%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE017+1 : 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 : n024.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 04:35:29 PM UTC 2026
% Result : Theorem 1.49s 1.72s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 45 unt; 0 def)
% Number of atoms : 141 ( 71 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 99 ( 35 ~; 39 |; 18 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 105 ( 0 sgn 54 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X4)
& test(X5)
& test(X6) )
=> ( leq(X6,multiplication(X4,X5))
<=> ( leq(X6,X4)
& leq(X6,X5) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_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(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(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(c_0_13,plain,
! [X65,X66] :
( ( multiplication(X65,X66) = zero
| ~ complement(X66,X65) )
& ( multiplication(X66,X65) = zero
| ~ complement(X66,X65) )
& ( addition(X65,X66) = one
| ~ complement(X66,X65) )
& ( multiplication(X65,X66) != zero
| multiplication(X66,X65) != zero
| addition(X65,X66) != one
| complement(X66,X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
fof(c_0_14,plain,
! [X61,X63,X64] :
( ( ~ test(X61)
| complement(esk1_1(X61),X61) )
& ( ~ complement(X64,X63)
| test(X63) ) ),
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_15,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X4)
& test(X5)
& test(X6) )
=> ( leq(X6,multiplication(X4,X5))
<=> ( leq(X6,X4)
& leq(X6,X5) ) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_16,plain,
! [X51,X52,X53] : multiplication(X51,addition(X52,X53)) = addition(multiplication(X51,X52),multiplication(X51,X53)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_17,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X44] : addition(X44,zero) = X44,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_20,plain,
! [X59,X60] :
( ( ~ leq(X59,X60)
| addition(X59,X60) = X60 )
& ( addition(X59,X60) != X60
| leq(X59,X60) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_21,negated_conjecture,
( test(esk2_0)
& test(esk3_0)
& test(esk4_0)
& ( ~ leq(esk4_0,multiplication(esk2_0,esk3_0))
| ~ leq(esk4_0,esk2_0)
| ~ leq(esk4_0,esk3_0) )
& ( leq(esk4_0,esk2_0)
| leq(esk4_0,multiplication(esk2_0,esk3_0)) )
& ( leq(esk4_0,esk3_0)
| leq(esk4_0,multiplication(esk2_0,esk3_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
fof(c_0_22,plain,
! [X41,X42,X43] : addition(X43,addition(X42,X41)) = addition(addition(X43,X42),X41),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_23,plain,
! [X45] : addition(X45,X45) = X45,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_24,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( multiplication(X1,esk1_1(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_28,plain,
! [X49] : multiplication(X49,one) = X49,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_29,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,negated_conjecture,
( leq(esk4_0,esk3_0)
| leq(esk4_0,multiplication(esk2_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
( multiplication(X1,addition(X2,esk1_1(X1))) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_34,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_35,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,negated_conjecture,
( addition(esk4_0,multiplication(esk2_0,esk3_0)) = multiplication(esk2_0,esk3_0)
| leq(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_37,plain,
! [X39,X40] : addition(X39,X40) = addition(X40,X39),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_38,plain,
! [X54,X55,X56] : multiplication(addition(X54,X55),X56) = addition(multiplication(X54,X56),multiplication(X55,X56)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_39,plain,
! [X50] : multiplication(one,X50) = X50,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_40,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_41,plain,
! [X46,X47,X48] : multiplication(X46,multiplication(X47,X48)) = multiplication(multiplication(X46,X47),X48),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_42,plain,
( multiplication(X1,X1) = X1
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_43,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_44,negated_conjecture,
( addition(esk4_0,addition(multiplication(esk2_0,esk3_0),X1)) = addition(multiplication(esk2_0,esk3_0),X1)
| leq(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_36]) ).
cnf(c_0_45,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
cnf(c_0_49,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_50,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,negated_conjecture,
multiplication(esk3_0,esk3_0) = esk3_0,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,negated_conjecture,
( addition(esk4_0,addition(X1,multiplication(esk2_0,esk3_0))) = addition(X1,multiplication(esk2_0,esk3_0))
| leq(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_45]) ).
cnf(c_0_54,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_45]) ).
cnf(c_0_55,plain,
( multiplication(X1,multiplication(X2,esk1_1(multiplication(X1,X2)))) = zero
| ~ test(multiplication(X1,X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_25]) ).
cnf(c_0_56,negated_conjecture,
multiplication(esk3_0,multiplication(esk3_0,X1)) = multiplication(esk3_0,X1),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
( multiplication(addition(X1,X2),esk1_1(X2)) = multiplication(X1,esk1_1(X2))
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_25]),c_0_26]) ).
cnf(c_0_58,negated_conjecture,
addition(esk4_0,esk3_0) = esk3_0,
inference(csr,[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(spm,[status(thm)],[c_0_52,c_0_53]),c_0_45]),c_0_54]),c_0_47]),c_0_45]),c_0_54]),c_0_47]),c_0_29]) ).
cnf(c_0_59,negated_conjecture,
multiplication(esk3_0,esk1_1(esk3_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_51]),c_0_51]),c_0_43])]) ).
cnf(c_0_60,negated_conjecture,
( leq(esk4_0,esk2_0)
| leq(esk4_0,multiplication(esk2_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_61,negated_conjecture,
multiplication(esk4_0,esk1_1(esk3_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_43])]) ).
cnf(c_0_62,negated_conjecture,
( addition(esk4_0,multiplication(esk2_0,esk3_0)) = multiplication(esk2_0,esk3_0)
| leq(esk4_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
multiplication(esk4_0,addition(X1,esk1_1(esk3_0))) = multiplication(esk4_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_61]),c_0_26]) ).
cnf(c_0_64,negated_conjecture,
( addition(esk4_0,addition(multiplication(esk2_0,esk3_0),X1)) = addition(multiplication(esk2_0,esk3_0),X1)
| leq(esk4_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_62]) ).
cnf(c_0_65,negated_conjecture,
( ~ leq(esk4_0,multiplication(esk2_0,esk3_0))
| ~ leq(esk4_0,esk2_0)
| ~ leq(esk4_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_66,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_67,negated_conjecture,
multiplication(esk4_0,esk3_0) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_34]),c_0_35]),c_0_43])]) ).
cnf(c_0_68,negated_conjecture,
( addition(esk4_0,addition(X1,multiplication(esk2_0,esk3_0))) = addition(X1,multiplication(esk2_0,esk3_0))
| leq(esk4_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_64,c_0_45]) ).
cnf(c_0_69,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_35]),c_0_45]) ).
cnf(c_0_70,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_43]),c_0_45]) ).
cnf(c_0_71,negated_conjecture,
( addition(esk4_0,multiplication(esk2_0,esk3_0)) != multiplication(esk2_0,esk3_0)
| ~ leq(esk4_0,esk2_0)
| ~ leq(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,negated_conjecture,
addition(esk4_0,multiplication(X1,esk3_0)) = multiplication(addition(esk4_0,X1),esk3_0),
inference(spm,[status(thm)],[c_0_46,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
addition(esk4_0,esk2_0) = esk2_0,
inference(csr,[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(spm,[status(thm)],[c_0_68,c_0_69]),c_0_45]),c_0_70]),c_0_35]),c_0_45]),c_0_70]),c_0_35]),c_0_29]) ).
cnf(c_0_74,negated_conjecture,
( ~ leq(esk4_0,esk2_0)
| ~ leq(esk4_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_75,negated_conjecture,
~ leq(esk4_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_66]),c_0_58])]) ).
cnf(c_0_76,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_66]),c_0_73])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : KLE017+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % 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
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 15:24:41 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.49/1.72 % Version : CSE_E---1.7
% 1.49/1.72 % Problem : theBenchmark.p
% 1.49/1.72 % SZS status Theorem for theBenchmark.p
% 1.49/1.72 % SZS output start CNFRefutation
% See solution above
% 1.49/1.72 % Total time : 1.362s
%------------------------------------------------------------------------------