%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE009+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.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 : Tue May 5 04:35:26 PM UTC 2026
% Result : Theorem 1.39s 1.76s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 84 ( 56 unt; 0 def)
% Number of atoms : 141 ( 79 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 103 ( 46 ~; 38 |; 12 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 1 sgn 38 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> one = addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(test_deMorgan1,axiom,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> c(addition(X4,X5)) = multiplication(c(X4),c(X5)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax',test_deMorgan1) ).
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(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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(c_0_9,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> one = addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_10,plain,
! [X63,X65,X66] :
( ( ~ test(X63)
| complement(esk1_1(X63),X63) )
& ( ~ complement(X66,X65)
| test(X65) ) ),
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_11,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& one != addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_12,plain,
! [X69,X70] :
( ( c(X69) != X70
| complement(X69,X70)
| ~ test(X69) )
& ( ~ complement(X69,X70)
| c(X69) = X70
| ~ test(X69) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_13,plain,
! [X67,X68] :
( ( multiplication(X67,X68) = zero
| ~ complement(X68,X67) )
& ( multiplication(X68,X67) = zero
| ~ complement(X68,X67) )
& ( addition(X67,X68) = one
| ~ complement(X68,X67) )
& ( multiplication(X67,X68) != zero
| multiplication(X68,X67) != zero
| addition(X67,X68) != one
| complement(X68,X67) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
fof(c_0_14,plain,
! [X41,X42] : addition(X41,X42) = addition(X42,X41),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_15,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,plain,
! [X72,X73] :
( ~ test(X72)
| ~ test(X73)
| c(addition(X72,X73)) = multiplication(c(X72),c(X73)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan1])]) ).
cnf(c_0_19,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,negated_conjecture,
complement(esk1_1(esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_25,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,negated_conjecture,
complement(esk1_1(esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
fof(c_0_27,plain,
! [X43,X44,X45] : addition(X45,addition(X44,X43)) = addition(addition(X45,X44),X43),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_28,plain,
( c(addition(X1,X2)) = multiplication(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
( complement(X1,X2)
| addition(X1,X2) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_31,negated_conjecture,
addition(esk2_0,esk1_1(esk2_0)) = one,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_32,negated_conjecture,
multiplication(esk2_0,esk1_1(esk2_0)) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_33,negated_conjecture,
multiplication(esk1_1(esk2_0),esk2_0) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_34,negated_conjecture,
addition(esk3_0,esk1_1(esk3_0)) = one,
inference(spm,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_35,negated_conjecture,
multiplication(esk3_0,esk1_1(esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_36,negated_conjecture,
multiplication(esk1_1(esk3_0),esk3_0) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_37,negated_conjecture,
one != addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_38,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,negated_conjecture,
( multiplication(c(X1),c(esk3_0)) = c(addition(X1,esk3_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_17]) ).
cnf(c_0_40,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_41,negated_conjecture,
complement(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_29,c_0_16]) ).
cnf(c_0_42,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_43,negated_conjecture,
complement(esk2_0,esk1_1(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_44,negated_conjecture,
complement(esk3_0,esk1_1(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_34]),c_0_35]),c_0_36])]) ).
cnf(c_0_45,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk2_0,c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),multiplication(c(esk2_0),c(esk3_0))))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_38]) ).
cnf(c_0_46,negated_conjecture,
multiplication(c(esk2_0),c(esk3_0)) = c(addition(esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_39,c_0_16]) ).
cnf(c_0_47,negated_conjecture,
test(c(esk2_0)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( c(esk1_1(esk2_0)) = esk2_0
| ~ test(esk1_1(esk2_0)) ),
inference(spm,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_49,negated_conjecture,
esk1_1(esk2_0) = c(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_16])]) ).
cnf(c_0_50,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_29,c_0_17]) ).
cnf(c_0_51,negated_conjecture,
( c(esk1_1(esk3_0)) = esk3_0
| ~ test(esk1_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_42,c_0_26]) ).
cnf(c_0_52,negated_conjecture,
test(esk1_1(esk3_0)),
inference(spm,[status(thm)],[c_0_40,c_0_44]) ).
cnf(c_0_53,negated_conjecture,
esk1_1(esk3_0) = c(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_44]),c_0_17])]) ).
cnf(c_0_54,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk2_0,c(esk3_0)),addition(c(addition(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_21]) ).
cnf(c_0_55,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_21]),c_0_38]) ).
cnf(c_0_56,negated_conjecture,
multiplication(c(c(esk2_0)),c(esk3_0)) = c(addition(c(esk2_0),esk3_0)),
inference(spm,[status(thm)],[c_0_39,c_0_47]) ).
cnf(c_0_57,negated_conjecture,
c(c(esk2_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49]),c_0_49]),c_0_47])]) ).
cnf(c_0_58,negated_conjecture,
test(c(esk3_0)),
inference(spm,[status(thm)],[c_0_40,c_0_50]) ).
cnf(c_0_59,negated_conjecture,
c(c(esk3_0)) = esk3_0,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]),c_0_53]) ).
fof(c_0_60,plain,
! [X56,X57,X58] : multiplication(addition(X56,X57),X58) = addition(multiplication(X56,X58),multiplication(X57,X58)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_61,plain,
! [X52] : multiplication(one,X52) = X52,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_62,negated_conjecture,
( multiplication(c(X1),c(esk2_0)) = c(addition(X1,esk2_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_63,negated_conjecture,
addition(c(addition(esk2_0,esk3_0)),addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk2_0,c(esk3_0)),multiplication(c(esk2_0),esk3_0)))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_55]) ).
cnf(c_0_64,negated_conjecture,
multiplication(esk2_0,c(esk3_0)) = c(addition(c(esk2_0),esk3_0)),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_65,negated_conjecture,
( multiplication(c(X1),esk3_0) = c(addition(X1,c(esk3_0)))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_58]),c_0_59]) ).
cnf(c_0_66,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_67,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_50]),c_0_21]) ).
cnf(c_0_68,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,negated_conjecture,
( multiplication(c(X1),esk2_0) = c(addition(X1,c(esk2_0)))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_47]),c_0_57]) ).
cnf(c_0_70,negated_conjecture,
multiplication(c(c(esk3_0)),c(esk2_0)) = c(addition(esk2_0,c(esk3_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_58]),c_0_21]) ).
cnf(c_0_71,negated_conjecture,
addition(c(addition(esk2_0,esk3_0)),addition(c(addition(c(esk2_0),esk3_0)),addition(multiplication(esk2_0,esk3_0),multiplication(c(esk2_0),esk3_0)))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_55]) ).
cnf(c_0_72,negated_conjecture,
multiplication(esk2_0,esk3_0) = c(addition(c(esk2_0),c(esk3_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_47]),c_0_57]) ).
cnf(c_0_73,negated_conjecture,
multiplication(c(esk2_0),esk3_0) = c(addition(esk2_0,c(esk3_0))),
inference(spm,[status(thm)],[c_0_65,c_0_16]) ).
cnf(c_0_74,negated_conjecture,
addition(multiplication(esk3_0,X1),multiplication(c(esk3_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_75,negated_conjecture,
multiplication(esk3_0,esk2_0) = c(addition(c(esk2_0),c(esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_58]),c_0_59]),c_0_21]) ).
cnf(c_0_76,negated_conjecture,
multiplication(c(esk3_0),esk2_0) = c(addition(c(esk2_0),esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_17]),c_0_21]) ).
cnf(c_0_77,negated_conjecture,
multiplication(c(esk3_0),c(esk2_0)) = c(addition(esk2_0,esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_17]),c_0_21]) ).
cnf(c_0_78,negated_conjecture,
multiplication(esk3_0,c(esk2_0)) = c(addition(esk2_0,c(esk3_0))),
inference(rw,[status(thm)],[c_0_70,c_0_59]) ).
cnf(c_0_79,negated_conjecture,
addition(c(addition(esk2_0,esk3_0)),addition(c(addition(esk2_0,c(esk3_0))),addition(c(addition(c(esk2_0),esk3_0)),c(addition(c(esk2_0),c(esk3_0)))))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_21]),c_0_55]) ).
cnf(c_0_80,negated_conjecture,
addition(c(addition(c(esk2_0),esk3_0)),c(addition(c(esk2_0),c(esk3_0)))) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_21]) ).
cnf(c_0_81,negated_conjecture,
addition(c(addition(esk2_0,esk3_0)),c(addition(esk2_0,c(esk3_0)))) = c(esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_77]),c_0_78]),c_0_21]) ).
cnf(c_0_82,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_41]),c_0_21]) ).
cnf(c_0_83,negated_conjecture,
$false,
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_79,c_0_80]),c_0_21]),c_0_55]),c_0_81]),c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE009+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n011.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 20:25:02 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.39/1.76 % Version : CSE_E---1.7
% 1.39/1.76 % Problem : theBenchmark.p
% 1.39/1.76 % SZS status Theorem for theBenchmark.p
% 1.39/1.76 % SZS output start CNFRefutation
% See solution above
% 1.39/1.76 % Total time : 1.371s
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