TSTP Solution File: KLE146+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE146+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 : n018.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 05:26:36 EDT 2023
% Result : Theorem 0.15s 0.58s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of formulae : 32 ( 21 unt; 8 typ; 0 def)
% Number of atoms : 29 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 3 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn; 20 !; 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 ).
fof(goals,conjecture,
! [X4] : leq(one,strong_iteration(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(c_0_6,negated_conjecture,
~ ! [X4] : leq(one,strong_iteration(X4)),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_7,plain,
! [X7,X8,X9] : addition(X9,addition(X8,X7)) = addition(addition(X9,X8),X7),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_8,plain,
! [X11] : addition(X11,X11) = X11,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_9,plain,
! [X32] : strong_iteration(X32) = addition(multiplication(X32,strong_iteration(X32)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_10,plain,
! [X5,X6] : addition(X5,X6) = addition(X6,X5),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_11,negated_conjecture,
~ leq(one,strong_iteration(esk1_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_12,plain,
! [X37,X38] :
( ( ~ leq(X37,X38)
| addition(X37,X38) = X38 )
& ( addition(X37,X38) != X38
| leq(X37,X38) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_13,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
~ leq(one,strong_iteration(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
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(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
addition(one,strong_iteration(esk1_0)) != strong_iteration(esk1_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
addition(one,strong_iteration(X1)) = strong_iteration(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
% 0.05/0.12 % Problem : KLE146+1 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.33 % Computer : n018.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Tue Aug 29 12:47:03 EDT 2023
% 0.10/0.33 % CPUTime :
% 0.15/0.55 start to proof: theBenchmark
% 0.15/0.58 % Version : CSE_E---1.5
% 0.15/0.58 % Problem : theBenchmark.p
% 0.15/0.58 % Proof found
% 0.15/0.58 % SZS status Theorem for theBenchmark.p
% 0.15/0.58 % SZS output start Proof
% See solution above
% 0.15/0.58 % Total time : 0.011000 s
% 0.15/0.58 % SZS output end Proof
% 0.15/0.58 % Total time : 0.013000 s
%------------------------------------------------------------------------------