%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG001-4 : 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 : n010.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 2.28s 0.80s
% Output : CNFRefutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 19 unt; 0 def)
% Number of atoms : 107 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 130 ( 67 ~; 63 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 150 ( 2 sgn 41 !; 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(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_4,plain,
sum(A,B,add(A,B)),
inference(clausify,[status(thm)],[closure_of_addition]) ).
fof(commutativity_of_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( sum(VAR_1,VAR_0,VAR_2)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_of_addition) ).
cnf(c_9,plain,
( sum(B,A,C)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_of_addition]) ).
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_12,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_13,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(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(distributivity4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( product(VAR_5,VAR_1,VAR_6)
| ~ sum(VAR_2,VAR_4,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',distributivity4) ).
cnf(c_15,plain,
( product(F,B,V6)
| ~ sum(C,E,V6)
| ~ sum(A,D,F)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity4]) ).
fof(cancellation2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_3
| ~ sum(VAR_3,VAR_1,VAR_2)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cancellation2) ).
cnf(c_19,plain,
( A = D
| ~ sum(D,B,C)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[cancellation2]) ).
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_20,plain,
~ product(a,additive_identity,additive_identity),
inference(clausify,[status(thm)],[prove_a_times_additive_id_is_additive_id]) ).
cnf(c_92,plain,
sum(A,B,add(B,A)),
inference(resolve,[status(thm)],[c_9,c_4]) ).
cnf(c_890,plain,
( sum(multiply(A,D),C,F)
| ~ product(A,E,F)
| ~ sum(D,B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_12,c_3]) ).
cnf(c_891,plain,
( sum(multiply(D,A),multiply(D,B),E)
| ~ product(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_890,c_3]) ).
cnf(c_892,plain,
( sum(multiply(A,B),multiply(A,additive_identity),C)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_891,c_2]) ).
cnf(c_98,plain,
sum(multiply(A,B),multiply(A,additive_identity),multiply(A,B)),
inference(resolve,[status(thm)],[c_892,c_3]) ).
cnf(c_893,plain,
( product(A,E,F)
| ~ sum(multiply(A,D),C,F)
| ~ sum(D,B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_13,c_3]) ).
cnf(c_894,plain,
( product(D,C,E)
| ~ sum(multiply(D,A),multiply(D,B),E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_893,c_3]) ).
cnf(c_895,plain,
( product(A,B,C)
| ~ sum(multiply(A,B),multiply(A,additive_identity),C) ),
inference(resolve,[status(thm)],[c_894,c_2]) ).
cnf(c_130,plain,
~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity),
inference(resolve,[status(thm)],[c_895,c_20]) ).
cnf(c_896,plain,
( sum(multiply(D,B),C,F)
| ~ product(E,B,F)
| ~ sum(D,A,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_897,plain,
( sum(multiply(A,D),multiply(B,D),E)
| ~ product(C,D,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_896,c_3]) ).
cnf(c_898,plain,
( sum(multiply(A,C),multiply(B,C),D)
| ~ product(add(A,B),C,D) ),
inference(resolve,[status(thm)],[c_897,c_4]) ).
cnf(c_224,plain,
~ product(add(a,a),additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_898,c_130]) ).
cnf(c_899,plain,
( additive_identity = A
| ~ sum(A,B,B) ),
inference(resolve,[status(thm)],[c_19,c_1]) ).
cnf(c_900,plain,
additive_identity = multiply(A,additive_identity),
inference(resolve,[status(thm)],[c_899,c_98]) ).
cnf(c_886,plain,
multiply(A,additive_identity) = additive_identity,
inference(copy,[status(thm)],[c_900]) ).
cnf(c_901,plain,
( product(E,B,F)
| ~ sum(multiply(D,B),C,F)
| ~ sum(D,A,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_902,plain,
( product(C,D,E)
| ~ sum(multiply(A,D),multiply(B,D),E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_901,c_3]) ).
cnf(c_903,plain,
( product(add(C,A),B,D)
| ~ sum(multiply(A,B),multiply(C,B),D) ),
inference(resolve,[status(thm)],[c_902,c_92]) ).
cnf(c_904,plain,
product(add(A,A),additive_identity,multiply(A,additive_identity)),
inference(resolve,[status(thm)],[c_903,c_98]) ).
cnf(c_888,plain,
product(add(A,A),additive_identity,additive_identity),
inference(paramod,[status(thm)],[c_886,c_904]) ).
cnf(c_889,plain,
$false,
inference(resolve,[status(thm)],[c_888,c_224]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG001-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n010.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 05:43:30 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2607887 was started by sandbox2 on n010,
% 0.17/0.43 % Sat Sep 26 05:43:30 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 2.28/0.80
% 2.28/0.80 % SZS status Unsatisfiable for theBenchmark
% 2.28/0.80
% 2.28/0.80 % Proof 1 at 0.24 (+ 0.11) seconds.
% 2.28/0.80 % Length of proof is 18.
% 2.28/0.80 % Level of proof is 4.
% 2.28/0.80 % Maximum clause weight is 25.000.
% 2.28/0.80 % Given clauses 45.
% 2.28/0.80
% 2.28/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------