%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE009+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 : n008.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 07:44:03 AM UTC 2026
% Result : Theorem 0.16s 10.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 20 unt; 0 def)
% Number of atoms : 109 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 115 ( 64 ~; 35 |; 10 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 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 : 52 ( 0 sgn 20 !; 2 ?)
% 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(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(X0)
& test(X1) )
=> ( leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(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(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ( ~ leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) )
& test(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(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_39,negated_conjecture,
test(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_40,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_44,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_50,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_51,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_50]) ).
cnf(c_53,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_55,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_57,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_58,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_208,negated_conjecture,
( ~ leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(paramod,[status(thm)],[c_51,c_38]) ).
cnf(c_209,negated_conjecture,
( ~ leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1)))),multiplication(c(sK0),c(sK1)))) ),
inference(paramod,[status(thm)],[c_58,c_208]) ).
cnf(c_210,negated_conjecture,
( ~ leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1)))))) ),
inference(paramod,[status(thm)],[c_58,c_209]) ).
cnf(c_211,negated_conjecture,
( ~ leq(addition(addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1)))))) ),
inference(paramod,[status(thm)],[c_51,c_210]) ).
cnf(c_212,negated_conjecture,
( ~ leq(addition(addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1)))),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1)))))) ),
inference(paramod,[status(thm)],[c_58,c_211]) ).
cnf(c_63,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1))))),one)
| ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1)))))) ),
inference(paramod,[status(thm)],[c_58,c_212]) ).
cnf(c_213,plain,
( addition(c(A),A) = one
| ~ test(A) ),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_67,plain,
( addition(A,c(A)) = one
| ~ test(A) ),
inference(paramod,[status(thm)],[c_58,c_213]) ).
cnf(c_149,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_55,c_44]) ).
cnf(c_214,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_58,c_57]) ).
cnf(c_175,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_57,c_214]) ).
cnf(c_215,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1))))),one)
| ~ leq(one,addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(sK0,addition(sK1,c(sK1)))))) ),
inference(paramod,[status(thm)],[c_175,c_63]) ).
cnf(c_178,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(sK0,addition(sK1,c(sK1))))),one)
| ~ leq(one,addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(sK0,addition(sK1,c(sK1)))))) ),
inference(paramod,[status(thm)],[c_175,c_215]) ).
cnf(c_205,plain,
addition(sK1,c(sK1)) = one,
inference(resolve,[status(thm)],[c_67,c_40]) ).
cnf(c_206,plain,
addition(sK0,c(sK0)) = one,
inference(resolve,[status(thm)],[c_67,c_39]) ).
cnf(c_216,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(sK0,addition(sK1,c(sK1))))),one)
| ~ leq(one,addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(sK0,one)))) ),
inference(paramod,[status(thm)],[c_205,c_178]) ).
cnf(c_217,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(sK0,addition(sK1,c(sK1))))),one)
| ~ leq(one,addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),sK0))) ),
inference(paramod,[status(thm)],[c_53,c_216]) ).
cnf(c_218,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(sK0,addition(sK1,c(sK1))))),one)
| ~ leq(one,addition(multiplication(c(sK0),sK1),addition(sK0,multiplication(c(sK0),c(sK1))))) ),
inference(paramod,[status(thm)],[c_58,c_217]) ).
cnf(c_219,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(sK0,addition(sK1,c(sK1))))),one)
| ~ leq(one,addition(sK0,addition(multiplication(c(sK0),sK1),multiplication(c(sK0),c(sK1))))) ),
inference(paramod,[status(thm)],[c_175,c_218]) ).
cnf(c_220,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(sK0,addition(sK1,c(sK1))))),one)
| ~ leq(one,addition(sK0,multiplication(c(sK0),addition(sK1,c(sK1))))) ),
inference(paramod,[status(thm)],[c_51,c_219]) ).
cnf(c_221,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(sK0,addition(sK1,c(sK1))))),one)
| ~ leq(one,addition(sK0,multiplication(c(sK0),one))) ),
inference(paramod,[status(thm)],[c_205,c_220]) ).
cnf(c_222,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(sK0,addition(sK1,c(sK1))))),one)
| ~ leq(one,addition(sK0,c(sK0))) ),
inference(paramod,[status(thm)],[c_53,c_221]) ).
cnf(c_223,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(sK0,addition(sK1,c(sK1))))),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_206,c_222]) ).
cnf(c_224,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(sK0,one))),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_205,c_223]) ).
cnf(c_225,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(c(sK0),c(sK1)),sK0)),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_53,c_224]) ).
cnf(c_226,negated_conjecture,
( ~ leq(addition(multiplication(c(sK0),sK1),addition(sK0,multiplication(c(sK0),c(sK1)))),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_58,c_225]) ).
cnf(c_227,negated_conjecture,
( ~ leq(addition(sK0,addition(multiplication(c(sK0),sK1),multiplication(c(sK0),c(sK1)))),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_175,c_226]) ).
cnf(c_228,negated_conjecture,
( ~ leq(addition(sK0,multiplication(c(sK0),addition(sK1,c(sK1)))),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_51,c_227]) ).
cnf(c_229,negated_conjecture,
( ~ leq(addition(sK0,multiplication(c(sK0),one)),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_205,c_228]) ).
cnf(c_230,negated_conjecture,
( ~ leq(addition(sK0,c(sK0)),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_53,c_229]) ).
cnf(c_231,negated_conjecture,
( ~ leq(one,one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_206,c_230]) ).
cnf(c_232,negated_conjecture,
~ leq(one,one),
inference(copy,[status(thm)],[c_231]) ).
cnf(c_207,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_149,c_232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/10.39 % Computer : n008.cluster.edu
% 0.13/10.39 % Model : x86_64 x86_64
% 0.13/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.39 % Memory : 8046.5625MB
% 0.13/10.39 % OS : Linux 6.8.0-71-generic
% 0.13/10.39 % CPULimit : 300
% 0.13/10.39 % WCLimit : 300
% 0.13/10.39 % DateTime : Fri Sep 25 19:12:08 UTC 2026
% 0.13/10.39 % CPUTime :
% 0.13/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/10.39 % Process 1651848 was started by sandbox2 on n008,
% 0.13/10.39 % Fri Sep 25 19:12:08 2026
% 0.13/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/10.40
% 0.13/10.40 % From the command line: assign(max_seconds, 300).
% 0.16/10.44
% 0.16/10.44 % SZS status Theorem for theBenchmark
% 0.16/10.44
% 0.16/10.44 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.16/10.44 % Length of proof is 30.
% 0.16/10.44 % Level of proof is 5.
% 0.16/10.44 % Maximum clause weight is 92.000.
% 0.16/10.44 % Given clauses 42.
% 0.16/10.44
% 0.16/10.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------