%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP124-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 0.93s 0.51s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 92 ( 37 unt; 0 def)
% Number of atoms : 211 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 219 ( 100 ~; 119 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 85 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(product_total_function2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_total_function2) ).
cnf(c_1,plain,
( equalish(C,D)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_total_function2]) ).
fof(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('theBenchmark.p',e_4_is_not_e_3) ).
cnf(c_2,plain,
~ equalish(e_4,e_3),
inference(clausify,[status(thm)],[e_4_is_not_e_3]) ).
fof(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('theBenchmark.p',e_4_is_not_e_2) ).
cnf(c_3,plain,
~ equalish(e_4,e_2),
inference(clausify,[status(thm)],[e_4_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_4,plain,
~ equalish(e_4,e_1),
inference(clausify,[status(thm)],[e_4_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_6,plain,
~ equalish(e_3,e_2),
inference(clausify,[status(thm)],[e_3_is_not_e_2]) ).
fof(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('theBenchmark.p',e_3_is_not_e_1) ).
cnf(c_7,plain,
~ equalish(e_3,e_1),
inference(clausify,[status(thm)],[e_3_is_not_e_1]) ).
fof(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_10,plain,
~ equalish(e_2,e_1),
inference(clausify,[status(thm)],[e_2_is_not_e_1]) ).
fof(product_right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_1,VAR_3)
| ~ product(VAR_0,VAR_3,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_right_cancellation) ).
cnf(c_14,plain,
( equalish(B,D)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_right_cancellation]) ).
fof(product_left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_0,VAR_3)
| ~ product(VAR_3,VAR_1,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_left_cancellation) ).
cnf(c_15,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
fof(qg2_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equalish(VAR_0,VAR_3)
| ~ product(VAR_5,VAR_3,VAR_4)
| ~ product(VAR_5,VAR_0,VAR_1)
| ~ product(VAR_3,VAR_4,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg2_1) ).
cnf(c_16,plain,
( equalish(A,D)
| ~ product(F,D,E)
| ~ product(F,A,B)
| ~ product(D,E,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg2_1]) ).
cnf(c_25,plain,
( ~ product(D,e_1,C)
| ~ product(D,e_3,A)
| ~ product(e_1,C,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_16,c_7]) ).
cnf(c_29,plain,
( ~ product(D,e_3,C)
| ~ product(D,e_4,A)
| ~ product(e_3,C,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_16,c_2]) ).
cnf(c_31,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_15,c_7]) ).
cnf(c_32,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_15,c_6]) ).
cnf(c_35,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_2]) ).
cnf(c_36,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_14,c_10]) ).
cnf(c_37,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_38,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_14,c_6]) ).
cnf(c_40,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_41,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_2]) ).
cnf(c_42,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_45,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_4) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_46,plain,
( ~ product(A,B,e_2)
| ~ product(A,B,e_4) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(product_idempotence,axiom,
! [VAR_0] : product(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product_idempotence) ).
cnf(c_48,plain,
product(A,A,A),
inference(clausify,[status(thm)],[product_idempotence]) ).
fof(product_total_function1,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,VAR_1,e_4)
| product(VAR_0,VAR_1,e_3)
| product(VAR_0,VAR_1,e_2)
| product(VAR_0,VAR_1,e_1)
| ~ group_element(VAR_1)
| ~ group_element(VAR_0) ),
file('theBenchmark.p',product_total_function1) ).
cnf(c_49,plain,
( product(A,B,e_4)
| product(A,B,e_3)
| product(A,B,e_2)
| product(A,B,e_1)
| ~ group_element(B)
| ~ group_element(A) ),
inference(clausify,[status(thm)],[product_total_function1]) ).
fof(element_4,axiom,
group_element(e_4),
file('theBenchmark.p',element_4) ).
cnf(c_50,plain,
group_element(e_4),
inference(clausify,[status(thm)],[element_4]) ).
fof(element_3,axiom,
group_element(e_3),
file('theBenchmark.p',element_3) ).
cnf(c_51,plain,
group_element(e_3),
inference(clausify,[status(thm)],[element_3]) ).
fof(element_2,axiom,
group_element(e_2),
file('theBenchmark.p',element_2) ).
cnf(c_52,plain,
group_element(e_2),
inference(clausify,[status(thm)],[element_2]) ).
fof(element_1,axiom,
group_element(e_1),
file('theBenchmark.p',element_1) ).
cnf(c_53,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
fof(row_surjectivity,axiom,
! [VAR_0,VAR_1] :
( product(e_4,VAR_0,VAR_1)
| product(e_3,VAR_0,VAR_1)
| product(e_2,VAR_0,VAR_1)
| product(e_1,VAR_0,VAR_1)
| ~ group_element(VAR_1)
| ~ group_element(VAR_0) ),
file('theBenchmark.p',row_surjectivity) ).
cnf(c_55,plain,
( product(e_4,A,B)
| product(e_3,A,B)
| product(e_2,A,B)
| product(e_1,A,B)
| ~ group_element(B)
| ~ group_element(A) ),
inference(clausify,[status(thm)],[row_surjectivity]) ).
cnf(c_1003,plain,
( ~ product(e_4,e_3,A)
| ~ product(e_3,A,e_4)
| ~ product(e_4,e_4,e_4) ),
inference(factor,[status(thm)],[c_29]) ).
cnf(c_100,plain,
( ~ product(e_4,e_3,A)
| ~ product(e_3,A,e_4) ),
inference(resolve,[status(thm)],[c_48,c_1003]) ).
cnf(c_112,plain,
~ product(e_2,e_2,e_1),
inference(resolve,[status(thm)],[c_48,c_42]) ).
cnf(c_113,plain,
~ product(e_4,e_3,e_4),
inference(resolve,[status(thm)],[c_48,c_41]) ).
cnf(c_114,plain,
~ product(e_4,e_2,e_4),
inference(resolve,[status(thm)],[c_48,c_40]) ).
cnf(c_116,plain,
~ product(e_3,e_2,e_3),
inference(resolve,[status(thm)],[c_48,c_38]) ).
cnf(c_123,plain,
~ product(e_1,e_3,e_3),
inference(resolve,[status(thm)],[c_48,c_31]) ).
cnf(c_141,plain,
( ~ product(e_1,e_3,A)
| ~ product(e_1,e_1,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_48,c_25]) ).
cnf(c_174,plain,
~ product(e_2,e_2,e_4),
inference(resolve,[status(thm)],[c_46,c_48]) ).
cnf(c_183,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_37,c_48]) ).
cnf(c_184,plain,
~ product(e_1,e_2,e_1),
inference(resolve,[status(thm)],[c_36,c_48]) ).
cnf(c_185,plain,
~ product(e_4,e_3,e_3),
inference(resolve,[status(thm)],[c_35,c_48]) ).
cnf(c_188,plain,
~ product(e_3,e_2,e_2),
inference(resolve,[status(thm)],[c_32,c_48]) ).
cnf(c_1004,plain,
( product(e_4,A,e_4)
| product(e_4,A,e_3)
| product(e_4,A,e_2)
| product(e_4,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_49,c_50]) ).
cnf(c_1005,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_1004,c_51]) ).
cnf(c_1006,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_185,c_1005]) ).
cnf(c_195,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_113,c_1006]) ).
cnf(c_1007,plain,
( product(e_3,A,e_4)
| product(e_3,A,e_3)
| product(e_3,A,e_2)
| product(e_3,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_49,c_51]) ).
cnf(c_1008,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_1007,c_52]) ).
cnf(c_1009,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_188,c_1008]) ).
cnf(c_199,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_116,c_1009]) ).
cnf(c_1010,plain,
( product(e_1,A,e_4)
| product(e_1,A,e_3)
| product(e_1,A,e_2)
| product(e_1,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_49,c_53]) ).
cnf(c_1011,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_1010,c_51]) ).
cnf(c_1012,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_183,c_1011]) ).
cnf(c_209,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_123,c_1012]) ).
cnf(c_1013,plain,
( product(e_4,e_2,A)
| product(e_3,e_2,A)
| product(e_2,e_2,A)
| product(e_1,e_2,A)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_55,c_52]) ).
cnf(c_1014,plain,
( product(e_4,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_1013,c_53]) ).
cnf(c_1015,plain,
( product(e_4,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_184,c_1014]) ).
cnf(c_242,plain,
( product(e_4,e_2,e_1)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_112,c_1015]) ).
cnf(c_1016,plain,
( product(e_4,e_2,A)
| product(e_3,e_2,A)
| product(e_2,e_2,A)
| product(e_1,e_2,A)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_55,c_52]) ).
cnf(c_1017,plain,
( product(e_4,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolve,[status(thm)],[c_1016,c_50]) ).
cnf(c_1018,plain,
( product(e_4,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolve,[status(thm)],[c_174,c_1017]) ).
cnf(c_244,plain,
( product(e_3,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolve,[status(thm)],[c_114,c_1018]) ).
cnf(c_1019,plain,
( product(e_3,e_2,e_1)
| ~ product(e_4,e_3,e_2) ),
inference(resolve,[status(thm)],[c_100,c_199]) ).
cnf(c_299,plain,
( product(e_4,e_3,e_1)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_1019,c_195]) ).
cnf(c_418,plain,
( ~ product(e_1,e_2,e_4)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_209,c_38]) ).
cnf(c_789,plain,
( ~ product(e_3,e_2,e_1)
| product(e_1,e_2,e_4) ),
inference(resolve,[status(thm)],[c_244,c_45]) ).
cnf(c_1020,plain,
( product(e_3,e_2,e_1)
| ~ product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_38,c_299]) ).
cnf(c_1021,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_1020,c_242]) ).
cnf(c_983,plain,
product(e_3,e_2,e_1),
inference(copy,[status(thm)],[c_1021]) ).
cnf(c_985,plain,
product(e_1,e_2,e_4),
inference(resolve,[status(thm)],[c_983,c_789]) ).
cnf(c_992,plain,
product(e_1,e_3,e_2),
inference(resolve,[status(thm)],[c_985,c_418]) ).
cnf(c_1022,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_983,c_141]) ).
cnf(c_1023,plain,
~ product(e_1,e_3,e_2),
inference(resolve,[status(thm)],[c_48,c_1022]) ).
cnf(c_1002,plain,
$false,
inference(resolve,[status(thm)],[c_992,c_1023]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:24:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 611848 was started by sandbox2 on n013,
% 0.10/0.37 % Fri Sep 25 14:24:51 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.93/0.51
% 0.93/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.93/0.51
% 0.93/0.51 % Proof 1 at 0.10 (+ 0.03) seconds.
% 0.93/0.51 % Length of proof is 54.
% 0.93/0.51 % Level of proof is 8.
% 0.93/0.51 % Maximum clause weight is 25.000.
% 0.93/0.51 % Given clauses 175.
% 0.93/0.51
% 0.93/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------