%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE004+1 : 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 : n009.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 07:44:01 AM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 19 unt; 0 def)
% Number of atoms : 52 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 21 ~; 15 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 7 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero,
file('theBenchmark.p',right_annihilation) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('theBenchmark.p',test_1) ).
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,
c(zero) = one,
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
c(zero) != one,
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_20,plain,
( ~ complement(A,B)
| c(A) = B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_23,plain,
( ~ complement(B,A)
| test(A) ),
inference(clausify,[status(thm)],[test_1]) ).
cnf(c_27,plain,
( ~ complement(B,C)
| c(B) = C
| ~ complement(A,B) ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_31,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_33,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_36,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_42,plain,
multiplication(A,zero) = zero,
inference(clausify,[status(thm)],[right_annihilation]) ).
cnf(c_43,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_47,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_48,negated_conjecture,
c(zero) != one,
inference(clausify,[status(thm)],[goals_neg]) ).
cnf(c_169,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_33,c_31]) ).
cnf(c_64,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_169]) ).
cnf(c_170,plain,
( multiplication(zero,one) != zero
| multiplication(one,zero) != zero
| complement(zero,one) ),
inference(resolve,[status(thm)],[c_47,c_33]) ).
cnf(c_171,plain,
( multiplication(zero,one) != zero
| complement(zero,one) ),
inference(resolve,[status(thm)],[c_42,c_170]) ).
cnf(c_133,plain,
complement(zero,one),
inference(resolve,[status(thm)],[c_36,c_171]) ).
cnf(c_172,plain,
( c(zero) = one
| ~ complement(A,zero) ),
inference(resolve,[status(thm)],[c_133,c_27]) ).
cnf(c_153,negated_conjecture,
~ complement(A,zero),
inference(resolve,[status(thm)],[c_48,c_172]) ).
cnf(c_173,plain,
( addition(zero,A) != one
| multiplication(A,zero) != zero
| multiplication(zero,A) != zero ),
inference(resolve,[status(thm)],[c_47,c_153]) ).
cnf(c_174,plain,
( addition(zero,A) != one
| multiplication(A,zero) != zero ),
inference(resolve,[status(thm)],[c_173,c_43]) ).
cnf(c_167,plain,
addition(zero,A) != one,
inference(resolve,[status(thm)],[c_174,c_42]) ).
cnf(c_168,plain,
$false,
inference(resolve,[status(thm)],[c_167,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE004+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 19:12:00 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2270230 was started by sandbox2 on n009,
% 0.10/0.37 % Fri Sep 25 19:12:00 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 24.
% 0.10/0.39 % Level of proof is 5.
% 0.10/0.39 % Maximum clause weight is 28.000.
% 0.10/0.39 % Given clauses 33.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------