%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE018+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 : n003.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 1.37s 1.73s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 58 ( 37 unt; 0 def)
% Number of atoms : 108 ( 55 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 79 ( 29 ~; 25 |; 16 &)
% ( 4 <=>; 5 =>; 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 50 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X4)
& test(X5)
& test(X6) )
=> ( leq(multiplication(X4,c(X5)),X6)
=> leq(X4,addition(X5,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
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(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(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(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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
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(c_0_12,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X4)
& test(X5)
& test(X6) )
=> ( leq(multiplication(X4,c(X5)),X6)
=> leq(X4,addition(X5,X6)) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_13,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_14,negated_conjecture,
( test(esk2_0)
& test(esk3_0)
& test(esk4_0)
& leq(multiplication(esk2_0,c(esk3_0)),esk4_0)
& ~ leq(esk2_0,addition(esk3_0,esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_15,plain,
! [X39,X40] : addition(X39,X40) = addition(X40,X39),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_16,plain,
! [X41,X42,X43] : addition(X43,addition(X42,X41)) = addition(addition(X43,X42),X41),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_17,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
leq(multiplication(esk2_0,c(esk3_0)),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
addition(esk4_0,multiplication(esk2_0,c(esk3_0))) = esk4_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
fof(c_0_22,plain,
! [X67,X68] :
( ( c(X67) != X68
| complement(X67,X68)
| ~ test(X67) )
& ( ~ complement(X67,X68)
| c(X67) = X68
| ~ test(X67) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
cnf(c_0_23,negated_conjecture,
addition(esk4_0,addition(multiplication(esk2_0,c(esk3_0)),X1)) = addition(esk4_0,X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_24,plain,
! [X51,X52,X53] : multiplication(X51,addition(X52,X53)) = addition(multiplication(X51,X52),multiplication(X51,X53)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_25,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])])]) ).
cnf(c_0_26,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
addition(esk4_0,addition(X1,multiplication(esk2_0,c(esk3_0)))) = addition(esk4_0,X1),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_28,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_26]) ).
fof(c_0_31,plain,
! [X49] : multiplication(X49,one) = X49,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_32,negated_conjecture,
addition(esk4_0,multiplication(esk2_0,addition(X1,c(esk3_0)))) = addition(esk4_0,multiplication(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_19]) ).
cnf(c_0_34,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_36,plain,
! [X45] : addition(X45,X45) = X45,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_37,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])])])])]) ).
cnf(c_0_38,negated_conjecture,
addition(esk4_0,multiplication(esk2_0,esk3_0)) = addition(esk2_0,esk4_0),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35])]),c_0_19]) ).
fof(c_0_39,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_40,plain,
! [X50] : multiplication(one,X50) = X50,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_41,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,negated_conjecture,
addition(esk4_0,addition(multiplication(esk2_0,esk3_0),X1)) = addition(esk2_0,addition(esk4_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_38]),c_0_20]) ).
cnf(c_0_44,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_41]) ).
cnf(c_0_47,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
addition(esk4_0,addition(X1,multiplication(esk2_0,esk3_0))) = addition(esk2_0,addition(esk4_0,X1)),
inference(spm,[status(thm)],[c_0_43,c_0_19]) ).
cnf(c_0_49,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_19]) ).
cnf(c_0_50,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
~ leq(esk2_0,addition(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_52,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_53,negated_conjecture,
addition(esk4_0,multiplication(addition(one,esk2_0),esk3_0)) = addition(esk2_0,addition(esk3_0,esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_19]),c_0_19]) ).
cnf(c_0_54,plain,
( addition(one,X1) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_56,negated_conjecture,
addition(esk2_0,addition(esk3_0,esk4_0)) != addition(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_45]),c_0_19]),c_0_55])]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : KLE018+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % 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
% 0.12/0.30 % Computer : n003.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Mon May 4 20:24:41 EDT 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.31 % start to proof: theBenchmark
% 1.37/1.73 % Version : CSE_E---1.7
% 1.37/1.73 % Problem : theBenchmark.p
% 1.37/1.73 % SZS status Theorem for theBenchmark.p
% 1.37/1.73 % SZS output start CNFRefutation
% See solution above
% 1.37/1.74 % Total time : 1.369s
%------------------------------------------------------------------------------