TSTP Solution File: KLE137+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE137+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 : n031.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 05:26:31 EDT 2023
% Result : Theorem 0.21s 0.60s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 69 ( 42 unt; 8 typ; 0 def)
% Number of atoms : 82 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 20 ~; 17 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 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 : 90 ( 5 sgn; 42 !; 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(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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
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(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
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(infty_coinduction,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(goals,conjecture,
! [X4] : leq(X4,strong_iteration(one)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_13,plain,
! [X29,X30,X31] :
( ~ leq(addition(multiplication(X31,X29),X30),X31)
| leq(multiplication(X30,star(X29)),X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction2])]) ).
fof(c_0_14,plain,
! [X15] : multiplication(X15,one) = X15,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_15,plain,
! [X7,X8,X9] : addition(X9,addition(X8,X7)) = addition(addition(X9,X8),X7),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_16,plain,
! [X11] : addition(X11,X11) = X11,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_17,plain,
! [X32] : strong_iteration(X32) = addition(multiplication(X32,strong_iteration(X32)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_18,plain,
! [X5,X6] : addition(X5,X6) = addition(X6,X5),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_19,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_28,plain,
! [X16] : multiplication(one,X16) = X16,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_29,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_30,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_32,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])]) ).
fof(c_0_33,plain,
! [X23] : multiplication(zero,X23) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_34,plain,
! [X10] : addition(X10,zero) = X10,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_35,plain,
( leq(star(one),strong_iteration(X1))
| ~ leq(strong_iteration(X1),strong_iteration(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_36,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_39,plain,
! [X25] : addition(one,multiplication(star(X25),X25)) = star(X25),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
cnf(c_0_40,plain,
leq(star(one),strong_iteration(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_22])]) ).
cnf(c_0_41,plain,
strong_iteration(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_37]),c_0_38]) ).
cnf(c_0_42,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,plain,
leq(star(one),one),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_26,c_0_42]) ).
cnf(c_0_46,plain,
star(one) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_24]),c_0_45]) ).
fof(c_0_47,plain,
! [X33,X34,X35] :
( ~ leq(X35,addition(multiplication(X33,X35),X34))
| leq(X35,multiplication(strong_iteration(X33),X34)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).
cnf(c_0_48,plain,
( leq(X1,X2)
| ~ leq(addition(X1,X2),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_46]),c_0_20]) ).
cnf(c_0_49,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_50,plain,
( leq(X1,X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_24]) ).
cnf(c_0_51,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_49,c_0_31]) ).
cnf(c_0_52,plain,
( leq(X1,X2)
| addition(X2,addition(X1,X2)) != X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_36]),c_0_21]) ).
fof(c_0_53,negated_conjecture,
~ ! [X4] : leq(X4,strong_iteration(one)),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_54,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X2,X1)) ),
inference(spm,[status(thm)],[c_0_51,c_0_24]) ).
cnf(c_0_55,plain,
( leq(X1,X2)
| addition(X2,X1) != X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_24]),c_0_26]) ).
fof(c_0_56,negated_conjecture,
~ leq(esk1_0,strong_iteration(one)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])]) ).
cnf(c_0_57,plain,
leq(X1,multiplication(strong_iteration(one),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_21]),c_0_22])]) ).
cnf(c_0_58,negated_conjecture,
~ leq(esk1_0,strong_iteration(one)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_59,plain,
leq(X1,strong_iteration(one)),
inference(spm,[status(thm)],[c_0_57,c_0_20]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE137+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 11:36:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.60 % Version : CSE_E---1.5
% 0.21/0.60 % Problem : theBenchmark.p
% 0.21/0.60 % Proof found
% 0.21/0.60 % SZS status Theorem for theBenchmark.p
% 0.21/0.60 % SZS output start Proof
% See solution above
% 0.21/0.61 % Total time : 0.020000 s
% 0.21/0.61 % SZS output end Proof
% 0.21/0.61 % Total time : 0.023000 s
%------------------------------------------------------------------------------