%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP040-4 : 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 07:26:21 AM UTC 2026
% Result : Unsatisfiable 1.03s 0.54s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 66 ( 36 unt; 0 def)
% Number of atoms : 124 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 104 ( 46 ~; 58 |; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 35 !; 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(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(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(closure_of_inverse,axiom,
! [VAR_0] :
( subgroup_member(inverse(VAR_0))
| ~ subgroup_member(VAR_0) ),
file('theBenchmark.p',closure_of_inverse) ).
cnf(c_11,plain,
( subgroup_member(inverse(A))
| ~ subgroup_member(A) ),
inference(clausify,[status(thm)],[closure_of_inverse]) ).
fof(product_right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( 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_12,plain,
( 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_14,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_15,plain,
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
inference(clausify,[status(thm)],[property_of_O2]) ).
fof(a_in_subgroup,axiom,
~ subgroup_member(a),
file('theBenchmark.p',a_in_subgroup) ).
cnf(c_16,plain,
~ subgroup_member(a),
inference(clausify,[status(thm)],[a_in_subgroup]) ).
fof(b_is_in_subgroup,axiom,
subgroup_member(b),
file('theBenchmark.p',b_is_in_subgroup) ).
cnf(c_17,plain,
subgroup_member(b),
inference(clausify,[status(thm)],[b_is_in_subgroup]) ).
fof(d_in_subgroup,axiom,
~ subgroup_member(d),
file('theBenchmark.p',d_in_subgroup) ).
cnf(c_18,plain,
~ subgroup_member(d),
inference(clausify,[status(thm)],[d_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_19,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_20,plain,
product(a,c,d),
inference(clausify,[status(thm)],[a_times_c_is_d]) ).
fof(prove_inverse_is_self_cancelling,axiom,
! [VAR_0] : inverse(inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',prove_inverse_is_self_cancelling) ).
cnf(c_21,plain,
inverse(inverse(A)) = A,
inference(clausify,[status(thm)],[prove_inverse_is_self_cancelling]) ).
cnf(c_720,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_40,plain,
multiply(A,identity) = A,
inference(resolve,[status(thm)],[c_720,c_2]) ).
cnf(c_721,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_41,plain,
multiply(identity,A) = A,
inference(resolve,[status(thm)],[c_721,c_1]) ).
cnf(c_190,plain,
subgroup_member(inverse(b)),
inference(resolve,[status(thm)],[c_17,c_11]) ).
cnf(c_722,plain,
( product(c,A,C)
| ~ product(b,B,C)
| ~ product(inverse(a),A,B) ),
inference(resolve,[status(thm)],[c_8,c_19]) ).
cnf(c_723,plain,
( product(c,inverse(inverse(a)),A)
| ~ product(b,identity,A) ),
inference(resolve,[status(thm)],[c_722,c_4]) ).
cnf(c_724,plain,
product(c,inverse(inverse(a)),multiply(b,identity)),
inference(resolve,[status(thm)],[c_723,c_5]) ).
cnf(c_725,plain,
product(c,a,multiply(b,identity)),
inference(paramod,[status(thm)],[c_21,c_724]) ).
cnf(c_219,plain,
product(c,a,b),
inference(paramod,[status(thm)],[c_40,c_725]) ).
cnf(c_726,plain,
( subgroup_member(A)
| subgroup_member(C)
| B = element_in_O2(A,C)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_12,c_15]) ).
cnf(c_727,plain,
( subgroup_member(a)
| subgroup_member(d)
| c = element_in_O2(a,d) ),
inference(resolve,[status(thm)],[c_726,c_20]) ).
cnf(c_728,plain,
( subgroup_member(a)
| subgroup_member(d)
| element_in_O2(a,d) = c ),
inference(copy,[status(thm)],[c_727]) ).
cnf(c_729,plain,
( subgroup_member(a)
| element_in_O2(a,d) = c ),
inference(resolve,[status(thm)],[c_18,c_728]) ).
cnf(c_244,plain,
element_in_O2(a,d) = c,
inference(resolve,[status(thm)],[c_16,c_729]) ).
cnf(c_730,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_731,plain,
( product(inverse(c),b,A)
| ~ product(identity,a,A) ),
inference(resolve,[status(thm)],[c_730,c_219]) ).
cnf(c_732,plain,
product(inverse(c),b,multiply(identity,a)),
inference(resolve,[status(thm)],[c_731,c_5]) ).
cnf(c_365,plain,
product(inverse(c),b,a),
inference(paramod,[status(thm)],[c_41,c_732]) ).
cnf(c_733,plain,
( subgroup_member(a)
| subgroup_member(d)
| subgroup_member(c) ),
inference(paramod,[status(thm)],[c_244,c_14]) ).
cnf(c_734,plain,
( subgroup_member(a)
| subgroup_member(c) ),
inference(resolve,[status(thm)],[c_18,c_733]) ).
cnf(c_669,plain,
subgroup_member(c),
inference(resolve,[status(thm)],[c_16,c_734]) ).
cnf(c_670,plain,
subgroup_member(inverse(c)),
inference(resolve,[status(thm)],[c_669,c_11]) ).
cnf(c_735,plain,
( subgroup_member(B)
| ~ product(inverse(c),inverse(A),B)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_9,c_670]) ).
cnf(c_736,plain,
( subgroup_member(A)
| ~ product(inverse(c),inverse(inverse(b)),A) ),
inference(resolve,[status(thm)],[c_735,c_190]) ).
cnf(c_737,plain,
~ product(inverse(c),inverse(inverse(b)),a),
inference(resolve,[status(thm)],[c_736,c_16]) ).
cnf(c_738,plain,
~ product(inverse(c),b,a),
inference(paramod,[status(thm)],[c_21,c_737]) ).
cnf(c_719,plain,
$false,
inference(resolve,[status(thm)],[c_365,c_738]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP040-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:19:22 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3348815 was started by sandbox on n004,
% 0.09/0.35 % Fri Sep 25 14:19:22 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 1.03/0.54
% 1.03/0.54 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 1.03/0.54
% 1.03/0.54 % SZS status Unsatisfiable for theBenchmark
% 1.03/0.54
% 1.03/0.54 % Proof 1 at 0.13 (+ 0.05) seconds.
% 1.03/0.54 % Length of proof is 28.
% 1.03/0.54 % Level of proof is 4.
% 1.03/0.54 % Maximum clause weight is 25.000.
% 1.03/0.54 % Given clauses 116.
% 1.03/0.54
% 1.03/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------