%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP124-8.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:27:38 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.55s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of formulae : 104 ( 43 unt; 0 def)
% Number of atoms : 209 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 189 ( 84 ~; 105 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 70 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_7,plain,
~ equalish(e_2,e_1),
inference(clausify,[status(thm)],[e_2_is_not_e_1]) ).
fof(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('theBenchmark.p',e_3_is_not_e_1) ).
cnf(c_10,plain,
~ equalish(e_3,e_1),
inference(clausify,[status(thm)],[e_3_is_not_e_1]) ).
fof(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_11,plain,
~ equalish(e_3,e_2),
inference(clausify,[status(thm)],[e_3_is_not_e_2]) ).
fof(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('theBenchmark.p',e_4_is_not_e_1) ).
cnf(c_13,plain,
~ equalish(e_4,e_1),
inference(clausify,[status(thm)],[e_4_is_not_e_1]) ).
fof(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('theBenchmark.p',e_4_is_not_e_2) ).
cnf(c_14,plain,
~ equalish(e_4,e_2),
inference(clausify,[status(thm)],[e_4_is_not_e_2]) ).
fof(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('theBenchmark.p',e_4_is_not_e_3) ).
cnf(c_15,plain,
~ equalish(e_4,e_3),
inference(clausify,[status(thm)],[e_4_is_not_e_3]) ).
fof(product1_right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_1,VAR_3)
| ~ product1(VAR_0,VAR_3,VAR_2)
| ~ product1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product1_right_cancellation) ).
cnf(c_17,plain,
( equalish(B,D)
| ~ product1(A,D,C)
| ~ product1(A,B,C) ),
inference(clausify,[status(thm)],[product1_right_cancellation]) ).
fof(product1_left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_0,VAR_3)
| ~ product1(VAR_3,VAR_1,VAR_2)
| ~ product1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product1_left_cancellation) ).
cnf(c_18,plain,
( equalish(A,D)
| ~ product1(D,B,C)
| ~ product1(A,B,C) ),
inference(clausify,[status(thm)],[product1_left_cancellation]) ).
fof(product2_total_function2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,VAR_3)
| ~ product2(VAR_0,VAR_1,VAR_3)
| ~ product2(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product2_total_function2) ).
cnf(c_19,plain,
( equalish(C,D)
| ~ product2(A,B,D)
| ~ product2(A,B,C) ),
inference(clausify,[status(thm)],[product2_total_function2]) ).
fof(element_1,axiom,
group_element(e_1),
file('theBenchmark.p',element_1) ).
cnf(c_39,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
fof(element_2,axiom,
group_element(e_2),
file('theBenchmark.p',element_2) ).
cnf(c_40,plain,
group_element(e_2),
inference(clausify,[status(thm)],[element_2]) ).
fof(element_3,axiom,
group_element(e_3),
file('theBenchmark.p',element_3) ).
cnf(c_41,plain,
group_element(e_3),
inference(clausify,[status(thm)],[element_3]) ).
fof(element_4,axiom,
group_element(e_4),
file('theBenchmark.p',element_4) ).
cnf(c_42,plain,
group_element(e_4),
inference(clausify,[status(thm)],[element_4]) ).
fof(product1_total_function1,axiom,
! [VAR_0,VAR_1] :
( product1(VAR_0,VAR_1,e_4)
| product1(VAR_0,VAR_1,e_3)
| product1(VAR_0,VAR_1,e_2)
| product1(VAR_0,VAR_1,e_1)
| ~ group_element(VAR_1)
| ~ group_element(VAR_0) ),
file('theBenchmark.p',product1_total_function1) ).
cnf(c_43,plain,
( product1(A,B,e_4)
| product1(A,B,e_3)
| product1(A,B,e_2)
| product1(A,B,e_1)
| ~ group_element(B)
| ~ group_element(A) ),
inference(clausify,[status(thm)],[product1_total_function1]) ).
fof(product1_idempotence,axiom,
! [VAR_0] : product1(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product1_idempotence) ).
cnf(c_44,plain,
product1(A,A,A),
inference(clausify,[status(thm)],[product1_idempotence]) ).
fof(product2_idempotence,axiom,
! [VAR_0] : product2(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product2_idempotence) ).
cnf(c_46,plain,
product2(A,A,A),
inference(clausify,[status(thm)],[product2_idempotence]) ).
fof(qg2a,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product2(VAR_3,VAR_1,VAR_0)
| ~ product1(VAR_2,VAR_0,VAR_3)
| ~ product1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg2a) ).
cnf(c_47,plain,
( product2(D,B,A)
| ~ product1(C,A,D)
| ~ product1(A,B,C) ),
inference(clausify,[status(thm)],[qg2a]) ).
cnf(c_84,plain,
( ~ product1(A,e_3,B)
| ~ product1(A,e_4,B) ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_85,plain,
( ~ product1(A,e_2,B)
| ~ product1(A,e_4,B) ),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_86,plain,
( ~ product1(A,e_1,B)
| ~ product1(A,e_4,B) ),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_87,plain,
( ~ product1(A,e_2,B)
| ~ product1(A,e_3,B) ),
inference(resolve,[status(thm)],[c_17,c_11]) ).
cnf(c_88,plain,
( ~ product1(A,e_1,B)
| ~ product1(A,e_3,B) ),
inference(resolve,[status(thm)],[c_17,c_10]) ).
cnf(c_89,plain,
( ~ product1(A,e_1,B)
| ~ product1(A,e_2,B) ),
inference(resolve,[status(thm)],[c_17,c_7]) ).
cnf(c_90,plain,
( ~ product1(e_3,A,B)
| ~ product1(e_4,A,B) ),
inference(resolve,[status(thm)],[c_18,c_15]) ).
cnf(c_91,plain,
( ~ product1(e_2,A,B)
| ~ product1(e_4,A,B) ),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_92,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_4,A,B) ),
inference(resolve,[status(thm)],[c_18,c_13]) ).
cnf(c_93,plain,
( ~ product1(e_2,A,B)
| ~ product1(e_3,A,B) ),
inference(resolve,[status(thm)],[c_18,c_11]) ).
cnf(c_94,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_3,A,B) ),
inference(resolve,[status(thm)],[c_18,c_10]) ).
cnf(c_97,plain,
( ~ product2(A,B,e_2)
| ~ product2(A,B,e_4) ),
inference(resolve,[status(thm)],[c_19,c_14]) ).
cnf(c_99,plain,
( ~ product2(A,B,e_2)
| ~ product2(A,B,e_3) ),
inference(resolve,[status(thm)],[c_19,c_11]) ).
cnf(c_166,plain,
( product1(e_4,A,e_4)
| product1(e_4,A,e_3)
| product1(e_4,A,e_2)
| product1(e_4,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_43,c_42]) ).
cnf(c_167,plain,
( product1(e_3,A,e_4)
| product1(e_3,A,e_3)
| product1(e_3,A,e_2)
| product1(e_3,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_43,c_41]) ).
cnf(c_255,plain,
~ product1(e_4,e_3,e_4),
inference(resolve,[status(thm)],[c_84,c_44]) ).
cnf(c_256,plain,
~ product1(e_3,e_4,e_3),
inference(resolve,[status(thm)],[c_84,c_44]) ).
cnf(c_257,plain,
~ product1(e_4,e_2,e_4),
inference(resolve,[status(thm)],[c_85,c_44]) ).
cnf(c_259,plain,
~ product1(e_4,e_1,e_4),
inference(resolve,[status(thm)],[c_86,c_44]) ).
cnf(c_261,plain,
~ product1(e_3,e_2,e_3),
inference(resolve,[status(thm)],[c_87,c_44]) ).
cnf(c_263,plain,
~ product1(e_3,e_1,e_3),
inference(resolve,[status(thm)],[c_88,c_44]) ).
cnf(c_267,plain,
~ product1(e_3,e_4,e_4),
inference(resolve,[status(thm)],[c_90,c_44]) ).
cnf(c_268,plain,
~ product1(e_4,e_3,e_3),
inference(resolve,[status(thm)],[c_90,c_44]) ).
cnf(c_270,plain,
~ product1(e_4,e_2,e_2),
inference(resolve,[status(thm)],[c_91,c_44]) ).
cnf(c_272,plain,
~ product1(e_4,e_1,e_1),
inference(resolve,[status(thm)],[c_92,c_44]) ).
cnf(c_274,plain,
~ product1(e_3,e_2,e_2),
inference(resolve,[status(thm)],[c_93,c_44]) ).
cnf(c_276,plain,
~ product1(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_94,c_44]) ).
cnf(c_282,plain,
~ product2(e_2,e_2,e_4),
inference(resolve,[status(thm)],[c_97,c_46]) ).
cnf(c_286,plain,
~ product2(e_2,e_2,e_3),
inference(resolve,[status(thm)],[c_99,c_46]) ).
cnf(c_433,plain,
( product1(e_4,e_3,e_4)
| product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_166,c_41]) ).
cnf(c_434,plain,
( product1(e_4,e_3,e_4)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_268,c_433]) ).
cnf(c_358,plain,
( product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_255,c_434]) ).
cnf(c_435,plain,
( product1(e_4,e_2,e_4)
| product1(e_4,e_2,e_3)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_166,c_40]) ).
cnf(c_436,plain,
( product1(e_4,e_2,e_4)
| product1(e_4,e_2,e_3)
| product1(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_270,c_435]) ).
cnf(c_359,plain,
( product1(e_4,e_2,e_3)
| product1(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_257,c_436]) ).
cnf(c_437,plain,
( product1(e_4,e_1,e_4)
| product1(e_4,e_1,e_3)
| product1(e_4,e_1,e_2)
| product1(e_4,e_1,e_1) ),
inference(resolve,[status(thm)],[c_166,c_39]) ).
cnf(c_438,plain,
( product1(e_4,e_1,e_4)
| product1(e_4,e_1,e_3)
| product1(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_272,c_437]) ).
cnf(c_360,plain,
( product1(e_4,e_1,e_3)
| product1(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_259,c_438]) ).
cnf(c_363,plain,
( product2(e_2,A,e_3)
| ~ product1(e_3,A,e_4)
| product1(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_358,c_47]) ).
cnf(c_366,plain,
( ~ product1(e_4,e_1,e_3)
| product1(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_359,c_89]) ).
cnf(c_368,plain,
( product2(A,e_2,e_4)
| ~ product1(e_3,e_4,A)
| product1(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_359,c_47]) ).
cnf(c_373,plain,
( product1(e_4,e_1,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_366,c_360]) ).
cnf(c_374,plain,
( ~ product1(e_3,e_2,e_1)
| product1(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_373,c_90]) ).
cnf(c_439,plain,
( product1(e_3,e_4,e_4)
| product1(e_3,e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_167,c_42]) ).
cnf(c_440,plain,
( product1(e_3,e_4,e_4)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_256,c_439]) ).
cnf(c_377,plain,
( product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_267,c_440]) ).
cnf(c_441,plain,
( product1(e_3,e_2,e_4)
| product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_167,c_40]) ).
cnf(c_442,plain,
( product1(e_3,e_2,e_4)
| product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_274,c_441]) ).
cnf(c_378,plain,
( product1(e_3,e_2,e_4)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_261,c_442]) ).
cnf(c_443,plain,
( product1(e_3,e_1,e_4)
| product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_167,c_39]) ).
cnf(c_444,plain,
( product1(e_3,e_1,e_4)
| product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_276,c_443]) ).
cnf(c_379,plain,
( product1(e_3,e_1,e_4)
| product1(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_263,c_444]) ).
cnf(c_445,plain,
( product2(e_2,e_2,e_4)
| product1(e_4,e_2,e_1)
| product1(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_377,c_368]) ).
cnf(c_381,plain,
( product1(e_4,e_2,e_1)
| product1(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_282,c_445]) ).
cnf(c_446,plain,
( product2(e_2,e_2,e_3)
| product1(e_4,e_3,e_1)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_378,c_363]) ).
cnf(c_386,plain,
( product1(e_4,e_3,e_1)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_286,c_446]) ).
cnf(c_388,plain,
( ~ product1(e_3,e_1,e_4)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_378,c_89]) ).
cnf(c_395,plain,
( ~ product1(e_3,e_2,e_1)
| product1(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_381,c_90]) ).
cnf(c_399,plain,
( ~ product1(e_4,e_2,e_1)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_386,c_87]) ).
cnf(c_403,plain,
( product1(e_3,e_1,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_388,c_379]) ).
cnf(c_405,plain,
( product1(e_4,e_1,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_399,c_373]) ).
cnf(c_406,plain,
( product1(e_3,e_4,e_1)
| product1(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_403,c_395]) ).
cnf(c_414,plain,
( ~ product1(e_3,e_1,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_405,c_90]) ).
cnf(c_419,plain,
( ~ product1(e_3,e_2,e_1)
| product1(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_406,c_85]) ).
cnf(c_447,plain,
( product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_419,c_403]) ).
cnf(c_425,plain,
product1(e_3,e_1,e_2),
inference(copy,[status(thm)],[c_447]) ).
cnf(c_426,plain,
product1(e_3,e_2,e_1),
inference(resolve,[status(thm)],[c_425,c_414]) ).
cnf(c_428,plain,
product1(e_4,e_1,e_2),
inference(resolve,[status(thm)],[c_426,c_374]) ).
cnf(c_448,plain,
~ product1(e_4,e_1,e_2),
inference(resolve,[status(thm)],[c_90,c_425]) ).
cnf(c_432,plain,
$false,
inference(resolve,[status(thm)],[c_428,c_448]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP124-8.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42 % Computer : n026.cluster.edu
% 0.11/0.42 % Model : x86_64 x86_64
% 0.11/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.42 % Memory : 8046.5625MB
% 0.11/0.42 % OS : Linux 6.8.0-71-generic
% 0.11/0.42 % CPULimit : 300
% 0.11/0.42 % WCLimit : 300
% 0.11/0.42 % DateTime : Fri Sep 25 14:27:39 UTC 2026
% 0.11/0.43 % CPUTime :
% 0.11/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.43 % Process 2736739 was started by sandbox on n026,
% 0.11/0.43 % Fri Sep 25 14:27:39 2026
% 0.11/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.43
% 0.11/0.43 % From the command line: assign(max_seconds, 300).
% 0.22/0.55
% 0.22/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.55
% 0.22/0.55 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.22/0.55 % Length of proof is 71.
% 0.22/0.55 % Level of proof is 12.
% 0.22/0.55 % Maximum clause weight is 20.000.
% 0.22/0.55 % Given clauses 244.
% 0.22/0.55
% 0.22/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------