TSTP Solution File: KLE045+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE045+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 05:25:51 EDT 2023
% Result : Theorem 38.95s 39.02s
% Output : CNFRefutation 38.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of formulae : 89 ( 56 unt; 9 typ; 0 def)
% Number of atoms : 106 ( 58 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 22 ~; 19 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 147 ( 1 sgn; 60 !; 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 ).
tff(decl_30,type,
esk3_0: $i ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
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(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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_left_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(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(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(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(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(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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_identity) ).
fof(c_0_14,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_15,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_16,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])]) ).
fof(c_0_17,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_18,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_21,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_22,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,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])]) ).
cnf(c_0_24,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_29,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_30,plain,
! [X29] : leq(addition(one,multiplication(X29,star(X29))),star(X29)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
cnf(c_0_31,plain,
( leq(multiplication(X1,star(one)),X2)
| addition(X1,X2) != X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19]),c_0_28]) ).
cnf(c_0_32,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_35,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_36,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_37,plain,
( leq(star(one),X1)
| addition(one,X1) != X1 ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,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_33,c_0_34]),c_0_19]),c_0_18]) ).
cnf(c_0_39,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_40,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_41,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_36])])]) ).
cnf(c_0_42,plain,
( addition(star(one),X1) = X1
| addition(one,X1) != X1 ),
inference(spm,[status(thm)],[c_0_33,c_0_37]) ).
fof(c_0_43,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_44,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_38]),c_0_19]),c_0_18]),c_0_39]) ).
cnf(c_0_45,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_32]),c_0_18]) ).
fof(c_0_46,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_47,negated_conjecture,
leq(multiplication(esk1_0,esk3_0),multiplication(esk3_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_39,c_0_38]) ).
cnf(c_0_49,plain,
( addition(X1,star(one)) = X1
| addition(one,X1) != X1 ),
inference(spm,[status(thm)],[c_0_18,c_0_42]) ).
fof(c_0_50,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_51,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_54,negated_conjecture,
addition(multiplication(esk1_0,esk3_0),multiplication(esk3_0,esk2_0)) = multiplication(esk3_0,esk2_0),
inference(spm,[status(thm)],[c_0_33,c_0_47]) ).
cnf(c_0_55,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_56,plain,
star(one) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_25])]) ).
cnf(c_0_57,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_58,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(X4,X2))) = multiplication(addition(X1,multiplication(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_40,c_0_51]) ).
cnf(c_0_59,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_52,c_0_18]) ).
cnf(c_0_60,plain,
addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_19,c_0_53]) ).
cnf(c_0_61,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(esk1_0,esk3_0)) = multiplication(esk3_0,esk2_0),
inference(rw,[status(thm)],[c_0_54,c_0_18]) ).
cnf(c_0_62,plain,
( leq(X1,addition(X1,X2))
| ~ leq(addition(X1,X2),addition(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_39]),c_0_56]),c_0_22]) ).
fof(c_0_63,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_64,plain,
( leq(multiplication(star(X1),addition(X2,multiplication(X1,X3))),X3)
| ~ leq(addition(X2,multiplication(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_28]) ).
cnf(c_0_65,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_58,c_0_59]),c_0_40]) ).
cnf(c_0_66,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_60,c_0_61]),c_0_53]),c_0_18]) ).
cnf(c_0_67,plain,
leq(X1,addition(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_27]),c_0_25])]) ).
cnf(c_0_68,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_69,plain,
( leq(multiplication(star(X1),multiplication(addition(X2,X1),X3)),X3)
| ~ leq(multiplication(addition(X2,X1),X3),X3) ),
inference(spm,[status(thm)],[c_0_64,c_0_40]) ).
cnf(c_0_70,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_65,c_0_66]),c_0_51]),c_0_59]),c_0_18]),c_0_45]),c_0_18]),c_0_51]) ).
cnf(c_0_71,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,plain,
( leq(multiplication(X1,X2),multiplication(X1,X3))
| ~ leq(multiplication(X1,addition(X2,X3)),multiplication(X1,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_53]),c_0_51]),c_0_56]),c_0_22]) ).
cnf(c_0_73,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_22]),c_0_18]) ).
cnf(c_0_74,negated_conjecture,
leq(multiplication(star(esk1_0),multiplication(esk3_0,star(esk2_0))),multiplication(esk3_0,star(esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]) ).
cnf(c_0_75,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(X4,X3)) = multiplication(addition(multiplication(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_40,c_0_51]) ).
cnf(c_0_76,plain,
( leq(multiplication(X1,X2),multiplication(X1,multiplication(X2,X3)))
| ~ leq(multiplication(X1,multiplication(X2,addition(X3,one))),multiplication(X1,multiplication(X2,X3))) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_77,negated_conjecture,
multiplication(star(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_33,c_0_74]),c_0_75]),c_0_18]),c_0_45]),c_0_18]),c_0_48]),c_0_51]) ).
cnf(c_0_78,negated_conjecture,
~ leq(multiplication(star(esk1_0),esk3_0),multiplication(esk3_0,star(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_79,negated_conjecture,
$false,
inference(sr,[status(thm)],[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_76,c_0_77]),c_0_18]),c_0_48]),c_0_77]),c_0_71])]),c_0_78]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE045+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n011.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 11:03:11 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 38.95/39.02 % Version : CSE_E---1.5
% 38.95/39.02 % Problem : theBenchmark.p
% 38.95/39.02 % Proof found
% 38.95/39.02 % SZS status Theorem for theBenchmark.p
% 38.95/39.02 % SZS output start Proof
% See solution above
% 38.95/39.03 % Total time : 38.445000 s
% 38.95/39.03 % SZS output end Proof
% 38.95/39.03 % Total time : 38.449000 s
%------------------------------------------------------------------------------