%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG001-3 : 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 : n014.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 0.08s 0.42s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 16 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 121 ( 63 ~; 58 |; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 136 ( 0 sgn 30 !; 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_inverse1,axiom,
! [VAR_0] : sum(additive_inverse(VAR_0),VAR_0,additive_identity),
file('theBenchmark.p',additive_inverse1) ).
cnf(c_2,plain,
sum(additive_inverse(A),A,additive_identity),
inference(clausify,[status(thm)],[additive_inverse1]) ).
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_3,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(associativity_of_addition2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( sum(VAR_2,VAR_3,VAR_5)
| ~ sum(VAR_0,VAR_4,VAR_5)
| ~ sum(VAR_1,VAR_3,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_addition2) ).
cnf(c_4,plain,
( sum(C,D,F)
| ~ sum(A,E,F)
| ~ sum(B,D,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_addition2]) ).
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_5,plain,
product(A,B,multiply(A,B)),
inference(clausify,[status(thm)],[closure_of_multiplication]) ).
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_6,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(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(prove_a_times_additive_id_is_additive_id,axiom,
~ product(a,additive_identity,additive_identity),
file('theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).
cnf(c_8,plain,
~ product(a,additive_identity,additive_identity),
inference(clausify,[status(thm)],[prove_a_times_additive_id_is_additive_id]) ).
cnf(c_143,plain,
( sum(additive_inverse(A),C,D)
| ~ sum(additive_identity,B,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_144,plain,
( sum(additive_inverse(additive_inverse(A)),additive_identity,B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_143,c_2]) ).
cnf(c_9,plain,
sum(additive_inverse(additive_inverse(A)),additive_identity,A),
inference(resolve,[status(thm)],[c_144,c_1]) ).
cnf(c_145,plain,
( sum(multiply(A,D),C,F)
| ~ product(A,E,F)
| ~ sum(D,B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_146,plain,
( sum(multiply(D,A),multiply(D,B),E)
| ~ product(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_145,c_5]) ).
cnf(c_147,plain,
( sum(multiply(A,additive_inverse(C)),multiply(A,C),B)
| ~ product(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_146,c_2]) ).
cnf(c_11,plain,
sum(multiply(A,additive_inverse(B)),multiply(A,B),multiply(A,additive_identity)),
inference(resolve,[status(thm)],[c_147,c_5]) ).
cnf(c_148,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_5]) ).
cnf(c_149,plain,
( product(D,C,E)
| ~ sum(multiply(D,A),multiply(D,B),E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_148,c_5]) ).
cnf(c_150,plain,
( product(A,additive_identity,C)
| ~ sum(multiply(A,additive_inverse(B)),multiply(A,B),C) ),
inference(resolve,[status(thm)],[c_149,c_2]) ).
cnf(c_16,plain,
~ sum(multiply(a,additive_inverse(A)),multiply(a,A),additive_identity),
inference(resolve,[status(thm)],[c_150,c_8]) ).
cnf(c_151,plain,
( sum(C,A,D)
| ~ sum(additive_inverse(additive_inverse(C)),B,D)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_4,c_9]) ).
cnf(c_152,plain,
( sum(A,B,C)
| ~ sum(additive_inverse(additive_inverse(A)),B,C) ),
inference(resolve,[status(thm)],[c_151,c_1]) ).
cnf(c_19,plain,
sum(A,additive_identity,A),
inference(resolve,[status(thm)],[c_152,c_9]) ).
cnf(c_153,plain,
( sum(multiply(A,D),C,F)
| ~ product(A,E,F)
| ~ sum(D,B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_154,plain,
( sum(multiply(D,A),multiply(D,B),E)
| ~ product(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_153,c_5]) ).
cnf(c_155,plain,
( sum(multiply(A,B),multiply(A,additive_identity),C)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_154,c_19]) ).
cnf(c_60,plain,
sum(multiply(A,B),multiply(A,additive_identity),multiply(A,B)),
inference(resolve,[status(thm)],[c_155,c_5]) ).
cnf(c_156,plain,
( sum(A,B,D)
| ~ sum(additive_identity,C,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_157,plain,
( sum(multiply(A,additive_inverse(C)),multiply(A,C),B)
| ~ sum(additive_identity,multiply(A,additive_identity),B) ),
inference(resolve,[status(thm)],[c_156,c_11]) ).
cnf(c_114,plain,
~ sum(additive_identity,multiply(a,additive_identity),additive_identity),
inference(resolve,[status(thm)],[c_157,c_16]) ).
cnf(c_158,plain,
( sum(additive_identity,B,D)
| ~ sum(additive_inverse(A),C,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_159,plain,
( sum(additive_identity,B,additive_identity)
| ~ sum(A,B,A) ),
inference(resolve,[status(thm)],[c_158,c_2]) ).
cnf(c_141,plain,
~ sum(A,multiply(a,additive_identity),A),
inference(resolve,[status(thm)],[c_159,c_114]) ).
cnf(c_142,plain,
$false,
inference(resolve,[status(thm)],[c_141,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 05:43:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2291095 was started by sandbox2 on n014,
% 0.08/0.36 % Sat Sep 26 05:43:02 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.42
% 0.08/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.42
% 0.08/0.42 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.08/0.42 % Length of proof is 16.
% 0.08/0.42 % Level of proof is 4.
% 0.08/0.42 % Maximum clause weight is 20.000.
% 0.08/0.42 % Given clauses 20.
% 0.08/0.42
% 0.08/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------