%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO011-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 06:55:04 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.51s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 9 unt; 0 def)
% Number of atoms : 17 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity1,axiom,
! [VAR_0] : sum(additive_identity,VAR_0,VAR_0),
file('theBenchmark.p',additive_identity1) ).
cnf(c_5,plain,
sum(additive_identity,A,A),
inference(clausify,[status(thm)],[additive_identity1]) ).
fof(additive_inverse2,axiom,
! [VAR_0] : sum(VAR_0,inverse(VAR_0),multiplicative_identity),
file('theBenchmark.p',additive_inverse2) ).
cnf(c_18,plain,
sum(A,inverse(A),multiplicative_identity),
inference(clausify,[status(thm)],[additive_inverse2]) ).
fof(addition_is_well_defined,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| ~ sum(VAR_0,VAR_1,VAR_3)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',addition_is_well_defined) ).
cnf(c_21,plain,
( C = D
| ~ sum(A,B,D)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[addition_is_well_defined]) ).
fof(prove_equation,axiom,
inverse(additive_identity) != multiplicative_identity,
file('theBenchmark.p',prove_equation) ).
cnf(c_23,plain,
inverse(additive_identity) != multiplicative_identity,
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_834,plain,
( multiplicative_identity = B
| ~ sum(A,inverse(A),B) ),
inference(resolve,[status(thm)],[c_21,c_18]) ).
cnf(c_835,plain,
multiplicative_identity = inverse(additive_identity),
inference(resolve,[status(thm)],[c_834,c_5]) ).
cnf(c_836,plain,
inverse(additive_identity) = multiplicative_identity,
inference(copy,[status(thm)],[c_835]) ).
cnf(c_833,plain,
$false,
inference(resolve,[status(thm)],[c_23,c_836]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41 % Computer : n016.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sat Sep 26 22:40:02 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.42 % Process 1888885 was started by sandbox on n016,
% 0.13/0.42 % Sat Sep 26 22:40:02 2026
% 0.13/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.42
% 0.13/0.42 % From the command line: assign(max_seconds, 300).
% 0.13/0.51
% 0.13/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.51
% 0.13/0.51 % Proof 1 at 0.06 (+ 0.03) seconds.
% 0.13/0.51 % Length of proof is 5.
% 0.13/0.51 % Level of proof is 1.
% 0.13/0.51 % Maximum clause weight is 16.000.
% 0.13/0.51 % Given clauses 21.
% 0.13/0.51
% 0.13/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------