TSTP Solution File: KLE145+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE145+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 : n024.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 05:26:35 EDT 2023
% Result : Theorem 88.73s 88.84s
% Output : CNFRefutation 88.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of formulae : 92 ( 70 unt; 8 typ; 0 def)
% Number of atoms : 100 ( 65 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 15 ~; 12 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 139 ( 3 sgn; 58 !; 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(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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
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_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
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(star_unfold1,axiom,
! [X1] : addition(one,multiplication(X1,star(X1))) = star(X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
fof(distributivity2,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
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(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(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
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(goals,conjecture,
! [X4] : star(strong_iteration(X4)) = strong_iteration(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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,
! [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_18,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_22,plain,
! [X5,X6] : addition(X5,X6) = addition(X6,X5),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_23,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_25,plain,
! [X25] : addition(one,multiplication(star(X25),X25)) = star(X25),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
fof(c_0_26,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])]) ).
cnf(c_0_27,plain,
leq(X1,addition(X2,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_29,plain,
! [X24] : addition(one,multiplication(X24,star(X24))) = star(X24),
inference(variable_rename,[status(thm)],[star_unfold1]) ).
cnf(c_0_30,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_32,plain,
leq(multiplication(star(X1),X1),star(X1)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_34,plain,
! [X20,X21,X22] : multiplication(addition(X20,X21),X22) = addition(multiplication(X20,X22),multiplication(X21,X22)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
fof(c_0_35,plain,
! [X16] : multiplication(one,X16) = X16,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_36,plain,
! [X17,X18,X19] : multiplication(X17,addition(X18,X19)) = addition(multiplication(X17,X18),multiplication(X17,X19)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
fof(c_0_37,plain,
! [X15] : multiplication(X15,one) = X15,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_38,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(X1,multiplication(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_39,plain,
addition(star(X1),multiplication(star(X1),X1)) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_24]) ).
cnf(c_0_40,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_41,plain,
leq(multiplication(X1,star(X1)),star(X1)),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
cnf(c_0_42,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
leq(multiplication(star(X1),star(X1)),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
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])]) ).
fof(c_0_48,plain,
! [X12,X13,X14] : multiplication(X12,multiplication(X13,X14)) = multiplication(multiplication(X12,X13),X14),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_49,plain,
addition(star(X1),multiplication(X1,star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_41]),c_0_24]) ).
cnf(c_0_50,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_24]) ).
fof(c_0_51,plain,
! [X32] : strong_iteration(X32) = addition(multiplication(X32,strong_iteration(X32)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
cnf(c_0_52,plain,
( leq(multiplication(X1,X2),multiplication(X3,X2))
| multiplication(addition(X1,X3),X2) != multiplication(X3,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_42]) ).
cnf(c_0_53,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_54,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_24]) ).
cnf(c_0_55,plain,
addition(star(X1),multiplication(star(X1),star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_46]),c_0_24]) ).
cnf(c_0_56,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_57,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_58,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_59,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_60,plain,
leq(X1,multiplication(star(X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_43]) ).
cnf(c_0_61,plain,
multiplication(star(X1),addition(X1,one)) = star(X1),
inference(rw,[status(thm)],[c_0_39,c_0_54]) ).
cnf(c_0_62,plain,
leq(multiplication(star(X1),star(star(X1))),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_55]),c_0_40])]) ).
cnf(c_0_63,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(X3,multiplication(X2,X1))) ),
inference(spm,[status(thm)],[c_0_56,c_0_24]) ).
cnf(c_0_64,plain,
addition(one,multiplication(X1,multiplication(X2,star(multiplication(X1,X2))))) = star(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_33,c_0_57]) ).
cnf(c_0_65,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_58,c_0_24]) ).
cnf(c_0_66,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_59,c_0_24]) ).
cnf(c_0_67,plain,
leq(addition(X1,one),star(X1)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,plain,
addition(star(X1),multiplication(star(X1),star(star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_62]),c_0_24]) ).
cnf(c_0_69,plain,
( leq(multiplication(X1,star(multiplication(X2,X1))),strong_iteration(X2))
| ~ leq(multiplication(X1,star(multiplication(X2,X1))),star(multiplication(X2,X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_45]) ).
cnf(c_0_70,plain,
multiplication(strong_iteration(X1),star(multiplication(X1,strong_iteration(X1)))) = star(multiplication(X1,strong_iteration(X1))),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,plain,
addition(one,addition(multiplication(X1,strong_iteration(X1)),X2)) = addition(strong_iteration(X1),X2),
inference(spm,[status(thm)],[c_0_18,c_0_66]) ).
cnf(c_0_72,plain,
addition(X1,star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_67]),c_0_18]),c_0_53]) ).
fof(c_0_73,negated_conjecture,
~ ! [X4] : star(strong_iteration(X4)) = strong_iteration(X4),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_74,plain,
multiplication(star(X1),star(star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_54]),c_0_24]),c_0_53]) ).
cnf(c_0_75,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_54]),c_0_24]),c_0_53]) ).
cnf(c_0_76,plain,
leq(star(multiplication(X1,strong_iteration(X1))),strong_iteration(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_40])]) ).
cnf(c_0_77,plain,
addition(strong_iteration(X1),star(multiplication(X1,strong_iteration(X1)))) = star(multiplication(X1,strong_iteration(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_53]) ).
fof(c_0_78,negated_conjecture,
star(strong_iteration(esk1_0)) != strong_iteration(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])])]) ).
cnf(c_0_79,plain,
star(star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_74]),c_0_75]),c_0_74]),c_0_53]) ).
cnf(c_0_80,plain,
star(multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_76]),c_0_24]),c_0_77]) ).
cnf(c_0_81,negated_conjecture,
star(strong_iteration(esk1_0)) != strong_iteration(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_82,plain,
star(strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE145+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 11:16:52 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 88.73/88.84 % Version : CSE_E---1.5
% 88.73/88.84 % Problem : theBenchmark.p
% 88.73/88.84 % Proof found
% 88.73/88.84 % SZS status Theorem for theBenchmark.p
% 88.73/88.84 % SZS output start Proof
% See solution above
% 88.73/88.85 % Total time : 88.275000 s
% 88.73/88.85 % SZS output end Proof
% 88.73/88.85 % Total time : 88.282000 s
%------------------------------------------------------------------------------