%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE010+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.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 04:35:27 PM UTC 2026
% Result : Theorem 1.91s 1.90s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 76 ( 50 unt; 0 def)
% Number of atoms : 130 ( 62 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 95 ( 41 ~; 33 |; 14 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 109 ( 9 sgn 54 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(goals,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
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_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
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(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
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(c_0_15,plain,
! [X65,X66] :
( ( c(X65) != X66
| complement(X65,X66)
| ~ test(X65) )
& ( ~ complement(X65,X66)
| c(X65) = X66
| ~ test(X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_16,plain,
! [X39,X40,X41] : addition(X41,addition(X40,X39)) = addition(addition(X41,X40),X39),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_17,plain,
! [X43] : addition(X43,X43) = X43,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_18,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_19,plain,
! [X63,X64] :
( ( multiplication(X63,X64) = zero
| ~ complement(X64,X63) )
& ( multiplication(X64,X63) = zero
| ~ complement(X64,X63) )
& ( addition(X63,X64) = one
| ~ complement(X64,X63) )
& ( multiplication(X63,X64) != zero
| multiplication(X64,X63) != zero
| addition(X63,X64) != one
| complement(X64,X63) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
cnf(c_0_20,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,plain,
! [X37,X38] : addition(X37,X38) = addition(X38,X37),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_22,plain,
! [X57,X58] :
( ( ~ leq(X57,X58)
| addition(X57,X58) = X58 )
& ( addition(X57,X58) != X58
| leq(X57,X58) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_23,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_25,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& ( ~ leq(one,addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))))
| ~ leq(addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_26,plain,
! [X52,X53,X54] : multiplication(addition(X52,X53),X54) = addition(multiplication(X52,X54),multiplication(X53,X54)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_27,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,negated_conjecture,
( ~ leq(one,addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))))
| ~ leq(addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_35,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_36,plain,
! [X48] : multiplication(one,X48) = X48,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_37,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
fof(c_0_39,plain,
! [X49,X50,X51] : multiplication(X49,addition(X50,X51)) = addition(multiplication(X49,X50),multiplication(X49,X51)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_40,negated_conjecture,
( ~ leq(one,addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))))
| ~ leq(addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))),one) ),
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_32,c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_33]),c_0_33]) ).
cnf(c_0_41,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_43,plain,
! [X47] : multiplication(X47,one) = X47,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_44,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_45,plain,
! [X59,X61,X62] :
( ( ~ test(X59)
| complement(esk1_1(X59),X59) )
& ( ~ complement(X62,X61)
| test(X61) ) ),
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_46,plain,
leq(X1,addition(X2,addition(X1,X3))),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,negated_conjecture,
( ~ leq(one,addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(esk2_0,esk3_0)))))
| ~ leq(addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(esk2_0,esk3_0)))),one) ),
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_40,c_0_41]),c_0_42]),c_0_29]),c_0_41]),c_0_42]),c_0_29]) ).
cnf(c_0_49,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_29]),c_0_23]) ).
cnf(c_0_51,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(spm,[status(thm)],[c_0_34,c_0_44]) ).
cnf(c_0_52,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,plain,
leq(multiplication(X1,X2),addition(X3,multiplication(X1,addition(X2,X4)))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_54,plain,
! [X42] : addition(X42,zero) = X42,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_55,plain,
! [X56] : multiplication(zero,X56) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_56,plain,
! [X55] : multiplication(X55,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_57,negated_conjecture,
( ~ leq(one,addition(esk2_0,addition(multiplication(esk2_0,esk3_0),c(esk2_0))))
| ~ leq(addition(esk2_0,addition(multiplication(esk2_0,esk3_0),c(esk2_0))),one) ),
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)],[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_48,c_0_38]),c_0_23]),c_0_38]),c_0_23]),c_0_47]),c_0_29]),c_0_41]),c_0_49]),c_0_38]),c_0_23]),c_0_38]),c_0_23]),c_0_47]),c_0_29]),c_0_41]),c_0_49]) ).
cnf(c_0_58,negated_conjecture,
addition(esk2_0,addition(X1,c(esk2_0))) = addition(X1,one),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_59,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_52]) ).
cnf(c_0_60,negated_conjecture,
leq(multiplication(X1,esk3_0),addition(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_41]),c_0_49]) ).
cnf(c_0_61,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_51]),c_0_29]) ).
cnf(c_0_62,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_63,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_64,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_65,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_66,negated_conjecture,
~ leq(addition(one,multiplication(esk2_0,esk3_0)),one),
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_57,c_0_58]),c_0_29]),c_0_37]),c_0_58]),c_0_29])]) ).
cnf(c_0_67,plain,
( leq(X1,one)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_59]) ).
cnf(c_0_68,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_69,negated_conjecture,
leq(multiplication(esk2_0,esk3_0),one),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_71,plain,
complement(zero,one),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_65])])]) ).
cnf(c_0_72,negated_conjecture,
~ test(addition(one,multiplication(esk2_0,esk3_0))),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
addition(one,multiplication(esk2_0,esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_29]) ).
cnf(c_0_74,plain,
test(one),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73]),c_0_74])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE010+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n005.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 20:25:00 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.91/1.90 % Version : CSE_E---1.7
% 1.91/1.90 % Problem : theBenchmark.p
% 1.91/1.90 % SZS status Theorem for theBenchmark.p
% 1.91/1.90 % SZS output start CNFRefutation
% See solution above
% 1.91/1.90 % Total time : 1.371s
%------------------------------------------------------------------------------