%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG001-2 : 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 : n012.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 08:26:16 AM UTC 2026
% Result : Unsatisfiable 50.07s 6.86s
% Output : CNFRefutation 50.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 16 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 89 ( 46 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 107 ( 3 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(theorem,axiom,
~ product(a,additive_identity,additive_identity),
file('theBenchmark.p',theorem) ).
cnf(c_4,plain,
~ product(a,additive_identity,additive_identity),
inference(clausify,[status(thm)],[theorem]) ).
fof(distributivity2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( product(VAR_0,VAR_5,VAR_6)
| ~ sum(VAR_2,VAR_4,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',distributivity2) ).
cnf(c_7,plain,
( product(A,F,V6)
| ~ sum(C,E,V6)
| ~ sum(B,D,F)
| ~ product(A,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity2]) ).
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_8,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(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_13,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(additive_inverse2,axiom,
! [VAR_0] : sum(VAR_0,additive_inverse(VAR_0),additive_identity),
file('theBenchmark.p',additive_inverse2) ).
cnf(c_14,plain,
sum(A,additive_inverse(A),additive_identity),
inference(clausify,[status(thm)],[additive_inverse2]) ).
fof(closure_of_addition,axiom,
! [VAR_0,VAR_1] : sum(VAR_0,VAR_1,add(VAR_0,VAR_1)),
file('theBenchmark.p',closure_of_addition) ).
cnf(c_16,plain,
sum(A,B,add(A,B)),
inference(clausify,[status(thm)],[closure_of_addition]) ).
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_17,plain,
product(A,B,multiply(A,B)),
inference(clausify,[status(thm)],[closure_of_multiplication]) ).
fof(additive_identity2,axiom,
! [VAR_0] : sum(VAR_0,additive_identity,VAR_0),
file('theBenchmark.p',additive_identity2) ).
cnf(c_18,plain,
sum(A,additive_identity,A),
inference(clausify,[status(thm)],[additive_identity2]) ).
cnf(c_39,plain,
( sum(A,D,D)
| ~ sum(B,C,D)
| ~ sum(A,B,B) ),
inference(factor,[status(thm)],[c_13]) ).
cnf(c_20104,plain,
( sum(A,C,D)
| ~ sum(additive_identity,B,D)
| ~ sum(additive_inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_13,c_14]) ).
cnf(c_20105,plain,
( sum(C,add(additive_inverse(C),A),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_20104,c_16]) ).
cnf(c_69,plain,
sum(A,add(additive_inverse(A),additive_inverse(additive_identity)),additive_identity),
inference(resolve,[status(thm)],[c_20105,c_14]) ).
cnf(c_20106,plain,
( sum(multiply(A,D),C,F)
| ~ product(A,E,F)
| ~ sum(D,B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_17]) ).
cnf(c_20107,plain,
( sum(multiply(D,A),multiply(D,B),E)
| ~ product(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_20106,c_17]) ).
cnf(c_20108,plain,
( sum(multiply(A,B),multiply(A,additive_identity),C)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_20107,c_18]) ).
cnf(c_132,plain,
sum(multiply(A,B),multiply(A,additive_identity),multiply(A,B)),
inference(resolve,[status(thm)],[c_20108,c_17]) ).
cnf(c_20109,plain,
( product(A,E,F)
| ~ sum(multiply(A,D),C,F)
| ~ sum(D,B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_17]) ).
cnf(c_20110,plain,
( product(D,C,E)
| ~ sum(multiply(D,A),multiply(D,B),E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_20109,c_17]) ).
cnf(c_20111,plain,
( product(A,B,C)
| ~ sum(multiply(A,B),multiply(A,additive_identity),C) ),
inference(resolve,[status(thm)],[c_20110,c_18]) ).
cnf(c_139,plain,
~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity),
inference(resolve,[status(thm)],[c_20111,c_4]) ).
cnf(c_20112,plain,
( sum(multiply(A,additive_identity),C,C)
| ~ sum(multiply(A,additive_identity),B,C) ),
inference(resolve,[status(thm)],[c_39,c_132]) ).
cnf(c_19838,plain,
sum(multiply(A,additive_identity),additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_20112,c_69]) ).
cnf(c_20113,plain,
( sum(multiply(A,D),C,E)
| ~ sum(multiply(A,D),B,E)
| ~ sum(multiply(A,additive_identity),B,C) ),
inference(resolve,[status(thm)],[c_13,c_132]) ).
cnf(c_20114,plain,
( sum(multiply(A,B),multiply(A,additive_identity),C)
| ~ sum(multiply(A,B),additive_identity,C) ),
inference(resolve,[status(thm)],[c_20113,c_18]) ).
cnf(c_20102,plain,
sum(multiply(A,additive_identity),multiply(A,additive_identity),additive_identity),
inference(resolve,[status(thm)],[c_20114,c_19838]) ).
cnf(c_20103,plain,
$false,
inference(resolve,[status(thm)],[c_20102,c_139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.51 % Computer : n012.cluster.edu
% 0.03/0.51 % Model : x86_64 x86_64
% 0.03/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.51 % Memory : 8046.5625MB
% 0.03/0.51 % OS : Linux 6.8.0-71-generic
% 0.03/0.51 % CPULimit : 300
% 0.03/0.51 % WCLimit : 300
% 0.03/0.51 % DateTime : Sat Sep 26 05:42:50 UTC 2026
% 0.03/0.51 % CPUTime :
% 0.03/0.51 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.51 % Process 4017627 was started by sandbox2 on n012,
% 0.03/0.51 % Sat Sep 26 05:42:50 2026
% 0.03/0.51 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.52
% 0.03/0.52 % From the command line: assign(max_seconds, 300).
% 50.07/6.86
% 50.07/6.86 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (7).
% 50.07/6.86
% 50.07/6.86 % SZS status Unsatisfiable for theBenchmark
% 50.07/6.86
% 50.07/6.86 % Proof 1 at 4.68 (+ 1.64) seconds.
% 50.07/6.86 % Length of proof is 15.
% 50.07/6.86 % Level of proof is 4.
% 50.07/6.86 % Maximum clause weight is 25.000.
% 50.07/6.86 % Given clauses 183.
% 50.07/6.86
% 50.07/6.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------