%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE148+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 : 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 04:35:49 PM UTC 2026
% Result : Theorem 1.60s 1.83s
% Output : CNFRefutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 36 unt; 0 def)
% Number of atoms : 64 ( 48 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 16 ~; 10 |; 4 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 3 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( ( multiplication(X4,X5) = zero
=> leq(multiplication(X4,strong_iteration(X5)),X4) )
& leq(X4,multiplication(X4,strong_iteration(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(distributivity1,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(c_0_11,negated_conjecture,
~ ! [X4,X5] :
( ( multiplication(X4,X5) = zero
=> leq(multiplication(X4,strong_iteration(X5)),X4) )
& leq(X4,multiplication(X4,strong_iteration(X5))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_12,plain,
! [X44,X45,X46] : addition(X46,addition(X45,X44)) = addition(addition(X46,X45),X44),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_13,plain,
! [X48] : addition(X48,X48) = X48,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_14,plain,
! [X69] : strong_iteration(X69) = addition(multiplication(X69,strong_iteration(X69)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_15,plain,
! [X42,X43] : addition(X42,X43) = addition(X43,X42),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_16,negated_conjecture,
( ( multiplication(esk1_0,esk2_0) = zero
| ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) )
& ( ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0)
| ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_17,plain,
! [X74,X75] :
( ( ~ leq(X74,X75)
| addition(X74,X75) = X75 )
& ( addition(X74,X75) != X75
| leq(X74,X75) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_18,plain,
! [X54,X55,X56] : multiplication(X54,addition(X55,X56)) = addition(multiplication(X54,X55),multiplication(X54,X56)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
fof(c_0_19,plain,
! [X52] : multiplication(X52,one) = X52,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_20,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( multiplication(esk1_0,esk2_0) = zero
| ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_30,plain,
! [X49,X50,X51] : multiplication(X49,multiplication(X50,X51)) = multiplication(multiplication(X49,X50),X51),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_31,negated_conjecture,
( multiplication(esk1_0,esk2_0) = zero
| addition(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) != multiplication(esk1_0,strong_iteration(esk2_0)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23]) ).
cnf(c_0_33,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_34,plain,
! [X60] : multiplication(zero,X60) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_35,negated_conjecture,
( ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0)
| ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_36,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
multiplication(esk1_0,esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_23]),c_0_33])]) ).
cnf(c_0_38,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_39,plain,
! [X47] : addition(X47,zero) = X47,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_40,negated_conjecture,
( addition(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) != esk1_0
| ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_25]),c_0_23]) ).
cnf(c_0_41,negated_conjecture,
multiplication(esk1_0,multiplication(esk2_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_42,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( addition(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) != multiplication(esk1_0,strong_iteration(esk2_0))
| addition(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) != esk1_0 ),
inference(spm,[status(thm)],[c_0_40,c_0_25]) ).
cnf(c_0_44,negated_conjecture,
multiplication(esk1_0,addition(one,multiplication(esk2_0,X1))) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_41]),c_0_42]),c_0_23]) ).
cnf(c_0_45,negated_conjecture,
multiplication(esk1_0,strong_iteration(esk2_0)) != esk1_0,
inference(cn,[status(thm)],[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_32]),c_0_23]),c_0_33]),c_0_32]),c_0_23]),c_0_33])]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_29]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE148+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n010.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 20:32:06 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.60/1.83 % Version : CSE_E---1.7
% 1.60/1.83 % Problem : theBenchmark.p
% 1.60/1.83 % SZS status Theorem for theBenchmark.p
% 1.60/1.83 % SZS output start CNFRefutation
% See solution above
% 1.60/1.84 % Total time : 1.370s
%------------------------------------------------------------------------------