%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE035+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 04:35:34 PM UTC 2026
% Result : Theorem 44.03s 26.45s
% Output : CNFRefutation 44.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 33 unt; 0 def)
% Number of atoms : 58 ( 30 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 26 ( 8 ~; 4 |; 11 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6,X7] :
( ( test(X7)
& test(X6)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& leq(multiplication(multiplication(X6,X5),c(X7)),zero) )
=> leq(multiplication(multiplication(X6,addition(X4,X5)),c(X7)),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(c_0_8,negated_conjecture,
~ ! [X4,X5,X6,X7] :
( ( test(X7)
& test(X6)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& leq(multiplication(multiplication(X6,X5),c(X7)),zero) )
=> leq(multiplication(multiplication(X6,addition(X4,X5)),c(X7)),zero) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_9,negated_conjecture,
( test(esk5_0)
& test(esk4_0)
& leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero)
& leq(multiplication(multiplication(esk4_0,esk3_0),c(esk5_0)),zero)
& ~ leq(multiplication(multiplication(esk4_0,addition(esk2_0,esk3_0)),c(esk5_0)),zero) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_10,plain,
! [X52,X53,X54] : multiplication(X52,multiplication(X53,X54)) = multiplication(multiplication(X52,X53),X54),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_11,plain,
! [X65,X66] :
( ( ~ leq(X65,X66)
| addition(X65,X66) = X66 )
& ( addition(X65,X66) != X66
| leq(X65,X66) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_12,negated_conjecture,
leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X50] : addition(X50,zero) = X50,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_15,plain,
! [X45,X46] : addition(X45,X46) = addition(X46,X45),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_16,plain,
! [X57,X58,X59] : multiplication(X57,addition(X58,X59)) = addition(multiplication(X57,X58),multiplication(X57,X59)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_17,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
leq(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),zero),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
leq(multiplication(multiplication(esk4_0,esk3_0),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_22,plain,
! [X60,X61,X62] : multiplication(addition(X60,X61),X62) = addition(multiplication(X60,X62),multiplication(X61,X62)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_23,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_25,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
leq(multiplication(esk4_0,multiplication(esk3_0,c(esk5_0))),zero),
inference(rw,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_27,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
multiplication(esk4_0,addition(multiplication(esk2_0,c(esk5_0)),X1)) = multiplication(esk4_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_29,negated_conjecture,
multiplication(esk4_0,multiplication(esk3_0,c(esk5_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_26]),c_0_19]) ).
fof(c_0_30,plain,
! [X51] : addition(X51,X51) = X51,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_31,negated_conjecture,
~ leq(multiplication(multiplication(esk4_0,addition(esk2_0,esk3_0)),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_32,negated_conjecture,
addition(multiplication(esk4_0,X1),multiplication(X2,addition(multiplication(esk2_0,c(esk5_0)),X1))) = multiplication(addition(esk4_0,X2),addition(multiplication(esk2_0,c(esk5_0)),X1)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
multiplication(esk4_0,addition(X1,multiplication(esk3_0,c(esk5_0)))) = multiplication(esk4_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_29]),c_0_19]) ).
cnf(c_0_34,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_36,negated_conjecture,
~ leq(multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))),zero),
inference(rw,[status(thm)],[c_0_31,c_0_13]) ).
cnf(c_0_37,negated_conjecture,
multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))) = zero,
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_32,c_0_33]),c_0_29]),c_0_24]),c_0_19]),c_0_34]),c_0_27]) ).
cnf(c_0_38,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE035+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n031.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 20:28:08 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 44.03/26.45 % Version : CSE_E---1.7
% 44.03/26.45 % Problem : theBenchmark.p
% 44.03/26.45 % SZS status Theorem for theBenchmark.p
% 44.03/26.45 % SZS output start CNFRefutation
% See solution above
% 44.23/26.64 % Total time : 19.406s
%------------------------------------------------------------------------------