TSTP Solution File: KLE169+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE169+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n013.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 05:26:42 EDT 2023
% Result : Theorem 234.74s 235.67s
% Output : CNFRefutation 234.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 25
% Syntax : Number of formulae : 103 ( 64 unt; 9 typ; 0 def)
% Number of atoms : 127 ( 56 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 32 ~; 29 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 149 ( 14 sgn; 52 !; 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,
sigma: $i ).
tff(decl_29,type,
a: $i ).
tff(decl_30,type,
b: $i ).
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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+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/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(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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_identity) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',right_annihilation) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',left_annihilation) ).
fof(star_induction_left,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X2)
=> leq(multiplication(star(X1),X3),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_induction_left) ).
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(a,conjecture,
leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
fof(an,axiom,
sigma = addition(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an) ).
fof(c_0_16,plain,
! [X31,X32,X33] :
( ~ leq(addition(multiplication(X31,X32),X33),X31)
| leq(multiplication(X33,star(X32)),X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_right])]) ).
fof(c_0_17,plain,
! [X14] : multiplication(X14,one) = X14,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_18,plain,
! [X6,X7,X8] : addition(X8,addition(X7,X6)) = addition(addition(X8,X7),X6),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_19,plain,
! [X10] : addition(X10,X10) = X10,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_20,plain,
! [X24,X25] :
( ( ~ leq(X24,X25)
| addition(X24,X25) = X25 )
& ( addition(X24,X25) != X25
| leq(X24,X25) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_21,plain,
! [X26] : leq(addition(one,multiplication(X26,star(X26))),star(X26)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
fof(c_0_22,plain,
! [X4,X5] : addition(X4,X5) = addition(X5,X4),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_23,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_25,plain,
! [X16,X17,X18] : multiplication(X16,addition(X17,X18)) = addition(multiplication(X16,X17),multiplication(X16,X18)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_26,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,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_28,c_0_29]),c_0_26]),c_0_30]) ).
cnf(c_0_35,plain,
( leq(multiplication(X1,star(one)),X1)
| ~ leq(X1,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_27]) ).
cnf(c_0_36,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_30]) ).
cnf(c_0_37,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
( multiplication(X1,star(one)) = X1
| ~ leq(X1,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_35]),c_0_30]),c_0_36]),c_0_30]),c_0_37]) ).
cnf(c_0_39,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_40,plain,
! [X9] : addition(X9,zero) = X9,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_41,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_42,plain,
multiplication(X1,star(one)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_27])]) ).
fof(c_0_43,plain,
! [X22] : multiplication(X22,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_44,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,plain,
( leq(X1,X2)
| ~ leq(addition(X1,X2),X2) ),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_47,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_30]) ).
fof(c_0_48,plain,
! [X15] : multiplication(one,X15) = X15,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_49,plain,
( leq(addition(X1,X2),X3)
| ~ leq(addition(X1,addition(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_26]) ).
cnf(c_0_50,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
fof(c_0_51,plain,
! [X23] : multiplication(zero,X23) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_52,plain,
( leq(multiplication(X1,star(zero)),X2)
| ~ leq(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_46]),c_0_47]) ).
cnf(c_0_53,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,plain,
( leq(addition(X1,X2),X1)
| ~ leq(addition(X2,X1),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_27]),c_0_26]),c_0_50]) ).
cnf(c_0_55,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,plain,
( leq(star(zero),X1)
| ~ leq(one,X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
( leq(addition(X1,X2),X1)
| addition(X2,X1) != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_39]),c_0_26]),c_0_27]) ).
fof(c_0_58,plain,
! [X28,X29,X30] :
( ~ leq(addition(multiplication(X28,X29),X30),X29)
| leq(multiplication(star(X28),X30),X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_left])]) ).
cnf(c_0_59,plain,
leq(one,star(zero)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_55]),c_0_44]) ).
cnf(c_0_60,plain,
( addition(star(zero),X1) = X1
| ~ leq(one,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_56]) ).
cnf(c_0_61,plain,
leq(addition(one,star(one)),star(one)),
inference(spm,[status(thm)],[c_0_29,c_0_53]) ).
cnf(c_0_62,plain,
leq(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_57]),c_0_27])]) ).
cnf(c_0_63,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_64,plain,
addition(one,star(zero)) = star(zero),
inference(spm,[status(thm)],[c_0_28,c_0_59]) ).
cnf(c_0_65,plain,
( addition(X1,star(zero)) = X1
| ~ leq(one,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_60]) ).
cnf(c_0_66,plain,
leq(star(one),star(one)),
inference(rw,[status(thm)],[c_0_61,c_0_37]) ).
cnf(c_0_67,plain,
star(one) = one,
inference(spm,[status(thm)],[c_0_53,c_0_42]) ).
cnf(c_0_68,plain,
leq(X1,addition(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_33]),c_0_62])]) ).
cnf(c_0_69,plain,
addition(X1,addition(X2,addition(X1,X3))) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_50]),c_0_26]),c_0_26]) ).
cnf(c_0_70,plain,
( leq(multiplication(star(zero),X1),X2)
| ~ leq(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_55]),c_0_47]) ).
cnf(c_0_71,plain,
( star(zero) = one
| ~ leq(one,one) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,plain,
leq(one,one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67]),c_0_67]) ).
fof(c_0_73,plain,
! [X19,X20,X21] : multiplication(addition(X19,X20),X21) = addition(multiplication(X19,X21),multiplication(X20,X21)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_74,plain,
leq(X1,addition(X2,addition(X1,X3))),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,plain,
( addition(multiplication(star(zero),X1),X2) = X2
| ~ leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_70]) ).
cnf(c_0_76,plain,
star(zero) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]) ).
cnf(c_0_77,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_78,plain,
( leq(X1,addition(X2,X3))
| ~ leq(X1,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_53]) ).
cnf(c_0_79,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_53]),c_0_30]) ).
cnf(c_0_80,plain,
( leq(X1,addition(X2,X3))
| ~ leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_78,c_0_30]) ).
cnf(c_0_81,plain,
leq(X1,multiplication(addition(X2,one),X1)),
inference(spm,[status(thm)],[c_0_68,c_0_79]) ).
cnf(c_0_82,plain,
( leq(X1,X2)
| ~ leq(X1,X3)
| ~ leq(X3,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_75]),c_0_76]),c_0_53]) ).
cnf(c_0_83,plain,
leq(X1,multiplication(addition(one,X2),X1)),
inference(spm,[status(thm)],[c_0_81,c_0_30]) ).
cnf(c_0_84,plain,
( leq(X1,X2)
| ~ leq(addition(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_82,c_0_68]) ).
cnf(c_0_85,plain,
leq(X1,multiplication(star(X2),X1)),
inference(spm,[status(thm)],[c_0_83,c_0_37]) ).
fof(c_0_86,negated_conjecture,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[a])]) ).
cnf(c_0_87,plain,
leq(X1,multiplication(star(X2),addition(X1,X3))),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,negated_conjecture,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_89,plain,
( leq(X1,multiplication(star(X2),X3))
| ~ leq(X1,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_75]),c_0_76]),c_0_53]) ).
cnf(c_0_90,plain,
sigma = addition(a,b),
inference(split_conjunct,[status(thm)],[an]) ).
cnf(c_0_91,negated_conjecture,
~ leq(multiplication(a,multiplication(b,a)),multiplication(a,multiplication(sigma,a))),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_92,plain,
addition(sigma,b) = sigma,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_90]),c_0_30]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_39]),c_0_32]),c_0_77]),c_0_30]),c_0_92])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE169+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n013.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 11:35:01 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 234.74/235.67 % Version : CSE_E---1.5
% 234.74/235.67 % Problem : theBenchmark.p
% 234.74/235.67 % Proof found
% 234.74/235.67 % SZS status Theorem for theBenchmark.p
% 234.74/235.67 % SZS output start Proof
% See solution above
% 234.74/235.68 % Total time : 234.088000 s
% 234.74/235.68 % SZS output end Proof
% 234.74/235.68 % Total time : 234.101000 s
%------------------------------------------------------------------------------