%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP127-3.004 : TPTP v9.3.1. Released v1.2.0.
% 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 07:27:41 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.42s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 27
% Syntax : Number of formulae : 163 ( 67 unt; 0 def)
% Number of atoms : 360 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 357 ( 160 ~; 197 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 102 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cycle7,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,VAR_3)
| ~ next(VAR_0,VAR_3)
| ~ greater(VAR_1,e_0)
| ~ product(VAR_0,e_1,VAR_2)
| ~ cycle(VAR_0,VAR_1) ),
file('theBenchmark.p',cycle7) ).
cnf(c_2,plain,
( equalish(C,D)
| ~ next(A,D)
| ~ greater(B,e_0)
| ~ product(A,e_1,C)
| ~ cycle(A,B) ),
inference(clausify,[status(thm)],[cycle7]) ).
fof(cycle4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( equalish(VAR_1,VAR_4)
| ~ next(VAR_3,VAR_4)
| ~ greater(VAR_1,e_0)
| ~ next(VAR_0,VAR_2)
| ~ cycle(VAR_2,VAR_3)
| ~ cycle(VAR_0,VAR_1) ),
file('theBenchmark.p',cycle4) ).
cnf(c_3,plain,
( equalish(B,E)
| ~ next(D,E)
| ~ greater(B,e_0)
| ~ next(A,C)
| ~ cycle(C,D)
| ~ cycle(A,B) ),
inference(clausify,[status(thm)],[cycle4]) ).
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_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('theBenchmark.p',e_2_is_not_e_4) ).
cnf(c_9,plain,
~ equalish(e_2,e_4),
inference(clausify,[status(thm)],[e_2_is_not_e_4]) ).
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(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_17,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_18,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
cnf(c_19,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolve,[status(thm)],[c_18,c_7]) ).
cnf(c_20,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_18,c_10]) ).
cnf(c_21,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_18,c_11]) ).
cnf(c_22,plain,
( ~ product(e_1,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_18,c_13]) ).
cnf(c_23,plain,
( ~ product(e_2,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_24,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_18,c_15]) ).
cnf(c_25,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_17,c_7]) ).
cnf(c_26,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_17,c_10]) ).
cnf(c_27,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_17,c_11]) ).
cnf(c_28,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_29,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_30,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_48,plain,
( ~ next(C,e_1)
| ~ greater(e_3,e_0)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_3) ),
inference(resolve,[status(thm)],[c_10,c_3]) ).
cnf(c_52,plain,
( ~ next(A,e_4)
| ~ greater(B,e_0)
| ~ product(A,e_1,e_2)
| ~ cycle(A,B) ),
inference(resolve,[status(thm)],[c_9,c_2]) ).
cnf(c_56,plain,
( ~ next(C,e_1)
| ~ greater(e_2,e_0)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_2) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
fof(qg3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_3,VAR_0,VAR_1)
| ~ product(VAR_2,VAR_0,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3) ).
cnf(c_67,plain,
( product(D,A,B)
| ~ product(C,A,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg3]) ).
fof(product_idempotence,axiom,
! [VAR_0] : product(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product_idempotence) ).
cnf(c_68,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_69,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_70,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_71,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_72,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_73,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
fof(cycle6,axiom,
! [VAR_0,VAR_1] :
( ~ greater(VAR_1,VAR_0)
| ~ product(VAR_0,e_1,VAR_1)
| ~ cycle(VAR_0,e_0) ),
file('theBenchmark.p',cycle6) ).
cnf(c_74,plain,
( ~ greater(B,A)
| ~ product(A,e_1,B)
| ~ cycle(A,e_0) ),
inference(clausify,[status(thm)],[cycle6]) ).
fof(cycle3,axiom,
cycle(e_4,e_0),
file('theBenchmark.p',cycle3) ).
cnf(c_76,plain,
cycle(e_4,e_0),
inference(clausify,[status(thm)],[cycle3]) ).
fof(cycle2,axiom,
! [VAR_0] :
( cycle(VAR_0,e_3)
| cycle(VAR_0,e_2)
| cycle(VAR_0,e_1)
| cycle(VAR_0,e_0)
| ~ group_element(VAR_0) ),
file('theBenchmark.p',cycle2) ).
cnf(c_77,plain,
( cycle(A,e_3)
| cycle(A,e_2)
| cycle(A,e_1)
| cycle(A,e_0)
| ~ group_element(A) ),
inference(clausify,[status(thm)],[cycle2]) ).
fof(e_4_greater_e_3,axiom,
greater(e_4,e_3),
file('theBenchmark.p',e_4_greater_e_3) ).
cnf(c_78,plain,
greater(e_4,e_3),
inference(clausify,[status(thm)],[e_4_greater_e_3]) ).
fof(e_3_greater_e_0,axiom,
greater(e_3,e_0),
file('theBenchmark.p',e_3_greater_e_0) ).
cnf(c_85,plain,
greater(e_3,e_0),
inference(clausify,[status(thm)],[e_3_greater_e_0]) ).
fof(e_2_greater_e_0,axiom,
greater(e_2,e_0),
file('theBenchmark.p',e_2_greater_e_0) ).
cnf(c_86,plain,
greater(e_2,e_0),
inference(clausify,[status(thm)],[e_2_greater_e_0]) ).
fof(e_1_greater_e_0,axiom,
greater(e_1,e_0),
file('theBenchmark.p',e_1_greater_e_0) ).
cnf(c_87,plain,
greater(e_1,e_0),
inference(clausify,[status(thm)],[e_1_greater_e_0]) ).
fof(e_3_then_e_4,axiom,
next(e_3,e_4),
file('theBenchmark.p',e_3_then_e_4) ).
cnf(c_88,plain,
next(e_3,e_4),
inference(clausify,[status(thm)],[e_3_then_e_4]) ).
fof(e_0_then_e_1,axiom,
next(e_0,e_1),
file('theBenchmark.p',e_0_then_e_1) ).
cnf(c_91,plain,
next(e_0,e_1),
inference(clausify,[status(thm)],[e_0_then_e_1]) ).
cnf(c_121,plain,
( ~ next(C,e_1)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_3) ),
inference(resolve,[status(thm)],[c_85,c_48]) ).
cnf(c_124,plain,
( ~ next(C,e_1)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_2) ),
inference(resolve,[status(thm)],[c_86,c_56]) ).
cnf(c_144,plain,
~ product(e_4,e_3,e_4),
inference(resolve,[status(thm)],[c_68,c_30]) ).
cnf(c_145,plain,
~ product(e_4,e_2,e_4),
inference(resolve,[status(thm)],[c_68,c_29]) ).
cnf(c_146,plain,
~ product(e_4,e_1,e_4),
inference(resolve,[status(thm)],[c_68,c_28]) ).
cnf(c_148,plain,
~ product(e_3,e_1,e_3),
inference(resolve,[status(thm)],[c_68,c_26]) ).
cnf(c_150,plain,
~ product(e_3,e_4,e_4),
inference(resolve,[status(thm)],[c_68,c_24]) ).
cnf(c_151,plain,
~ product(e_2,e_4,e_4),
inference(resolve,[status(thm)],[c_68,c_23]) ).
cnf(c_152,plain,
~ product(e_1,e_4,e_4),
inference(resolve,[status(thm)],[c_68,c_22]) ).
cnf(c_154,plain,
~ product(e_1,e_3,e_3),
inference(resolve,[status(thm)],[c_68,c_20]) ).
cnf(c_155,plain,
~ product(e_1,e_2,e_2),
inference(resolve,[status(thm)],[c_68,c_19]) ).
cnf(c_162,plain,
~ product(e_3,e_4,e_3),
inference(resolve,[status(thm)],[c_30,c_68]) ).
cnf(c_163,plain,
~ product(e_2,e_4,e_2),
inference(resolve,[status(thm)],[c_29,c_68]) ).
cnf(c_164,plain,
~ product(e_1,e_4,e_1),
inference(resolve,[status(thm)],[c_28,c_68]) ).
cnf(c_166,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_26,c_68]) ).
cnf(c_167,plain,
~ product(e_1,e_2,e_1),
inference(resolve,[status(thm)],[c_25,c_68]) ).
cnf(c_168,plain,
~ product(e_4,e_3,e_3),
inference(resolve,[status(thm)],[c_24,c_68]) ).
cnf(c_169,plain,
~ product(e_4,e_2,e_2),
inference(resolve,[status(thm)],[c_23,c_68]) ).
cnf(c_170,plain,
~ product(e_4,e_1,e_1),
inference(resolve,[status(thm)],[c_22,c_68]) ).
cnf(c_172,plain,
~ product(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_20,c_68]) ).
cnf(c_174,plain,
( product(A,e_4,e_4)
| product(A,e_4,e_3)
| product(A,e_4,e_2)
| product(A,e_4,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_70,c_69]) ).
cnf(c_175,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_70,c_69]) ).
cnf(c_176,plain,
( product(A,e_3,e_4)
| product(A,e_3,e_3)
| product(A,e_3,e_2)
| product(A,e_3,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_71,c_69]) ).
cnf(c_177,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_71,c_69]) ).
cnf(c_178,plain,
( product(A,e_2,e_4)
| product(A,e_2,e_3)
| product(A,e_2,e_2)
| product(A,e_2,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_72,c_69]) ).
cnf(c_185,plain,
( cycle(e_3,e_3)
| cycle(e_3,e_2)
| cycle(e_3,e_1)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_77,c_71]) ).
cnf(c_419,plain,
( ~ next(e_0,e_1)
| ~ next(A,e_4)
| ~ cycle(A,e_3) ),
inference(resolve,[status(thm)],[c_121,c_76]) ).
cnf(c_420,plain,
( ~ next(e_0,e_1)
| ~ cycle(e_3,e_3) ),
inference(resolve,[status(thm)],[c_419,c_88]) ).
cnf(c_231,plain,
~ cycle(e_3,e_3),
inference(resolve,[status(thm)],[c_420,c_91]) ).
cnf(c_232,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_1)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_231,c_185]) ).
cnf(c_421,plain,
( ~ next(e_0,e_1)
| ~ next(A,e_4)
| ~ cycle(A,e_2) ),
inference(resolve,[status(thm)],[c_124,c_76]) ).
cnf(c_422,plain,
( ~ next(e_0,e_1)
| ~ cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_421,c_88]) ).
cnf(c_240,plain,
~ cycle(e_3,e_2),
inference(resolve,[status(thm)],[c_422,c_91]) ).
cnf(c_241,plain,
( cycle(e_3,e_1)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_240,c_232]) ).
cnf(c_423,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(resolve,[status(thm)],[c_174,c_73]) ).
cnf(c_424,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_164,c_423]) ).
cnf(c_259,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_152,c_424]) ).
cnf(c_425,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_174,c_72]) ).
cnf(c_426,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_163,c_425]) ).
cnf(c_260,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_151,c_426]) ).
cnf(c_427,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_174,c_71]) ).
cnf(c_428,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_162,c_427]) ).
cnf(c_261,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_150,c_428]) ).
cnf(c_263,plain,
( product(A,e_1,e_4)
| ~ product(e_3,e_1,A)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_259,c_67]) ).
cnf(c_265,plain,
( product(e_3,e_4,A)
| ~ product(e_4,A,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_260,c_67]) ).
cnf(c_271,plain,
( ~ product(e_3,e_1,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_261,c_28]) ).
cnf(c_429,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(resolve,[status(thm)],[c_175,c_73]) ).
cnf(c_430,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_170,c_429]) ).
cnf(c_277,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_146,c_430]) ).
cnf(c_431,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_175,c_72]) ).
cnf(c_432,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_169,c_431]) ).
cnf(c_278,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_145,c_432]) ).
cnf(c_433,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_175,c_71]) ).
cnf(c_434,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_168,c_433]) ).
cnf(c_279,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_144,c_434]) ).
cnf(c_291,plain,
( ~ product(e_4,e_1,e_3)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_278,c_25]) ).
cnf(c_292,plain,
( ~ product(e_1,e_2,e_3)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_278,c_22]) ).
cnf(c_435,plain,
( product(e_3,e_4,e_3)
| product(e_2,e_4,e_1)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_279,c_265]) ).
cnf(c_293,plain,
( product(e_2,e_4,e_1)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_162,c_435]) ).
cnf(c_301,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_291,c_277]) ).
cnf(c_304,plain,
( ~ product(e_4,e_2,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_293,c_27]) ).
cnf(c_310,plain,
( product(e_4,e_1,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_304,c_301]) ).
cnf(c_436,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_176,c_73]) ).
cnf(c_437,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_166,c_436]) ).
cnf(c_312,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_154,c_437]) ).
cnf(c_322,plain,
( ~ product(e_3,e_1,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_310,c_24]) ).
cnf(c_328,plain,
( ~ product(e_1,e_2,e_4)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_312,c_27]) ).
cnf(c_438,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_177,c_73]) ).
cnf(c_439,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_172,c_438]) ).
cnf(c_329,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_148,c_439]) ).
cnf(c_440,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_178,c_73]) ).
cnf(c_441,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(resolve,[status(thm)],[c_167,c_440]) ).
cnf(c_338,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3) ),
inference(resolve,[status(thm)],[c_155,c_441]) ).
cnf(c_442,plain,
( product(e_4,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_329,c_263]) ).
cnf(c_340,plain,
( product(e_1,e_4,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_146,c_442]) ).
cnf(c_443,plain,
( ~ greater(e_4,e_3)
| ~ cycle(e_3,e_0)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_329,c_74]) ).
cnf(c_341,plain,
( ~ cycle(e_3,e_0)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_78,c_443]) ).
cnf(c_348,plain,
( cycle(e_3,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_341,c_241]) ).
cnf(c_349,plain,
( product(e_2,e_4,e_1)
| cycle(e_3,e_1) ),
inference(resolve,[status(thm)],[c_348,c_322]) ).
cnf(c_350,plain,
( product(e_3,e_4,e_1)
| cycle(e_3,e_1) ),
inference(resolve,[status(thm)],[c_348,c_271]) ).
cnf(c_367,plain,
( ~ product(e_2,e_4,e_1)
| cycle(e_3,e_1) ),
inference(resolve,[status(thm)],[c_350,c_21]) ).
cnf(c_444,plain,
( cycle(e_3,e_1)
| cycle(e_3,e_1) ),
inference(resolve,[status(thm)],[c_367,c_349]) ).
cnf(c_369,plain,
cycle(e_3,e_1),
inference(copy,[status(thm)],[c_444]) ).
cnf(c_445,plain,
( ~ next(e_3,e_4)
| ~ greater(e_1,e_0)
| ~ product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_52,c_369]) ).
cnf(c_446,plain,
( ~ next(e_3,e_4)
| ~ product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_445,c_87]) ).
cnf(c_387,plain,
~ product(e_3,e_1,e_2),
inference(resolve,[status(thm)],[c_446,c_88]) ).
cnf(c_396,plain,
product(e_1,e_4,e_2),
inference(resolve,[status(thm)],[c_387,c_340]) ).
cnf(c_405,plain,
~ product(e_1,e_3,e_2),
inference(resolve,[status(thm)],[c_396,c_30]) ).
cnf(c_447,plain,
( product(e_2,e_4,A)
| ~ product(e_4,A,e_1) ),
inference(resolve,[status(thm)],[c_67,c_396]) ).
cnf(c_406,plain,
~ product(e_4,e_2,e_1),
inference(resolve,[status(thm)],[c_447,c_163]) ).
cnf(c_409,plain,
~ product(e_1,e_2,e_4),
inference(resolve,[status(thm)],[c_405,c_328]) ).
cnf(c_413,plain,
~ product(e_1,e_2,e_3),
inference(resolve,[status(thm)],[c_406,c_292]) ).
cnf(c_448,plain,
product(e_1,e_2,e_4),
inference(resolve,[status(thm)],[c_413,c_338]) ).
cnf(c_418,plain,
$false,
inference(resolve,[status(thm)],[c_409,c_448]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP127-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 14:26:53 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 613406 was started by sandbox2 on n013,
% 0.08/0.36 % Fri Sep 25 14:26:53 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.42
% 0.08/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.42
% 0.08/0.42 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.08/0.42 % Length of proof is 106.
% 0.08/0.42 % Level of proof is 15.
% 0.08/0.42 % Maximum clause weight is 20.000.
% 0.08/0.42 % Given clauses 234.
% 0.08/0.42
% 0.08/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------