%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE027+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 : n029.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 04:35:32 PM UTC 2026
% Result : Theorem 1.44s 1.78s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 35 unt; 0 def)
% Number of atoms : 97 ( 51 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 73 ( 30 ~; 24 |; 13 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 83 ( 3 sgn 52 !; 0 ?)
% 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(goals,conjecture,
! [X4,X5,X6,X7,X8] :
( ( test(X7)
& test(X8) )
=> ( leq(addition(multiplication(X7,addition(multiplication(X7,X4),multiplication(c(X7),X5))),multiplication(c(X7),X6)),addition(multiplication(X7,X4),multiplication(c(X7),X6)))
& leq(addition(multiplication(X7,X4),multiplication(c(X7),X6)),addition(multiplication(X7,addition(multiplication(X7,X4),multiplication(c(X7),X5))),multiplication(c(X7),X6))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(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_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(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
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(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_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(c_0_12,plain,
! [X71,X72] :
( ( c(X71) != X72
| complement(X71,X72)
| ~ test(X71) )
& ( ~ complement(X71,X72)
| c(X71) = X72
| ~ test(X71) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_13,negated_conjecture,
~ ! [X4,X5,X6,X7,X8] :
( ( test(X7)
& test(X8) )
=> ( leq(addition(multiplication(X7,addition(multiplication(X7,X4),multiplication(c(X7),X5))),multiplication(c(X7),X6)),addition(multiplication(X7,X4),multiplication(c(X7),X6)))
& leq(addition(multiplication(X7,X4),multiplication(c(X7),X6)),addition(multiplication(X7,addition(multiplication(X7,X4),multiplication(c(X7),X5))),multiplication(c(X7),X6))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_14,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,negated_conjecture,
( test(esk5_0)
& test(esk6_0)
& ( ~ leq(addition(multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0))),multiplication(c(esk5_0),esk4_0)),addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)))
| ~ leq(addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),addition(multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0))),multiplication(c(esk5_0),esk4_0))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_16,plain,
! [X43,X44] : addition(X43,X44) = addition(X44,X43),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_17,plain,
! [X69,X70] :
( ( multiplication(X69,X70) = zero
| ~ complement(X70,X69) )
& ( multiplication(X70,X69) = zero
| ~ complement(X70,X69) )
& ( addition(X69,X70) = one
| ~ complement(X70,X69) )
& ( multiplication(X69,X70) != zero
| multiplication(X70,X69) != zero
| addition(X69,X70) != one
| complement(X70,X69) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
cnf(c_0_18,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
test(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( ~ leq(addition(multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0))),multiplication(c(esk5_0),esk4_0)),addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)))
| ~ leq(addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),addition(multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0))),multiplication(c(esk5_0),esk4_0))) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X55,X56,X57] : multiplication(X55,addition(X56,X57)) = addition(multiplication(X55,X56),multiplication(X55,X57)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_23,plain,
! [X50,X51,X52] : multiplication(X50,multiplication(X51,X52)) = multiplication(multiplication(X50,X51),X52),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_24,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
complement(esk5_0,c(esk5_0)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_26,plain,
! [X62] : multiplication(zero,X62) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_27,plain,
! [X58,X59,X60] : multiplication(addition(X58,X59),X60) = addition(multiplication(X58,X60),multiplication(X59,X60)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_28,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_29,plain,
! [X54] : multiplication(one,X54) = X54,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_30,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_31,negated_conjecture,
( ~ leq(addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),addition(multiplication(c(esk5_0),esk4_0),multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0)))))
| ~ leq(addition(multiplication(c(esk5_0),esk4_0),multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0)))),addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
cnf(c_0_32,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,negated_conjecture,
multiplication(esk5_0,c(esk5_0)) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_35,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_36,plain,
! [X48] : addition(X48,zero) = X48,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_37,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,negated_conjecture,
addition(esk5_0,c(esk5_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_25]),c_0_21]) ).
cnf(c_0_39,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,negated_conjecture,
multiplication(c(esk5_0),esk5_0) = zero,
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
fof(c_0_41,plain,
! [X63,X64] :
( ( ~ leq(X63,X64)
| addition(X63,X64) = X64 )
& ( addition(X63,X64) != X64
| leq(X63,X64) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_42,plain,
! [X49] : addition(X49,X49) = X49,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_43,negated_conjecture,
( ~ leq(addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),addition(multiplication(c(esk5_0),esk4_0),addition(multiplication(esk5_0,multiplication(esk5_0,esk2_0)),multiplication(esk5_0,multiplication(c(esk5_0),esk3_0)))))
| ~ leq(addition(multiplication(c(esk5_0),esk4_0),addition(multiplication(esk5_0,multiplication(esk5_0,esk2_0)),multiplication(esk5_0,multiplication(c(esk5_0),esk3_0)))),addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]) ).
cnf(c_0_44,negated_conjecture,
multiplication(esk5_0,multiplication(c(esk5_0),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_45,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,negated_conjecture,
addition(multiplication(esk5_0,X1),multiplication(c(esk5_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_47,negated_conjecture,
multiplication(c(esk5_0),multiplication(esk5_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_40]),c_0_35]) ).
cnf(c_0_48,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( ~ leq(addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),addition(multiplication(esk5_0,multiplication(esk5_0,esk2_0)),multiplication(c(esk5_0),esk4_0)))
| ~ leq(addition(multiplication(esk5_0,multiplication(esk5_0,esk2_0)),multiplication(c(esk5_0),esk4_0)),addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0))) ),
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_43,c_0_44]),c_0_45]),c_0_21]),c_0_44]),c_0_45]),c_0_21]) ).
cnf(c_0_51,negated_conjecture,
multiplication(esk5_0,multiplication(esk5_0,X1)) = multiplication(esk5_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_45]) ).
cnf(c_0_52,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_51]),c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE027+2 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % 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
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 20:26:44 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.44/1.78 % Version : CSE_E---1.7
% 1.44/1.78 % Problem : theBenchmark.p
% 1.44/1.78 % SZS status Theorem for theBenchmark.p
% 1.44/1.78 % SZS output start CNFRefutation
% See solution above
% 1.44/1.79 % Total time : 1.374s
%------------------------------------------------------------------------------