%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE021+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 : n016.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 0.14s 17.11s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 62 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 27 ~; 16 |; 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 : 39 ( 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_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',left_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(X1,X0),multiplication(c(X1),X0)),X0)
& leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> ( leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0)
& leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) ) ),
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(X1,X0),multiplication(c(X1),X0)),X0)
| ~ leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) )
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ( ~ leq(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),sK0)
| ~ leq(sK0,addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0))) )
& 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(sK1,sK0),multiplication(c(sK1),sK0)),sK0)
| ~ leq(sK0,addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0))) ),
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_45,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_49,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_50,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_53,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_56,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_59,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_134,negated_conjecture,
( ~ leq(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),sK0)
| ~ leq(sK0,multiplication(addition(sK1,c(sK1)),sK0)) ),
inference(paramod,[status(thm)],[c_50,c_38]) ).
cnf(c_64,negated_conjecture,
( ~ leq(multiplication(addition(sK1,c(sK1)),sK0),sK0)
| ~ leq(sK0,multiplication(addition(sK1,c(sK1)),sK0)) ),
inference(paramod,[status(thm)],[c_50,c_134]) ).
cnf(c_135,negated_conjecture,
( addition(A,sK1) = one
| c(sK1) != A ),
inference(resolve,[status(thm)],[c_33,c_39]) ).
cnf(c_136,plain,
addition(c(sK1),sK1) = one,
inference(xxres,[status(thm)],[c_135]) ).
cnf(c_73,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_59,c_136]) ).
cnf(c_137,negated_conjecture,
( ~ leq(multiplication(addition(sK1,c(sK1)),sK0),sK0)
| ~ leq(sK0,multiplication(one,sK0)) ),
inference(paramod,[status(thm)],[c_73,c_64]) ).
cnf(c_138,negated_conjecture,
( ~ leq(multiplication(addition(sK1,c(sK1)),sK0),sK0)
| ~ leq(sK0,sK0) ),
inference(paramod,[status(thm)],[c_53,c_137]) ).
cnf(c_139,negated_conjecture,
( ~ leq(multiplication(one,sK0),sK0)
| ~ leq(sK0,sK0) ),
inference(paramod,[status(thm)],[c_73,c_138]) ).
cnf(c_140,negated_conjecture,
( ~ leq(sK0,sK0)
| ~ leq(sK0,sK0) ),
inference(paramod,[status(thm)],[c_53,c_139]) ).
cnf(c_78,negated_conjecture,
~ leq(sK0,sK0),
inference(copy,[status(thm)],[c_140]) ).
cnf(c_132,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_56,c_45]) ).
cnf(c_133,plain,
$false,
inference(resolve,[status(thm)],[c_132,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE021+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.04/17.09 % CPULimit : 300
% 0.04/17.09 % WCLimit : 300
% 0.04/17.09 % DateTime : Fri Sep 25 19:14:25 UTC 2026
% 0.04/17.09 % CPUTime :
% 0.04/17.09 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/17.09 % Process 2746031 was started by sandbox2 on n012,
% 0.04/17.09 % Fri Sep 25 19:14:25 2026
% 0.04/17.09 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/17.10
% 0.04/17.10 % From the command line: assign(max_seconds, 300).
% 0.14/17.11
% 0.14/17.11 % SZS status Theorem for theBenchmark
% 0.14/17.11
% 0.14/17.11 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/17.11 % Length of proof is 24.
% 0.14/17.11 % Level of proof is 5.
% 0.14/17.11 % Maximum clause weight is 40.000.
% 0.14/17.11 % Given clauses 24.
% 0.14/17.11
% 0.14/17.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------