%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE142+1 : 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 : n027.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 04:35:48 PM UTC 2026
% Result : Theorem 1.26s 1.73s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 30 unt; 0 def)
% Number of atoms : 52 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 12 ~; 9 |; 1 &)
% ( 1 <=>; 1 =>; 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; 3 con; 0-2 aty)
% Number of variables : 52 ( 10 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(infty_coinduction,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(isolation,axiom,
! [X1] : strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',isolation) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(goals,conjecture,
! [X4] : strong_iteration(strong_iteration(X4)) = strong_iteration(one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_8,plain,
! [X68,X69,X70] :
( ~ leq(X70,addition(multiplication(X68,X70),X69))
| leq(X70,multiplication(strong_iteration(X68),X69)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).
fof(c_0_9,plain,
! [X51] : multiplication(one,X51) = X51,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_10,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X45] : addition(X45,zero) = X45,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_13,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X72,X73] :
( ( ~ leq(X72,X73)
| addition(X72,X73) = X73 )
& ( addition(X72,X73) != X73
| leq(X72,X73) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_16,plain,
! [X46] : addition(X46,X46) = X46,
inference(variable_rename,[status(thm)],[idempotence]) ).
cnf(c_0_17,plain,
( leq(X1,multiplication(strong_iteration(one),zero))
| ~ leq(X1,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X71] : strong_iteration(X71) = addition(star(X71),multiplication(strong_iteration(X71),zero)),
inference(variable_rename,[status(thm)],[isolation]) ).
cnf(c_0_21,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
leq(X1,multiplication(strong_iteration(one),zero)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_23,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
addition(X1,multiplication(strong_iteration(one),zero)) = multiplication(strong_iteration(one),zero),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
addition(X1,strong_iteration(one)) = strong_iteration(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_25]) ).
cnf(c_0_27,plain,
leq(X1,strong_iteration(one)),
inference(rw,[status(thm)],[c_0_22,c_0_25]) ).
fof(c_0_28,plain,
! [X40,X41] : addition(X40,X41) = addition(X41,X40),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_29,plain,
( leq(X1,multiplication(strong_iteration(X2),zero))
| ~ leq(X1,multiplication(X2,X1)) ),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_30,plain,
leq(X1,multiplication(strong_iteration(X2),strong_iteration(one))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_26]),c_0_27])]) ).
cnf(c_0_31,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_32,negated_conjecture,
~ ! [X4] : strong_iteration(strong_iteration(X4)) = strong_iteration(one),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_33,plain,
leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X1)),zero)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_31,c_0_26]) ).
fof(c_0_35,negated_conjecture,
strong_iteration(strong_iteration(esk1_0)) != strong_iteration(one),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).
cnf(c_0_36,plain,
multiplication(strong_iteration(strong_iteration(X1)),zero) = strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_33]),c_0_34]) ).
cnf(c_0_37,negated_conjecture,
strong_iteration(strong_iteration(esk1_0)) != strong_iteration(one),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_38,plain,
strong_iteration(strong_iteration(X1)) = strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_36]),c_0_26]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE142+1 : 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
% 0.14/0.32 % Computer : n027.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 20:31:05 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.26/1.73 % Version : CSE_E---1.7
% 1.26/1.73 % Problem : theBenchmark.p
% 1.26/1.73 % SZS status Theorem for theBenchmark.p
% 1.26/1.73 % SZS output start CNFRefutation
% See solution above
% 1.26/1.73 % Total time : 1.372s
%------------------------------------------------------------------------------