%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG038-2 : 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 : n011.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 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 3 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity2,axiom,
! [VAR_0] : sum(VAR_0,additive_identity,VAR_0),
file('theBenchmark.p',additive_identity2) ).
cnf(c_10,plain,
sum(A,additive_identity,A),
inference(clausify,[status(thm)],[additive_identity2]) ).
fof(addition_is_well_defined,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(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_23,plain,
( equalish(C,D)
| ~ sum(A,B,D)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[addition_is_well_defined]) ).
fof(multiplication_is_well_defined,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',multiplication_is_well_defined) ).
cnf(c_24,plain,
( equalish(C,D)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[multiplication_is_well_defined]) ).
fof(multiplicative_identity1,axiom,
! [VAR_0] : product(additive_identity,VAR_0,additive_identity),
file('theBenchmark.p',multiplicative_identity1) ).
cnf(c_25,plain,
product(additive_identity,A,additive_identity),
inference(clausify,[status(thm)],[multiplicative_identity1]) ).
fof(some_property,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,h(VAR_0,VAR_1),VAR_1)
| ~ equalish(VAR_0,additive_identity) ),
file('theBenchmark.p',some_property) ).
cnf(c_27,plain,
( product(A,h(A,B),B)
| ~ equalish(A,additive_identity) ),
inference(clausify,[status(thm)],[some_property]) ).
fof(a_not_additive_identity,axiom,
~ equalish(a,additive_identity),
file('theBenchmark.p',a_not_additive_identity) ).
cnf(c_29,plain,
~ equalish(a,additive_identity),
inference(clausify,[status(thm)],[a_not_additive_identity]) ).
cnf(c_453,plain,
( equalish(A,B)
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_23,c_10]) ).
cnf(c_80,plain,
equalish(A,A),
inference(resolve,[status(thm)],[c_453,c_10]) ).
cnf(c_454,plain,
( equalish(B,additive_identity)
| ~ product(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_24,c_25]) ).
cnf(c_224,plain,
~ product(additive_identity,A,a),
inference(resolve,[status(thm)],[c_454,c_29]) ).
cnf(c_455,plain,
~ equalish(additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_224,c_27]) ).
cnf(c_452,plain,
$false,
inference(resolve,[status(thm)],[c_80,c_455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG038-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.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 05:51:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3932337 was started by sandbox on n011,
% 0.09/0.37 % Sat Sep 26 05:51:14 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.42
% 0.13/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.42
% 0.13/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.42 % Length of proof is 9.
% 0.13/0.42 % Level of proof is 2.
% 0.13/0.42 % Maximum clause weight is 19.000.
% 0.13/0.42 % Given clauses 36.
% 0.13/0.42
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------