TSTP Solution File: KLE039+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE039+2 : 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 : n001.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 05:25:49 EDT 2023
% Result : Theorem 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of formulae : 76 ( 56 unt; 7 typ; 0 def)
% Number of atoms : 84 ( 50 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 16 ~; 10 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 111 ( 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,
leq: ( $i * $i ) > $o ).
tff(decl_27,type,
star: $i > $i ).
tff(decl_28,type,
esk1_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/KLE002+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).
fof(star_unfold_right,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
fof(star_induction_right,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X1)
=> leq(multiplication(X3,star(X2)),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_induction_right) ).
fof(star_unfold_left,axiom,
! [X1] : leq(addition(one,multiplication(star(X1),X1)),star(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(goals,conjecture,
! [X4] :
( leq(star(star(X4)),star(X4))
& leq(star(X4),star(star(X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_associativity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',left_distributivity) ).
fof(c_0_13,plain,
! [X7,X8,X9] : addition(X9,addition(X8,X7)) = addition(addition(X9,X8),X7),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_14,plain,
! [X11] : addition(X11,X11) = X11,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_15,plain,
! [X25,X26] :
( ( ~ leq(X25,X26)
| addition(X25,X26) = X26 )
& ( addition(X25,X26) != X26
| leq(X25,X26) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_16,plain,
! [X27] : leq(addition(one,multiplication(X27,star(X27))),star(X27)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
fof(c_0_17,plain,
! [X5,X6] : addition(X5,X6) = addition(X6,X5),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_18,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18]),c_0_22]) ).
fof(c_0_25,plain,
! [X32,X33,X34] :
( ~ leq(addition(multiplication(X32,X33),X34),X32)
| leq(multiplication(X34,star(X33)),X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_right])]) ).
fof(c_0_26,plain,
! [X28] : leq(addition(one,multiplication(star(X28),X28)),star(X28)),
inference(variable_rename,[status(thm)],[star_unfold_left]) ).
cnf(c_0_27,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_29,plain,
! [X16] : multiplication(one,X16) = X16,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_30,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
addition(one,addition(star(X1),X2)) = addition(star(X1),X2),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_32,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(X1,multiplication(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_33,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,plain,
addition(star(X1),multiplication(star(X1),X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_30]),c_0_18]),c_0_22]),c_0_31]) ).
cnf(c_0_35,plain,
leq(star(X1),star(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_33]) ).
cnf(c_0_36,plain,
leq(multiplication(star(X1),star(X1)),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_34]),c_0_35])]) ).
cnf(c_0_37,plain,
addition(star(X1),multiplication(star(X1),star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_36]),c_0_22]) ).
fof(c_0_38,plain,
! [X17,X18,X19] : multiplication(X17,addition(X18,X19)) = addition(multiplication(X17,X18),multiplication(X17,X19)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_39,plain,
! [X15] : multiplication(X15,one) = X15,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_40,negated_conjecture,
~ ! [X4] :
( leq(star(star(X4)),star(X4))
& leq(star(X4),star(star(X4))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_41,plain,
! [X12,X13,X14] : multiplication(X12,multiplication(X13,X14)) = multiplication(multiplication(X12,X13),X14),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_42,plain,
leq(multiplication(star(X1),star(star(X1))),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_35])]) ).
cnf(c_0_43,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
fof(c_0_46,plain,
! [X20,X21,X22] : multiplication(addition(X20,X21),X22) = addition(multiplication(X20,X22),multiplication(X21,X22)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_47,negated_conjecture,
( ~ leq(star(star(esk1_0)),star(esk1_0))
| ~ leq(star(esk1_0),star(star(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])]) ).
cnf(c_0_48,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
addition(star(X1),multiplication(star(X1),star(star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_42]),c_0_22]) ).
cnf(c_0_50,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_22]) ).
cnf(c_0_52,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_45,c_0_19]) ).
cnf(c_0_53,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_54,negated_conjecture,
( ~ leq(star(star(esk1_0)),star(esk1_0))
| ~ leq(star(esk1_0),star(star(esk1_0))) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_56,plain,
leq(addition(one,multiplication(X1,multiplication(X2,star(multiplication(X1,X2))))),star(multiplication(X1,X2))),
inference(spm,[status(thm)],[c_0_21,c_0_48]) ).
cnf(c_0_57,plain,
multiplication(star(X1),star(star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_27]) ).
cnf(c_0_58,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_51]),c_0_22]),c_0_27]) ).
cnf(c_0_59,plain,
addition(star(X1),multiplication(X1,star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_24]),c_0_18]),c_0_22]),c_0_23]) ).
cnf(c_0_60,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_33]),c_0_22]) ).
cnf(c_0_61,negated_conjecture,
( addition(star(esk1_0),star(star(esk1_0))) != star(esk1_0)
| ~ leq(star(esk1_0),star(star(esk1_0))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_22]) ).
cnf(c_0_62,plain,
leq(star(X1),star(star(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_57]),c_0_27]) ).
cnf(c_0_63,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
addition(star(esk1_0),star(star(esk1_0))) != star(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]) ).
cnf(c_0_65,plain,
addition(X1,star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_63]),c_0_18]),c_0_27]),c_0_27]),c_0_63]) ).
cnf(c_0_66,negated_conjecture,
star(star(esk1_0)) != star(esk1_0),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_67,plain,
star(star(X1)) = star(X1),
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_60,c_0_57]),c_0_22]),c_0_27]),c_0_57]),c_0_22]),c_0_65]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE039+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n001.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 11:54:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.60 % Version : CSE_E---1.5
% 0.19/0.60 % Problem : theBenchmark.p
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark.p
% 0.19/0.60 % SZS output start Proof
% See solution above
% 0.19/0.61 % Total time : 0.034000 s
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time : 0.037000 s
%------------------------------------------------------------------------------