%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG040-2 : 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 : n004.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 08:26:28 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 17 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 33 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_of_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_of_addition) ).
cnf(c_9,plain,
( sum(B,A,C)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_of_addition]) ).
fof(distributivity1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( sum(VAR_2,VAR_4,VAR_6)
| ~ product(VAR_0,VAR_5,VAR_6)
| ~ sum(VAR_1,VAR_3,VAR_5)
| ~ product(VAR_0,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity1) ).
cnf(c_12,plain,
( sum(C,E,V6)
| ~ product(A,F,V6)
| ~ sum(B,D,F)
| ~ product(A,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity1]) ).
fof(product_symmetry,axiom,
! [VAR_0,VAR_1,VAR_2] :
( product(VAR_1,VAR_0,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_symmetry) ).
cnf(c_22,plain,
( product(B,A,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_symmetry]) ).
fof(b_plus_c,axiom,
sum(b,c,d),
file('theBenchmark.p',b_plus_c) ).
cnf(c_23,plain,
sum(b,c,d),
inference(clausify,[status(thm)],[b_plus_c]) ).
fof(d_plus_a,axiom,
product(d,a,additive_identity),
file('theBenchmark.p',d_plus_a) ).
cnf(c_24,plain,
product(d,a,additive_identity),
inference(clausify,[status(thm)],[d_plus_a]) ).
fof(b_plus_a,axiom,
product(b,a,l),
file('theBenchmark.p',b_plus_a) ).
cnf(c_25,plain,
product(b,a,l),
inference(clausify,[status(thm)],[b_plus_a]) ).
fof(c_plus_a,axiom,
product(c,a,n),
file('theBenchmark.p',c_plus_a) ).
cnf(c_26,plain,
product(c,a,n),
inference(clausify,[status(thm)],[c_plus_a]) ).
fof(prove_equation,axiom,
~ sum(l,n,additive_identity),
file('theBenchmark.p',prove_equation) ).
cnf(c_27,plain,
~ sum(l,n,additive_identity),
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_162,plain,
sum(c,b,d),
inference(resolve,[status(thm)],[c_23,c_9]) ).
cnf(c_169,plain,
product(a,d,additive_identity),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_177,plain,
product(a,b,l),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_185,plain,
product(a,c,n),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_196,plain,
~ sum(n,l,additive_identity),
inference(resolve,[status(thm)],[c_9,c_27]) ).
cnf(c_355,plain,
( sum(B,l,D)
| ~ product(a,C,D)
| ~ sum(A,b,C)
| ~ product(a,A,B) ),
inference(resolve,[status(thm)],[c_12,c_177]) ).
cnf(c_356,plain,
( sum(A,l,B)
| ~ product(a,d,B)
| ~ product(a,c,A) ),
inference(resolve,[status(thm)],[c_355,c_162]) ).
cnf(c_357,plain,
( sum(A,l,additive_identity)
| ~ product(a,c,A) ),
inference(resolve,[status(thm)],[c_356,c_169]) ).
cnf(c_358,plain,
~ product(a,c,n),
inference(resolve,[status(thm)],[c_357,c_196]) ).
cnf(c_354,plain,
$false,
inference(resolve,[status(thm)],[c_185,c_358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG040-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 05:51:23 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 957226 was started by sandbox on n004,
% 0.09/0.36 % Sat Sep 26 05:51:23 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.41
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.41
% 0.13/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.41 % Length of proof is 14.
% 0.13/0.41 % Level of proof is 2.
% 0.13/0.41 % Maximum clause weight is 25.000.
% 0.13/0.41 % Given clauses 50.
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------