%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 07:26:09 AM UTC 2026
% Result : Unsatisfiable 0.10s 5.59s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 19 unt; 0 def)
% Number of atoms : 55 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 29 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(right_identity,axiom,
! [VAR_0] : product(VAR_0,identity,VAR_0),
file('theBenchmark.p',right_identity) ).
cnf(c_2,plain,
product(A,identity,A),
inference(clausify,[status(thm)],[right_identity]) ).
fof(right_inverse,axiom,
! [VAR_0] : product(VAR_0,inverse(VAR_0),identity),
file('theBenchmark.p',right_inverse) ).
cnf(c_4,plain,
product(A,inverse(A),identity),
inference(clausify,[status(thm)],[right_inverse]) ).
fof(total_function1,axiom,
! [VAR_0,VAR_1] : product(VAR_0,VAR_1,multiply(VAR_0,VAR_1)),
file('theBenchmark.p',total_function1) ).
cnf(c_5,plain,
product(A,B,multiply(A,B)),
inference(clausify,[status(thm)],[total_function1]) ).
fof(total_function2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',total_function2) ).
cnf(c_6,plain,
( C = D
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[total_function2]) ).
fof(associativity1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( product(VAR_0,VAR_4,VAR_5)
| ~ product(VAR_2,VAR_3,VAR_5)
| ~ product(VAR_1,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity1) ).
cnf(c_7,plain,
( product(A,E,F)
| ~ product(C,D,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity1]) ).
fof(associativity2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( product(VAR_2,VAR_3,VAR_5)
| ~ product(VAR_0,VAR_4,VAR_5)
| ~ product(VAR_1,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity2) ).
cnf(c_8,plain,
( product(C,D,F)
| ~ product(A,E,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity2]) ).
fof(a_is_an_inverse_of_b,axiom,
product(a,b,identity),
file('theBenchmark.p',a_is_an_inverse_of_b) ).
cnf(c_9,plain,
product(a,b,identity),
inference(clausify,[status(thm)],[a_is_an_inverse_of_b]) ).
fof(c_is_an_inverse_of_b,axiom,
product(c,b,identity),
file('theBenchmark.p',c_is_an_inverse_of_b) ).
cnf(c_10,plain,
product(c,b,identity),
inference(clausify,[status(thm)],[c_is_an_inverse_of_b]) ).
fof(prove_a_equals_c,axiom,
a != c,
file('theBenchmark.p',prove_a_equals_c) ).
cnf(c_11,plain,
a != c,
inference(clausify,[status(thm)],[prove_a_equals_c]) ).
cnf(c_12,plain,
c != a,
inference(copy,[status(thm)],[c_11]) ).
cnf(c_67,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_15,plain,
multiply(A,identity) = A,
inference(resolve,[status(thm)],[c_67,c_2]) ).
cnf(c_68,plain,
( product(identity,A,C)
| ~ product(c,B,C)
| ~ product(b,A,B) ),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_69,plain,
( product(identity,inverse(b),A)
| ~ product(c,identity,A) ),
inference(resolve,[status(thm)],[c_68,c_4]) ).
cnf(c_70,plain,
product(identity,inverse(b),multiply(c,identity)),
inference(resolve,[status(thm)],[c_69,c_5]) ).
cnf(c_50,plain,
product(identity,inverse(b),c),
inference(paramod,[status(thm)],[c_15,c_70]) ).
cnf(c_71,plain,
( B = A
| ~ product(A,identity,B) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_58,plain,
~ product(a,identity,c),
inference(resolve,[status(thm)],[c_71,c_12]) ).
cnf(c_72,plain,
( product(a,B,C)
| ~ product(identity,A,C)
| ~ product(b,A,B) ),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_73,plain,
( product(a,identity,A)
| ~ product(identity,inverse(b),A) ),
inference(resolve,[status(thm)],[c_72,c_4]) ).
cnf(c_65,plain,
~ product(identity,inverse(b),c),
inference(resolve,[status(thm)],[c_73,c_58]) ).
cnf(c_66,plain,
$false,
inference(resolve,[status(thm)],[c_65,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.57 % Computer : n004.cluster.edu
% 0.10/5.57 % Model : x86_64 x86_64
% 0.10/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.57 % Memory : 8046.5625MB
% 0.10/5.57 % OS : Linux 6.8.0-71-generic
% 0.10/5.57 % CPULimit : 300
% 0.10/5.57 % WCLimit : 300
% 0.10/5.57 % DateTime : Fri Sep 25 14:16:13 UTC 2026
% 0.10/5.57 % CPUTime :
% 0.10/5.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.58 % Process 3343388 was started by sandbox on n004,
% 0.10/5.58 % Fri Sep 25 14:16:13 2026
% 0.10/5.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.58
% 0.10/5.58 % From the command line: assign(max_seconds, 300).
% 0.10/5.59
% 0.10/5.59 % SZS status Unsatisfiable for theBenchmark
% 0.10/5.59
% 0.10/5.59 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/5.59 % Length of proof is 15.
% 0.10/5.59 % Level of proof is 4.
% 0.10/5.59 % Maximum clause weight is 16.000.
% 0.10/5.59 % Given clauses 13.
% 0.10/5.59
% 0.10/5.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------