TSTP Solution File: KLE042+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE042+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 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 : 300s
% DateTime : Thu Aug 31 05:25:50 EDT 2023
% Result : Theorem 4.09s 4.16s
% Output : CNFRefutation 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 78 ( 50 unt; 8 typ; 0 def)
% Number of atoms : 92 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 23 ~; 16 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% 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 : 133 ( 0 sgn; 58 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
addition: ( $i * $i ) > $i ).
tff(decl_23,type,
zero: $i ).
tff(decl_24,type,
multiplication: ( $i * $i ) > $i ).
tff(decl_25,type,
one: $i ).
tff(decl_26,type,
leq: ( $i * $i ) > $o ).
tff(decl_27,type,
star: $i > $i ).
tff(decl_28,type,
esk1_0: $i ).
tff(decl_29,type,
esk2_0: $i ).
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(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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
fof(goals,conjecture,
! [X4,X5] :
( leq(multiplication(star(multiplication(X4,X5)),X4),multiplication(X4,star(multiplication(X5,X4))))
& leq(multiplication(X4,star(multiplication(X5,X4))),multiplication(star(multiplication(X4,X5)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(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_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
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(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(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(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(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]) ).
fof(c_0_16,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_17,plain,
! [X28] : leq(addition(one,multiplication(X28,star(X28))),star(X28)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
fof(c_0_18,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_19,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,negated_conjecture,
~ ! [X4,X5] :
( leq(multiplication(star(multiplication(X4,X5)),X4),multiplication(X4,star(multiplication(X5,X4))))
& leq(multiplication(X4,star(multiplication(X5,X4))),multiplication(star(multiplication(X4,X5)),X4)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_25,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_26,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_27,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,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_21,c_0_22]),c_0_19]),c_0_23]) ).
fof(c_0_29,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_30,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])]) ).
fof(c_0_31,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_32,negated_conjecture,
( ~ leq(multiplication(star(multiplication(esk1_0,esk2_0)),esk1_0),multiplication(esk1_0,star(multiplication(esk2_0,esk1_0))))
| ~ leq(multiplication(esk1_0,star(multiplication(esk2_0,esk1_0))),multiplication(star(multiplication(esk1_0,esk2_0)),esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
cnf(c_0_33,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_35,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_39,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_40,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_41,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_42,plain,
! [X29] : leq(addition(one,multiplication(star(X29),X29)),star(X29)),
inference(variable_rename,[status(thm)],[star_unfold_left]) ).
cnf(c_0_43,negated_conjecture,
( ~ leq(multiplication(star(multiplication(esk1_0,esk2_0)),esk1_0),multiplication(esk1_0,star(multiplication(esk2_0,esk1_0))))
| ~ leq(multiplication(esk1_0,star(multiplication(esk2_0,esk1_0))),multiplication(star(multiplication(esk1_0,esk2_0)),esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,plain,
( leq(multiplication(X1,star(X2)),X3)
| addition(multiplication(X3,X2),addition(X1,X3)) != X3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_19]) ).
cnf(c_0_45,plain,
addition(X1,multiplication(star(X2),X1)) = multiplication(star(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_46,plain,
( leq(multiplication(star(X1),X2),X3)
| addition(multiplication(X1,X3),addition(X2,X3)) != X3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_34]),c_0_19]) ).
cnf(c_0_47,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_48,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
leq(addition(one,multiplication(X1,multiplication(X2,star(multiplication(X1,X2))))),star(multiplication(X1,X2))),
inference(spm,[status(thm)],[c_0_22,c_0_41]) ).
cnf(c_0_51,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,negated_conjecture,
( addition(multiplication(star(multiplication(esk1_0,esk2_0)),esk1_0),multiplication(star(multiplication(esk1_0,esk2_0)),multiplication(esk1_0,multiplication(esk2_0,esk1_0)))) != multiplication(star(multiplication(esk1_0,esk2_0)),esk1_0)
| ~ leq(multiplication(star(multiplication(esk1_0,esk2_0)),esk1_0),multiplication(esk1_0,star(multiplication(esk2_0,esk1_0)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_41]),c_0_45]),c_0_23]) ).
cnf(c_0_53,plain,
( leq(multiplication(star(X1),X2),X3)
| addition(X3,addition(multiplication(X1,X3),X2)) != X3 ),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_23]),c_0_19]) ).
cnf(c_0_55,plain,
addition(X1,multiplication(X1,star(X2))) = multiplication(X1,star(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_36]),c_0_49]) ).
cnf(c_0_56,plain,
addition(one,addition(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,star(multiplication(X1,X2)))))) = star(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_50]),c_0_19]),c_0_23]) ).
cnf(c_0_57,plain,
addition(one,addition(star(X1),X2)) = addition(star(X1),X2),
inference(spm,[status(thm)],[c_0_19,c_0_36]) ).
cnf(c_0_58,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_27,c_0_23]) ).
cnf(c_0_59,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_21,c_0_51]),c_0_19]),c_0_23]) ).
cnf(c_0_60,negated_conjecture,
( addition(esk1_0,addition(multiplication(esk1_0,star(multiplication(esk2_0,esk1_0))),multiplication(esk1_0,multiplication(esk2_0,multiplication(esk1_0,star(multiplication(esk2_0,esk1_0))))))) != multiplication(esk1_0,star(multiplication(esk2_0,esk1_0)))
| addition(multiplication(star(multiplication(esk1_0,esk2_0)),esk1_0),multiplication(star(multiplication(esk1_0,esk2_0)),multiplication(esk1_0,multiplication(esk2_0,esk1_0)))) != multiplication(star(multiplication(esk1_0,esk2_0)),esk1_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_41]),c_0_23]),c_0_54]) ).
cnf(c_0_61,plain,
addition(X1,addition(multiplication(X1,star(X2)),X3)) = addition(multiplication(X1,star(X2)),X3),
inference(spm,[status(thm)],[c_0_19,c_0_55]) ).
cnf(c_0_62,plain,
addition(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,star(multiplication(X1,X2))))) = star(multiplication(X1,X2)),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,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_58,c_0_59]),c_0_19]),c_0_23]),c_0_27]) ).
cnf(c_0_64,negated_conjecture,
( addition(multiplication(esk1_0,star(multiplication(esk2_0,esk1_0))),multiplication(esk1_0,multiplication(esk2_0,multiplication(esk1_0,star(multiplication(esk2_0,esk1_0)))))) != multiplication(esk1_0,star(multiplication(esk2_0,esk1_0)))
| addition(multiplication(star(multiplication(esk1_0,esk2_0)),esk1_0),multiplication(star(multiplication(esk1_0,esk2_0)),multiplication(esk1_0,multiplication(esk2_0,esk1_0)))) != multiplication(star(multiplication(esk1_0,esk2_0)),esk1_0) ),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,plain,
addition(multiplication(X1,star(multiplication(X2,X3))),multiplication(X1,multiplication(X2,multiplication(X3,star(multiplication(X2,X3)))))) = multiplication(X1,star(multiplication(X2,X3))),
inference(spm,[status(thm)],[c_0_48,c_0_62]) ).
cnf(c_0_66,plain,
addition(multiplication(star(X1),X2),multiplication(star(X1),multiplication(X1,X2))) = multiplication(star(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_63]),c_0_41]) ).
cnf(c_0_67,negated_conjecture,
addition(multiplication(star(multiplication(esk1_0,esk2_0)),esk1_0),multiplication(star(multiplication(esk1_0,esk2_0)),multiplication(esk1_0,multiplication(esk2_0,esk1_0)))) != multiplication(star(multiplication(esk1_0,esk2_0)),esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
cnf(c_0_68,plain,
addition(multiplication(star(multiplication(X1,X2)),X3),multiplication(star(multiplication(X1,X2)),multiplication(X1,multiplication(X2,X3)))) = multiplication(star(multiplication(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_66,c_0_41]) ).
cnf(c_0_69,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE042+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 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 : 300
% 0.14/0.35 % DateTime : Tue Aug 29 12:43:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.55 start to proof: theBenchmark
% 4.09/4.16 % Version : CSE_E---1.5
% 4.09/4.16 % Problem : theBenchmark.p
% 4.09/4.16 % Proof found
% 4.09/4.16 % SZS status Theorem for theBenchmark.p
% 4.09/4.16 % SZS output start Proof
% See solution above
% 4.09/4.17 % Total time : 3.601000 s
% 4.09/4.17 % SZS output end Proof
% 4.09/4.17 % Total time : 3.604000 s
%------------------------------------------------------------------------------