%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG001-5 : 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 : n018.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 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 15 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 71 ( 38 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(product_substitution3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_2,VAR_3,VAR_1)
| ~ product(VAR_2,VAR_3,VAR_0)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',product_substitution3) ).
cnf(c_12,plain,
( product(C,D,B)
| ~ product(C,D,A)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[product_substitution3]) ).
fof(additive_identity1,axiom,
! [VAR_0] : sum(additive_identity,VAR_0,VAR_0),
file('theBenchmark.p',additive_identity1) ).
cnf(c_13,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_14,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_15,plain,
product(A,B,multiply(A,B)),
inference(clausify,[status(thm)],[closure_of_multiplication]) ).
fof(right_inverse,axiom,
! [VAR_0] : sum(VAR_0,additive_inverse(VAR_0),additive_identity),
file('theBenchmark.p',right_inverse) ).
cnf(c_18,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_19,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(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_24,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(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_28,plain,
( equalish(C,D)
| ~ sum(A,B,D)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[addition_is_well_defined]) ).
fof(prove_multiplicative_identity_axiom,axiom,
~ product(a,additive_identity,additive_identity),
file('theBenchmark.p',prove_multiplicative_identity_axiom) ).
cnf(c_30,plain,
~ product(a,additive_identity,additive_identity),
inference(clausify,[status(thm)],[prove_multiplicative_identity_axiom]) ).
cnf(c_277,plain,
( sum(multiply(A,D),C,F)
| ~ product(A,E,F)
| ~ sum(D,B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_24,c_15]) ).
cnf(c_278,plain,
( sum(multiply(D,A),multiply(D,B),E)
| ~ product(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_277,c_15]) ).
cnf(c_279,plain,
( sum(multiply(A,additive_identity),multiply(A,B),C)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_278,c_13]) ).
cnf(c_109,plain,
sum(multiply(A,additive_identity),multiply(A,B),multiply(A,B)),
inference(resolve,[status(thm)],[c_279,c_15]) ).
cnf(c_280,plain,
( product(A,B,C)
| ~ equalish(multiply(A,B),C) ),
inference(resolve,[status(thm)],[c_12,c_15]) ).
cnf(c_152,plain,
~ equalish(multiply(a,additive_identity),additive_identity),
inference(resolve,[status(thm)],[c_280,c_30]) ).
cnf(c_281,plain,
( equalish(A,B)
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_28,c_14]) ).
cnf(c_230,plain,
~ sum(multiply(a,additive_identity),additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_281,c_152]) ).
cnf(c_282,plain,
( sum(A,additive_identity,D)
| ~ sum(C,additive_inverse(B),D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_19,c_18]) ).
cnf(c_283,plain,
( sum(A,additive_identity,additive_identity)
| ~ sum(A,B,B) ),
inference(resolve,[status(thm)],[c_282,c_18]) ).
cnf(c_275,plain,
~ sum(multiply(a,additive_identity),A,A),
inference(resolve,[status(thm)],[c_283,c_230]) ).
cnf(c_276,plain,
$false,
inference(resolve,[status(thm)],[c_275,c_109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 05:45:21 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 3854630 was started by sandbox2 on n018,
% 0.09/0.37 % Sat Sep 26 05:45:21 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.41
% 0.15/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.41
% 0.15/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.15/0.41 % Length of proof is 14.
% 0.15/0.41 % Level of proof is 4.
% 0.15/0.41 % Maximum clause weight is 20.000.
% 0.15/0.41 % Given clauses 35.
% 0.15/0.41
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------