multiplication(addition(X20,X21),X22) = addition(multiplication(X20,X22),multiplication(X21,X22)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
fof(c_0_19,plain,
! [X16] : multiplication(one,X16) = X16,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_20,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_24,plain,
! [X12,X13,X14] : multiplication(X12,multiplication(X13,X14)) = multiplication(multiplication(X12,X13),X14),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_25,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).
cnf(c_0_31,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_27,c_0_23]) ).
cnf(c_0_32,plain,
addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
addition(X1,multiplication(X2,multiplication(X3,X1))) = multiplication(addition(one,multiplication(X2,X3)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_29]),c_0_23]) ).
fof(c_0_34,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])]) ).
fof(c_0_35,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])]) ).
cnf(c_0_36,plain,
multiplication(addition(one,multiplication(X1,X2)),strong_iteration(multiplication(X1,X2))) = strong_iteration(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_23]),c_0_33]) ).
cnf(c_0_37,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_39,plain,
! [X23] : multiplication(zero,X23) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_40,plain,
! [X10] : addition(X10,zero) = X10,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_41,plain,
multiplication(strong_iteration(X1),strong_iteration(multiplication(X1,strong_iteration(X1)))) = strong_iteration(multiplication(X1,strong_iteration(X1))),
inference(spm,[status(thm)],[c_0_36,c_0_28]) ).
fof(c_0_42,plain,
! [X15] : multiplication(X15,one) = X15,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_43,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| addition(X1,addition(multiplication(X2,X1),X3)) != addition(multiplication(X2,X1),X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_46,plain,
! [X17,X18,X19] : multiplication(X17,addition(X18,X19)) = addition(multiplication(X17,X18),multiplication(X17,X19)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
cnf(c_0_47,plain,
multiplication(strong_iteration(multiplication(X1,X2)),strong_iteration(multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2)))))) = strong_iteration(multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))),
inference(spm,[status(thm)],[c_0_41,c_0_29]) ).
cnf(c_0_48,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(X3,multiplication(X2,X1))) ),
inference(spm,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_49,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
leq(X1,multiplication(strong_iteration(X2),X1)),
inference(spm,[status(thm)],[c_0_43,c_0_31]) ).
cnf(c_0_51,plain,
strong_iteration(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_44]),c_0_45]) ).
cnf(c_0_52,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,plain,
multiplication(strong_iteration(multiplication(X1,strong_iteration(X1))),strong_iteration(multiplication(X1,strong_iteration(multiplication(X1,strong_iteration(X1)))))) = strong_iteration(multiplication(X1,strong_iteration(multiplication(X1,strong_iteration(X1))))),
inference(spm,[status(thm)],[c_0_47,c_0_41]) ).
cnf(c_0_54,plain,
( leq(multiplication(X1,strong_iteration(multiplication(X2,X1))),strong_iteration(X2))
| ~ leq(multiplication(X1,strong_iteration(multiplication(X2,X1))),strong_iteration(multiplication(X2,X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_32]),c_0_49]) ).
cnf(c_0_55,plain,
leq(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_26]) ).
cnf(c_0_56,plain,
addition(multiplication(strong_iteration(X1),X2),strong_iteration(multiplication(X1,strong_iteration(X1)))) = multiplication(strong_iteration(X1),addition(X2,strong_iteration(multiplication(X1,strong_iteration(X1))))),
inference(spm,[status(thm)],[c_0_52,c_0_41]) ).
cnf(c_0_57,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_58,negated_conjecture,
~ ! [X4] : multiplication(strong_iteration(X4),strong_iteration(X4)) = strong_iteration(X4),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_59,plain,
multiplication(strong_iteration(multiplication(X1,strong_iteration(X1))),multiplication(strong_iteration(multiplication(X1,strong_iteration(multiplication(X1,strong_iteration(X1))))),X2)) = multiplication(strong_iteration(multiplication(X1,strong_iteration(multiplication(X1,strong_iteration(X1))))),X2),
inference(spm,[status(thm)],[c_0_29,c_0_53]) ).
cnf(c_0_60,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_61,plain,
leq(strong_iteration(multiplication(X1,strong_iteration(X1))),strong_iteration(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_41]),c_0_55])]) ).
cnf(c_0_62,plain,
addition(strong_iteration(X1),strong_iteration(multiplication(X1,strong_iteration(X1)))) = strong_iteration(multiplication(X1,strong_iteration(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_57]),c_0_41]) ).
fof(c_0_63,negated_conjecture,
multiplication(strong_iteration(esk1_0),strong_iteration(esk1_0)) != strong_iteration(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])]) ).
cnf(c_0_64,plain,
multiplication(strong_iteration(multiplication(X1,strong_iteration(X1))),strong_iteration(multiplication(X1,strong_iteration(multiplication(X1,strong_iteration(multiplication(X1,strong_iteration(X1)))))))) = strong_iteration(multiplication(X1,strong_iteration(multiplication(X1,strong_iteration(multiplication(X1,strong_iteration(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_41]),c_0_29]),c_0_53]),c_0_29]),c_0_53]) ).
cnf(c_0_65,plain,
strong_iteration(multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_23]),c_0_62]) ).
cnf(c_0_66,negated_conjecture,
multiplication(strong_iteration(esk1_0),strong_iteration(esk1_0)) != strong_iteration(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_67,plain,
multiplication(strong_iteration(X1),strong_iteration(X1)) = strong_iteration(X1),
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)],[c_0_64,c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : KLE143+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14 % Command : enigmatic-eprover.py %s %d 1
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 12:37:22 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.48 # ENIGMATIC: Selected SinE mode:
% 0.21/0.49 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.49 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.21/0.49 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.21/0.49 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 13.94/3.25 # ENIGMATIC: Solved by autoschedule:
% 13.94/3.25 # No SInE strategy applied
% 13.94/3.25 # Trying AutoSched0 for 150 seconds
% 13.94/3.25 # AutoSched0-Mode selected heuristic G_____0010_evo
% 13.94/3.25 # and selection function SelectMaxLComplexAvoidPosPred.
% 13.94/3.25 #
% 13.94/3.25 # Preprocessing time : 0.024 s
% 13.94/3.25
% 13.94/3.25 # Proof found!
% 13.94/3.25 # SZS status Theorem
% 13.94/3.25 # SZS output start CNFRefutation
% See solution above
% 13.94/3.25 # Training examples: 0 positive, 0 negative
% 13.94/3.25
% 13.94/3.25 # -------------------------------------------------
% 13.94/3.25 # User time : 0.712 s
% 13.94/3.25 # System time : 0.040 s
% 13.94/3.25 # Total time : 0.751 s
% 13.94/3.25 # Maximum resident set size: 7120 pages
% 13.94/3.25
%------------------------------------------------------------------------------