%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE009+3 : 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 : n005.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 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 24 unt; 0 def)
% Number of atoms : 110 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 111 ( 62 ~; 33 |; 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 : 50 ( 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_20,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
fof(nnf_17,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(sK1,sK0),multiplication(sK1,c(sK0))),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0)))) )
& test(sK1)
& test(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK1),skolemize(X1,sK0)],[nnf_17]) ).
cnf(c_23,negated_conjecture,
test(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_24,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_26,negated_conjecture,
( complement(sK1,A)
| c(sK1) != A ),
inference(resolve,[status(thm)],[c_24,c_20]) ).
cnf(c_29,negated_conjecture,
( complement(sK0,A)
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_37,negated_conjecture,
( ~ leq(addition(addition(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0)))) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_39,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_42,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_48,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_49,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_51,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_53,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_55,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_56,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_136,negated_conjecture,
( ~ leq(addition(addition(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(addition(multiplication(sK1,addition(sK0,c(sK0))),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0)))) ),
inference(paramod,[status(thm)],[c_49,c_37]) ).
cnf(c_137,negated_conjecture,
( ~ leq(addition(addition(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(sK0,c(sK0)))),multiplication(c(sK1),c(sK0)))) ),
inference(paramod,[status(thm)],[c_56,c_136]) ).
cnf(c_138,negated_conjecture,
( ~ leq(addition(addition(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(sK0,c(sK0)))))) ),
inference(paramod,[status(thm)],[c_56,c_137]) ).
cnf(c_139,negated_conjecture,
( ~ leq(addition(addition(multiplication(sK1,addition(sK0,c(sK0))),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(sK0,c(sK0)))))) ),
inference(paramod,[status(thm)],[c_49,c_138]) ).
cnf(c_140,negated_conjecture,
( ~ leq(addition(addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(sK0,c(sK0)))),multiplication(c(sK1),c(sK0))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(sK0,c(sK0)))))) ),
inference(paramod,[status(thm)],[c_56,c_139]) ).
cnf(c_60,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(sK0,c(sK0))))),one)
| ~ leq(one,addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(sK0,c(sK0)))))) ),
inference(paramod,[status(thm)],[c_56,c_140]) ).
cnf(c_61,plain,
complement(sK1,c(sK1)),
inference(xxres,[status(thm)],[c_26]) ).
cnf(c_62,plain,
complement(sK0,c(sK0)),
inference(xxres,[status(thm)],[c_29]) ).
cnf(c_95,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_53,c_42]) ).
cnf(c_141,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_56,c_55]) ).
cnf(c_116,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_55,c_141]) ).
cnf(c_142,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(sK0,c(sK0))))),one)
| ~ leq(one,addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,addition(sK0,c(sK0)))))) ),
inference(paramod,[status(thm)],[c_116,c_60]) ).
cnf(c_117,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,addition(sK0,c(sK0))))),one)
| ~ leq(one,addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,addition(sK0,c(sK0)))))) ),
inference(paramod,[status(thm)],[c_116,c_142]) ).
cnf(c_143,plain,
addition(c(sK1),sK1) = one,
inference(resolve,[status(thm)],[c_61,c_39]) ).
cnf(c_120,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_56,c_143]) ).
cnf(c_144,plain,
addition(c(sK0),sK0) = one,
inference(resolve,[status(thm)],[c_62,c_39]) ).
cnf(c_131,plain,
addition(sK0,c(sK0)) = one,
inference(paramod,[status(thm)],[c_56,c_144]) ).
cnf(c_145,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,addition(sK0,c(sK0))))),one)
| ~ leq(one,addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,one)))) ),
inference(paramod,[status(thm)],[c_131,c_117]) ).
cnf(c_146,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,addition(sK0,c(sK0))))),one)
| ~ leq(one,addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),sK1))) ),
inference(paramod,[status(thm)],[c_51,c_145]) ).
cnf(c_147,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,addition(sK0,c(sK0))))),one)
| ~ leq(one,addition(multiplication(c(sK1),sK0),addition(sK1,multiplication(c(sK1),c(sK0))))) ),
inference(paramod,[status(thm)],[c_56,c_146]) ).
cnf(c_148,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,addition(sK0,c(sK0))))),one)
| ~ leq(one,addition(sK1,addition(multiplication(c(sK1),sK0),multiplication(c(sK1),c(sK0))))) ),
inference(paramod,[status(thm)],[c_116,c_147]) ).
cnf(c_149,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,addition(sK0,c(sK0))))),one)
| ~ leq(one,addition(sK1,multiplication(c(sK1),addition(sK0,c(sK0))))) ),
inference(paramod,[status(thm)],[c_49,c_148]) ).
cnf(c_150,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,addition(sK0,c(sK0))))),one)
| ~ leq(one,addition(sK1,multiplication(c(sK1),one))) ),
inference(paramod,[status(thm)],[c_131,c_149]) ).
cnf(c_151,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,addition(sK0,c(sK0))))),one)
| ~ leq(one,addition(sK1,c(sK1))) ),
inference(paramod,[status(thm)],[c_51,c_150]) ).
cnf(c_152,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,addition(sK0,c(sK0))))),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_120,c_151]) ).
cnf(c_153,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,one))),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_131,c_152]) ).
cnf(c_154,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),sK1)),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_51,c_153]) ).
cnf(c_155,negated_conjecture,
( ~ leq(addition(multiplication(c(sK1),sK0),addition(sK1,multiplication(c(sK1),c(sK0)))),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_56,c_154]) ).
cnf(c_156,negated_conjecture,
( ~ leq(addition(sK1,addition(multiplication(c(sK1),sK0),multiplication(c(sK1),c(sK0)))),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_116,c_155]) ).
cnf(c_157,negated_conjecture,
( ~ leq(addition(sK1,multiplication(c(sK1),addition(sK0,c(sK0)))),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_49,c_156]) ).
cnf(c_158,negated_conjecture,
( ~ leq(addition(sK1,multiplication(c(sK1),one)),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_131,c_157]) ).
cnf(c_159,negated_conjecture,
( ~ leq(addition(sK1,c(sK1)),one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_51,c_158]) ).
cnf(c_160,negated_conjecture,
( ~ leq(one,one)
| ~ leq(one,one) ),
inference(paramod,[status(thm)],[c_120,c_159]) ).
cnf(c_161,negated_conjecture,
~ leq(one,one),
inference(copy,[status(thm)],[c_160]) ).
cnf(c_135,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_95,c_161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 19:11:03 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 4116811 was started by sandbox2 on n005,
% 0.11/0.37 % Fri Sep 25 19:11:03 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.39
% 0.11/0.39 % SZS status Theorem for theBenchmark
% 0.11/0.39
% 0.11/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.11/0.39 % Length of proof is 32.
% 0.11/0.39 % Level of proof is 5.
% 0.11/0.39 % Maximum clause weight is 42.000.
% 0.11/0.39 % Given clauses 37.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------