%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE144+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 : n002.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 3.79s 3.18s
% Output : CNFRefutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 64 unt; 0 def)
% Number of atoms : 88 ( 63 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 10 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 115 ( 15 sgn 48 !; 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/sandbox/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
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(distributivity2,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_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(star_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(isolation,axiom,
! [X1] : strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',isolation) ).
fof(goals,conjecture,
! [X4] : strong_iteration(star(X4)) = strong_iteration(one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_14,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_15,plain,
! [X51] : multiplication(one,X51) = X51,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_16,plain,
! [X42,X43,X44] : addition(X44,addition(X43,X42)) = addition(addition(X44,X43),X42),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_17,plain,
! [X46] : addition(X46,X46) = X46,
inference(variable_rename,[status(thm)],[idempotence]) ).
cnf(c_0_18,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,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])]) ).
cnf(c_0_21,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_26,plain,
! [X50] : multiplication(X50,one) = X50,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_27,plain,
! [X67] : strong_iteration(X67) = addition(multiplication(X67,strong_iteration(X67)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_28,plain,
! [X40,X41] : addition(X40,X41) = addition(X41,X40),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_29,plain,
! [X55,X56,X57] : multiplication(addition(X55,X56),X57) = addition(multiplication(X55,X57),multiplication(X56,X57)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
cnf(c_0_30,plain,
leq(X1,multiplication(strong_iteration(one),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_31,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_35,plain,
! [X45] : addition(X45,zero) = X45,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_36,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_37,plain,
leq(X1,strong_iteration(one)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
addition(X1,addition(X2,addition(X1,X2))) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_39,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_19]),c_0_33]) ).
cnf(c_0_41,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
addition(X1,strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_43,plain,
! [X47,X48,X49] : multiplication(X47,multiplication(X48,X49)) = multiplication(multiplication(X47,X48),X49),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_44,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_33]),c_0_25]) ).
cnf(c_0_45,plain,
addition(one,multiplication(addition(X1,one),strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_33]),c_0_40]) ).
fof(c_0_46,plain,
! [X60] : addition(one,multiplication(star(X60),X60)) = star(X60),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
fof(c_0_47,plain,
! [X71] : strong_iteration(X71) = addition(star(X71),multiplication(strong_iteration(X71),zero)),
inference(variable_rename,[status(thm)],[isolation]) ).
cnf(c_0_48,plain,
( leq(X1,multiplication(strong_iteration(X2),zero))
| ~ leq(X1,multiplication(X2,X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_41]) ).
cnf(c_0_49,plain,
leq(X1,multiplication(strong_iteration(X2),strong_iteration(one))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_42]),c_0_37])]) ).
cnf(c_0_50,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_33,c_0_42]) ).
cnf(c_0_51,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
multiplication(addition(X1,one),strong_iteration(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_33]),c_0_40]),c_0_21]),c_0_22]) ).
cnf(c_0_53,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_54,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,plain,
leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X1)),zero)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,plain,
multiplication(addition(X1,one),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_50,c_0_40]) ).
cnf(c_0_57,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(X3,multiplication(X2,X1))) ),
inference(spm,[status(thm)],[c_0_18,c_0_33]) ).
cnf(c_0_58,plain,
addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_39,c_0_51]) ).
cnf(c_0_59,plain,
multiplication(addition(one,X1),strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_52,c_0_33]) ).
cnf(c_0_60,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_25,c_0_53]) ).
cnf(c_0_61,plain,
addition(multiplication(strong_iteration(X1),zero),star(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_54,c_0_33]) ).
cnf(c_0_62,plain,
multiplication(strong_iteration(strong_iteration(X1)),zero) = strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_55]),c_0_50]) ).
cnf(c_0_63,plain,
multiplication(addition(one,X1),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_56,c_0_33]) ).
cnf(c_0_64,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_25,c_0_39]) ).
fof(c_0_65,negated_conjecture,
~ ! [X4] : strong_iteration(star(X4)) = strong_iteration(one),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_66,plain,
( leq(multiplication(X1,strong_iteration(multiplication(X2,X1))),strong_iteration(X2))
| ~ leq(multiplication(X1,strong_iteration(multiplication(X2,X1))),strong_iteration(multiplication(X2,X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_31]) ).
cnf(c_0_67,plain,
multiplication(star(X1),strong_iteration(star(X1))) = strong_iteration(star(X1)),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,plain,
strong_iteration(strong_iteration(X1)) = strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_50]) ).
cnf(c_0_69,plain,
multiplication(strong_iteration(X1),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
fof(c_0_70,negated_conjecture,
strong_iteration(star(esk1_0)) != strong_iteration(one),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])]) ).
cnf(c_0_71,plain,
leq(strong_iteration(one),strong_iteration(star(X1))),
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)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_69]),c_0_68]),c_0_69]),c_0_68]),c_0_37])]) ).
cnf(c_0_72,negated_conjecture,
strong_iteration(star(esk1_0)) != strong_iteration(one),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_73,plain,
strong_iteration(star(X1)) = strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_71]),c_0_50]) ).
cnf(c_0_74,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE144+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 : n002.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 20:32:01 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 3.79/3.18 % Version : CSE_E---1.7
% 3.79/3.18 % Problem : theBenchmark.p
% 3.79/3.18 % SZS status Theorem for theBenchmark.p
% 3.79/3.18 % SZS output start CNFRefutation
% See solution above
% 3.79/3.19 % Total time : 2.369s
%------------------------------------------------------------------------------