%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG038-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 0.16s 0.54s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 20 unt; 0 def)
% Number of atoms : 68 ( 11 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 70 ( 38 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 79 ( 2 sgn 25 !; 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(additive_identity2,axiom,
! [VAR_0] : sum(VAR_0,additive_identity,VAR_0),
file('theBenchmark.p',additive_identity2) ).
cnf(c_2,plain,
sum(A,additive_identity,A),
inference(clausify,[status(thm)],[additive_identity2]) ).
fof(closure_of_multiplication,axiom,
! [VAR_0,VAR_1] : product(VAR_0,VAR_1,multiply(VAR_0,VAR_1)),
file('theBenchmark.p',closure_of_multiplication) ).
cnf(c_3,plain,
product(A,B,multiply(A,B)),
inference(clausify,[status(thm)],[closure_of_multiplication]) ).
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(right_inverse,axiom,
! [VAR_0] : sum(VAR_0,additive_inverse(VAR_0),additive_identity),
file('theBenchmark.p',right_inverse) ).
cnf(c_6,plain,
sum(A,additive_inverse(A),additive_identity),
inference(clausify,[status(thm)],[right_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(distributivity3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( sum(VAR_2,VAR_4,VAR_6)
| ~ product(VAR_5,VAR_1,VAR_6)
| ~ sum(VAR_0,VAR_3,VAR_5)
| ~ product(VAR_3,VAR_1,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity3) ).
cnf(c_14,plain,
( sum(C,E,V6)
| ~ product(F,B,V6)
| ~ sum(A,D,F)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity3]) ).
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(some_property,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,h(VAR_0,VAR_1),VAR_1)
| VAR_0 != additive_identity ),
file('theBenchmark.p',some_property) ).
cnf(c_18,plain,
( product(A,h(A,B),B)
| A != additive_identity ),
inference(clausify,[status(thm)],[some_property]) ).
cnf(c_19,plain,
( product(A,h(A,B),B)
| additive_identity != A ),
inference(copy,[status(thm)],[c_18]) ).
fof(a_not_additive_identity,axiom,
a != additive_identity,
file('theBenchmark.p',a_not_additive_identity) ).
cnf(c_21,plain,
a != additive_identity,
inference(clausify,[status(thm)],[a_not_additive_identity]) ).
cnf(c_329,plain,
( additive_identity = B
| ~ sum(A,additive_inverse(A),B) ),
inference(resolve,[status(thm)],[c_16,c_6]) ).
cnf(c_330,plain,
additive_identity = additive_inverse(additive_identity),
inference(resolve,[status(thm)],[c_329,c_1]) ).
cnf(c_191,plain,
additive_inverse(additive_identity) = additive_identity,
inference(copy,[status(thm)],[c_330]) ).
cnf(c_196,plain,
product(additive_identity,h(additive_identity,A),A),
inference(xxres,[status(thm)],[c_19]) ).
cnf(c_331,plain,
( A = B
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_16,c_2]) ).
cnf(c_237,plain,
~ sum(a,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_331,c_21]) ).
cnf(c_332,plain,
( sum(A,additive_identity,D)
| ~ sum(C,additive_inverse(B),D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_333,plain,
( sum(A,additive_identity,additive_identity)
| ~ sum(A,B,B) ),
inference(resolve,[status(thm)],[c_332,c_6]) ).
cnf(c_262,plain,
~ sum(a,A,A),
inference(resolve,[status(thm)],[c_333,c_237]) ).
cnf(c_334,plain,
( sum(C,multiply(D,B),F)
| ~ product(E,B,F)
| ~ sum(A,D,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_335,plain,
( sum(C,multiply(A,B),D)
| ~ product(additive_identity,B,D)
| ~ product(additive_inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_334,c_5]) ).
cnf(c_336,plain,
( sum(C,multiply(A,B),multiply(additive_identity,B))
| ~ product(additive_inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_335,c_3]) ).
cnf(c_337,plain,
~ product(additive_inverse(additive_identity),A,a),
inference(resolve,[status(thm)],[c_336,c_262]) ).
cnf(c_327,plain,
~ product(additive_identity,A,a),
inference(paramod,[status(thm)],[c_191,c_337]) ).
cnf(c_328,plain,
$false,
inference(resolve,[status(thm)],[c_327,c_196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG038-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n011.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 05:50:44 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.45 % Process 3930123 was started by sandbox2 on n011,
% 0.16/0.45 % Sat Sep 26 05:50:44 2026
% 0.16/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.54
% 0.16/0.54 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (10).
% 0.16/0.54
% 0.16/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.54
% 0.16/0.54 % Proof 1 at 0.05 (+ 0.03) seconds.
% 0.16/0.54 % Length of proof is 17.
% 0.16/0.54 % Level of proof is 4.
% 0.16/0.54 % Maximum clause weight is 25.000.
% 0.16/0.54 % Given clauses 42.
% 0.16/0.54
% 0.16/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------