%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE010+1 : 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 : n018.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 0.13s 5.72s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 61 unt; 0 def)
% Number of atoms : 89 ( 68 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 24 ~; 5 |; 8 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 22 !; 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(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_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(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',left_distributivity) ).
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) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,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) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0,X1] :
( addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) != one
& test(X0)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( addition(addition(addition(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK1)),multiplication(sK1,sK0)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))) != one
& test(sK1)
& test(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK1),skolemize(X1,sK0)],[nnf_17]) ).
cnf(c_22,negated_conjecture,
test(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_23,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_24,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_33,negated_conjecture,
( complement(sK1,A)
| c(sK1) != A ),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_34,negated_conjecture,
( complement(sK0,A)
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_39,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_40,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_42,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_44,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_45,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_46,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_47,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_48,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_49,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_54,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_56,negated_conjecture,
addition(addition(addition(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK1)),multiplication(sK1,sK0)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))) != one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_533,negated_conjecture,
addition(addition(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(sK1,sK0)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))) != one,
inference(paramod,[status(thm)],[c_49,c_56]) ).
cnf(c_534,negated_conjecture,
addition(addition(addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))) != one,
inference(paramod,[status(thm)],[c_39,c_533]) ).
cnf(c_535,negated_conjecture,
addition(addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1))),multiplication(c(sK1),c(sK0))) != one,
inference(paramod,[status(thm)],[c_39,c_534]) ).
cnf(c_57,negated_conjecture,
addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),addition(multiplication(sK1,sK0),multiplication(addition(sK0,c(sK0)),sK1)))) != one,
inference(paramod,[status(thm)],[c_39,c_535]) ).
cnf(c_65,plain,
complement(sK1,c(sK1)),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_66,plain,
complement(sK0,c(sK0)),
inference(xxres,[status(thm)],[c_34]) ).
cnf(c_536,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_39,c_40]) ).
cnf(c_73,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_40,c_536]) ).
cnf(c_537,negated_conjecture,
addition(multiplication(c(sK1),c(sK0)),addition(multiplication(sK1,sK0),addition(multiplication(c(sK1),sK0),multiplication(addition(sK0,c(sK0)),sK1)))) != one,
inference(paramod,[status(thm)],[c_73,c_57]) ).
cnf(c_538,negated_conjecture,
addition(multiplication(sK1,sK0),addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),multiplication(addition(sK0,c(sK0)),sK1)))) != one,
inference(paramod,[status(thm)],[c_73,c_537]) ).
cnf(c_74,negated_conjecture,
addition(multiplication(sK1,sK0),addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(addition(sK0,c(sK0)),sK1)))) != one,
inference(paramod,[status(thm)],[c_73,c_538]) ).
cnf(c_539,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_80,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_539]) ).
cnf(c_540,plain,
addition(multiplication(A,addition(B,C)),D) = addition(multiplication(A,B),addition(multiplication(A,C),D)),
inference(paramod,[status(thm)],[c_47,c_40]) ).
cnf(c_83,plain,
addition(multiplication(A,B),addition(multiplication(A,C),D)) = addition(multiplication(A,addition(B,C)),D),
inference(copy,[status(thm)],[c_540]) ).
cnf(c_541,negated_conjecture,
addition(multiplication(sK1,sK0),addition(multiplication(c(sK1),addition(sK0,c(sK0))),multiplication(addition(sK0,c(sK0)),sK1))) != one,
inference(paramod,[status(thm)],[c_83,c_74]) ).
cnf(c_86,negated_conjecture,
addition(multiplication(sK1,sK0),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(c(sK1),addition(sK0,c(sK0))))) != one,
inference(paramod,[status(thm)],[c_39,c_541]) ).
cnf(c_542,plain,
addition(c(sK1),sK1) = one,
inference(resolve,[status(thm)],[c_65,c_54]) ).
cnf(c_118,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_39,c_542]) ).
cnf(c_543,plain,
addition(c(sK0),sK0) = one,
inference(resolve,[status(thm)],[c_66,c_54]) ).
cnf(c_124,plain,
addition(sK0,c(sK0)) = one,
inference(paramod,[status(thm)],[c_39,c_543]) ).
cnf(c_544,negated_conjecture,
addition(multiplication(sK1,sK0),addition(multiplication(one,sK1),multiplication(c(sK1),addition(sK0,c(sK0))))) != one,
inference(paramod,[status(thm)],[c_124,c_86]) ).
cnf(c_545,negated_conjecture,
addition(multiplication(sK1,sK0),addition(sK1,multiplication(c(sK1),addition(sK0,c(sK0))))) != one,
inference(paramod,[status(thm)],[c_45,c_544]) ).
cnf(c_546,negated_conjecture,
addition(multiplication(sK1,sK0),addition(sK1,multiplication(c(sK1),one))) != one,
inference(paramod,[status(thm)],[c_124,c_545]) ).
cnf(c_547,negated_conjecture,
addition(multiplication(sK1,sK0),addition(sK1,c(sK1))) != one,
inference(paramod,[status(thm)],[c_44,c_546]) ).
cnf(c_548,negated_conjecture,
addition(multiplication(sK1,sK0),one) != one,
inference(paramod,[status(thm)],[c_118,c_547]) ).
cnf(c_131,negated_conjecture,
addition(one,multiplication(sK1,sK0)) != one,
inference(paramod,[status(thm)],[c_39,c_548]) ).
cnf(c_549,plain,
addition(sK1,one) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_118,c_80]) ).
cnf(c_550,plain,
addition(one,sK1) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_39,c_549]) ).
cnf(c_209,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_118,c_550]) ).
cnf(c_551,plain,
addition(one,A) = addition(one,addition(sK1,A)),
inference(paramod,[status(thm)],[c_209,c_40]) ).
cnf(c_211,plain,
addition(one,addition(sK1,A)) = addition(one,A),
inference(copy,[status(thm)],[c_551]) ).
cnf(c_552,plain,
addition(sK0,one) = addition(sK0,c(sK0)),
inference(paramod,[status(thm)],[c_124,c_80]) ).
cnf(c_553,plain,
addition(one,sK0) = addition(sK0,c(sK0)),
inference(paramod,[status(thm)],[c_39,c_552]) ).
cnf(c_229,plain,
addition(one,sK0) = one,
inference(paramod,[status(thm)],[c_124,c_553]) ).
cnf(c_554,plain,
addition(multiplication(A,one),multiplication(A,sK0)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_229,c_47]) ).
cnf(c_555,plain,
addition(A,multiplication(A,sK0)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_44,c_554]) ).
cnf(c_233,plain,
addition(A,multiplication(A,sK0)) = A,
inference(paramod,[status(thm)],[c_44,c_555]) ).
cnf(c_556,plain,
addition(one,sK1) = addition(one,multiplication(sK1,sK0)),
inference(paramod,[status(thm)],[c_233,c_211]) ).
cnf(c_557,plain,
one = addition(one,multiplication(sK1,sK0)),
inference(paramod,[status(thm)],[c_209,c_556]) ).
cnf(c_558,plain,
addition(one,multiplication(sK1,sK0)) = one,
inference(copy,[status(thm)],[c_557]) ).
cnf(c_532,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_131,c_558]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE010+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.40 % Computer : n018.cluster.edu
% 0.09/5.40 % Model : x86_64 x86_64
% 0.09/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.40 % Memory : 8046.5625MB
% 0.09/5.40 % OS : Linux 6.8.0-71-generic
% 0.09/5.40 % CPULimit : 300
% 0.09/5.40 % WCLimit : 300
% 0.09/5.40 % DateTime : Fri Sep 25 19:14:56 UTC 2026
% 0.09/5.40 % CPUTime :
% 0.09/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.41 % Process 2610363 was started by sandbox on n018,
% 0.09/5.41 % Fri Sep 25 19:14:56 2026
% 0.09/5.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.41
% 0.09/5.41 % From the command line: assign(max_seconds, 300).
% 0.13/5.72
% 0.13/5.72 % SZS status Theorem for theBenchmark
% 0.13/5.72
% 0.13/5.72 % Proof 1 at 0.08 (+ 0.04) seconds.
% 0.13/5.72 % Length of proof is 42.
% 0.13/5.72 % Level of proof is 7.
% 0.13/5.72 % Maximum clause weight is 62.000.
% 0.13/5.72 % Given clauses 136.
% 0.13/5.72
% 0.13/5.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------