%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP036-3 : 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 : n009.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 07:26:20 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 16 unt; 0 def)
% Number of atoms : 43 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 21 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 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 : 33 ( 0 sgn 12 !; 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(closure_of_product_and_inverse,axiom,
! [VAR_0,VAR_1,VAR_2] :
( subgroup_member(VAR_2)
| ~ product(VAR_0,inverse(VAR_1),VAR_2)
| ~ subgroup_member(VAR_1)
| ~ subgroup_member(VAR_0) ),
file('theBenchmark.p',closure_of_product_and_inverse) ).
cnf(c_9,plain,
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(clausify,[status(thm)],[closure_of_product_and_inverse]) ).
fof(another_left_identity,axiom,
! [VAR_0] :
( product(another_identity,VAR_0,VAR_0)
| ~ subgroup_member(VAR_0) ),
file('theBenchmark.p',another_left_identity) ).
cnf(c_10,plain,
( product(another_identity,A,A)
| ~ subgroup_member(A) ),
inference(clausify,[status(thm)],[another_left_identity]) ).
fof(another_identity_in_subgroup,axiom,
subgroup_member(another_identity),
file('theBenchmark.p',another_identity_in_subgroup) ).
cnf(c_15,plain,
subgroup_member(another_identity),
inference(clausify,[status(thm)],[another_identity_in_subgroup]) ).
fof(prove_identity_equals_another_identity,axiom,
identity != another_identity,
file('theBenchmark.p',prove_identity_equals_another_identity) ).
cnf(c_16,plain,
identity != another_identity,
inference(clausify,[status(thm)],[prove_identity_equals_another_identity]) ).
cnf(c_50,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_17,plain,
multiply(A,inverse(A)) = identity,
inference(resolve,[status(thm)],[c_50,c_4]) ).
cnf(c_51,plain,
( subgroup_member(B)
| ~ product(another_identity,inverse(A),B)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_9,c_15]) ).
cnf(c_52,plain,
( subgroup_member(A)
| ~ product(another_identity,inverse(another_identity),A) ),
inference(resolve,[status(thm)],[c_51,c_15]) ).
cnf(c_53,plain,
subgroup_member(multiply(another_identity,inverse(another_identity))),
inference(resolve,[status(thm)],[c_52,c_5]) ).
cnf(c_42,plain,
subgroup_member(identity),
inference(paramod,[status(thm)],[c_17,c_53]) ).
cnf(c_54,plain,
( B = A
| ~ product(A,identity,B) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_43,plain,
~ product(another_identity,identity,identity),
inference(resolve,[status(thm)],[c_54,c_16]) ).
cnf(c_48,plain,
~ subgroup_member(identity),
inference(resolve,[status(thm)],[c_10,c_43]) ).
cnf(c_49,plain,
$false,
inference(resolve,[status(thm)],[c_48,c_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP036-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n009.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Fri Sep 25 14:18:58 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 1781045 was started by sandbox2 on n009,
% 0.19/0.44 % Fri Sep 25 14:18:58 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 0.19/0.47
% 0.19/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.47
% 0.19/0.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.19/0.47 % Length of proof is 13.
% 0.19/0.47 % Level of proof is 3.
% 0.19/0.47 % Maximum clause weight is 11.000.
% 0.19/0.47 % Given clauses 18.
% 0.19/0.47
% 0.19/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------