%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE002+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 : n010.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 1.27s 1.74s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 17 unt; 0 def)
% Number of atoms : 33 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 16 ( 7 ~; 4 |; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( leq(X4,X5)
=> leq(multiplication(X4,X6),multiplication(X5,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(c_0_5,plain,
! [X34,X35,X36] : addition(X36,addition(X35,X34)) = addition(addition(X36,X35),X34),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_6,plain,
! [X38] : addition(X38,X38) = X38,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_7,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])]) ).
cnf(c_0_8,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
~ ! [X4,X5,X6] :
( leq(X4,X5)
=> leq(multiplication(X4,X6),multiplication(X5,X6)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_11,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
fof(c_0_13,plain,
! [X47,X48,X49] : multiplication(addition(X47,X48),X49) = addition(multiplication(X47,X49),multiplication(X48,X49)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_14,negated_conjecture,
( leq(esk1_0,esk2_0)
& ~ leq(multiplication(esk1_0,esk3_0),multiplication(esk2_0,esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_15,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
leq(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
leq(multiplication(X1,X2),multiplication(addition(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
addition(esk1_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ leq(multiplication(esk1_0,esk3_0),multiplication(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
leq(multiplication(esk1_0,X1),multiplication(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE002+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 20:24:06 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.27/1.74 % Version : CSE_E---1.7
% 1.27/1.74 % Problem : theBenchmark.p
% 1.27/1.74 % SZS status Theorem for theBenchmark.p
% 1.27/1.74 % SZS output start CNFRefutation
% See solution above
% 1.27/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------