%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP039-4 : 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 : n019.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 07:26:21 AM UTC 2026
% Result : Unsatisfiable 13.57s 2.30s
% Output : CNFRefutation 13.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 65 ( 28 unt; 0 def)
% Number of atoms : 136 ( 4 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 125 ( 54 ~; 71 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 29 !; 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(left_inverse,axiom,
! [VAR_0] : product(inverse(VAR_0),VAR_0,identity),
file('theBenchmark.p',left_inverse) ).
cnf(c_3,plain,
product(inverse(A),A,identity),
inference(clausify,[status(thm)],[left_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(closure_of_inverse,axiom,
! [VAR_0] :
( subgroup_member(inverse(VAR_0))
| ~ subgroup_member(VAR_0) ),
file('theBenchmark.p',closure_of_inverse) ).
cnf(c_9,plain,
( subgroup_member(inverse(A))
| ~ subgroup_member(A) ),
inference(clausify,[status(thm)],[closure_of_inverse]) ).
fof(closure_of_product,axiom,
! [VAR_0,VAR_1,VAR_2] :
( subgroup_member(VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2)
| ~ subgroup_member(VAR_1)
| ~ subgroup_member(VAR_0) ),
file('theBenchmark.p',closure_of_product) ).
cnf(c_10,plain,
( subgroup_member(C)
| ~ product(A,B,C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(clausify,[status(thm)],[closure_of_product]) ).
fof(identity_is_in_subgroup,axiom,
subgroup_member(identity),
file('theBenchmark.p',identity_is_in_subgroup) ).
cnf(c_11,plain,
subgroup_member(identity),
inference(clausify,[status(thm)],[identity_is_in_subgroup]) ).
fof(an_element_in_O2,axiom,
! [VAR_0,VAR_1] :
( subgroup_member(VAR_0)
| subgroup_member(VAR_1)
| subgroup_member(element_in_O2(VAR_0,VAR_1)) ),
file('theBenchmark.p',an_element_in_O2) ).
cnf(c_12,plain,
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
inference(clausify,[status(thm)],[an_element_in_O2]) ).
fof(property_of_O2,axiom,
! [VAR_0,VAR_1] :
( subgroup_member(VAR_0)
| subgroup_member(VAR_1)
| product(VAR_0,element_in_O2(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',property_of_O2) ).
cnf(c_13,plain,
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
inference(clausify,[status(thm)],[property_of_O2]) ).
fof(b_is_in_subgroup,axiom,
subgroup_member(b),
file('theBenchmark.p',b_is_in_subgroup) ).
cnf(c_14,plain,
subgroup_member(b),
inference(clausify,[status(thm)],[b_is_in_subgroup]) ).
fof(b_times_a_inverse_is_c,axiom,
product(b,inverse(a),c),
file('theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(c_15,plain,
product(b,inverse(a),c),
inference(clausify,[status(thm)],[b_times_a_inverse_is_c]) ).
fof(a_times_c_is_d,axiom,
product(a,c,d),
file('theBenchmark.p',a_times_c_is_d) ).
cnf(c_16,plain,
product(a,c,d),
inference(clausify,[status(thm)],[a_times_c_is_d]) ).
fof(prove_d_is_in_subgroup,axiom,
~ subgroup_member(d),
file('theBenchmark.p',prove_d_is_in_subgroup) ).
cnf(c_17,plain,
~ subgroup_member(d),
inference(clausify,[status(thm)],[prove_d_is_in_subgroup]) ).
cnf(c_32,plain,
( B = A
| ~ product(A,identity,B) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_41,plain,
( product(A,identity,D)
| ~ product(C,B,D)
| ~ product(A,inverse(B),C) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_48,plain,
( product(A,D,C)
| ~ product(B,C,D)
| ~ product(A,B,identity) ),
inference(resolve,[status(thm)],[c_7,c_1]) ).
cnf(c_54,plain,
( product(identity,B,D)
| ~ product(inverse(A),C,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_3]) ).
cnf(c_75,plain,
( subgroup_member(D)
| ~ product(C,element_in_O2(B,A),D)
| ~ subgroup_member(C)
| subgroup_member(B)
| subgroup_member(A) ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_108,plain,
( subgroup_member(B)
| ~ product(A,b,B)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_14,c_10]) ).
cnf(c_2738,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(resolve,[status(thm)],[c_15,c_10]) ).
cnf(c_111,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(resolve,[status(thm)],[c_14,c_2738]) ).
cnf(c_2739,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(resolve,[status(thm)],[c_16,c_10]) ).
cnf(c_121,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(resolve,[status(thm)],[c_17,c_2739]) ).
cnf(c_636,plain,
( product(b,identity,A)
| ~ product(c,a,A) ),
inference(resolve,[status(thm)],[c_41,c_15]) ).
cnf(c_686,plain,
product(b,identity,multiply(c,a)),
inference(resolve,[status(thm)],[c_636,c_5]) ).
cnf(c_699,plain,
multiply(c,a) = b,
inference(resolve,[status(thm)],[c_686,c_32]) ).
cnf(c_700,plain,
product(c,a,b),
inference(paramod,[status(thm)],[c_699,c_5]) ).
cnf(c_807,plain,
( product(A,b,a)
| ~ product(A,c,identity) ),
inference(resolve,[status(thm)],[c_48,c_700]) ).
cnf(c_809,plain,
( product(A,d,c)
| ~ product(A,a,identity) ),
inference(resolve,[status(thm)],[c_48,c_16]) ).
cnf(c_812,plain,
product(inverse(c),b,a),
inference(resolve,[status(thm)],[c_807,c_3]) ).
cnf(c_813,plain,
product(inverse(a),d,c),
inference(resolve,[status(thm)],[c_809,c_3]) ).
cnf(c_835,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(resolve,[status(thm)],[c_812,c_108]) ).
cnf(c_1298,plain,
( product(identity,A,c)
| ~ product(a,A,d) ),
inference(resolve,[status(thm)],[c_54,c_813]) ).
cnf(c_2740,plain,
( subgroup_member(a)
| subgroup_member(d)
| product(identity,element_in_O2(a,d),c) ),
inference(resolve,[status(thm)],[c_1298,c_13]) ).
cnf(c_1338,plain,
( subgroup_member(a)
| product(identity,element_in_O2(a,d),c) ),
inference(resolve,[status(thm)],[c_17,c_2740]) ).
cnf(c_2741,plain,
( subgroup_member(c)
| ~ subgroup_member(identity)
| subgroup_member(a)
| subgroup_member(d)
| subgroup_member(a) ),
inference(resolve,[status(thm)],[c_1338,c_75]) ).
cnf(c_2742,plain,
( subgroup_member(c)
| ~ subgroup_member(identity)
| subgroup_member(d)
| subgroup_member(a) ),
inference(copy,[status(thm)],[c_2741]) ).
cnf(c_2743,plain,
( subgroup_member(c)
| ~ subgroup_member(identity)
| subgroup_member(a) ),
inference(resolve,[status(thm)],[c_17,c_2742]) ).
cnf(c_2542,plain,
( subgroup_member(c)
| subgroup_member(a) ),
inference(resolve,[status(thm)],[c_11,c_2743]) ).
cnf(c_2596,plain,
( subgroup_member(inverse(c))
| subgroup_member(a) ),
inference(resolve,[status(thm)],[c_2542,c_9]) ).
cnf(c_2744,plain,
( subgroup_member(a)
| subgroup_member(a) ),
inference(resolve,[status(thm)],[c_2596,c_835]) ).
cnf(c_2708,plain,
subgroup_member(a),
inference(copy,[status(thm)],[c_2744]) ).
cnf(c_2710,plain,
~ subgroup_member(c),
inference(resolve,[status(thm)],[c_2708,c_121]) ).
cnf(c_2718,plain,
~ subgroup_member(inverse(a)),
inference(resolve,[status(thm)],[c_2710,c_111]) ).
cnf(c_2745,plain,
subgroup_member(inverse(a)),
inference(resolve,[status(thm)],[c_2708,c_9]) ).
cnf(c_2737,plain,
$false,
inference(resolve,[status(thm)],[c_2718,c_2745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP039-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 14:19:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 2935650 was started by sandbox2 on n019,
% 0.08/0.37 % Fri Sep 25 14:19:19 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 13.57/2.30
% 13.57/2.30 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 13.57/2.30
% 13.57/2.30 % SZS status Unsatisfiable for theBenchmark
% 13.57/2.30
% 13.57/2.30 % Proof 1 at 1.34 (+ 0.56) seconds.
% 13.57/2.30 % Length of proof is 41.
% 13.57/2.30 % Level of proof is 12.
% 13.57/2.30 % Maximum clause weight is 24.000.
% 13.57/2.30 % Given clauses 399.
% 13.57/2.30
% 13.57/2.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------