TSTP Solution File: KLE167+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE167+1 : 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 : n006.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 05:26:42 EDT 2023
% Result : Theorem 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 19
% Syntax : Number of formulae : 51 ( 28 unt; 9 typ; 0 def)
% Number of atoms : 62 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 17 ~; 12 |; 4 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 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 : 62 ( 0 sgn; 38 !; 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(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(goals,conjecture,
! [X4,X5] :
( ( multiplication(X4,X5) = zero
=> leq(multiplication(X4,star(X5)),X4) )
& leq(X4,multiplication(X4,star(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(star_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(distributivity1,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(star_induction2,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X3,X1),X2),X3)
=> leq(multiplication(X2,star(X1)),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_induction2) ).
fof(c_0_10,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_11,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_12,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]) ).
cnf(c_0_13,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X26] : addition(one,multiplication(star(X26),X26)) = star(X26),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
fof(c_0_16,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_12])])])]) ).
fof(c_0_17,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_18,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_19,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_22,negated_conjecture,
( multiplication(esk1_0,esk2_0) = zero
| ~ leq(esk1_0,multiplication(esk1_0,star(esk2_0))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_28,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_29,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])]) ).
cnf(c_0_30,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_22,c_0_23]) ).
cnf(c_0_31,plain,
addition(X1,multiplication(X1,star(X2))) = multiplication(X1,star(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_32,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
multiplication(esk1_0,esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_36,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,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_16]) ).
cnf(c_0_38,negated_conjecture,
( leq(multiplication(X1,star(esk2_0)),esk1_0)
| ~ leq(X1,esk1_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( ~ leq(esk1_0,multiplication(esk1_0,star(esk2_0)))
| ~ leq(esk1_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,negated_conjecture,
~ leq(esk1_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_23]),c_0_31])]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_23]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE167+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 12:13:21 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.57 % Version : CSE_E---1.5
% 0.19/0.57 % Problem : theBenchmark.p
% 0.19/0.57 % Proof found
% 0.19/0.57 % SZS status Theorem for theBenchmark.p
% 0.19/0.57 % SZS output start Proof
% See solution above
% 0.19/0.58 % Total time : 0.016000 s
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58 % Total time : 0.019000 s
%------------------------------------------------------------------------------