TSTP Solution File: KLE002+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE002+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 : n012.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 05:25:30 EDT 2023
% Result : Theorem 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 32 ( 17 unt; 8 typ; 0 def)
% Number of atoms : 33 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 16 ( 7 ~; 4 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 2 sgn; 24 !; 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,
esk1_0: $i ).
tff(decl_28,type,
esk2_0: $i ).
tff(decl_29,type,
esk3_0: $i ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( leq(X4,X5)
=> leq(multiplication(X4,X6),multiplication(X5,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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/KLE001+0.ax',left_distributivity) ).
fof(c_0_5,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_6,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_7,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_8,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
~ ! [X4,X5,X6] :
( leq(X4,X5)
=> leq(multiplication(X4,X6),multiplication(X5,X6)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_11,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
fof(c_0_13,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_14,negated_conjecture,
( leq(esk1_0,esk2_0)
& ~ leq(multiplication(esk1_0,esk3_0),multiplication(esk2_0,esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_15,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
leq(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
leq(multiplication(X1,X2),multiplication(addition(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
addition(esk1_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ leq(multiplication(esk1_0,esk3_0),multiplication(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
leq(multiplication(esk1_0,X1),multiplication(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE002+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 11:55:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.53 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.59 % Total time : 0.045000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.048000 s
%------------------------------------------------------------------------------