%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP035-3 : 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 : n003.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 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 29 unt; 0 def)
% Number of atoms : 82 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 37 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : product(identity,VAR_0,VAR_0),
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
product(identity,A,A),
inference(clausify,[status(thm)],[left_identity]) ).
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(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(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(a_is_in_subgroup,axiom,
subgroup_member(a),
file('theBenchmark.p',a_is_in_subgroup) ).
cnf(c_10,plain,
subgroup_member(a),
inference(clausify,[status(thm)],[a_is_in_subgroup]) ).
fof(b_is_in_subgroup,axiom,
subgroup_member(b),
file('theBenchmark.p',b_is_in_subgroup) ).
cnf(c_11,plain,
subgroup_member(b),
inference(clausify,[status(thm)],[b_is_in_subgroup]) ).
fof(a_times_b_is_c,axiom,
product(a,b,c),
file('theBenchmark.p',a_times_b_is_c) ).
cnf(c_12,plain,
product(a,b,c),
inference(clausify,[status(thm)],[a_times_b_is_c]) ).
fof(prove_c_is_in_subgroup,axiom,
~ subgroup_member(c),
file('theBenchmark.p',prove_c_is_in_subgroup) ).
cnf(c_13,plain,
~ subgroup_member(c),
inference(clausify,[status(thm)],[prove_c_is_in_subgroup]) ).
cnf(c_290,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_21,plain,
multiply(A,inverse(A)) = identity,
inference(resolve,[status(thm)],[c_290,c_4]) ).
cnf(c_291,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_23,plain,
multiply(A,identity) = A,
inference(resolve,[status(thm)],[c_291,c_2]) ).
cnf(c_292,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_24,plain,
multiply(identity,A) = A,
inference(resolve,[status(thm)],[c_292,c_1]) ).
cnf(c_293,plain,
( subgroup_member(B)
| ~ product(a,inverse(A),B)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_294,plain,
( subgroup_member(A)
| ~ product(a,inverse(a),A) ),
inference(resolve,[status(thm)],[c_293,c_10]) ).
cnf(c_295,plain,
subgroup_member(multiply(a,inverse(a))),
inference(resolve,[status(thm)],[c_294,c_5]) ).
cnf(c_75,plain,
subgroup_member(identity),
inference(paramod,[status(thm)],[c_21,c_295]) ).
cnf(c_296,plain,
( product(c,A,C)
| ~ product(a,B,C)
| ~ product(b,A,B) ),
inference(resolve,[status(thm)],[c_8,c_12]) ).
cnf(c_297,plain,
( product(c,inverse(b),A)
| ~ product(a,identity,A) ),
inference(resolve,[status(thm)],[c_296,c_4]) ).
cnf(c_298,plain,
product(c,inverse(b),multiply(a,identity)),
inference(resolve,[status(thm)],[c_297,c_5]) ).
cnf(c_91,plain,
product(c,inverse(b),a),
inference(paramod,[status(thm)],[c_23,c_298]) ).
cnf(c_299,plain,
( subgroup_member(B)
| ~ product(identity,inverse(A),B)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_9,c_75]) ).
cnf(c_300,plain,
( subgroup_member(A)
| ~ product(identity,inverse(b),A) ),
inference(resolve,[status(thm)],[c_299,c_11]) ).
cnf(c_301,plain,
subgroup_member(multiply(identity,inverse(b))),
inference(resolve,[status(thm)],[c_300,c_5]) ).
cnf(c_131,plain,
subgroup_member(inverse(b)),
inference(paramod,[status(thm)],[c_24,c_301]) ).
cnf(c_302,plain,
( subgroup_member(B)
| ~ product(a,inverse(A),B)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_303,plain,
( subgroup_member(A)
| ~ product(a,inverse(inverse(b)),A) ),
inference(resolve,[status(thm)],[c_302,c_131]) ).
cnf(c_206,plain,
~ product(a,inverse(inverse(b)),c),
inference(resolve,[status(thm)],[c_303,c_13]) ).
cnf(c_304,plain,
( product(a,A,C)
| ~ product(c,B,C)
| ~ product(inverse(b),A,B) ),
inference(resolve,[status(thm)],[c_8,c_91]) ).
cnf(c_305,plain,
( product(a,inverse(inverse(b)),A)
| ~ product(c,identity,A) ),
inference(resolve,[status(thm)],[c_304,c_4]) ).
cnf(c_306,plain,
product(a,inverse(inverse(b)),multiply(c,identity)),
inference(resolve,[status(thm)],[c_305,c_5]) ).
cnf(c_307,plain,
product(a,inverse(inverse(b)),c),
inference(paramod,[status(thm)],[c_23,c_306]) ).
cnf(c_289,plain,
$false,
inference(resolve,[status(thm)],[c_206,c_307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP035-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:20:37 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 359463 was started by sandbox2 on n003,
% 0.09/0.37 % Fri Sep 25 14:20:37 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.40
% 0.14/0.40 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 0.14/0.40
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.40 % Length of proof is 19.
% 0.14/0.40 % Level of proof is 5.
% 0.14/0.40 % Maximum clause weight is 26.000.
% 0.14/0.40 % Given clauses 53.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------