%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP124-6.004 : 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 : n009.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 0.07s 0.48s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 96 ( 40 unt; 0 def)
% Number of atoms : 193 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 181 ( 84 ~; 97 |; 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 : 78 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(product1_total_function2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,VAR_3)
| ~ product1(VAR_0,VAR_1,VAR_3)
| ~ product1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product1_total_function2) ).
cnf(c_1,plain,
( equalish(C,D)
| ~ product1(A,B,D)
| ~ product1(A,B,C) ),
inference(clausify,[status(thm)],[product1_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(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_14,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_15,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_16,plain,
( equalish(C,D)
| ~ product2(A,B,D)
| ~ product2(A,B,C) ),
inference(clausify,[status(thm)],[product2_total_function2]) ).
cnf(c_36,plain,
( ~ product2(A,B,e_3)
| ~ product2(A,B,e_4) ),
inference(resolve,[status(thm)],[c_16,c_2]) ).
cnf(c_37,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_2,A,B) ),
inference(resolve,[status(thm)],[c_15,c_10]) ).
cnf(c_38,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_3,A,B) ),
inference(resolve,[status(thm)],[c_15,c_7]) ).
cnf(c_39,plain,
( ~ product1(e_2,A,B)
| ~ product1(e_3,A,B) ),
inference(resolve,[status(thm)],[c_15,c_6]) ).
cnf(c_40,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_4]) ).
cnf(c_41,plain,
( ~ product1(e_2,A,B)
| ~ product1(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_42,plain,
( ~ product1(e_3,A,B)
| ~ product1(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_2]) ).
cnf(c_44,plain,
( ~ product1(A,e_1,B)
| ~ product1(A,e_3,B) ),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_45,plain,
( ~ product1(A,e_2,B)
| ~ product1(A,e_3,B) ),
inference(resolve,[status(thm)],[c_14,c_6]) ).
cnf(c_46,plain,
( ~ product1(A,e_1,B)
| ~ product1(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_4]) ).
cnf(c_47,plain,
( ~ product1(A,e_2,B)
| ~ product1(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_48,plain,
( ~ product1(A,e_3,B)
| ~ product1(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_2]) ).
cnf(c_49,plain,
( ~ product1(A,B,e_1)
| ~ product1(A,B,e_2) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
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_55,plain,
( product2(D,B,A)
| ~ product1(C,A,D)
| ~ product1(A,B,C) ),
inference(clausify,[status(thm)],[qg2a]) ).
fof(product2_idempotence,axiom,
! [VAR_0] : product2(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product2_idempotence) ).
cnf(c_56,plain,
product2(A,A,A),
inference(clausify,[status(thm)],[product2_idempotence]) ).
fof(product1_idempotence,axiom,
! [VAR_0] : product1(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product1_idempotence) ).
cnf(c_58,plain,
product1(A,A,A),
inference(clausify,[status(thm)],[product1_idempotence]) ).
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_59,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(element_4,axiom,
group_element(e_4),
file('theBenchmark.p',element_4) ).
cnf(c_60,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_61,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_62,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_63,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_66,plain,
~ product2(e_4,e_4,e_3),
inference(resolve,[status(thm)],[c_56,c_36]) ).
cnf(c_116,plain,
~ product1(e_3,e_4,e_4),
inference(resolve,[status(thm)],[c_58,c_42]) ).
cnf(c_117,plain,
~ product1(e_2,e_4,e_4),
inference(resolve,[status(thm)],[c_58,c_41]) ).
cnf(c_118,plain,
~ product1(e_1,e_4,e_4),
inference(resolve,[status(thm)],[c_58,c_40]) ).
cnf(c_119,plain,
~ product1(e_2,e_3,e_3),
inference(resolve,[status(thm)],[c_58,c_39]) ).
cnf(c_120,plain,
~ product1(e_1,e_3,e_3),
inference(resolve,[status(thm)],[c_58,c_38]) ).
cnf(c_128,plain,
~ product1(e_3,e_4,e_3),
inference(resolve,[status(thm)],[c_48,c_58]) ).
cnf(c_129,plain,
~ product1(e_2,e_4,e_2),
inference(resolve,[status(thm)],[c_47,c_58]) ).
cnf(c_130,plain,
~ product1(e_1,e_4,e_1),
inference(resolve,[status(thm)],[c_46,c_58]) ).
cnf(c_131,plain,
~ product1(e_2,e_3,e_2),
inference(resolve,[status(thm)],[c_45,c_58]) ).
cnf(c_132,plain,
~ product1(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_44,c_58]) ).
cnf(c_140,plain,
( product1(A,e_4,e_4)
| product1(A,e_4,e_3)
| product1(A,e_4,e_2)
| product1(A,e_4,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_60,c_59]) ).
cnf(c_144,plain,
( product1(A,e_3,e_4)
| product1(A,e_3,e_3)
| product1(A,e_3,e_2)
| product1(A,e_3,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_61,c_59]) ).
cnf(c_424,plain,
( product1(e_1,e_4,e_4)
| product1(e_1,e_4,e_3)
| product1(e_1,e_4,e_2)
| product1(e_1,e_4,e_1) ),
inference(resolve,[status(thm)],[c_140,c_63]) ).
cnf(c_425,plain,
( product1(e_1,e_4,e_4)
| product1(e_1,e_4,e_3)
| product1(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_130,c_424]) ).
cnf(c_156,plain,
( product1(e_1,e_4,e_3)
| product1(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_118,c_425]) ).
cnf(c_426,plain,
( product1(e_2,e_4,e_4)
| product1(e_2,e_4,e_3)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_140,c_62]) ).
cnf(c_427,plain,
( product1(e_2,e_4,e_4)
| product1(e_2,e_4,e_3)
| product1(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_129,c_426]) ).
cnf(c_157,plain,
( product1(e_2,e_4,e_3)
| product1(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_117,c_427]) ).
cnf(c_428,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_140,c_61]) ).
cnf(c_429,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_128,c_428]) ).
cnf(c_158,plain,
( product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_116,c_429]) ).
cnf(c_171,plain,
( ~ product1(e_1,e_4,e_3)
| product1(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_157,c_37]) ).
cnf(c_173,plain,
( product2(A,e_4,e_3)
| ~ product1(e_1,e_3,A)
| product1(e_3,e_4,e_2) ),
inference(resolve,[status(thm)],[c_158,c_55]) ).
cnf(c_175,plain,
( ~ product1(e_2,e_4,e_1)
| product1(e_3,e_4,e_2) ),
inference(resolve,[status(thm)],[c_158,c_39]) ).
cnf(c_179,plain,
( ~ product1(e_1,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_158,c_38]) ).
cnf(c_180,plain,
( product1(e_1,e_4,e_2)
| product1(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_171,c_156]) ).
cnf(c_183,plain,
( product1(e_3,e_4,e_2)
| product1(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_180,c_175]) ).
cnf(c_187,plain,
( product1(e_3,e_4,e_1)
| product1(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_180,c_179]) ).
cnf(c_209,plain,
( ~ product1(e_1,e_3,e_2)
| product1(e_3,e_4,e_2) ),
inference(resolve,[status(thm)],[c_183,c_48]) ).
cnf(c_216,plain,
( ~ product1(e_2,e_3,e_1)
| product1(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_187,c_48]) ).
cnf(c_430,plain,
( product1(e_1,e_3,e_4)
| product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_144,c_63]) ).
cnf(c_431,plain,
( product1(e_1,e_3,e_4)
| product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_132,c_430]) ).
cnf(c_249,plain,
( product1(e_1,e_3,e_4)
| product1(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_120,c_431]) ).
cnf(c_432,plain,
( product1(e_2,e_3,e_4)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_144,c_62]) ).
cnf(c_433,plain,
( product1(e_2,e_3,e_4)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_131,c_432]) ).
cnf(c_250,plain,
( product1(e_2,e_3,e_4)
| product1(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_119,c_433]) ).
cnf(c_288,plain,
( product1(e_3,e_4,e_2)
| product1(e_1,e_3,e_4) ),
inference(resolve,[status(thm)],[c_249,c_209]) ).
cnf(c_296,plain,
( product1(e_3,e_4,e_1)
| product1(e_2,e_3,e_4) ),
inference(resolve,[status(thm)],[c_250,c_216]) ).
cnf(c_434,plain,
( product2(e_4,e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_2) ),
inference(resolve,[status(thm)],[c_288,c_173]) ).
cnf(c_435,plain,
( product2(e_4,e_4,e_3)
| product1(e_3,e_4,e_2) ),
inference(copy,[status(thm)],[c_434]) ).
cnf(c_405,plain,
product1(e_3,e_4,e_2),
inference(resolve,[status(thm)],[c_66,c_435]) ).
cnf(c_413,plain,
~ product1(e_3,e_4,e_1),
inference(resolve,[status(thm)],[c_405,c_49]) ).
cnf(c_436,plain,
( product2(A,e_4,e_3)
| ~ product1(e_2,e_3,A) ),
inference(resolve,[status(thm)],[c_55,c_405]) ).
cnf(c_417,plain,
~ product1(e_2,e_3,e_4),
inference(resolve,[status(thm)],[c_436,c_66]) ).
cnf(c_437,plain,
product1(e_3,e_4,e_1),
inference(resolve,[status(thm)],[c_417,c_296]) ).
cnf(c_423,plain,
$false,
inference(resolve,[status(thm)],[c_413,c_437]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP124-6.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.39 % Computer : n009.cluster.edu
% 0.07/0.39 % Model : x86_64 x86_64
% 0.07/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.39 % Memory : 8046.5625MB
% 0.07/0.39 % OS : Linux 6.8.0-71-generic
% 0.07/0.39 % CPULimit : 300
% 0.07/0.39 % WCLimit : 300
% 0.07/0.39 % DateTime : Fri Sep 25 14:25:13 UTC 2026
% 0.07/0.39 % CPUTime :
% 0.07/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.39 % Process 1802878 was started by sandbox on n009,
% 0.07/0.39 % Fri Sep 25 14:25:13 2026
% 0.07/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.40
% 0.07/0.40 % From the command line: assign(max_seconds, 300).
% 0.07/0.48
% 0.07/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.48
% 0.07/0.48 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.07/0.48 % Length of proof is 64.
% 0.07/0.48 % Level of proof is 11.
% 0.07/0.48 % Maximum clause weight is 25.000.
% 0.07/0.48 % Given clauses 238.
% 0.07/0.48
% 0.07/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------