%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG002-1 : 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 : n003.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 08:26:17 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 15 unt; 0 def)
% Number of atoms : 49 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 28 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 48 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity1,axiom,
! [VAR_0] : sum(additive_identity,VAR_0,VAR_0),
file('theBenchmark.p',additive_identity1) ).
cnf(c_1,plain,
sum(additive_identity,A,A),
inference(clausify,[status(thm)],[additive_identity1]) ).
fof(left_inverse,axiom,
! [VAR_0] : sum(additive_inverse(VAR_0),VAR_0,additive_identity),
file('theBenchmark.p',left_inverse) ).
cnf(c_5,plain,
sum(additive_inverse(A),A,additive_identity),
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity_of_addition1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( sum(VAR_0,VAR_4,VAR_5)
| ~ sum(VAR_2,VAR_3,VAR_5)
| ~ sum(VAR_1,VAR_3,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_addition1) ).
cnf(c_7,plain,
( sum(A,E,F)
| ~ sum(C,D,F)
| ~ sum(B,D,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_addition1]) ).
fof(associativity_of_addition2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( sum(VAR_2,VAR_3,VAR_5)
| ~ sum(VAR_0,VAR_4,VAR_5)
| ~ sum(VAR_1,VAR_3,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_addition2) ).
cnf(c_8,plain,
( sum(C,D,F)
| ~ sum(A,E,F)
| ~ sum(B,D,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_addition2]) ).
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_16,plain,
( C = D
| ~ sum(A,B,D)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[addition_is_well_defined]) ).
fof(a_plus_b_is_d,axiom,
sum(a,b,d),
file('theBenchmark.p',a_plus_b_is_d) ).
cnf(c_18,plain,
sum(a,b,d),
inference(clausify,[status(thm)],[a_plus_b_is_d]) ).
fof(a_plus_c_is_d,axiom,
sum(a,c,d),
file('theBenchmark.p',a_plus_c_is_d) ).
cnf(c_19,plain,
sum(a,c,d),
inference(clausify,[status(thm)],[a_plus_c_is_d]) ).
fof(prove_b_equals_c,axiom,
b != c,
file('theBenchmark.p',prove_b_equals_c) ).
cnf(c_20,plain,
b != c,
inference(clausify,[status(thm)],[prove_b_equals_c]) ).
cnf(c_21,plain,
c != b,
inference(copy,[status(thm)],[c_20]) ).
cnf(c_386,plain,
( sum(additive_inverse(A),C,D)
| ~ sum(additive_identity,B,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_387,plain,
( sum(additive_inverse(a),d,A)
| ~ sum(additive_identity,c,A) ),
inference(resolve,[status(thm)],[c_386,c_19]) ).
cnf(c_169,plain,
sum(additive_inverse(a),d,c),
inference(resolve,[status(thm)],[c_387,c_1]) ).
cnf(c_388,plain,
( B = A
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_16,c_1]) ).
cnf(c_178,plain,
~ sum(additive_identity,b,c),
inference(resolve,[status(thm)],[c_388,c_21]) ).
cnf(c_389,plain,
( sum(additive_identity,B,D)
| ~ sum(additive_inverse(A),C,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_390,plain,
( sum(additive_identity,b,A)
| ~ sum(additive_inverse(a),d,A) ),
inference(resolve,[status(thm)],[c_389,c_18]) ).
cnf(c_391,plain,
~ sum(additive_inverse(a),d,c),
inference(resolve,[status(thm)],[c_390,c_178]) ).
cnf(c_385,plain,
$false,
inference(resolve,[status(thm)],[c_169,c_391]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.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 : Sat Sep 26 05:45:08 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2156488 was started by sandbox on n003,
% 0.10/0.36 % Sat Sep 26 05:45:08 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.39
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.39
% 0.12/0.39 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.12/0.39 % Length of proof is 12.
% 0.12/0.39 % Level of proof is 3.
% 0.12/0.39 % Maximum clause weight is 21.000.
% 0.12/0.39 % Given clauses 24.
% 0.12/0.39
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------