%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE022+4 : 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 : n013.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 07:44:06 AM UTC 2026
% Result : Theorem 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 14 unt; 0 def)
% Number of atoms : 63 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 28 ~; 17 |; 6 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 17 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_idempotence) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',right_distributivity) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('theBenchmark.p',test_2) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('theBenchmark.p',test_3) ).
fof(goals,conjecture,
! [X0,X1] :
( test(X1)
=> ( leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0)
& leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> ( leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0)
& leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_24,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_26,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_33,plain,
( addition(B,A) = one
| c(A) != B
| ~ test(A) ),
inference(resolve,[status(thm)],[c_26,c_24]) ).
fof(nnf_19,plain,
? [X0,X1] :
( ( ~ leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0)
| ~ leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) )
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ( ~ leq(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),sK0)
| ~ leq(sK0,addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1)))) )
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_19]) ).
cnf(c_38,negated_conjecture,
( ~ leq(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),sK0)
| ~ leq(sK0,addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1)))) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_39,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_43,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_49,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_50,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_52,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_54,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_57,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_186,negated_conjecture,
( ~ leq(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),sK0)
| ~ leq(sK0,multiplication(sK0,addition(sK1,c(sK1)))) ),
inference(paramod,[status(thm)],[c_50,c_38]) ).
cnf(c_62,negated_conjecture,
( ~ leq(multiplication(sK0,addition(sK1,c(sK1))),sK0)
| ~ leq(sK0,multiplication(sK0,addition(sK1,c(sK1)))) ),
inference(paramod,[status(thm)],[c_50,c_186]) ).
cnf(c_187,plain,
( addition(c(A),A) = one
| ~ test(A) ),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_66,plain,
( addition(A,c(A)) = one
| ~ test(A) ),
inference(paramod,[status(thm)],[c_57,c_187]) ).
cnf(c_134,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_54,c_43]) ).
cnf(c_184,plain,
addition(sK1,c(sK1)) = one,
inference(resolve,[status(thm)],[c_66,c_39]) ).
cnf(c_188,negated_conjecture,
( ~ leq(multiplication(sK0,addition(sK1,c(sK1))),sK0)
| ~ leq(sK0,multiplication(sK0,one)) ),
inference(paramod,[status(thm)],[c_184,c_62]) ).
cnf(c_189,negated_conjecture,
( ~ leq(multiplication(sK0,addition(sK1,c(sK1))),sK0)
| ~ leq(sK0,sK0) ),
inference(paramod,[status(thm)],[c_52,c_188]) ).
cnf(c_190,negated_conjecture,
( ~ leq(multiplication(sK0,one),sK0)
| ~ leq(sK0,sK0) ),
inference(paramod,[status(thm)],[c_184,c_189]) ).
cnf(c_191,negated_conjecture,
( ~ leq(sK0,sK0)
| ~ leq(sK0,sK0) ),
inference(paramod,[status(thm)],[c_52,c_190]) ).
cnf(c_192,negated_conjecture,
~ leq(sK0,sK0),
inference(copy,[status(thm)],[c_191]) ).
cnf(c_185,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_134,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE022+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n013.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Fri Sep 25 19:13:38 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 978901 was started by sandbox2 on n013,
% 0.18/0.46 % Fri Sep 25 19:13:38 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 0.18/0.50
% 0.18/0.50 % SZS status Theorem for theBenchmark
% 0.18/0.50
% 0.18/0.50 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.18/0.50 % Length of proof is 24.
% 0.18/0.50 % Level of proof is 5.
% 0.18/0.50 % Maximum clause weight is 40.000.
% 0.18/0.50 % Given clauses 41.
% 0.18/0.50
% 0.18/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------