TSTP Solution File: KLE020+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE020+2 : 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 : 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 05:25:40 EDT 2023
% Result : Theorem 0.64s 0.70s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 74 ( 38 unt; 12 typ; 0 def)
% Number of atoms : 109 ( 59 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 82 ( 35 ~; 26 |; 16 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn; 48 !; 1 ?; 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,
test: $i > $o ).
tff(decl_28,type,
complement: ( $i * $i ) > $o ).
tff(decl_29,type,
c: $i > $i ).
tff(decl_30,type,
esk1_1: $i > $i ).
tff(decl_31,type,
esk2_0: $i ).
tff(decl_32,type,
esk3_0: $i ).
tff(decl_33,type,
esk4_0: $i ).
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X4)
& test(X5)
& test(X6) )
=> ( leq(addition(X4,multiplication(X5,X6)),multiplication(addition(X4,X5),addition(X4,X6)))
& leq(multiplication(addition(X4,X5),addition(X4,X6)),addition(X4,multiplication(X5,X6))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(c_0_12,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X4)
& test(X5)
& test(X6) )
=> ( leq(addition(X4,multiplication(X5,X6)),multiplication(addition(X4,X5),addition(X4,X6)))
& leq(multiplication(addition(X4,X5),addition(X4,X6)),addition(X4,multiplication(X5,X6))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_13,negated_conjecture,
( test(esk2_0)
& test(esk3_0)
& test(esk4_0)
& ( ~ leq(addition(esk2_0,multiplication(esk3_0,esk4_0)),multiplication(addition(esk2_0,esk3_0),addition(esk2_0,esk4_0)))
| ~ leq(multiplication(addition(esk2_0,esk3_0),addition(esk2_0,esk4_0)),addition(esk2_0,multiplication(esk3_0,esk4_0))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_14,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_15,negated_conjecture,
( ~ leq(addition(esk2_0,multiplication(esk3_0,esk4_0)),multiplication(addition(esk2_0,esk3_0),addition(esk2_0,esk4_0)))
| ~ leq(multiplication(addition(esk2_0,esk3_0),addition(esk2_0,esk4_0)),addition(esk2_0,multiplication(esk3_0,esk4_0))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_18,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_19,plain,
! [X33,X34] :
( ( multiplication(X33,X34) = zero
| ~ complement(X34,X33) )
& ( multiplication(X34,X33) = zero
| ~ complement(X34,X33) )
& ( addition(X33,X34) = one
| ~ complement(X34,X33) )
& ( multiplication(X33,X34) != zero
| multiplication(X34,X33) != zero
| addition(X33,X34) != one
| complement(X34,X33) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
fof(c_0_20,plain,
! [X29,X31,X32] :
( ( ~ test(X29)
| complement(esk1_1(X29),X29) )
& ( ~ complement(X32,X31)
| test(X31) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[test_1])])])])]) ).
fof(c_0_21,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_22,negated_conjecture,
( ~ leq(addition(esk2_0,multiplication(esk3_0,esk4_0)),addition(multiplication(addition(esk2_0,esk3_0),esk2_0),multiplication(addition(esk2_0,esk3_0),esk4_0)))
| ~ leq(addition(multiplication(addition(esk2_0,esk3_0),esk2_0),multiplication(addition(esk2_0,esk3_0),esk4_0)),addition(esk2_0,multiplication(esk3_0,esk4_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
cnf(c_0_23,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X27,X28] :
( ( ~ leq(X27,X28)
| addition(X27,X28) = X28 )
& ( addition(X27,X28) != X28
| leq(X27,X28) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_26,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_29,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
( ~ leq(addition(esk2_0,multiplication(esk3_0,esk4_0)),addition(multiplication(esk2_0,esk2_0),addition(multiplication(esk3_0,esk2_0),addition(multiplication(esk2_0,esk4_0),multiplication(esk3_0,esk4_0)))))
| ~ leq(addition(multiplication(esk2_0,esk2_0),addition(multiplication(esk3_0,esk2_0),addition(multiplication(esk2_0,esk4_0),multiplication(esk3_0,esk4_0)))),addition(esk2_0,multiplication(esk3_0,esk4_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_24]),c_0_23]),c_0_24]) ).
cnf(c_0_31,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_33,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_36,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_37,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_38,negated_conjecture,
( addition(multiplication(esk2_0,esk2_0),addition(multiplication(esk3_0,esk2_0),addition(multiplication(esk2_0,esk4_0),addition(multiplication(esk3_0,esk4_0),addition(esk2_0,multiplication(esk3_0,esk4_0)))))) != addition(esk2_0,multiplication(esk3_0,esk4_0))
| ~ leq(addition(esk2_0,multiplication(esk3_0,esk4_0)),addition(multiplication(esk2_0,esk2_0),addition(multiplication(esk3_0,esk2_0),addition(multiplication(esk2_0,esk4_0),multiplication(esk3_0,esk4_0))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_24]),c_0_24]),c_0_24]) ).
cnf(c_0_39,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
( addition(multiplication(X1,X2),multiplication(esk1_1(X1),X2)) = X2
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_33]),c_0_34]) ).
cnf(c_0_41,plain,
( multiplication(esk1_1(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_27]) ).
cnf(c_0_42,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_33]) ).
cnf(c_0_44,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_45,negated_conjecture,
test(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_46,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_47,negated_conjecture,
( addition(esk2_0,addition(multiplication(esk3_0,esk4_0),addition(multiplication(esk2_0,esk2_0),addition(multiplication(esk3_0,esk2_0),addition(multiplication(esk2_0,esk4_0),multiplication(esk3_0,esk4_0)))))) != addition(multiplication(esk2_0,esk2_0),addition(multiplication(esk3_0,esk2_0),addition(multiplication(esk2_0,esk4_0),multiplication(esk3_0,esk4_0))))
| addition(multiplication(esk2_0,esk2_0),addition(multiplication(esk3_0,esk2_0),addition(multiplication(esk2_0,esk4_0),addition(multiplication(esk3_0,esk4_0),addition(esk2_0,multiplication(esk3_0,esk4_0)))))) != addition(esk2_0,multiplication(esk3_0,esk4_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_31]),c_0_24]) ).
cnf(c_0_48,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_39]),c_0_24]) ).
cnf(c_0_49,plain,
( multiplication(X1,X1) = X1
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_50,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_51,negated_conjecture,
addition(esk3_0,one) = one,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
addition(esk4_0,one) = one,
inference(spm,[status(thm)],[c_0_43,c_0_45]) ).
cnf(c_0_53,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_54,negated_conjecture,
( addition(esk2_0,addition(multiplication(esk2_0,esk2_0),addition(multiplication(esk3_0,esk2_0),addition(multiplication(esk2_0,esk4_0),multiplication(esk3_0,esk4_0))))) != addition(multiplication(esk2_0,esk2_0),addition(multiplication(esk3_0,esk2_0),addition(multiplication(esk2_0,esk4_0),multiplication(esk3_0,esk4_0))))
| addition(esk2_0,addition(multiplication(esk2_0,esk2_0),addition(multiplication(esk3_0,esk2_0),addition(multiplication(esk2_0,esk4_0),multiplication(esk3_0,esk4_0))))) != addition(esk2_0,multiplication(esk3_0,esk4_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_48]),c_0_48]),c_0_29]),c_0_48]),c_0_29]),c_0_48]),c_0_48]),c_0_48]) ).
cnf(c_0_55,negated_conjecture,
multiplication(esk2_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
addition(X1,multiplication(esk3_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_51]),c_0_34]),c_0_34]),c_0_39]) ).
cnf(c_0_57,negated_conjecture,
addition(X1,multiplication(X1,esk4_0)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_52]),c_0_53]),c_0_53]),c_0_39]) ).
cnf(c_0_58,negated_conjecture,
addition(esk2_0,addition(multiplication(esk3_0,esk2_0),addition(multiplication(esk2_0,esk4_0),multiplication(esk3_0,esk4_0)))) != addition(esk2_0,multiplication(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_37]),c_0_55]),c_0_55]),c_0_37])]) ).
cnf(c_0_59,negated_conjecture,
addition(X1,addition(multiplication(esk3_0,X1),X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
addition(X1,addition(multiplication(X1,esk4_0),X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_57]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : KLE020+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35 % Computer : n013.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 29 11:49:47 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.57 start to proof: theBenchmark
% 0.64/0.70 % Version : CSE_E---1.5
% 0.64/0.70 % Problem : theBenchmark.p
% 0.64/0.70 % Proof found
% 0.64/0.70 % SZS status Theorem for theBenchmark.p
% 0.64/0.70 % SZS output start Proof
% See solution above
% 0.64/0.71 % Total time : 0.111000 s
% 0.64/0.71 % SZS output end Proof
% 0.64/0.71 % Total time : 0.115000 s
%------------------------------------------------------------------------------