%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD054-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 07:11:38 AM UTC 2026
% Result : Unsatisfiable 12.08s 2.10s
% Output : CNFRefutation 12.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of formulae : 95 ( 51 unt; 0 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 187 ( 106 ~; 81 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 125 ( 7 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_addition_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ sum(VAR_3,VAR_5,VAR_2)
| ~ sum(VAR_4,VAR_1,VAR_5)
| ~ sum(VAR_3,VAR_4,VAR_0)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_addition_2) ).
cnf(c_2,plain,
( ~ sum(D,F,C)
| ~ sum(E,B,F)
| ~ sum(D,E,A)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_addition_2]) ).
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_identity,VAR_0,VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_3,plain,
( ~ defined(A)
| sum(additive_identity,A,A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(existence_of_inverse_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_inverse(VAR_0),VAR_0,additive_identity) ),
file('theBenchmark.p',existence_of_inverse_addition) ).
cnf(c_4,plain,
( ~ defined(A)
| sum(additive_inverse(A),A,additive_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_addition]) ).
fof(commutativity_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_addition) ).
cnf(c_5,plain,
( ~ sum(B,A,C)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_addition]) ).
fof(associativity_multiplication_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ product(VAR_4,VAR_5,VAR_2)
| ~ product(VAR_3,VAR_5,VAR_1)
| ~ product(VAR_0,VAR_3,VAR_4)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_multiplication_1) ).
cnf(c_6,plain,
( ~ product(E,F,C)
| ~ product(D,F,B)
| ~ product(A,D,E)
| product(A,B,C) ),
inference(clausify,[status(thm)],[associativity_multiplication_1]) ).
fof(existence_of_identity_multiplication,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| product(multiplicative_identity,VAR_0,VAR_0) ),
file('theBenchmark.p',existence_of_identity_multiplication) ).
cnf(c_8,plain,
( ~ defined(A)
| product(multiplicative_identity,A,A) ),
inference(clausify,[status(thm)],[existence_of_identity_multiplication]) ).
fof(existence_of_inverse_multiplication,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_identity,VAR_0,additive_identity)
| product(multiplicative_inverse(VAR_0),VAR_0,multiplicative_identity) ),
file('theBenchmark.p',existence_of_inverse_multiplication) ).
cnf(c_9,plain,
( ~ defined(A)
| sum(additive_identity,A,additive_identity)
| product(multiplicative_inverse(A),A,multiplicative_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_multiplication]) ).
fof(commutativity_multiplication,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ product(VAR_1,VAR_0,VAR_2)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_multiplication) ).
cnf(c_10,plain,
( ~ product(B,A,C)
| product(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_multiplication]) ).
fof(distributivity_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( ~ product(VAR_4,VAR_6,VAR_1)
| ~ product(VAR_3,VAR_6,VAR_0)
| ~ product(VAR_5,VAR_6,VAR_2)
| ~ sum(VAR_3,VAR_4,VAR_5)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity_1) ).
cnf(c_11,plain,
( ~ product(E,V6,B)
| ~ product(D,V6,A)
| ~ product(F,V6,C)
| ~ sum(D,E,F)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[distributivity_1]) ).
fof(distributivity_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( ~ sum(VAR_5,VAR_6,VAR_2)
| ~ product(VAR_4,VAR_1,VAR_6)
| ~ product(VAR_3,VAR_1,VAR_5)
| ~ sum(VAR_3,VAR_4,VAR_0)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity_2) ).
cnf(c_12,plain,
( ~ sum(F,V6,C)
| ~ product(E,B,V6)
| ~ product(D,B,F)
| ~ sum(D,E,A)
| product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity_2]) ).
fof(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('theBenchmark.p',well_definedness_of_additive_identity) ).
cnf(c_14,plain,
defined(additive_identity),
inference(clausify,[status(thm)],[well_definedness_of_additive_identity]) ).
fof(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_27,plain,
defined(a),
inference(clausify,[status(thm)],[a_is_defined]) ).
fof(b_is_defined,axiom,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_28,plain,
defined(b),
inference(clausify,[status(thm)],[b_is_defined]) ).
fof(u_is_defined,axiom,
defined(u),
file('theBenchmark.p',u_is_defined) ).
cnf(c_29,plain,
defined(u),
inference(clausify,[status(thm)],[u_is_defined]) ).
fof(l_is_defined,axiom,
defined(l),
file('theBenchmark.p',l_is_defined) ).
cnf(c_31,plain,
defined(l),
inference(clausify,[status(thm)],[l_is_defined]) ).
fof(not_sum_6,axiom,
~ sum(additive_identity,a,additive_identity),
file('theBenchmark.p',not_sum_6) ).
cnf(c_32,plain,
~ sum(additive_identity,a,additive_identity),
inference(clausify,[status(thm)],[not_sum_6]) ).
fof(not_sum_7,axiom,
~ sum(additive_identity,b,additive_identity),
file('theBenchmark.p',not_sum_7) ).
cnf(c_33,plain,
~ sum(additive_identity,b,additive_identity),
inference(clausify,[status(thm)],[not_sum_7]) ).
fof(sum_8,axiom,
sum(multiplicative_inverse(a),multiplicative_inverse(b),u),
file('theBenchmark.p',sum_8) ).
cnf(c_34,plain,
sum(multiplicative_inverse(a),multiplicative_inverse(b),u),
inference(clausify,[status(thm)],[sum_8]) ).
fof(sum_9,axiom,
sum(a,b,k),
file('theBenchmark.p',sum_9) ).
cnf(c_35,plain,
sum(a,b,k),
inference(clausify,[status(thm)],[sum_9]) ).
fof(product_10,axiom,
product(a,b,l),
file('theBenchmark.p',product_10) ).
cnf(c_36,plain,
product(a,b,l),
inference(clausify,[status(thm)],[product_10]) ).
fof(not_product_11,axiom,
~ product(k,multiplicative_inverse(l),u),
file('theBenchmark.p',not_product_11) ).
cnf(c_37,plain,
~ product(k,multiplicative_inverse(l),u),
inference(clausify,[status(thm)],[not_product_11]) ).
cnf(c_40,plain,
( ~ sum(D,B,D)
| ~ sum(C,D,A)
| sum(A,B,A) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_46,plain,
( ~ product(D,E,B)
| ~ product(C,E,A)
| ~ sum(C,D,C)
| sum(A,B,A) ),
inference(factor,[status(thm)],[c_11]) ).
cnf(c_59,plain,
( ~ product(B,C,A)
| ~ sum(B,B,B)
| sum(A,A,A) ),
inference(factor,[status(thm)],[c_46]) ).
cnf(c_64,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_66,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_11753,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_27,c_9]) ).
cnf(c_103,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(resolve,[status(thm)],[c_32,c_11753]) ).
cnf(c_104,plain,
product(multiplicative_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_8]) ).
cnf(c_105,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_11754,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_28,c_9]) ).
cnf(c_119,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(resolve,[status(thm)],[c_33,c_11754]) ).
cnf(c_120,plain,
product(multiplicative_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_8]) ).
cnf(c_136,plain,
product(multiplicative_identity,u,u),
inference(resolve,[status(thm)],[c_29,c_8]) ).
cnf(c_167,plain,
( sum(additive_identity,l,additive_identity)
| product(multiplicative_inverse(l),l,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_31,c_9]) ).
cnf(c_168,plain,
product(multiplicative_identity,l,l),
inference(resolve,[status(thm)],[c_31,c_8]) ).
cnf(c_170,plain,
sum(additive_identity,l,l),
inference(resolve,[status(thm)],[c_31,c_3]) ).
cnf(c_176,plain,
sum(multiplicative_inverse(b),multiplicative_inverse(a),u),
inference(resolve,[status(thm)],[c_34,c_5]) ).
cnf(c_198,plain,
product(b,a,l),
inference(resolve,[status(thm)],[c_36,c_10]) ).
cnf(c_203,plain,
( ~ product(C,b,B)
| ~ product(A,a,C)
| product(A,l,B) ),
inference(resolve,[status(thm)],[c_36,c_6]) ).
cnf(c_208,plain,
~ product(multiplicative_inverse(l),k,u),
inference(resolve,[status(thm)],[c_10,c_37]) ).
cnf(c_275,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_64,c_10]) ).
cnf(c_399,plain,
product(a,multiplicative_identity,a),
inference(resolve,[status(thm)],[c_104,c_10]) ).
cnf(c_403,plain,
( ~ product(C,a,B)
| ~ product(A,C,multiplicative_identity)
| product(A,B,a) ),
inference(resolve,[status(thm)],[c_104,c_6]) ).
cnf(c_571,plain,
product(l,multiplicative_identity,l),
inference(resolve,[status(thm)],[c_168,c_10]) ).
cnf(c_11755,plain,
( ~ sum(B,a,B)
| ~ sum(A,B,additive_identity) ),
inference(resolve,[status(thm)],[c_40,c_32]) ).
cnf(c_1421,plain,
~ sum(a,a,a),
inference(resolve,[status(thm)],[c_11755,c_105]) ).
cnf(c_11756,plain,
( ~ product(A,B,a)
| ~ sum(A,A,A) ),
inference(resolve,[status(thm)],[c_59,c_1421]) ).
cnf(c_1473,plain,
~ product(additive_identity,A,a),
inference(resolve,[status(thm)],[c_11756,c_66]) ).
cnf(c_1641,plain,
~ product(A,additive_identity,a),
inference(resolve,[status(thm)],[c_10,c_1473]) ).
cnf(c_11757,plain,
( ~ product(C,D,a)
| ~ product(B,D,additive_identity)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_1641]) ).
cnf(c_11758,plain,
( ~ product(multiplicative_identity,A,a)
| ~ product(b,A,additive_identity) ),
inference(resolve,[status(thm)],[c_11757,c_119]) ).
cnf(c_1715,plain,
~ product(b,a,additive_identity),
inference(resolve,[status(thm)],[c_11758,c_104]) ).
cnf(c_11759,plain,
( ~ product(B,C,additive_identity)
| ~ product(A,C,a)
| ~ product(b,A,B) ),
inference(resolve,[status(thm)],[c_6,c_1715]) ).
cnf(c_11760,plain,
( ~ product(l,A,additive_identity)
| ~ product(a,A,a) ),
inference(resolve,[status(thm)],[c_11759,c_198]) ).
cnf(c_1770,plain,
~ product(l,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_11760,c_399]) ).
cnf(c_11761,plain,
( ~ sum(C,D,additive_identity)
| ~ product(B,multiplicative_identity,D)
| ~ product(A,multiplicative_identity,C)
| ~ sum(A,B,l) ),
inference(resolve,[status(thm)],[c_12,c_1770]) ).
cnf(c_11762,plain,
( ~ sum(A,B,additive_identity)
| ~ product(l,multiplicative_identity,B)
| ~ product(additive_identity,multiplicative_identity,A) ),
inference(resolve,[status(thm)],[c_11761,c_170]) ).
cnf(c_11763,plain,
( ~ sum(additive_identity,A,additive_identity)
| ~ product(l,multiplicative_identity,A) ),
inference(resolve,[status(thm)],[c_11762,c_275]) ).
cnf(c_1819,plain,
~ sum(additive_identity,l,additive_identity),
inference(resolve,[status(thm)],[c_11763,c_571]) ).
cnf(c_1820,plain,
product(multiplicative_inverse(l),l,multiplicative_identity),
inference(resolve,[status(thm)],[c_1819,c_167]) ).
cnf(c_2587,plain,
( ~ product(A,a,multiplicative_identity)
| product(A,l,b) ),
inference(resolve,[status(thm)],[c_203,c_120]) ).
cnf(c_2968,plain,
product(multiplicative_inverse(a),l,b),
inference(resolve,[status(thm)],[c_2587,c_103]) ).
cnf(c_11214,plain,
( ~ product(A,b,multiplicative_identity)
| product(A,l,a) ),
inference(resolve,[status(thm)],[c_403,c_198]) ).
cnf(c_11226,plain,
product(multiplicative_inverse(b),l,a),
inference(resolve,[status(thm)],[c_11214,c_119]) ).
cnf(c_11764,plain,
( ~ product(B,C,u)
| ~ product(A,C,k)
| ~ product(multiplicative_inverse(l),A,B) ),
inference(resolve,[status(thm)],[c_6,c_208]) ).
cnf(c_11765,plain,
( ~ product(multiplicative_identity,A,u)
| ~ product(l,A,k) ),
inference(resolve,[status(thm)],[c_11764,c_1820]) ).
cnf(c_11439,plain,
~ product(l,u,k),
inference(resolve,[status(thm)],[c_11765,c_136]) ).
cnf(c_11511,plain,
~ product(u,l,k),
inference(resolve,[status(thm)],[c_10,c_11439]) ).
cnf(c_11766,plain,
( ~ sum(C,D,k)
| ~ product(B,l,D)
| ~ product(A,l,C)
| ~ sum(A,B,u) ),
inference(resolve,[status(thm)],[c_12,c_11511]) ).
cnf(c_11767,plain,
( ~ sum(A,B,k)
| ~ product(multiplicative_inverse(a),l,B)
| ~ product(multiplicative_inverse(b),l,A) ),
inference(resolve,[status(thm)],[c_11766,c_176]) ).
cnf(c_11768,plain,
( ~ sum(A,b,k)
| ~ product(multiplicative_inverse(b),l,A) ),
inference(resolve,[status(thm)],[c_11767,c_2968]) ).
cnf(c_11769,plain,
~ product(multiplicative_inverse(b),l,a),
inference(resolve,[status(thm)],[c_11768,c_35]) ).
cnf(c_11752,plain,
$false,
inference(resolve,[status(thm)],[c_11226,c_11769]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD054-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.53 % Computer : n006.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.53 % CPULimit : 300
% 0.10/0.53 % WCLimit : 300
% 0.10/0.53 % DateTime : Sun Sep 27 02:31:20 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.53 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.53 % Process 2596378 was started by sandbox on n006,
% 0.10/0.53 % Sun Sep 27 02:31:20 2026
% 0.10/0.53 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.54
% 0.10/0.54 % From the command line: assign(max_seconds, 300).
% 12.08/2.10
% 12.08/2.10 % given #500 (W,wt=13): 1716 sum(additive_identity,A,additive_identity) | -sum(b,A,b). [resolve(121,a,40,b)].
% 12.08/2.10
% 12.08/2.10 % given #1000 (F,wt=15): 2966 -sum(additive_identity,additive_identity,multiplicative_inverse(b)). [ur(50,a,1708,a,c,275,a,d,66,a)].
% 12.08/2.10
% 12.08/2.10 % SZS status Unsatisfiable for theBenchmark
% 12.08/2.10
% 12.08/2.10 % Proof 1 at 1.32 (+ 0.22) seconds.
% 12.08/2.10 % Length of proof is 57.
% 12.08/2.10 % Level of proof is 11.
% 12.08/2.10 % Maximum clause weight is 25.000.
% 12.08/2.10 % Given clauses 1238.
% 12.08/2.10
% 12.08/2.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------