%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE001+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 : n026.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 04:35:25 PM UTC 2026
% Result : Theorem 0.22s 1.59s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 31
% Syntax : Number of formulae : 61 ( 38 unt; 0 def)
% Number of atoms : 92 ( 70 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 29 ~; 26 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 122 ( 2 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6] :
( leq(X4,X5)
=> leq(addition(X4,X6),addition(X4,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(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(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(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_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
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(i_0_13,negated_conjecture,
~ ! [X4,X5,X6] :
( leq(X4,X5)
=> leq(addition(X4,X6),addition(X4,X6)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(i_0_14,plain,
! [X47,X48,X49] : multiplication(addition(X47,X48),X49) = addition(multiplication(X47,X49),multiplication(X48,X49)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(i_0_15,plain,
! [X44,X45,X46] : multiplication(X44,addition(X45,X46)) = addition(multiplication(X44,X45),multiplication(X44,X46)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(i_0_16,negated_conjecture,
( leq(esk1_0,esk2_0)
& ~ leq(addition(esk1_0,esk3_0),addition(esk1_0,esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_13])])]) ).
fof(i_0_17,plain,
! [X39,X40,X41] : multiplication(X39,multiplication(X40,X41)) = multiplication(multiplication(X39,X40),X41),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(i_0_18,plain,
! [X34,X35,X36] : addition(X36,addition(X35,X34)) = addition(addition(X36,X35),X34),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(i_0_19,plain,
! [X52,X53] :
( ( ~ leq(X52,X53)
| addition(X52,X53) = X53 )
& ( addition(X52,X53) != X53
| leq(X52,X53) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(i_0_20,plain,
! [X32,X33] : addition(X32,X33) = addition(X33,X32),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(i_0_21,plain,
! [X38] : addition(X38,X38) = X38,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(i_0_22,plain,
! [X43] : multiplication(one,X43) = X43,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(i_0_23,plain,
! [X42] : multiplication(X42,one) = X42,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(i_0_24,plain,
! [X37] : addition(X37,zero) = X37,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(i_0_25,plain,
! [X51] : multiplication(zero,X51) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(i_0_26,plain,
! [X50] : multiplication(X50,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(i_0_27,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_28,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_29,negated_conjecture,
~ leq(addition(esk1_0,esk3_0),addition(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_30,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_31,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_32,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_33,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_34,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_35,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_36,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_37,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_38,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_39,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_40,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_41,negated_conjecture,
leq(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_42,axiom,
X1 = X1 ).
cnf(i_0_43,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_44,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_45,axiom,
( X1 != X2
| multiplication(X1,X3) = multiplication(X2,X3) ) ).
cnf(i_0_46,axiom,
( X1 != X2
| multiplication(X3,X1) = multiplication(X3,X2) ) ).
cnf(i_0_47,axiom,
( X1 != X2
| addition(X1,X3) = addition(X2,X3) ) ).
cnf(i_0_48,axiom,
( X1 != X2
| addition(X3,X1) = addition(X3,X2) ) ).
cnf(i_0_49,axiom,
( X1 != X2
| ~ leq(X1,X3)
| leq(X2,X3) ) ).
cnf(i_0_50,axiom,
( X1 != X2
| ~ leq(X3,X1)
| leq(X3,X2) ) ).
cnf(i_0_42_001,axiom,
X1 = X1 ).
cnf(i_0_43_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_44_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_45_004,axiom,
( X1 != X2
| multiplication(X1,X3) = multiplication(X2,X3) ) ).
cnf(i_0_46_005,axiom,
( X1 != X2
| multiplication(X3,X1) = multiplication(X3,X2) ) ).
cnf(i_0_47_006,axiom,
( X1 != X2
| addition(X1,X3) = addition(X2,X3) ) ).
cnf(i_0_48_007,axiom,
( X1 != X2
| addition(X3,X1) = addition(X3,X2) ) ).
cnf(i_0_49_008,axiom,
( X1 != X2
| ~ leq(X1,X3)
| leq(X2,X3) ) ).
cnf(i_0_50_009,axiom,
( X1 != X2
| ~ leq(X3,X1)
| leq(X3,X2) ) ).
cnf(i_0_51,plain,
$false,
inference(scs_inference,[],[i_0_29,i_0_35,i_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : KLE001+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
% 0.12/0.31 % Computer : n026.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon May 4 20:24:23 EDT 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.32 % start to proof: theBenchmark
% 0.22/1.59 % Version : CSE_E---1.7
% 0.22/1.59 % Problem : theBenchmark.p
% 0.22/1.59 % SZS status Theorem for theBenchmark.p
% 0.22/1.59 % SZS output start CNFRefutation
% See solution above
% 0.24/1.60 % Total time : 1.271s
%------------------------------------------------------------------------------