%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD014-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 07:11:28 AM UTC 2026
% Result : Unsatisfiable 6.15s 1.18s
% Output : CNFRefutation 6.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 20 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 28 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 32 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_addition_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ sum(VAR_4,VAR_5,VAR_2)
| ~ sum(VAR_3,VAR_5,VAR_1)
| ~ sum(VAR_0,VAR_3,VAR_4)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_addition_1) ).
cnf(c_1,plain,
( ~ sum(E,F,C)
| ~ sum(D,F,B)
| ~ sum(A,D,E)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_addition_1]) ).
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_identity,VAR_0,VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_3,plain,
( ~ defined(A)
| sum(additive_identity,A,A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(existence_of_inverse_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_inverse(VAR_0),VAR_0,additive_identity) ),
file('theBenchmark.p',existence_of_inverse_addition) ).
cnf(c_4,plain,
( ~ defined(A)
| sum(additive_inverse(A),A,additive_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_addition]) ).
fof(commutativity_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ sum(VAR_1,VAR_0,VAR_2)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_addition) ).
cnf(c_5,plain,
( ~ sum(B,A,C)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_addition]) ).
fof(well_definedness_of_additive_inverse,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| defined(additive_inverse(VAR_0)) ),
file('theBenchmark.p',well_definedness_of_additive_inverse) ).
cnf(c_15,plain,
( ~ defined(A)
| defined(additive_inverse(A)) ),
inference(clausify,[status(thm)],[well_definedness_of_additive_inverse]) ).
fof(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_27,plain,
defined(a),
inference(clausify,[status(thm)],[a_is_defined]) ).
fof(b_is_defined,axiom,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_28,plain,
defined(b),
inference(clausify,[status(thm)],[b_is_defined]) ).
fof(sum_3,axiom,
sum(additive_identity,a,b),
file('theBenchmark.p',sum_3) ).
cnf(c_29,plain,
sum(additive_identity,a,b),
inference(clausify,[status(thm)],[sum_3]) ).
fof(not_sum_4,axiom,
~ sum(additive_identity,additive_inverse(a),additive_inverse(b)),
file('theBenchmark.p',not_sum_4) ).
cnf(c_30,plain,
~ sum(additive_identity,additive_inverse(a),additive_inverse(b)),
inference(clausify,[status(thm)],[not_sum_4]) ).
cnf(c_93,plain,
defined(additive_inverse(a)),
inference(resolve,[status(thm)],[c_27,c_15]) ).
cnf(c_98,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_109,plain,
defined(additive_inverse(b)),
inference(resolve,[status(thm)],[c_28,c_15]) ).
cnf(c_114,plain,
sum(additive_inverse(b),b,additive_identity),
inference(resolve,[status(thm)],[c_28,c_4]) ).
cnf(c_127,plain,
( ~ sum(C,a,B)
| ~ sum(A,additive_identity,C)
| sum(A,b,B) ),
inference(resolve,[status(thm)],[c_29,c_1]) ).
cnf(c_129,plain,
~ sum(additive_inverse(a),additive_identity,additive_inverse(b)),
inference(resolve,[status(thm)],[c_5,c_30]) ).
cnf(c_571,plain,
sum(additive_identity,additive_inverse(a),additive_inverse(a)),
inference(resolve,[status(thm)],[c_93,c_3]) ).
cnf(c_609,plain,
sum(additive_identity,additive_inverse(b),additive_inverse(b)),
inference(resolve,[status(thm)],[c_109,c_3]) ).
cnf(c_1985,plain,
sum(b,additive_inverse(b),additive_identity),
inference(resolve,[status(thm)],[c_114,c_5]) ).
cnf(c_4500,plain,
sum(additive_inverse(a),additive_identity,additive_inverse(a)),
inference(resolve,[status(thm)],[c_571,c_5]) ).
cnf(c_4563,plain,
( ~ sum(B,C,additive_inverse(b))
| ~ sum(A,C,additive_identity)
| ~ sum(additive_inverse(a),A,B) ),
inference(resolve,[status(thm)],[c_1,c_129]) ).
cnf(c_4564,plain,
( ~ sum(A,additive_inverse(b),additive_inverse(b))
| ~ sum(additive_inverse(a),b,A) ),
inference(resolve,[status(thm)],[c_4563,c_1985]) ).
cnf(c_4557,plain,
~ sum(additive_inverse(a),b,additive_identity),
inference(resolve,[status(thm)],[c_4564,c_609]) ).
cnf(c_4565,plain,
( ~ sum(A,a,additive_identity)
| ~ sum(additive_inverse(a),additive_identity,A) ),
inference(resolve,[status(thm)],[c_127,c_4557]) ).
cnf(c_4566,plain,
~ sum(additive_inverse(a),additive_identity,additive_inverse(a)),
inference(resolve,[status(thm)],[c_4565,c_98]) ).
cnf(c_4562,plain,
$false,
inference(resolve,[status(thm)],[c_4500,c_4566]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD014-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 02:23:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 529124 was started by sandbox2 on n010,
% 0.08/0.37 % Sun Sep 27 02:23:02 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 6.15/1.18
% 6.15/1.18 % given #500 (A,wt=21): 194 product(A,B,additive_identity) | -sum(C,D,A) | -product(C,B,additive_inverse(additive_identity)) | -product(D,B,additive_identity). [resolve(58,a,12,e)].
% 6.15/1.18
% 6.15/1.18 % SZS status Unsatisfiable for theBenchmark
% 6.15/1.18
% 6.15/1.18 % Proof 1 at 0.63 (+ 0.16) seconds.
% 6.15/1.18 % Length of proof is 21.
% 6.15/1.18 % Level of proof is 4.
% 6.15/1.18 % Maximum clause weight is 18.000.
% 6.15/1.18 % Given clauses 510.
% 6.15/1.18
% 6.15/1.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------