%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP040-3 : 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 : 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 0.21s 5.73s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 86 ( 44 unt; 0 def)
% Number of atoms : 172 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 140 ( 54 ~; 86 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 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 : 118 ( 4 sgn 30 !; 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(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_10,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_11,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_12,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_13,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_14,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_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_inverse_is_self_cancelling,axiom,
! [VAR_0] : inverse(inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',prove_inverse_is_self_cancelling) ).
cnf(c_17,plain,
inverse(inverse(A)) = A,
inference(clausify,[status(thm)],[prove_inverse_is_self_cancelling]) ).
cnf(c_27,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_33,plain,
( B = A
| ~ product(identity,A,B) ),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_1792,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_36,plain,
multiply(A,identity) = A,
inference(resolve,[status(thm)],[c_1792,c_2]) ).
cnf(c_1793,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_37,plain,
multiply(identity,A) = A,
inference(resolve,[status(thm)],[c_1793,c_1]) ).
cnf(c_87,plain,
( subgroup_member(inverse(A))
| ~ subgroup_member(A)
| ~ subgroup_member(identity) ),
inference(resolve,[status(thm)],[c_9,c_1]) ).
cnf(c_1794,plain,
( subgroup_member(B)
| subgroup_member(C)
| subgroup_member(D)
| ~ product(element_in_O2(B,C),inverse(A),D)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_1795,plain,
( subgroup_member(C)
| subgroup_member(D)
| subgroup_member(A)
| subgroup_member(B)
| subgroup_member(E)
| ~ product(element_in_O2(A,B),inverse(element_in_O2(C,D)),E) ),
inference(resolve,[status(thm)],[c_1794,c_10]) ).
cnf(c_1796,plain,
( subgroup_member(B)
| subgroup_member(A)
| subgroup_member(B)
| subgroup_member(A)
| subgroup_member(identity) ),
inference(resolve,[status(thm)],[c_1795,c_4]) ).
cnf(c_1797,plain,
( subgroup_member(B)
| subgroup_member(B)
| subgroup_member(A)
| subgroup_member(identity) ),
inference(copy,[status(thm)],[c_1796]) ).
cnf(c_89,plain,
( subgroup_member(B)
| subgroup_member(A)
| subgroup_member(identity) ),
inference(copy,[status(thm)],[c_1797]) ).
cnf(c_96,plain,
( subgroup_member(A)
| subgroup_member(identity) ),
inference(factor,[status(thm)],[c_89]) ).
cnf(c_103,plain,
subgroup_member(identity),
inference(factor,[status(thm)],[c_96]) ).
cnf(c_104,plain,
( subgroup_member(inverse(A))
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_103,c_87]) ).
cnf(c_1798,plain,
( product(c,A,C)
| ~ product(b,B,C)
| ~ product(inverse(a),A,B) ),
inference(resolve,[status(thm)],[c_8,c_15]) ).
cnf(c_1799,plain,
( product(c,inverse(inverse(a)),A)
| ~ product(b,identity,A) ),
inference(resolve,[status(thm)],[c_1798,c_4]) ).
cnf(c_1800,plain,
product(c,inverse(inverse(a)),multiply(b,identity)),
inference(resolve,[status(thm)],[c_1799,c_5]) ).
cnf(c_1801,plain,
product(c,a,multiply(b,identity)),
inference(paramod,[status(thm)],[c_17,c_1800]) ).
cnf(c_192,plain,
product(c,a,b),
inference(paramod,[status(thm)],[c_36,c_1801]) ).
cnf(c_1802,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_1803,plain,
( product(inverse(a),d,A)
| ~ product(identity,c,A) ),
inference(resolve,[status(thm)],[c_1802,c_16]) ).
cnf(c_1804,plain,
product(inverse(a),d,multiply(identity,c)),
inference(resolve,[status(thm)],[c_1803,c_5]) ).
cnf(c_233,plain,
product(inverse(a),d,c),
inference(paramod,[status(thm)],[c_37,c_1804]) ).
cnf(c_1805,plain,
( subgroup_member(B)
| ~ product(identity,inverse(A),B)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_9,c_103]) ).
cnf(c_1806,plain,
( subgroup_member(A)
| ~ product(identity,inverse(b),A) ),
inference(resolve,[status(thm)],[c_1805,c_13]) ).
cnf(c_1807,plain,
subgroup_member(multiply(identity,inverse(b))),
inference(resolve,[status(thm)],[c_1806,c_5]) ).
cnf(c_293,plain,
subgroup_member(inverse(b)),
inference(paramod,[status(thm)],[c_37,c_1807]) ).
cnf(c_1808,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_1809,plain,
( product(inverse(c),b,A)
| ~ product(identity,a,A) ),
inference(resolve,[status(thm)],[c_1808,c_192]) ).
cnf(c_1810,plain,
product(inverse(c),b,multiply(identity,a)),
inference(resolve,[status(thm)],[c_1809,c_5]) ).
cnf(c_327,plain,
product(inverse(c),b,a),
inference(paramod,[status(thm)],[c_37,c_1810]) ).
cnf(c_1811,plain,
( product(identity,B,D)
| ~ product(A,C,D)
| ~ product(inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_1812,plain,
( subgroup_member(inverse(A))
| subgroup_member(B)
| product(identity,element_in_O2(inverse(A),B),C)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_1811,c_11]) ).
cnf(c_1813,plain,
( subgroup_member(inverse(inverse(a)))
| subgroup_member(d)
| product(identity,element_in_O2(inverse(inverse(a)),d),c) ),
inference(resolve,[status(thm)],[c_1812,c_233]) ).
cnf(c_1814,plain,
( subgroup_member(inverse(inverse(a)))
| subgroup_member(d)
| product(identity,element_in_O2(a,d),c) ),
inference(paramod,[status(thm)],[c_17,c_1813]) ).
cnf(c_1815,plain,
( subgroup_member(a)
| subgroup_member(d)
| product(identity,element_in_O2(a,d),c) ),
inference(paramod,[status(thm)],[c_17,c_1814]) ).
cnf(c_1816,plain,
( subgroup_member(a)
| product(identity,element_in_O2(a,d),c) ),
inference(resolve,[status(thm)],[c_14,c_1815]) ).
cnf(c_652,plain,
product(identity,element_in_O2(a,d),c),
inference(resolve,[status(thm)],[c_12,c_1816]) ).
cnf(c_731,plain,
multiply(inverse(c),b) = a,
inference(resolve,[status(thm)],[c_327,c_27]) ).
cnf(c_1817,plain,
c = element_in_O2(a,d),
inference(resolve,[status(thm)],[c_652,c_33]) ).
cnf(c_1758,plain,
element_in_O2(a,d) = c,
inference(copy,[status(thm)],[c_1817]) ).
cnf(c_1818,plain,
( subgroup_member(a)
| subgroup_member(d)
| subgroup_member(c) ),
inference(paramod,[status(thm)],[c_1758,c_10]) ).
cnf(c_1819,plain,
( subgroup_member(a)
| subgroup_member(c) ),
inference(resolve,[status(thm)],[c_14,c_1818]) ).
cnf(c_1759,plain,
subgroup_member(c),
inference(resolve,[status(thm)],[c_12,c_1819]) ).
cnf(c_1760,plain,
subgroup_member(inverse(c)),
inference(resolve,[status(thm)],[c_1759,c_104]) ).
cnf(c_1820,plain,
( subgroup_member(B)
| ~ product(inverse(c),inverse(A),B)
| ~ subgroup_member(A) ),
inference(resolve,[status(thm)],[c_9,c_1760]) ).
cnf(c_1821,plain,
( subgroup_member(A)
| ~ product(inverse(c),inverse(inverse(b)),A) ),
inference(resolve,[status(thm)],[c_1820,c_293]) ).
cnf(c_1822,plain,
subgroup_member(multiply(inverse(c),inverse(inverse(b)))),
inference(resolve,[status(thm)],[c_1821,c_5]) ).
cnf(c_1823,plain,
subgroup_member(multiply(inverse(c),b)),
inference(paramod,[status(thm)],[c_17,c_1822]) ).
cnf(c_1824,plain,
subgroup_member(a),
inference(paramod,[status(thm)],[c_731,c_1823]) ).
cnf(c_1791,plain,
$false,
inference(resolve,[status(thm)],[c_12,c_1824]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP040-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.44 % Computer : n004.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Fri Sep 25 14:19:27 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.45 % Process 3349013 was started by sandbox2 on n004,
% 0.17/5.45 % Fri Sep 25 14:19:27 2026
% 0.17/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.45
% 0.17/5.45 % From the command line: assign(max_seconds, 300).
% 0.21/5.73
% 0.21/5.73 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 0.21/5.73
% 0.21/5.73 % SZS status Unsatisfiable for theBenchmark
% 0.21/5.73
% 0.21/5.73 % Proof 1 at 0.18 (+ 0.08) seconds.
% 0.21/5.73 % Length of proof is 36.
% 0.21/5.73 % Level of proof is 7.
% 0.21/5.73 % Maximum clause weight is 25.000.
% 0.21/5.73 % Given clauses 189.
% 0.21/5.73
% 0.21/5.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------