%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE141+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 0.22s 5.51s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 15 unt; 0 def)
% Number of atoms : 35 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 6 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 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 : 36 ( 4 sgn 13 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(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),multiplication(strong_iteration(one),X0))
& leq(multiplication(strong_iteration(one),X0),strong_iteration(one)) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(one),multiplication(strong_iteration(one),X0))
& leq(multiplication(strong_iteration(one),X0),strong_iteration(one)) ),
inference(assume_negation,[status(cth)],[goals]) ).
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_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),multiplication(strong_iteration(one),X0))
| ~ leq(multiplication(strong_iteration(one),X0),strong_iteration(one)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(strong_iteration(one),multiplication(strong_iteration(one),sK0))
| ~ leq(multiplication(strong_iteration(one),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),multiplication(strong_iteration(one),sK0))
| ~ leq(multiplication(strong_iteration(one),sK0),strong_iteration(one)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_163,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_163]) ).
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_133,negated_conjecture,
~ leq(multiplication(strong_iteration(one),sK0),strong_iteration(one)),
inference(resolve,[status(thm)],[c_132,c_45]) ).
cnf(c_161,plain,
leq(A,strong_iteration(one)),
inference(paramod,[status(thm)],[c_25,c_132]) ).
cnf(c_162,plain,
$false,
inference(resolve,[status(thm)],[c_161,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE141+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.45 % Computer : n010.cluster.edu
% 0.16/5.45 % Model : x86_64 x86_64
% 0.16/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.45 % Memory : 8046.5625MB
% 0.16/5.45 % OS : Linux 6.8.0-71-generic
% 0.16/5.45 % CPULimit : 300
% 0.16/5.45 % WCLimit : 300
% 0.16/5.45 % DateTime : Fri Sep 25 19:26:49 UTC 2026
% 0.16/5.46 % CPUTime :
% 0.16/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.46 % Process 1458496 was started by sandbox2 on n010,
% 0.16/5.46 % Fri Sep 25 19:26:49 2026
% 0.16/5.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.47
% 0.16/5.47 % From the command line: assign(max_seconds, 300).
% 0.22/5.51
% 0.22/5.51 % SZS status Theorem for theBenchmark
% 0.22/5.51
% 0.22/5.51 % Proof 1 at 0.02 (+ 0.02) seconds.
% 0.22/5.51 % Length of proof is 21.
% 0.22/5.51 % Level of proof is 6.
% 0.22/5.51 % Maximum clause weight is 14.000.
% 0.22/5.51 % Given clauses 37.
% 0.22/5.51
% 0.22/5.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------