%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD049-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 07:11:37 AM UTC 2026
% Result : Unsatisfiable 2.12s 0.78s
% Output : CNFRefutation 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 33 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 38 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 34 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_multiplication_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ product(VAR_3,VAR_5,VAR_2)
| ~ product(VAR_4,VAR_1,VAR_5)
| ~ product(VAR_3,VAR_4,VAR_0)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_multiplication_2) ).
cnf(c_7,plain,
( ~ product(D,F,C)
| ~ product(E,B,F)
| ~ product(D,E,A)
| product(A,B,C) ),
inference(clausify,[status(thm)],[associativity_multiplication_2]) ).
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(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(c_is_defined,axiom,
defined(c),
file('theBenchmark.p',c_is_defined) ).
cnf(c_29,plain,
defined(c),
inference(clausify,[status(thm)],[c_is_defined]) ).
fof(d_is_defined,axiom,
defined(d),
file('theBenchmark.p',d_is_defined) ).
cnf(c_30,plain,
defined(d),
inference(clausify,[status(thm)],[d_is_defined]) ).
fof(k_is_defined,axiom,
defined(k),
file('theBenchmark.p',k_is_defined) ).
cnf(c_31,plain,
defined(k),
inference(clausify,[status(thm)],[k_is_defined]) ).
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(not_sum_8,axiom,
~ sum(additive_identity,d,additive_identity),
file('theBenchmark.p',not_sum_8) ).
cnf(c_34,plain,
~ sum(additive_identity,d,additive_identity),
inference(clausify,[status(thm)],[not_sum_8]) ).
fof(product_9,axiom,
product(a,multiplicative_inverse(b),s),
file('theBenchmark.p',product_9) ).
cnf(c_35,plain,
product(a,multiplicative_inverse(b),s),
inference(clausify,[status(thm)],[product_9]) ).
fof(product_10,axiom,
product(c,multiplicative_inverse(d),s),
file('theBenchmark.p',product_10) ).
cnf(c_36,plain,
product(c,multiplicative_inverse(d),s),
inference(clausify,[status(thm)],[product_10]) ).
fof(product_11,axiom,
product(a,d,k),
file('theBenchmark.p',product_11) ).
cnf(c_37,plain,
product(a,d,k),
inference(clausify,[status(thm)],[product_11]) ).
fof(not_product_12,axiom,
~ product(b,c,k),
file('theBenchmark.p',not_product_12) ).
cnf(c_38,plain,
~ product(b,c,k),
inference(clausify,[status(thm)],[not_product_12]) ).
cnf(c_2539,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_28,c_9]) ).
cnf(c_120,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(resolve,[status(thm)],[c_33,c_2539]) ).
cnf(c_137,plain,
product(multiplicative_identity,c,c),
inference(resolve,[status(thm)],[c_29,c_8]) ).
cnf(c_2540,plain,
( sum(additive_identity,d,additive_identity)
| product(multiplicative_inverse(d),d,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_30,c_9]) ).
cnf(c_152,plain,
product(multiplicative_inverse(d),d,multiplicative_identity),
inference(resolve,[status(thm)],[c_34,c_2540]) ).
cnf(c_169,plain,
product(multiplicative_identity,k,k),
inference(resolve,[status(thm)],[c_31,c_8]) ).
cnf(c_208,plain,
product(d,a,k),
inference(resolve,[status(thm)],[c_37,c_10]) ).
cnf(c_215,plain,
~ product(c,b,k),
inference(resolve,[status(thm)],[c_10,c_38]) ).
cnf(c_469,plain,
product(c,multiplicative_identity,c),
inference(resolve,[status(thm)],[c_137,c_10]) ).
cnf(c_564,plain,
product(k,multiplicative_identity,k),
inference(resolve,[status(thm)],[c_169,c_10]) ).
cnf(c_2541,plain,
( ~ product(A,C,k)
| ~ product(B,b,C)
| ~ product(A,B,c) ),
inference(resolve,[status(thm)],[c_7,c_215]) ).
cnf(c_2542,plain,
( ~ product(A,multiplicative_identity,k)
| ~ product(A,multiplicative_inverse(b),c) ),
inference(resolve,[status(thm)],[c_2541,c_120]) ).
cnf(c_1710,plain,
~ product(k,multiplicative_inverse(b),c),
inference(resolve,[status(thm)],[c_2542,c_564]) ).
cnf(c_2543,plain,
( ~ product(A,C,c)
| ~ product(B,multiplicative_inverse(b),C)
| ~ product(A,B,k) ),
inference(resolve,[status(thm)],[c_7,c_1710]) ).
cnf(c_2544,plain,
( ~ product(d,A,c)
| ~ product(a,multiplicative_inverse(b),A) ),
inference(resolve,[status(thm)],[c_2543,c_208]) ).
cnf(c_2528,plain,
~ product(d,s,c),
inference(resolve,[status(thm)],[c_2544,c_35]) ).
cnf(c_2529,plain,
~ product(s,d,c),
inference(resolve,[status(thm)],[c_10,c_2528]) ).
cnf(c_2545,plain,
( ~ product(A,C,c)
| ~ product(B,d,C)
| ~ product(A,B,s) ),
inference(resolve,[status(thm)],[c_7,c_2529]) ).
cnf(c_2546,plain,
( ~ product(A,multiplicative_identity,c)
| ~ product(A,multiplicative_inverse(d),s) ),
inference(resolve,[status(thm)],[c_2545,c_152]) ).
cnf(c_2547,plain,
~ product(c,multiplicative_inverse(d),s),
inference(resolve,[status(thm)],[c_2546,c_469]) ).
cnf(c_2538,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_2547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD049-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 02:30:35 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 3025632 was started by sandbox2 on n020,
% 0.10/0.38 % Sun Sep 27 02:30:35 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 2.12/0.78
% 2.12/0.78 % SZS status Unsatisfiable for theBenchmark
% 2.12/0.78
% 2.12/0.78 % Proof 1 at 0.30 (+ 0.08) seconds.
% 2.12/0.78 % Length of proof is 26.
% 2.12/0.78 % Level of proof is 6.
% 2.12/0.78 % Maximum clause weight is 21.000.
% 2.12/0.78 % Given clauses 436.
% 2.12/0.78
% 2.12/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------