%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE142+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:44:23 AM UTC 2026
% Result : Theorem 0.80s 0.57s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 29 unt; 0 def)
% Number of atoms : 53 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 13 ~; 8 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 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 : 70 ( 11 sgn 19 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('theBenchmark.p',additive_associativity) ).
fof(idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',idempotence) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
fof(distributivity2,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',distributivity2) ).
fof(infty_unfold1,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('theBenchmark.p',infty_unfold1) ).
fof(infty_coinduction,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('theBenchmark.p',infty_coinduction) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(goals,conjecture,
! [X0] :
( leq(strong_iteration(one),strong_iteration(strong_iteration(X0)))
& leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(one),strong_iteration(strong_iteration(X0)))
& leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_20,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_21,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_23,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[idempotence]) ).
cnf(c_25,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_26,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_29,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[distributivity2]) ).
cnf(c_30,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_38,plain,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(clausify,[status(thm)],[infty_unfold1]) ).
cnf(c_649,plain,
strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))),
inference(paramod,[status(thm)],[c_20,c_38]) ).
cnf(c_39,plain,
addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A),
inference(copy,[status(thm)],[c_649]) ).
cnf(c_40,plain,
( leq(A,multiplication(strong_iteration(B),C))
| ~ leq(A,addition(multiplication(B,A),C)) ),
inference(clausify,[status(thm)],[infty_coinduction]) ).
cnf(c_44,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
fof(nnf_19,plain,
? [X0] :
( ~ leq(strong_iteration(one),strong_iteration(strong_iteration(X0)))
| ~ leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(strong_iteration(one),strong_iteration(strong_iteration(sK0)))
| ~ leq(strong_iteration(strong_iteration(sK0)),strong_iteration(one)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_19]) ).
cnf(c_45,negated_conjecture,
( ~ leq(strong_iteration(one),strong_iteration(strong_iteration(sK0)))
| ~ leq(strong_iteration(strong_iteration(sK0)),strong_iteration(one)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_650,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_23,c_21]) ).
cnf(c_49,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_650]) ).
cnf(c_651,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_26,c_30]) ).
cnf(c_58,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_651]) ).
cnf(c_97,plain,
( leq(A,multiplication(strong_iteration(one),B))
| ~ leq(A,addition(A,B)) ),
inference(paramod,[status(thm)],[c_26,c_40]) ).
cnf(c_123,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_44,c_49]) ).
cnf(c_132,plain,
leq(A,multiplication(strong_iteration(one),B)),
inference(resolve,[status(thm)],[c_123,c_97]) ).
cnf(c_159,plain,
leq(A,strong_iteration(one)),
inference(paramod,[status(thm)],[c_25,c_132]) ).
cnf(c_160,negated_conjecture,
~ leq(strong_iteration(one),strong_iteration(strong_iteration(sK0))),
inference(resolve,[status(thm)],[c_159,c_45]) ).
cnf(c_652,plain,
( leq(A,multiplication(strong_iteration(addition(one,B)),C))
| ~ leq(A,addition(addition(A,multiplication(B,A)),C)) ),
inference(paramod,[status(thm)],[c_58,c_40]) ).
cnf(c_653,plain,
( leq(A,multiplication(strong_iteration(addition(one,B)),C))
| ~ leq(A,addition(A,addition(multiplication(B,A),C))) ),
inference(paramod,[status(thm)],[c_21,c_652]) ).
cnf(c_363,plain,
leq(A,multiplication(strong_iteration(addition(one,B)),C)),
inference(resolve,[status(thm)],[c_123,c_653]) ).
cnf(c_639,plain,
leq(A,strong_iteration(addition(one,B))),
inference(paramod,[status(thm)],[c_25,c_363]) ).
cnf(c_647,plain,
leq(A,strong_iteration(strong_iteration(B))),
inference(paramod,[status(thm)],[c_39,c_639]) ).
cnf(c_648,plain,
$false,
inference(resolve,[status(thm)],[c_647,c_160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE142+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 19:29:10 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3234666 was started by sandbox on n026,
% 0.09/0.37 % Fri Sep 25 19:29:10 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.80/0.57
% 0.80/0.57 % SZS status Theorem for theBenchmark
% 0.80/0.57
% 0.80/0.57 % Proof 1 at 0.10 (+ 0.06) seconds.
% 0.80/0.57 % Length of proof is 33.
% 0.80/0.57 % Level of proof is 7.
% 0.80/0.57 % Maximum clause weight is 13.000.
% 0.80/0.57 % Given clauses 98.
% 0.80/0.57
% 0.80/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------