%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE150+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 : n019.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 07:44:25 AM UTC 2026
% Result : Theorem 1.14s 0.69s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 18 unt; 0 def)
% Number of atoms : 36 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 6 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 1 sgn 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',idempotence) ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('theBenchmark.p',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(infty_unfold1,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('theBenchmark.p',infty_unfold1) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(goals,conjecture,
! [X0] :
( leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
& leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
& leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_20,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_23,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[idempotence]) ).
cnf(c_24,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_31,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_38,plain,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(clausify,[status(thm)],[infty_unfold1]) ).
cnf(c_897,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_897]) ).
cnf(c_44,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
fof(nnf_19,plain,
? [X0] :
( ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
| ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_19]) ).
cnf(c_45,negated_conjecture,
( ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_87,plain,
addition(one,multiplication(A,multiplication(B,strong_iteration(multiplication(A,B))))) = strong_iteration(multiplication(A,B)),
inference(paramod,[status(thm)],[c_24,c_39]) ).
cnf(c_102,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_44,c_23]) ).
cnf(c_898,plain,
addition(one,multiplication(A,zero)) = strong_iteration(multiplication(A,zero)),
inference(paramod,[status(thm)],[c_31,c_87]) ).
cnf(c_870,plain,
strong_iteration(multiplication(A,zero)) = addition(one,multiplication(A,zero)),
inference(copy,[status(thm)],[c_898]) ).
cnf(c_899,negated_conjecture,
( ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| ~ leq(addition(one,multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
inference(paramod,[status(thm)],[c_870,c_45]) ).
cnf(c_900,negated_conjecture,
( ~ leq(addition(one,multiplication(sK0,zero)),addition(one,multiplication(sK0,zero)))
| ~ leq(addition(one,multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
inference(paramod,[status(thm)],[c_870,c_899]) ).
cnf(c_901,negated_conjecture,
~ leq(addition(one,multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))),
inference(copy,[status(thm)],[c_900]) ).
cnf(c_896,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_102,c_901]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n019.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 19:27:48 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 3471449 was started by sandbox on n019,
% 0.18/0.44 % Fri Sep 25 19:27:48 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 1.14/0.69
% 1.14/0.69 % SZS status Theorem for theBenchmark
% 1.14/0.69
% 1.14/0.69 % Proof 1 at 0.15 (+ 0.08) seconds.
% 1.14/0.69 % Length of proof is 19.
% 1.14/0.69 % Level of proof is 5.
% 1.14/0.69 % Maximum clause weight is 50.000.
% 1.14/0.69 % Given clauses 111.
% 1.14/0.69
% 1.14/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------