TSTP Solution File: KLE151+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE151+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 : n029.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 05:26:38 EDT 2023
% Result : Theorem 117.88s 117.90s
% Output : CNFRefutation 117.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 60 ( 42 unt; 9 typ; 0 def)
% Number of atoms : 62 ( 43 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 8 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn; 50 !; 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,
star: $i > $i ).
tff(decl_27,type,
leq: ( $i * $i ) > $o ).
tff(decl_28,type,
strong_iteration: $i > $i ).
tff(decl_29,type,
esk1_0: $i ).
tff(decl_30,type,
esk2_0: $i ).
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(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(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(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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
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(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(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(goals,conjecture,
! [X4,X5] : leq(multiplication(X4,strong_iteration(multiplication(X5,X4))),multiplication(strong_iteration(multiplication(X4,X5)),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(c_0_12,plain,
! [X33] : strong_iteration(X33) = addition(multiplication(X33,strong_iteration(X33)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_13,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_14,plain,
! [X34,X35,X36] :
( ~ leq(X36,addition(multiplication(X34,X36),X35))
| leq(X36,multiplication(strong_iteration(X34),X35)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).
fof(c_0_15,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_16,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
fof(c_0_17,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_18,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_22,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_23,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_24,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
cnf(c_0_25,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_28,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_29,negated_conjecture,
~ ! [X4,X5] : leq(multiplication(X4,strong_iteration(multiplication(X5,X4))),multiplication(strong_iteration(multiplication(X4,X5)),X4)),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_30,plain,
( leq(X1,multiplication(strong_iteration(multiplication(X2,X3)),X4))
| ~ leq(X1,addition(multiplication(X2,multiplication(X3,X1)),X4)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_31,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,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_19]) ).
cnf(c_0_35,plain,
addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
fof(c_0_36,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_37,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_38,negated_conjecture,
~ leq(multiplication(esk1_0,strong_iteration(multiplication(esk2_0,esk1_0))),multiplication(strong_iteration(multiplication(esk1_0,esk2_0)),esk1_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
cnf(c_0_39,plain,
( leq(X1,multiplication(strong_iteration(multiplication(X2,X3)),X4))
| addition(X1,addition(multiplication(X2,multiplication(X3,X1)),X4)) != addition(multiplication(X2,multiplication(X3,X1)),X4) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,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_34,c_0_21]),c_0_19]) ).
cnf(c_0_42,plain,
addition(one,addition(multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2)))),X3)) = addition(strong_iteration(multiplication(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_43,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
~ leq(multiplication(esk1_0,strong_iteration(multiplication(esk2_0,esk1_0))),multiplication(strong_iteration(multiplication(esk1_0,esk2_0)),esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
( leq(multiplication(X1,X2),multiplication(strong_iteration(multiplication(X1,X3)),X4))
| addition(multiplication(X1,multiplication(addition(one,multiplication(X3,X1)),X2)),X4) != addition(multiplication(X1,multiplication(X3,multiplication(X1,X2))),X4) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_47,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_42,c_0_37]),c_0_35]),c_0_41]) ).
cnf(c_0_48,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_43]),c_0_19]) ).
cnf(c_0_49,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_44,c_0_27]) ).
cnf(c_0_50,negated_conjecture,
$false,
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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_19]),c_0_48]),c_0_19]),c_0_49]),c_0_19]),c_0_48]),c_0_19]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE151+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 11:14:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 117.88/117.90 % Version : CSE_E---1.5
% 117.88/117.90 % Problem : theBenchmark.p
% 117.88/117.90 % Proof found
% 117.88/117.90 % SZS status Theorem for theBenchmark.p
% 117.88/117.90 % SZS output start Proof
% See solution above
% 117.88/117.91 % Total time : 117.315000 s
% 117.88/117.91 % SZS output end Proof
% 117.88/117.91 % Total time : 117.323000 s
%------------------------------------------------------------------------------