TSTP Solution File: KLE023+2 by Enigma---0.5.1
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%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : KLE023+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n009.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 : 600s
% DateTime : Sun Jul 17 01:49:39 EDT 2022
% Result : Theorem 8.87s 2.59s
% Output : CNFRefutation 8.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 49 unt; 0 def)
% Number of atoms : 127 ( 75 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 90 ( 36 ~; 32 |; 13 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 96 ( 3 sgn 54 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( addition(multiplication(X5,X4),multiplication(X4,X6)) = multiplication(X4,X6)
=> addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(test_deMorgan2,axiom,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> c(multiplication(X4,X5)) = addition(c(X4),c(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax',test_deMorgan2) ).
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/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
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/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(c_0_14,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_15,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_16,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_17,plain,
! [X26] : multiplication(zero,X26) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_18,plain,
! [X25] : multiplication(X25,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_19,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_25,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( addition(multiplication(X5,X4),multiplication(X4,X6)) = multiplication(X4,X6)
=> addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_26,plain,
! [X35,X36] :
( ( c(X35) != X36
| complement(X35,X36)
| ~ test(X35) )
& ( ~ complement(X35,X36)
| c(X35) = X36
| ~ test(X35) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
cnf(c_0_27,plain,
( complement(zero,X1)
| X1 != one ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_22]),c_0_23])]) ).
fof(c_0_28,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])])])])]) ).
cnf(c_0_29,plain,
( complement(X1,zero)
| X1 != one ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_24]),c_0_23]),c_0_22])]) ).
fof(c_0_30,negated_conjecture,
( test(esk3_0)
& test(esk4_0)
& addition(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) = multiplication(esk2_0,esk4_0)
& addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) != multiplication(c(esk3_0),esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
fof(c_0_31,plain,
! [X40,X41] :
( ~ test(X40)
| ~ test(X41)
| c(multiplication(X40,X41)) = addition(c(X40),c(X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan2])]) ).
cnf(c_0_32,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
complement(zero,one),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
complement(one,zero),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,negated_conjecture,
test(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
( c(multiplication(X1,X2)) = addition(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,plain,
( c(zero) = one
| ~ test(zero) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
test(zero),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
( complement(esk3_0,X1)
| c(esk3_0) != X1 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_43,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_44,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_45,negated_conjecture,
( complement(esk4_0,X1)
| c(esk4_0) != X1 ),
inference(spm,[status(thm)],[c_0_36,c_0_38]) ).
fof(c_0_46,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_47,negated_conjecture,
( c(multiplication(X1,esk4_0)) = addition(c(X1),c(esk4_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_38]) ).
cnf(c_0_48,plain,
c(zero) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
fof(c_0_49,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_50,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_51,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(er,[status(thm)],[c_0_42]) ).
fof(c_0_52,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_53,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_54,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) = multiplication(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_55,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_57,negated_conjecture,
complement(esk4_0,c(esk4_0)),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_58,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_59,negated_conjecture,
addition(one,c(esk4_0)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_41]),c_0_22]),c_0_48]),c_0_48]) ).
cnf(c_0_60,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_20]) ).
cnf(c_0_62,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_63,negated_conjecture,
addition(multiplication(esk3_0,multiplication(esk2_0,X1)),multiplication(esk2_0,multiplication(esk4_0,X1))) = multiplication(esk2_0,multiplication(esk4_0,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_55]),c_0_55]) ).
cnf(c_0_64,negated_conjecture,
multiplication(esk4_0,c(esk4_0)) = zero,
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_65,negated_conjecture,
addition(X1,multiplication(X1,c(esk4_0))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_60]) ).
cnf(c_0_66,negated_conjecture,
addition(multiplication(esk3_0,X1),multiplication(c(esk3_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_61]),c_0_62]) ).
cnf(c_0_67,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_23]),c_0_19]),c_0_23]) ).
cnf(c_0_68,negated_conjecture,
addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) != multiplication(c(esk3_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_69,negated_conjecture,
addition(multiplication(X1,X2),multiplication(X1,multiplication(X2,c(esk4_0)))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_58,c_0_65]) ).
cnf(c_0_70,negated_conjecture,
multiplication(c(esk3_0),multiplication(esk2_0,c(esk4_0))) = multiplication(esk2_0,c(esk4_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_24]) ).
cnf(c_0_71,negated_conjecture,
addition(multiplication(c(esk3_0),esk2_0),multiplication(esk2_0,c(esk4_0))) != multiplication(c(esk3_0),esk2_0),
inference(rw,[status(thm)],[c_0_68,c_0_20]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE023+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : enigmatic-eprover.py %s %d 1
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 07:04:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.45 # ENIGMATIC: Selected SinE mode:
% 0.21/0.46 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.46 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.21/0.46 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.21/0.46 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 8.87/2.59 # ENIGMATIC: Solved by autoschedule:
% 8.87/2.59 # No SInE strategy applied
% 8.87/2.59 # Trying AutoSched0 for 150 seconds
% 8.87/2.59 # AutoSched0-Mode selected heuristic G_E___107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S071I
% 8.87/2.59 # and selection function SelectCQArEqLast.
% 8.87/2.59 #
% 8.87/2.59 # Preprocessing time : 0.025 s
% 8.87/2.59 # Presaturation interreduction done
% 8.87/2.59
% 8.87/2.59 # Proof found!
% 8.87/2.59 # SZS status Theorem
% 8.87/2.59 # SZS output start CNFRefutation
% See solution above
% 8.87/2.60 # Training examples: 0 positive, 0 negative
% 8.87/2.60
% 8.87/2.60 # -------------------------------------------------
% 8.87/2.60 # User time : 0.103 s
% 8.87/2.60 # System time : 0.011 s
% 8.87/2.60 # Total time : 0.114 s
% 8.87/2.60 # Maximum resident set size: 7124 pages
% 8.87/2.60
%------------------------------------------------------------------------------