%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP039-6 : 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 : n026.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 10.42s 1.76s
% Output : CNFRefutation 10.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 56 ( 21 unt; 0 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 116 ( 50 ~; 66 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subgroup_member_substitution,axiom,
! [VAR_0,VAR_1] :
( subgroup_member(VAR_1)
| ~ subgroup_member(VAR_0)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',subgroup_member_substitution) ).
cnf(c_1,plain,
( subgroup_member(B)
| ~ subgroup_member(A)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[subgroup_member_substitution]) ).
fof(closure_of_inverse,axiom,
! [VAR_0] :
( subgroup_member(inverse(VAR_0))
| ~ subgroup_member(VAR_0) ),
file('theBenchmark.p',closure_of_inverse) ).
cnf(c_5,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_6,plain,
( subgroup_member(C)
| ~ product(A,B,C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(clausify,[status(thm)],[closure_of_product]) ).
fof(left_identity,axiom,
! [VAR_0] : product(identity,VAR_0,VAR_0),
file('theBenchmark.p',left_identity) ).
cnf(c_7,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_8,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_9,plain,
product(inverse(A),A,identity),
inference(clausify,[status(thm)],[left_inverse]) ).
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_11,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_12,plain,
( product(C,D,F)
| ~ product(A,E,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity2]) ).
fof(product_right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_3,VAR_1)
| ~ product(VAR_0,VAR_3,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_right_cancellation) ).
cnf(c_15,plain,
( equalish(D,B)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_right_cancellation]) ).
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_17,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_18,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_19,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_20,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_21,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_22,plain,
~ subgroup_member(d),
inference(clausify,[status(thm)],[prove_d_is_in_subgroup]) ).
cnf(c_50,plain,
( product(A,D,C)
| ~ product(B,C,D)
| ~ product(A,B,identity) ),
inference(resolve,[status(thm)],[c_11,c_7]) ).
cnf(c_57,plain,
( product(C,B,D)
| ~ product(A,identity,D)
| ~ product(A,inverse(B),C) ),
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_92,plain,
( subgroup_member(C)
| ~ equalish(element_in_O2(B,A),C)
| subgroup_member(B)
| subgroup_member(A) ),
inference(resolve,[status(thm)],[c_17,c_1]) ).
cnf(c_137,plain,
( subgroup_member(B)
| ~ product(A,b,B)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_19,c_6]) ).
cnf(c_2720,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(resolve,[status(thm)],[c_20,c_6]) ).
cnf(c_153,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(resolve,[status(thm)],[c_19,c_2720]) ).
cnf(c_160,plain,
( equalish(A,c)
| ~ product(a,A,d) ),
inference(resolve,[status(thm)],[c_21,c_15]) ).
cnf(c_2721,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(resolve,[status(thm)],[c_21,c_6]) ).
cnf(c_169,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(resolve,[status(thm)],[c_22,c_2721]) ).
cnf(c_2722,plain,
( subgroup_member(a)
| subgroup_member(d)
| equalish(element_in_O2(a,d),c) ),
inference(resolve,[status(thm)],[c_160,c_18]) ).
cnf(c_340,plain,
( subgroup_member(a)
| equalish(element_in_O2(a,d),c) ),
inference(resolve,[status(thm)],[c_22,c_2722]) ).
cnf(c_1442,plain,
( product(c,a,A)
| ~ product(b,identity,A) ),
inference(resolve,[status(thm)],[c_57,c_20]) ).
cnf(c_1459,plain,
product(c,a,b),
inference(resolve,[status(thm)],[c_1442,c_8]) ).
cnf(c_1467,plain,
( product(A,b,a)
| ~ product(A,c,identity) ),
inference(resolve,[status(thm)],[c_1459,c_50]) ).
cnf(c_1547,plain,
product(inverse(c),b,a),
inference(resolve,[status(thm)],[c_1467,c_9]) ).
cnf(c_1613,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(resolve,[status(thm)],[c_1547,c_137]) ).
cnf(c_2723,plain,
( subgroup_member(a)
| subgroup_member(c)
| subgroup_member(a)
| subgroup_member(d) ),
inference(resolve,[status(thm)],[c_92,c_340]) ).
cnf(c_2724,plain,
( subgroup_member(c)
| subgroup_member(a)
| subgroup_member(d) ),
inference(copy,[status(thm)],[c_2723]) ).
cnf(c_2557,plain,
( subgroup_member(c)
| subgroup_member(a) ),
inference(resolve,[status(thm)],[c_22,c_2724]) ).
cnf(c_2571,plain,
( subgroup_member(inverse(c))
| subgroup_member(a) ),
inference(resolve,[status(thm)],[c_2557,c_5]) ).
cnf(c_2725,plain,
( subgroup_member(a)
| subgroup_member(a) ),
inference(resolve,[status(thm)],[c_2571,c_1613]) ).
cnf(c_2655,plain,
subgroup_member(a),
inference(copy,[status(thm)],[c_2725]) ).
cnf(c_2656,plain,
~ subgroup_member(c),
inference(resolve,[status(thm)],[c_2655,c_169]) ).
cnf(c_2706,plain,
~ subgroup_member(inverse(a)),
inference(resolve,[status(thm)],[c_2656,c_153]) ).
cnf(c_2726,plain,
subgroup_member(inverse(a)),
inference(resolve,[status(thm)],[c_2655,c_5]) ).
cnf(c_2719,plain,
$false,
inference(resolve,[status(thm)],[c_2706,c_2726]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:21:54 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2718318 was started by sandbox2 on n026,
% 0.08/0.36 % Fri Sep 25 14:21:54 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 10.42/1.76
% 10.42/1.76 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 10.42/1.76
% 10.42/1.76 % SZS status Unsatisfiable for theBenchmark
% 10.42/1.76
% 10.42/1.76 % Proof 1 at 0.98 (+ 0.38) seconds.
% 10.42/1.76 % Length of proof is 34.
% 10.42/1.76 % Level of proof is 10.
% 10.42/1.76 % Maximum clause weight is 23.000.
% 10.42/1.76 % Given clauses 472.
% 10.42/1.76
% 10.42/1.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------