%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE170+1.002 : TPTP v9.2.1. Released v5.2.0.
% 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 : 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 04:35:52 PM UTC 2026
% Result : Theorem 11.78s 8.12s
% Output : CNFRefutation 11.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 47 unt; 0 def)
% Number of atoms : 57 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 13 ( 7 ~; 4 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).
fof(star_unfold_left,axiom,
! [X1] : leq(addition(one,multiplication(star(X1),X1)),star(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(star_unfold_right,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
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/KLE002+0.ax',left_distributivity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(a,conjecture,
leq(multiplication(a,a),star(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
fof(c_0_11,plain,
! [X34,X35] : addition(X34,X35) = addition(X35,X34),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_12,plain,
! [X36,X37,X38] : addition(X38,addition(X37,X36)) = addition(addition(X38,X37),X36),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_13,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X40] : addition(X40,X40) = X40,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_16,plain,
! [X54,X55] :
( ( ~ leq(X54,X55)
| addition(X54,X55) = X55 )
& ( addition(X54,X55) != X55
| leq(X54,X55) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_17,plain,
! [X57] : leq(addition(one,multiplication(star(X57),X57)),star(X57)),
inference(variable_rename,[status(thm)],[star_unfold_left]) ).
cnf(c_0_18,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X46,X47,X48] : multiplication(X46,addition(X47,X48)) = addition(multiplication(X46,X47),multiplication(X46,X48)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_23,plain,
! [X44] : multiplication(X44,one) = X44,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_24,plain,
! [X56] : leq(addition(one,multiplication(X56,star(X56))),star(X56)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
fof(c_0_25,plain,
! [X49,X50,X51] : multiplication(addition(X49,X50),X51) = addition(multiplication(X49,X51),multiplication(X50,X51)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_26,plain,
! [X45] : multiplication(one,X45) = X45,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_27,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,plain,
addition(one,addition(star(X1),multiplication(star(X1),X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14]),c_0_13]) ).
cnf(c_0_29,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_30,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
addition(star(X1),multiplication(star(X1),X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_14]),c_0_13]),c_0_29]) ).
cnf(c_0_36,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_13]) ).
cnf(c_0_37,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_32]),c_0_14]),c_0_13]) ).
cnf(c_0_38,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_13]) ).
cnf(c_0_39,plain,
multiplication(star(X1),addition(X1,one)) = star(X1),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
fof(c_0_41,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[a])]) ).
cnf(c_0_42,plain,
addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
cnf(c_0_43,plain,
addition(X1,star(X1)) = star(X1),
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_38,c_0_39]),c_0_14]),c_0_40]),c_0_13]),c_0_40]),c_0_39]) ).
cnf(c_0_44,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_46,plain,
addition(multiplication(X1,addition(X2,one)),star(X2)) = multiplication(addition(X1,star(X2)),addition(X2,one)),
inference(spm,[status(thm)],[c_0_33,c_0_39]) ).
cnf(c_0_47,plain,
addition(multiplication(X1,addition(X2,X3)),star(multiplication(X1,X3))) = addition(multiplication(X1,X2),star(multiplication(X1,X3))),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
addition(multiplication(a,a),star(a)) != star(a),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
addition(multiplication(X1,X1),star(X1)) = star(X1),
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_46,c_0_47]),c_0_31]),c_0_31]),c_0_31]),c_0_43]),c_0_31]),c_0_39]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE170+1.002 : TPTP v9.2.1. Released v5.2.0.
% 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 : n027.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 20:35:35 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 11.78/8.12 % Version : CSE_E---1.7
% 11.78/8.12 % Problem : theBenchmark.p
% 11.78/8.12 % SZS status Theorem for theBenchmark.p
% 11.78/8.12 % SZS output start CNFRefutation
% See solution above
% 11.88/8.15 % Total time : 6.382s
%------------------------------------------------------------------------------